The argument from contingency

0. Introduction

The ‘argument from contingency’ is a version of the cosmological argument. It has various forms, and historians of philosophy trace it as far back as Avicenna in the 10th century. It is one of Aquinas’ five proofs, and is part of the repertoire of the classical apologetical method. I have an objection that I will explain here. It is probably not new (as it is such an old argument), but I like it, so I want to spell it out.

  1. The argument

There are various ways to phrase the argument, and there will doubtless be ways to spell it out that avoid my particular objection, but this is a classic way of presenting the argument.

The driving idea is that the universe, if its existence is contingent (i.e. if its existence is neither necessary nor impossible), requires an explanation. Contingent things cannot just exist with no reason for them. Take this pillow. Its existence is contingent, in that it could have not existed. The fact that it does exist is a fact which can be explained (at least in principle); there is some answer to the question ‘why does this pillow exist?’. One way of thinking about the explanation for its existence is in terms of the causal conditions that brought it into existence. So perhaps it was made in a factory, by some Chinese pillow-manufacturer or whatever. There is some causal story we could tell which would explain why this pillow exists. Not only that, but it has to have some story or other like this which explains its existence. If it wasn’t made in a Chinese factory, then it was made somehow, somewhere. It couldn’t be that it just was. A thing which is contingent, whose existence is neither necessary nor impossible, but which just existed for no reason, is (so the argument goes) itself impossible. Contingent things, like pillows, porcupines, pineapples, or people, etc, are contingent, and they all have explanations for their existence. Sometimes, this principle is called the ‘principle of sufficient reason’.

But consider something whose existence is necessary; something which couldn’t not exist.  Let’s say that the number 9 exists (it doesn’t matter if you don’t like this example, just plug in your own favourite example of something which necessarily exists). If the number 9 exists, its existence is not the sort of thing that could have failed to be the case. No matter what happens in the world, no matter the coming or goings of physical things, the existence of the number 9 is completely independent of it. Thus, there could be no causal explanation for the number 9, as it exists over and above the causal chains that contingent things exist within the world. It doesn’t make sense to explain why something exists, if it couldn’t not exist. Unlike contingent things, like me or my pillow, there is no answer to the question: ‘why does the number 9 exist?’.

Given this distinction between contingent things, whose existence requires explanation, and necessary things, whose existence doesn’t require explanation, we seem to be faced with a trilemma. That is, there seem to be only three possible options. The options seem to be:

  1. Each contingent thing has as its explanation another contingent thing. So my pillow was made by a person, who was made by another person, and ultimately life was created by contingent physical processes, which themselves were contingent outcomes of contingent events. The chain of contingent things stretches back forever, with each contingent thing having a contingent explanatory thing that it depends on for its existence.
  2. Most contingent things have as their explanation other contingent things, but the chain of dependency doesn’t go backwards forever; rather, it terminates at some point. The point at which the chain terminates is itself a contingently existing thing. Perhaps there was a burst of energy at the big bang, which was itself a contingently existing thing, but (contra the principle of sufficient reason) the existence of this thing has no explanation whatsoever. It just happened for no reason.
  3. Most contingent things have as their explanation other contingent things, but the chain of dependency doesn’t go backwards forever; rather, it terminates at some point. The point at which the chain terminates is itself a necessarily existing thing. This necessarily existing thing is the ultimate cause and explanation for the existence of all of the contingently existing things. Let’s call this first mover, this necessarily exiting thing, ‘God’.

It seems that these are the only possible options, and so all one has to do to prove that God exists is to rule out the first two options. Here, the principle of sufficient reason does most of the heavy lifting. Take option 2. The idea of something contingent just happening for no reason is supposed to be impossible. Contingent things don’t just happen. Imagine you came across a pattern in the sand while walking along the beach that read ‘Hello’. This is obviously the sort of thing that could have not existed, and so it is a contingently existing thing. It is also the sort of thing that it would make sense to ask ‘why does this exist?’, and there will be an answer to this question. Someone probably drew the lines in the  sand with a stick. It may have happened by some very unlikely process of the wind working in just the right way so as to make the letters appear in the sand. However it happened though, there is some explanation for it. It couldn’t be that it exists but without an explanation. It would be like thinking that each domino fell because the previous one fell into it, but that at some point a domino just falls over without anything falling into it, for no reason.

Similar reasoning applies to option 1. Obviously, in this case (unlike in option 2) there is no contingently existing thing that has no explanation for its existence; each contingently existing thing has a contingently existing thing as the explanation for its existence. So on this picture, each thing has an explanation. However, there is no explanation for why the whole sequence of contingent things exists. Where did it come from, ultimately? As the infinite chain of contingent things recedes off into the distance, one is left with the feeling that this infinite bunch of contingency is just as strange as the brute contingent fact that we found so strange in option 2. If the dominos each fall because the previous one fell into it, and this goes on forever without a starting point, it is ultimately a complete mystery why any of them started to fall over at all.

The last option then is the only one that could have any hope of offering any explanation for the contingency of the world. On this option, the necessarily existing starting point caused the first contingent thing to exist; it pushed the first cosmic domino over. As it is not a contingently existing thing, it doesn’t require an explanation for it’s own existence, so the termination point of the chain is not arbitrary, as on option 2. Thus we seem to have found the only option that is acceptable, according to the principle of sufficient reason. There are contingently existing things in the world (like pillows), so there must have been a necessarily existing thing that caused them to come into being.

2. Some Responses 

So how should someone respond to this argument? One could of course reject the idea that contingently existing things need an explanation. This would allow one to embrace option 2. The problem with this is supposed to be that the idea that contingently existing things require explanations is a fundamental assumption to science, and to any rational understanding of the world. If things could just exist without explanation, then there would be no way of knowing with any given contingent thing whether it was one of those things. One would always have to wrestle with the option that the given phenomenon, such as the spread of the disease across the population, or the fact that the bowling ball falls to the earth with such and such velocity, could just be a brute fact with no explanation. Science, it seems, requires that option 2 is false.

One could accept the idea that contingently existing things require an explanation, but reject the idea that there are contingently existing things at all. Maybe there is just the appearance of contingency, whereas in reality everything is necessary. The cost of this view is that it seems intuitively very obvious that most things are only contingently existing. Most of them could not exist. It is obviously possible that I could have not existed. In fact, if you consider how many contingent things are required for my existence, my parents meeting, their parents meeting, their parents meeting, etc, my existence should be almost impossibly unlikely. I quite obviously do not exist necessarily. Saying that everything which exists does so necessarily seems very hard to maintain.

Lastly, one could try to opt for option 1, where each domino falls because of the previous one, in a never ending sequence back into infinity. Here, the well-rehersed absurdities resultant from infinite sequences come into play. Imagine someone who was counting up from minus-infinity. As you come across him you hear him saying ‘…minus 3, minus 2, minus 1, 0 …’. The idea that he has come to 0 at the precise moment that you come across him seems to have no explanation. Why had he not arrived at this point before? Why does he not come to this point tomorrow instead? After all, it must have taken him an infinite amount of time for him to get here, whether he got here yesterday, today or tomorrow. There can be no explanation for one over the other. Thus, we seem to be back in the boat of option 2.

3. My response

My response is not to take any of these options. I do not really offer a solution to the problem as such. My tactic is to point out that option 3 is no better off than options 1 or 2. Here is how I see the problem. On this option it is God, the necessarily existing thing, that set the contingent sequence of things off. But when he did so, what was the nature of the choice? Specifically, was there something in virtue of which God made the choice to create this sequence of contingent things rather than another sequence, or rather than no sequence at all? There seem to be two options here:

i) Yes, there was something in virtue of which God made this choice.

ii) No, there was nothing in virtue of which God made this choice.

Note, that we are not asking whether there is something that explains God’s existence. We do not need to say that God is not necessary, or that necessary things require explanations. Rather, we are asking whether God’s choice is the sort of thing that has an explanation.

Let’s explore option i). On this view, God made his choice because of something; there is something which explains his choice. Familiar candidates for such a thing might include his nature (perhaps he is by nature something which wants to be in a loving relationship with certain contingent things), or God’s nature plus the nature of this world (perhaps God always wants the best thing, and perhaps this is the best of all possible worlds). On any view like this, it seems that God’s choice is not completely free. In some sense he has to make this choice, as a result of his nature. If that is right, then the existence of the world, and all the apparently contingent things in it, is in fact necessary; they had to happen, and couldn’t have not happened. The existence of the world is as necessary as the existence of the first mover. Neither could happen without the other.

Let’s look at option ii). On this view, there is nothing in virtue of which God made the world. He chose to make this world completely free of any determining factor. He wasn’t dictated by his nature, or by the nature of the world. He could have made any world just as easily as this. On this view, there is nothing which explains why he made this world rather than another, or rather than none at all. On this world, the existence of the universe is indeed contingent, but also without explanation, which violates the principle of sufficient reason after all.

4. Conclusion

Thus, it seems that the third option in our original trilemma really has nothing to offer over and above the first two. If the chain of contingent things terminates in a necessarily existing thing, then either the existence of the world is itself necessary and thus requiring no explanation, or contingent but itself without an explanation.

Problems with ‘The Lord of non-Contradiction’

0. Introduction

In this post, I will not be focusing on a blog post or a non-professional apologetical argument. Rather, I will be focusing on an argument in a peer-reviewed academic journal, called Philosophia Christi (it is published by the Evangelical Philosophical Society). The paper is entitled ‘The Lord of Non-Contradiction‘, and the authors are James Anderson and Greg Welty. They are professional academics, with PhDs in respected institutions (Edinburgh and Oxford, respectively). These guys are proper academics, by any standards. I believe this to be the most philosophically rigorous version of their argument that I have come across.

The argument they present in the paper is a version of the ‘argument from logic’, in which the existence of God is argued for using the nature of logic as the motivating factor. This is a sophisticated version of the familiar presuppositionalist refrain, and is the sort of thing I imagine Matt Slick would be arguing for had he received a graduate education in philosophy as well as theology. It is an interesting paper, which certainly doesn’t fall prey to the usual fallacies that we see repeated over and over again in the non-professional internet apologetics communities. They are presuppositionalists (as far as I can gather), but this is not a presuppositional argument as such.

Despite their obvious qualities as theologians and philosophers, I still see reason to reject the argument, which I will explain here. Before we get to my reasons for criticising the argument, we should have a look at the argument as they present it.

  1. The argument

The paper is divided into nine sections, the first eight of which have headings that are claims about the laws of logic; ‘the laws of logic are truths’, ‘the laws of logic are truths about truths’, ‘the laws of logic are necessary truths’, ‘the laws of logic really exist’, ‘the laws of logic necessarily exist’, ‘the laws of logic are non-physical’, ‘the laws of logic are thoughts’, and ‘the laws of logic are divine thoughts’. Here is how they summarise the argument in their conclusion:

“The laws of logic are necessary truths about truths; they are necessarily true propositions. Propositions are real entities, but cannot be physical entities; they are essentially thoughts. So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. But if there are necessarily existent thoughts, there must be a necessarily existent mind; and if there is a necessarily existent mind, there must be a necessarily existent person. A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily. Thus, if there are laws of logic, there must also be a necessarily existent, personal, spiritual being. The laws of logic imply the existence of God.” (p. 20)

So we see a plausible looking string of inferences from various claims, each of which has a section in the paper defending it, and often presenting citations to other papers for elaborations. We seem to be moving from simple observations about the nature of the laws of logic, that they are necessary truths, etc, to the claim that they indicate the presence of a divine mind.

Here is the argument from above in something closer to premise/conclusion form. I have had to construct this, as the authors leave the logical form of the argument informal, and in doing so, I have tried to represent the reasoning as we find it above:

  1. The laws of logic are necessarily true propositions.
  2. Propositions are real entities, but cannot be physical entities; they are essentially thoughts.
  3. But if there are necessarily existent thoughts, there must be a necessarily existent mind.
  4. If there is a necessarily existent mind, there must be a necessarily existent person.
  5.  A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily.
  6. If there are laws of logic, there must also be a necessarily existent, personal, spiritual being.
  7. A necessarily existent, personal, spiritual being is God
  8. The laws of logic imply the existence of God.
  9. Therefore, God exists.

The final step I have had to add in myself, as Anderson and Welty do not explicitly draw it out as such. They stop their argument at the conditional ‘logic implies God’, leaving the reader to join the dots. There are some terms that don’t quite match up properly in the above (true propositions and real entities, etc), which stop it from being formally valid.

1.1 A more formal version of the argument

Here is a more formal way of thinking about the argument, with the presentation cleaned up a bit, and as a result more stilted:

 

1.  If something is a law of logic, then it is necessarily true. (premise)

1a. If something is necessarily true, then it is true all possible worlds. (premise).

 1b. There is something which is a law of logic. (premise)

 1c. There is something such that it exists in all possible worlds. (from 1 and 1b.)

2. For everything that exists, it is either a physical thing or a thought. (premise)

2a. If something is a law of logic, then it is either a physical thing or a thought. (from 1 and 2.).

2b. If a thing exists necessarily, then it is not a physical thing. (premise)

2c. If something is a law of logic, then it is not a physical thing. (from 1 and 2b.)

2d. If something is a law of logic, then it is a thought. (from 2a. and 2c.)

2e. There is something which is a thought. (from 1a. and 2d.)

 2f. There is something such that it is is a thought and that it is necessary that it exists. (from 1b and 2e)

3. If there is a thought, then there is a mind (of which it is a part). (premise)

3a. There is a thought and there is a mind (of which it is part). (from 2e. and 3)

3b. There is something such that it is is a thought and that it is necessary that it exists, and that there is a mind (of which it is part). (from 2f., 3.)

4. If something is a mind, then it is a person. (premise)

4a. There is a person. (from 3a and 4)

4b. There is something such that it is is a thought and that it is necessary that it exists, and that there is a mind (of which it is part) and this is a person. (from 3b. and 4)

 5. If it is necessary that there is a person, that person must be spiritual. (premise)

5a. It is necessary that there is a person such that they are spiritual. (from 4b and 5).

6. If the laws of logic exist, then it is necessary that there is person who is spiritual. (1a and 5a)

7. If it is necessary that there is a spiritual person, that person is God. (premise)

8. Therefore, God exists (from 5a. and 7)

 

The argument presented above is valid. It has the advantage of showing what the various inferences are and how many assumptions need to be given in order for the argument to work. I will present two initial problems, before going into more detail about three more serious problems.

1.2 Initial problems

There are two initial problems with the argument. Firstly, the conclusion arrived at is actually weaker than ‘God exists’, and secondly there is a false dichotomy involved in one of the premises.

1.2.1 Polytheism

The first problem is in premise 3, the inference from the existence of thoughts to the existence of a mind. Take a particular law, say the law of non-contradiction. We can run through the argument up to premise 3 and show that there is a thought, then we deduce the existence of a mind from it; call that mind ‘M1’. But now run the argument again, this time with the law of excluded middle as the example. Once again, when we arrive at step 3, we deduce the existence of a mind; call it ‘M2’. The question is, does M1 = M2? It doesn’t follow logically that they are the same mind, and they could be distinct minds for all the truth of the premises entail. If so, then we would end up with two Gods at the end. Given that there are three laws of logic considered in the paper, Anderson and Welty’s argument is compatible with there being three non-identical necessarily existing minds, or Gods, which would be polytheism. The argument is not specific to laws of logic, but could use any necessary proposition, such as those of mathematics, meaning that we could be looking at an infinite number of minds.

In order to avoid this, we would have to add in as an additional premise that in all cases such as this, M1 = M2. But this seems rather implausible. Now the argument basically says, ‘laws of logic are thoughts, and so are all necessary propositions, and they are all had by the same mind, and that mind is God’. The addition of this premise is ad hoc, meaning it has no intuitive support apart from the fact that it gets us to the conclusion. For it to be considered at all plausible, there should be some independent reason given to think that it is true. Anderson and Welty consider something close to this objection:

“It might be objected that the necessary existence of certain thoughts entails only that, necessarily, some minds exist.” (p.19)

However, they cash this out with a scenario in which there are multiple contingent minds, and then produce a counter-argument against this. They seem to miss the possibility that there are multiple necessary minds (i.e. polytheism), and as such their counter-argument misses my point entirely.

At the moment, even if you grant all the premises and assumptions, the argument establishes only that at least one god exists, which is presumably a lot weaker than the conclusion they intend to establish.

1.2.2 False dichotomy

Another problem with the argument above is that premise 2 (everything is either a physical thing or a thought) is a false dichotomy. In addition to arguing that laws of logic are not physical, one would have to present an argument for why the only two options are physical or thought. Anderson and Welty do not present any such argument, and as such there is no reason to accept premise 2. One might want to argue that everything has to be in one of two categories, but then one has to say something about difficult cases. We often say things like ‘there is an opportunity for a promotion’. On the face of it, we are quantifying existentially over opportunities. So opportunities exist. Are they physical things? Are they thoughts? Take haircuts as another example. Are they physical things? Are they thoughts? We could come up with some way of categorising things such that opportunities are a kind of mental entity, and haircuts are a type of physical entity, or explain away the apparent existential quantification as a mere turn of phrase, but the point is that is it is not straightforward to merely claim that everything is either mental or physical, and any argument which relies on this as a basic assumption inherits all the difficulties associated with it.

However, if I left things like that, then I think I would be seriously misrepresenting their actual argument. In reality, this premise is a product of trying to stick to the wording of what they say in the quoted section above. In the paper, they actually provide a positive argument for why laws of logic have to be considered as thoughts. So we could just change premise 2 to ‘the laws of logic are thoughts’, and have it supported independently by their sub-argument. I will come to their sub-argument, that the laws of logic have to be thoughts, in section 3 below.

In what follows, I will look at three aspects of their argument where I think there are weaknesses. These aspects will be with a) the claim that the laws of logic are necessary (part 2), b) with the inference from intentionality to mentality (part 3), and c) with a modal shift from necessary thoughts to necessary minds (part 4). They are not presented in order of importance, or any particular order.

2. The Necessary Truth Hypothesis

The first premise of the argument as stated above (‘If something is a law of logic, then it is necessarily true’) is ambiguous over the variety of necessity involved. There are several likely contenders for the type of modality involved: epistemic modality, metaphysical modality, logical modality. I consider each in turn.

2.1 Epistemic Modality

Anderson and Welty are clearly not attempting to make an epistemological claim about the status of the laws of logic. They say they are not interested in exploring the epistemological connection between the laws of logic and God (“In this paper we do not propose to explore or contest those epistemological relationships”, p. 1), so I think it is safe to assume that when they say the laws of logic are necessary, they do not merely mean epistemologically necessary.

 

2.2 Metaphysical Modality

More likely, when Anderson and Welty say the laws of logic are necessary, they mean the laws of logic are metaphysically necessary. They are fairly explicit about this:

“…we will argue for a substantive metaphysical relationship between the laws of logic and the existence of God … In other words, we will argue that there are laws of logic because God exists; indeed, there are laws of logic only because God exists.” (p. 1)

Nonetheless, on this reading, I find the reasons they offer for thinking the laws of logic are necessary rather strange. They say,

“…we cannot imagine the possibility of the law of noncontradiction being false” (p. 6),

And in a footnote they say that they

“…rely on the widely-shared intuition that conceivability is a reliable guide to possibility” (ibid)

The suggestion then is that the reason for thinking that non-contradiction is metaphysically necessary because they cannot imagine true contradictions. I want to bring up three issues with this methodology:

  1. Conceivability is often a poor guide to metaphysical possibility
  2. The falsity of non-classical laws is conceivable
  3. The falsity of excluded middle is conceivable

2.2.1 Metaphysical modality and conceivability

Firstly, in contrast to their ‘widely-shared intuition’, conceivability seems to me to be a relatively poor guide to metaphysical possibility. Ever since Kripke’s celebrated examples of necessary a posteriori truths in Naming and Necessity, the epistemic and metaphysical modalities have been recognised to be properly distinct from one another. One could easily adapt those famous examples to show the independence of metaphysical possibility and conceivability.

For example, one might not be able to conceive of the morning star being identical to the evening star (if you were an ancient Babylonian astrologer, etc), but we now know that their identity is metaphysically necessary. Again, one might be able to conceive of the mind existing without the brain, but it is quite plausible their independence is metaphysically impossible. Kant famously thought Euclidian geometry was a synthetic a priori truth; one must presuppose Euclidean geometry to be true when we think about the world, which would make its falsity inconceivable. Yet our world is non-Euclidian. It took pioneering and brilliant mathematicians to imagine what geometry would be like in this case, but once their work has filtered down into mainstream educated society, this otherwise inconceivable metaphysical truth has become entirely conceivable.

A somewhat similar situation is now the case with non-contradiction. Graham Priest is a very widely respected, if controversial, logician and metaphysician who has argued for the thesis that there are true contradictions. One may disagree with his methodology and conclusions, and I am in no way asserting that dialethism is anywhere as near as well supported as non-euclidian geometry, but it seems odd to rule out all the work on dialethism and paraconsistent logic simply on the basis that one cannot conceive of it being true. It could quite easily be true regardless of your particular inability to conceive of it, as history seems to show.

To push this even further, it is worth noting that conceivability (like epistemic modality, and unlike metaphysical possibility) is agent-dependent, in the sense that what is, and is not, conceivable varies from agent to agent. I may be able to conceive of something you cannot. To take an example of an agent who cannot conceive of a thesis, and then to couple that with the claim that ‘conceivability is a reliable guide to possibility’, seems to be ad hoc. Had we started with someone else’s outlook (say Graham Priest’s), we would be using exactly the same argument to reach the opposite conclusion. The strength of the argument then would depend entirely on the choice of agent.

Anderson and Welty cannot conceive of true contradictions. But should we be consulting their notion of conceivability when trying to draw metaphysical conclusions? If we are going to use conceivability as a guide to metaphysical possibility, we had better make sure we pick an agent who’s idea of what his conceivable is suitable for the job. An agent who’s idea of what is conceivable differed radically from what is in fact metaphysically possible would be unsuitable for that purpose (a five year old child, for example). Ideally,  you would want an agent who’s idea of what is conceivable supervened perfectly on what is in fact metaphysically possible. The extent to which they differed, for some particular agent, is the extent to which conceivability, for that particular agent, is not a ‘reliable guide to (metaphysical) possibility’. Whether something is metaphysically possible could be determined by consulting whether it was conceivable for a given agent only on the assumption that what is conceivable for that agent supervenes on what is in fact metaphysically possible. But this means that what is relevant here is simply whether or not contradictions are in fact metaphysically possible, as this would itself determine whether it was conceivable for that agent; not the other way round. So we have been taken on a long and winding route, via the notion of conceivability, which ultimately is seen to be relevant only to the extent that is maps to metaphysical possibility, to get to this destination.

So, is Anderson and Welty’s inability to imagine what true contradictions would be like actually any kind of evidence that true contradictions are metaphysically impossible? The answer is: only if what they can conceive of matches perfectly (at least with respect to this issue) what is in fact metaphysically possible. We have to assume that they are right for the inference to be seen as valid. And we have been given no reason to think that this is the case. Until we are, we should draw no conclusions about what is metaphysically possible based on what they are able to conceive of. If they could produce some reason to think that what they can conceive of always tracks what is metaphysically possible, or at least successfully tracks what is metaphysically possible in this case, then we would have been given some reasonwe have been given no reason to buy the claim that true contradictions are metaphysically impossible.

There might be other reasons to think that contradictions are metaphysically impossible of course, but they are not mentioned in this paper. So the argument as stated has an unjustified premise, it seems to me.

2.2.2 Conceivability and non-classical laws

In the introduction to their paper, Anderson and Welty attempt to pre-empt a response about alternative laws of logic by saying that their argument is not dependent in any way on the  choice of these particular laws. They say:

“Readers who favor other examples [of logical laws – AM] should substitute them at the appropriate points.”

I am not saying we should use any particular laws rather than the ones that they use here either. But I do want to point out that this part of the argument (about the laws being metaphysically necessary) does depend for its plausibility on the choice of laws, in contrast to the claim above. What we are being asked to accept is the inconceivability of the falsity of the laws of logic. I suggest that this far more likely to be considered true if we start with classical laws, than if we had substituted in other non-classical laws at the beginning. For example, would Anderson and Welty be prepared to defend that the falsity of the laws of quantum logic is also inconceivable? Or equally inconceivable as the falsity of the classical laws? The laws of quantum logic may well be true or false (at least from my perspective), and so their falsity is certainly conceivable to me.

Even if it turns out that they are big enthusiasts for quantum logic as well as for classical logic, finding each equally intuitive (which seems unlikely), there will surely be some far-out system of logic which has some law they find down-right implausible, for which its falsity is entirely conceivable to them. Then, their argument would not work if we substituted the laws from these logical systems instead.

This would mean that, to this extent then, their argument is only an argument for the sorts of logical systems they happen to find plausible. Thus, if a logic happens to be the one that God thinks, which also happens to be entirely implausible to Anderson and Welty (for which they find the falsity of its principles entirely conceivable), they would have failed to articulate an argument here which established a route from logic to God.

2.2.3 Excluded middle

The general argument for the laws of logic being metaphysically necessary is that their falsity is inconceivable. Here is Anderson and Welty:

“Not only are the laws of logic truths, they are necessary truths. This is just to say that they are true propositions that could not have been false. The proposition that the Allies won the Second World War is a contingent truth; it could have been false, since it was at least possible for the Allies to lose the war. But the laws of logic are not contingent truths. While we can easily imagine the possibility of the Allies losing the war, and thus of the proposition that the Allies won the Second World War being false, we cannot imagine the possibility of the Law of Non-Contradiction being false. That is to say, we cannot imagine any possible circumstances in which a truth could also be a falsehood.” (p. 6, emphasis mine)

It is telling that Anderson and Welty use the law of non-contradiction as their example here, as it is admittedly rather difficult to get one’s head around the idea of it being false (none other than David Lewis famously claimed not to be able to do so).

However, this reasoning does not really work for the law of excluded middle. What we have to do to imagine that this is the case is to imagine that there is a proposition for which neither it nor its negation is true. Aristotle makes various comments in De Interpretione IX, which he (seems to) make an argument according to which statements about the future concerning contingent events, such as ‘Tomorrow there will be a sea battle’, should be considered neither true nor false. It follows from this that the law of excluded middle would be false, at least for future contingents such as this. There is controversy as to whether Aristotle was making this argument, with the issue being one of the longest logico-metaphysical debates in the history of philosophy (being discussed by Arabic logicians, medieval logicians, and modern logicians), and there is nothing like a consensus that Aristotle was correct in making this argument, if indeed he was actually making it. However, the thesis he was putting forward (that future contingents are neither true nor false) is clearly conceivable by a great many philosophers. Indeed, it is a textbook philosophical position.

So the argument was that the laws of logic are metaphysically necessary, and the support for this is that the falsity of the laws of logic is inconceivable. Yet, while it is perhaps true for the law of non-contradiction, this seems plainly false for the law of excluded middle. It is patently conceivable that it is false. Thus, the support for the laws of logic being metaphysically necessary only covers two of the three laws they themselves provide.

If we were to respond by dropping excluded middle just to get around this problem, that would be ad hoc. To respond to this, they should explain how the falsity of excluded middle is in fact inconceivable, or provide another reason for thinking that it is metaphysically necessary.

2.3 Possible worlds 

Anderson and Welty attempt to provide additional support for the metaphysical necessity of the laws of logic by asserting the laws of logic are true in all possible worlds. Again, leaning heavily on the notion of conceivability, they say:

“[w]e cannot imagine a possible world in which the law of noncontradiction is false…Now you may insist that you can imagine a possible world—albeit a very chaotic and confusing world—in which the Law of Non-Contradiction is false. If so, we would simply invite you to reflect on whether you really can conceive of a possible world in which contradictions abound. What would that look like? Can you imagine an alternate reality in which, for example, trees both exist and do not exist?” (p. 6).

Firstly, for the law of non-contradiction to be false, there only has to be one true contradiction, and it is not required that contradictions ‘abound’. I think I could conceive of a possible world where there is a contradiction; and it might be the actual world. Perhaps the liar sentence (‘this sentence is false’) is an example. Maybe in the actual world everything else is classical apart from the liar sentence. If so I have conceived of a world in which the law of non-contradiction is false. This does not mean that ‘contradictions abound’, and we do no have to imagine trees both existing and not existing. I seem to have met their challenge.

Remember, I do not have to show that the liar sentence is in fact both true and false at the actual world. All I have to do is be able to conceive of a world in which the law of non-contradiction is false. It seems to me that, given the work of dialethists on this area, it is conceivable.

Perhaps sensing the need for further argument, they say that contradictory worlds cannot be conceived of, because possible worlds are by definition consistent:

“The criterion of logical consistency—conformity to the law of noncontradiction—is surely the first criterion we apply when determining whether a world is possible or impossible. A world in which some proposition is both true and false, in which some fact both obtains and does not obtain, is by definition an impossible world. The notion of noncontradiction lies at the core of our understanding of possibility.” (p. 6 – 7)

This passage is quite hard to interpret. However, Anderson and Welty seem to argue in a circle. They seem to think non-contradiction is necessary because inconsistent possible worlds are inconceivable. But the only reason they give for thinking inconsistent worlds are inconceivable is, by definition, we use consistency as a sort of yard-stick to ‘determine’ whether a given world is indeed possible. Thus, laws of logic are necessary because they are true in all possible worlds, but laws of logic are true in all possible worlds because the laws of logic are necessary.

I think the direction of travel from possible worlds to possibilities is misguided. Anderson and Welty appear to be under the impression there is some metaphysically significant sense in which we can check possible worlds to see if they really are possible or not; as if possible worlds were conceptually prior to possibilities. The picture painted is that there is a sort of a priori rationalistic access we have to the set of possible worlds which we can consult in order to find out about what is really possible. This idea is actually warned against by Kripke in Naming and Necessity. There he argues against the identification of a prioricity and necessity:

“I think people have thought that these two things [a prioricity and necessity – AM] must mean the same of these reasons: … if something not only happens to be true in the actual world but is also true in all possible worlds, then, of course, just by running through all the possible worlds in our heads, we ought to be able with enough effort to see, if a statement is necessary, that it is necessary, and thus know it a priori. But really this is not so obviously feasible at all.” (p. 38)

It also seems to fly in the face of Kripke’s famous telescope remark:

“One thinks, in this picture, of a possible world as if it were like a foreign country. … it seems to me not to be the right way of thinking about the possible worlds. A possible world isn’t a distant country that we are coming across, or viewing through a telescope.… A possible world is given by the descriptive conditions we associate with it” (Kripke,Naming and Necessity, p 43-44).

I think, apparently in contrast to A&W, possible worlds are just a way of cashing out our notion(s) of possibility. If we are thinking about what is logically possible (with classical logic in mind), then when constructing the possible worlds we make sure to get them consistent (to keep non-contradiction) and also maximal (to keep the law of excluded middle). So a truth assignment for a formula in classical propositional logic is a ‘possible world’, so long as the truth assignment covers all cases and gives each formula only one truth value.

However, different notions of logical consequence lead to different constructions of worlds. In intuitionist logic, where we want to have mathematical propositions for which there is no formal proof to be neither true nor false, the ‘possible worlds’ (or ‘constructions’) are not maximal. They may simply leave both p and not-p out altogether. Equally, for a dialetheist who believes there are true contradictions in the actual world, where both p and not-p are true, the notion of ‘possible world’ leaves out the notion of consistency (or, if you prefer, the dialetheist includes both possible worlds and ‘impossible worlds’ in his semantics). In the actual practice of formal and philosophical logic, one normally starts with a notion of logical consequence (or of ‘laws’) and then uses logical consequence to cash out what the appropriate semantic apparatus will be like. On this understanding (the usual understanding), one cannot use the fact that maximal and consistent possible worlds do not have contradictions to tell us which logical laws to accept as true, as we need an idea of which logical laws to accept prior to accepting anything about possible worlds. So the circularity of A&W’s reasoning here is completely avoidable. They just need to appreciate the role possible worlds semantics plays in philosophical logic. If they were able to see the restrictions they put on possible worlds (maximal, consistent, etc) are not mandatory, they would be able to more readily conceive of how a possible world could be inconsistent or non-maximal. Anderson and Welty appear to resemble the 17th century geometer who cannot imagine parallel lines ever meeting and concludes the meeting of parallel lines is metaphysically impossible. Thus, Anderson and Welty’s failure to imagine what non-classical worlds would be like seems to be a limitation on their part and should not be used as a support for their argument.

In sum, Anderson and Welty provide two reasons for thinking LOL are metaphysically necessary: (i) their falsity is inconceivable and (ii) they are true in every possible world. We have shown (i) provides flimsy support for their subconclusions and (ii) is based on several confusions concerning philosophical logic and possible worlds.

2.4 Logical Necessity

Finally, the claim could instead be read as saying the laws of logic are logically necessary truths. In some sense, one cannot deny the laws of logic are logically necessary truths, but this sense is trivial. Usually, the claim that p is logically necessary, with respect to a system S, simply means the truth of p does not violate any logical law of S. When p is an instance of a logical law of S, the claim becomes vacuous. If we said ‘p is chessessary’ means ‘the truth of p does not violate any of the laws of chess’, then, provided p is one of the laws of chess, obviously, p is chessessary. The claim, while true, is trivial. The necessary truth of laws of logic, if construed as logical necessity, is not a substantive claim, such as that associated with the necessary truth of the existence of platonic objects, or of God. Logical necessity is more like the way that statements about numbers depend on which number system you have in mind; is there a number between 1 and 2? No, if you mean ‘natural number’, yes if you mean a more complex notion of number. To ask ‘but is there really a number there?’ is arguably not a sensible question at all. If this is correct, then there may be no more to the notion of logical necessity than ‘necessary given system S’, and as such each logical law is true in its own system and (in general) is not in another system.

In sum, Anderson and Welty claim that the laws of logic are necessary truths. They do not seem to be making a claim about epistemological necessity; their arguments for a claim about metaphysical necessity are highly dubious; the claim that it is about logical necessity makes it vacuous. Thus, either this part of the argument is unsupported, or trivial.

3. Propositions are intentional

The most controversial aspect of Anderson and Welty’s argument is the move from the laws of logic being propositions, through them being intentional, to them being mental (or thoughts). In order to see what is at stake here, we need to be clear about both intentionality and propositions.

Anderson and Welty’s argument at this stage seems to be of the following form:

  1. All propositions are intentional.
  2. Everything intentional is mental.
  3. Therefore, all propositions are mental.

This little argument is clearly valid, so if the premises are also true, we would have to accept the conclusion.

I think there are reasons to doubt both premises. More specifically, there is reason to doubt that the arguments presented in Anderson and Welty’s paper support these premises.

3.1 Intentionality

The central idea behind intentionality is aboutness. Typical examples of intentional things are thoughts. So if I have a thought, it is always a thought which is about something, and it seems that there couldn’t be a thought which is not about anything. The typical philosophical authority referred to in this context is Brentano:

“Every mental phenomenon is characterized by what the Scholastics of the Middle Ages called the intentional (or mental) inexistence of an object, and what we might call, though not wholly unambiguously, reference to a content, direction towards an object (which is not to be understood here as meaning a thing), or immanent objectivity. In presentation something is presented, in judgement something is affirmed or denied, in love loved, in hate hated, in desire desired, and so on.” (Psychology from an empirical standpoint, Franz Brentano, 1874, p 68)

It has become customary to call the following claim ‘Brentano’s Thesis’:

x is intentional iff x is metnal

As this is a biconditional claim, it can be split into two conditionals:

  1. Everything intentional is mental
  2. Everything mental is intentional

It is standard for philosophers to argue that there are mental states which are non-intentional (Searle’s example is a vague an undirected feeling of anxiety), and thus that the second condition in Brentano’s thesis is false.

Anderson and Welty say that they are really concerned with the first of these conditions, and that

“…the argument is unaffected if it turns out that there are some non-intentional mental states” (p. 17)

What they need to do is show that there is nothing which is both intentional and non-mental. There seem to be counter-examples here though. Firstly, sentences of natural language seem to be intentional, in that they are about things. The sentence ‘Quine was a philosopher’ is about Quine. Yet that sentence is not itself mental. I can think about the sentence, of course, but the sentence itself is not mental.

The common response to this is to say that sentences are only derivatively intentional. On their own sentences are not about anything, but when read by a mind they become invested with meaning and this makes them about something. Sentences are just non-intentional  vehicles for communicating intentional thoughts. Anderson and Welty want to say that, while there may be instances of derivatively intentional phenomena (like sentences), anything which is inherently intentional is mental.

There are other approaches which hold that there are inherently intentional non-mental phenomena, such as that of Fred Dretske, according to which intentionality is best understood as the property of containing information. So an object is intentional if it contains some information. The content of the information is what makes the object about something else. So, an example is that there is no smoke without fire. In this sense, the smoke contains information about the presence of fire. Other examples stated on the Stanford page include:

“A fingerprint carries information about the identity of the human being whose finger was imprinted. Spots on a human face carry information about a disease. The height of the column of mercury in a thermometer carries information about the temperature. A gas-gauge on the dashboard of a car carries information about the amount of fuel in the car tank. The position of a needle in a galvanometer carries information about the flow of electric current. A compass carries information about the location of the North pole.“

All these objects are not mental, yet they carry information about things, and so are intentional in Dretske’s sense of the word. If this approach is correct, then Anderson and Welty’s inference is blocked (as there are things which are non-mental yet intentional), and with it the rest of the argument is blocked. You could not argue from the laws of logic being propositions, to them being intentional, to them being thoughts, to them being the thoughts of God. The jump from being intentional to being mental would be invalid if Dretske’s approach, or one like it, were correct.

There are problems with Dretske’s account of intentionality, as you would expect from a philosophical theory, but if Anderson and Welty want to advance the thesis that all intentional things are mental, they need to provide counter-arguments to proposals such as Dretske’s.

3.1.1 The mark of the mental

In fairness, Anderson and Welty do point to a paper by Tim Crane, about which they claim:

“Following Brentano, Crane argues (against some contemporary philosophers of mind) that intentionality, properly understood, is not only a sufficient condition of the mental but also a necessary condition” (p. 17, footnote)

If this were right, then they would have some support for their claim that everything which is intentional is mental. However, I think they are using Crane to argue for a thesis that his paper does not support, and I will explain why I think this.

Crane’s main concern in his paper is to deal with intentionality being a necessary condition for being mental (i.e. that everything mental is intentional). The sufficiency claim (that everything intentional is mental), which is the only thing that Anderson and Welty are really concerned with for their argument, is only tangentially addressed by Crane in that paper. Crane’s motivation, as he explains, is to account for why Brentano would have asserted his thesis if there were so many seemingly obvious counter-examples to it:

“If it is so obvious that Brentano’s thesis is false, why did Brentano propose it? If a moment’s reflection on one’s states of mind refutes the thesis that all mental states are intentional, then why would anyone (including Brentano, Husserl, Sartre and their followers) think otherwise? Did Brentano have a radically different inner life from the inner lives of contemporary philosophers? Or was the originator of phenomenology spectacularly inattentive to phenomenological facts, rather as Freud is supposed to have been a bad analyst? Or—surely more plausibly—did Brentano mean something different by ‘intentionality’ than what many contemporary philosophers mean?“(Crane, Intentionality as the mark of the mental, p. 2)

He says that he is not specifically interested in the historical and exegetical question of what Brentano and his followers actually said, but rather with the following question:

“…what would you have to believe about intentionality to believe that it is the mark of the mental?” (Crane, Intentionality as the mark of the mental, p. 2)

Thus, when Crane talks about ‘intentionality’, we should remember that he does not mean “what many contemporary philosophers mean” by the term. Rather, he has a specific aim in mind: to cash out what intentionality would be like if it was, by definition, the ‘mark of the mental’, i.e. not what intentionality is like, but what it would be like if Brentano’s thesis was true.

Most of the paper is directed at supposed examples of mental phenomena that are non-intentional, such as sense perception and undirected emotion. He gives an account of what it would mean to consider these as intentional. This effort is being addressed to defend the first part of Brentano’s thesis (that everything mental is intentional).

Although the focus of the paper is on the first part of Brentano’s thesis, Crane does directly confront the second part, i.e. the notion that everything intentional is mental:

“I have been defending the claim that all mental phenomena exhibit intentionality. Now I want to return to the other part of Brentano’s thesis, the claim that intentionality is exclusive to the mental domain. This will give me the opportunity to air some speculations about why we should be interested in the idea of a mark of the mental.” (Crane, Intentionality as the mark of the mental, p. 14)

Crane addresses the Chisholm-Quine idea that sentences are intentional and non-mental phenomena. Chisholm (1957) proposed a criterion whereby we can tell if a sentence is intentional or not, which is basically if it is used in non-extensional (i.e. in intensional) contexts. Crane calls this the ‘linguistic criterion’. In response to this, Crane recommends that the position he is defending (intentionalism) should reject the linguistic criterion altogether. I will quote his reasons for recommending such a position in full:

“And given the way I have been proceeding in this paper, [the rejection of the linguistic criterion] should not be suprising. Intentionality, like consciousness, is one of the concepts which we use in an elucidation of what it is to have a mind. On this conception of intentionality, to consider the question of whether intentionality is present in some creature is of a piece with considering what it is like for that creature—that is, with a consideration of that creature’s mental life as a whole. To say this is not to reject by stipulation the idea that there are primitive forms of intentionality which are only remotely connected with conscious mental life—say, the intentionality of the information-processing which goes on in our brains. It is rather to emphasise the priority of intentionality as a phenomenological notion. So intentionalists will reject the linguistic criterion of intentionality precisely because the criterion will count phenomena as intentional which are clearly not mental.” (Crane, Intentionality as the mark of the mental, p. 15)

Thus we can see here that Crane rejects the criteria by which one says that some sentences are intentional, not because sentences are only ‘derivatively’ intentional, but “precisely because the criterion will count phenomena as intentional which are clearly not mental“. Ultimately, on Crane’s picture of intentionality, sentences are not intentional because they are not mental.

When it comes to propositions, it is actually quite controversial and non-standard to consider propositions to be mental (i.e. to be thoughts). Just like sentences, they are usually considered to be intentional (in the standard sense, in that they are about things) yet not mental. Anderson and Welty point to Crane as someone who has defended the thesis that everything intentional is mental. Yet, when we come to consider Crane’s special sense of intentionality, we see the author recommending that we should resist applying it to propositions just because we would end up classifying “phenomena as intentional which are clearly not mental“. Crane doesn’t deduce mentality from things that are otherwise obviously intentional; rather he ensures that everything intentional is mental by restricting the application of intentionality to only things which are obviously mental. It is a recommendation to change the meaning of intentional to get the desired result. If Anderson and  Welty want to say that the reason they have for claiming that propositions are mental is that they are intentional in Crane’s sense, then it is doubtful that this is true. It is doubtful that propositions are intentional in this sense precisely because they are not obviously mental. We could only use Crane’s sense of intentionality if we already thought that propositions were mental. Prima facie, it seems that are only as intentional as sentences, and if sentences are deemed non-intentional for Crane, then so should propositions. Thus, I see no benefit for Anderson and Welty for pointing us in the direction of Crane here.

 

4. Modal shift

Let’s say we grant that the laws of logic are (metaphysically/logically) necessary, and that they exist in every (metaphysically/logically) possible world. Let’s also grant that they are inherently intentional, and that they are therefore thoughts. What we would have established at this juncture is that there are some necessarily existing thoughts, which are constitutive of the laws of logic (and all other metaphysically necessary propositions). From this, Anderson and Welty draw the conclusion that this implies the presence of a divine mind:

“But now an obvious question arises. Just whose thoughts are the laws of logic? There are no more thoughts without minds than there is smoke without fire … In any case, the laws of logic couldn’t be our thoughts—or the thoughts of any other contingent being for that matter—for as we’ve seen, the laws of logic exist necessarily if they exist at all. For any human person S, S might not have existed, along with S’s thoughts. The Law of Non-Contradiction, on the other hand, could not have failed to exist—otherwise it could have failed to be true. If the laws of logic are necessarily existent thoughts, they can only be the thoughts of a necessarily existent mind.” (p. 19)

So the inference from thoughts to a mind is as follows:

  1. There are no thoughts without minds.
  2. Necessarily there are thoughts.
  3. Therefore, necessarily there is a mind.

The scope of the necessity claim in the conclusion needs to be cashed out properly, for us to be able to judge whether the inference is valid. The precise logical form of the argument is not entirely clear to me, but here is my best shot:

  1. (∃x (Tx) → ∃y (My))    (If there is a thought, then there is a mind)
  2. □(∃x (Tx))                     (Necessarily, there is a thought)
  3. □(∃x (Mx))                   (Therefore, necessarily, there is a mind)

This argument follows, as it requires nothing but modus ponens, and the closure of necessity with respect to the theorems of propositional logic. The problem is that 3 is a de dicto necessity, where Anderson and Welty presumably want to have a de re necessity. They presumably want the conclusion to be that there is something that is a necessary mind (de re necessity), rather than it being necessary that there something which is a mind (de dicto necessity).

Here is an illustration of the difference between them. It is necessary that there is someone who is the oldest person alive. Say someone, let’s call them Raj, is the oldest person alive. It is not necessary of Raj that he is the oldest person, because he could die and the title of oldest person would pass to someone else. It is necessary that someone has the title (at least so long as there are people), but there is nobody of whom it is necessary that they have the title.

A&W want to say that there is a mind (God’s mind) of which it necessarily exists, which is a de re claim, and not just that it is necessary that some mind or other exists, which is a de dicto claim. The difference is between □(∃x (Mx)) (‘It is necessary that there is a mind’), and (∃x □(Mx)) (‘There is a necessary mind’).

If we change their argument to put the de re conclusion in that they want, it becomes the following:

  1. (∃x (Tx) → ∃y (Mx))
  2. □(∃x (Tx))
  3. (∃x □(Mx))

The problem is that 3 does not follow from 1 and 2. For an illustration of the counterexample (where premise 1 and 2 are true, but this de re reading of the conclusion is false), consider the following:

It may be that each possible world has its own unique mind, which thinks the laws of logic. This would mean that premise 1 is true, as whenever there is thought, there is a mind; and it would mean that premise 2 is true, as there is thought that exists in every possible world  (specifically, the laws of logic). However, on this model, no mind exists at more than one world; each logic-thinking mind is contingent. So, ‘□(∃x (Mx))’ is true, in that at every world there is a mind, but ‘(∃x □(Mx))’ is false, in that there isn’t a thing which is a mind in every world.

Anderson and Welty do anticipate this response:

“It might be objected that the necessary existence of certain thoughts entails only that, necessarily, some minds exist. Presumably the objector envisages a scenario in which every possible world contains one or more contingent minds, and those minds necessarily produce certain thoughts (among which are the laws of logic). Since those thoughts are produced in every possible world, they enjoy necessary existence.” (p. 19, footnote 31)

This is essentially exactly the issue laid out above. They are saying that the inference to the de dicto conclusion might be seen as invalid, on the basis of a model in which there are multiple contingent minds. This is how my counter-example above worked; it involved each world having its own unique contingent mind.

They have two responses to such a move:

“One problem with this suggestion is that thoughts belong essentially to the minds that produce them. Your thoughts necessarily belong to you. We could not have had your thoughts (except in the weaker sense that we could have thoughts with the same content as your thoughts, which presupposes a distinction between human thoughts and the content of those thoughts, e.g., propositions). Consequently, the thoughts of contingent minds must be themselves contingent. Another problem, less serious but still significant, is that this alternative scenario violates the principle of parsimony.” (p. 19-20, ibid)

To begin with we have the claim that “thoughts belong essentially to the minds that produce them“. So I have this particular thought about how lovely the weather is today. While you may also be thinking that the weather is lovely today, you are not literally having the same thought as me; rather you are having a different thought, even if it has the same content. Thus, this thought is had by me (and only me) in every world in which it exists. So being a thought of mine is an essential property of that thought. Because I am a contingent being, and do not exist in every possible world, it follows that there are worlds in which my particular thought about how lovely the weather is today also does not exist. Thus, given that thoughts are essentially of the minds that think them, contingent beings can only have contingent thoughts.

I am quite sympathetic to this response. It seems right to me that contingent beings can only have thoughts that are contingent too. While the content of my thought can be necessary, the thought itself cannot be. The counterexample above does seem to require there being contingent minds. Thus, in order for the thought to have the necessity required, the mind also has to be necessary.

However, while I find all this quite agreeable, there still seems to be a problem here, although I do find this quite hard to put into words completely clearly, and maybe it is something that could be cleared up with a little more detail on the ontology of how the laws of logic relate to God’s thoughts on A&W’s part. Anyway, here is how I see it.

The distinction between the thought and the content of the thought is that the former cannot be shared across minds (I cannot have the same thought as you), while the latter can be (I can have a thought with the same content as yours). This, it seems to me, generates a little problem for the divine conceptualist. It seems like the categories of thought and content are mutually exclusive; if I think of my coffee mug, then the thought is not the content of the thought. If I think about the thought I just had about the coffee mug, then my previous thought (about the mug) is the content of a new thought (about the thought about the mug). It seems unintelligible that one and the same thought could be the content of itself. Self-reflection, it seems, is hierarchical, not circular. Call this ‘the principle of the Distinctness of Thought from Content‘ (or PDTC). If PDTC is true, then it is impossible for a thought to be the content of itself.

Of course, there is the discussion in Metaphysics about God being thought that thinks thought. The idea is that God, the pure actuality, has to be thinking which has itself as it’s own object of thought. Aristotle seems to anticipate something like the PDTC, when he says the following:

“[God’s] Mind thinks itself, if it is that which is best; and its thinking is a thinking of thinking.

Yet it seems that knowledge and perception and opinion and understanding are always of something else, and only incidentally of themselves. And further, if to think is not the same as to be thought, in respect of which does goodness belong to thought? for the act of thinking and the object of thought have not the same essence.

The answer is that in some cases the knowledge is the object. In the productive sciences, if we disregard the matter, the substance, i.e. the essence, is the object; but in the speculative sciences the formula or the act of thinking is the object. Therefore since thought and the object of thought are not different in the case of things which contain no matter, they will be the same, and the act of thinking will be one with the object of thought.” (Aristotle, Metaphysics, book 12, 1074b-1075a)

So the claim is that the divine mind thinks itself. Then in the second paragraph the objection is posed that thoughts are always about something distinct from themselves. The ‘answer’ provided by Aristotle is that “in the speculative sciences the formula or the act of thinking is the object”. Logic certainly counts as an example of a speculative science (par excellence), and so it seems that Aristotle’s claim is that when God thinks about logic, his thought is identical to the object of the thought. If this is the case, Aristotle presents no argument for it (at least not that I know of). And it seems quite strange, if taken to be the claim that when one thinks about logic, the thought is the content of the thought. It seems quite clear that when I think of the laws of logic, they are the content of my thought, and not the thought itself.

Here is an argument for my claim:

  1. If p can be thought by a mind m and a mind m’ , where m ≠ m’, then p is the content of their thought. (Contents of thoughts can be shared by minds)
  2. If t is a thought had by m, then t cannot be had by any mind m’, where m ≠ m’. (Thoughts cannot be shared by minds)
  3. Two people can both think of the law of non-contradiction.
  4. Therefore, the law of non-contradiction can be the content of thoughts. (from 1 + 3, modus ponens)
  5. Therefore, the law of non-contradiction cannot be a thought. (from 2 + 4, modus tollens)

The first two premises of this argument make the distinction between thought and contents of thoughts made by A&W above, and the third just says that two people can both think the LnC. It follows that the LnC cannot be a thought.

For the divine conceptualism of A&W, the law of non-contradiction is ultimately supposed to be God’s thought. So take the law of non-contradiction, ‘LnC’, and some thought had by God, T. If LnC = T, then (by the PDTC) it is not the content of T. But what is the content of T? What is God thinking about when he has the thought T which is the law of non-contradiction? The obvious answer would be that God is thinking about propositions, and how each proposition cannot be true along with its negation. But the problem with that is that it is the law of non-contradiction. That would make the LnC the content of T, and (if thoughts cannot be their own content) that would mean that T isn’t LnC. So when God thinks T, he must think about something other than the LnC.

 

But why is it then that T is LnC, if the content of T is something other than that propositions cannot be true with their negations? Nothing else is relevant! It seems incredible to consider that the content of T is (say) this coffee mug, while also insisting that T is the LnC. If the content of T, whatever it is, is not the mutual exclusivity of propositions and their negations, then it can only be arbitrarily connected with LnC. This makes it a mystery, ultimately, why it has anything to do with LnC, let alone being the LnC.

The question is: in virtue of what could a thought T, whose content is irrelevant to the LnC, be said to be the LnC?

There are three ways out of this problem, it seems to me.

One is to bite the bullet and say that God thinks something with completely arbitrary content, and this just is the LnC. It is a hard pill to swallow.

The next escape route would be to say that the LnC is in fact the content of T. This explains why it is that I can also think about LnC; both me and God think about the same thing. However, this option is rather like the horn of the Euthyphro dilemma that says that God likes good actions because they are good. If God has a thought which has LnC as its content, then the LnC is not to be associated with God’s thought any more than it is if I have a thought with the LnC as its content. The significance of God in the equation has been completely removed. It seems that the central claim of a divine conceptualist has been undermined if we take this route.

The only other escape route I can see here is to deny that LnC cannot be both T and the content of T. Perhaps when it comes to God’s thoughts, they can be both thought and content together. So the LnC is the content of God’s thought (i.e. he is thinking about how propositions and their negations cannot both be true) and that this thought is the law itself. It may seem unintelligible for us humans to have such a thought, but maybe this is how God thinks.

The problem with this route, it seems to me, is that it undermines the analogy between divine thoughts and mere human thoughts. When the divine conceptualist says that laws of logic are divine thoughts, we take it that the claim is saying that they are thoughts that are at least a somewhat similar to human thoughts. This seems to be required for the argument from propositions being intentional in section 3 (above). Propositions don’t seem to be mental on their face, but the idea is that they are because they are intentional, and everything intentional is mental. This last claim is undermined significantly if the extension of ‘mental’ includes things which are significantly unlike human thoughts. To the extent then that we have to broaden the category of thoughts to include the seemingly unintelligible idea of a thought being at once its own content, the universal claim is also undermined. Consider the claim spelled out in full:

“Everything intentional is mental, and and under the term ‘mental’ I include things which are very unlike human thoughts because they have properties which are unintelligible if applied to human thoughts (such as a human thought which is its own content)”

Where we have arrived at, is a destination where the central claim of the divine conceptualist is that the laws of logic are to be associated with some aspect of God, which in some sense resembles human thoughts, but that in another sense is nothing like human thoughts. Saying that the laws of logic are thoughts at all on this picture seems quite a difficult thing to maintain.

5. Conclusion

It seems to me that there are quite a few problems with the argument presented in The Lord of Non-Contradiction. Some of them are quite subtle, like the final one concerning the precise relationship between the laws and the thoughts of God, and it is entirely possible that they could be cleared up. Some of them are quite technical, such as the details of how possible worlds are cashed out in the metaphysics of modality, and A&W could be forgiven for not realising them. Some of them, I suggest, are quite a lot more serious, such as the inference from intentionality to mentality. I don’t see this being fixed up with a little revision or by spelling something out a bit more clearly. It is utterly foundational to the argument and it seems to me that it is just fallacious.

Transcendental arguments and the logic of presupposition.

0. Introduction 

In this post I will look at the transcendental methodology employed in philosophy and how far it can be said to be similarly employed in the presuppositional apologetics of Van Til. There is some controversy over the correct logical form of the so-called ‘transcendental argument for God’ (TAG), and I contrast looking at it cashed out using implication, with presupposition, and with ontological dependence. Each has its own difficulties as a rendering of what Van Til says, so in the end I am not sure which way it is supposed to be taken. On the way I discuss how Putnam thought he had refuted the sceptical hypothesis that I could be a brain in a vat, various features of validity in the non-classical logic of presupposition, and end with a discussion about metaphysical dependence.

1 Transcendental arguments.  

Transcendental arguments are somewhat controversial in philosophy. They go back at least to Kant, who used them in his Critique of Pure Reason. There, he was responding to the scepticism of philosophers like Descartes and Hume. It could be that one’s sense data are radically divorced from the external world and it would be impossible to tell, etc. Kant’s strategy is essentially to show that this seemingly neutral starting point between the sceptic and the philosopher, such as the basic fact of one’s own sense-data etc, itself has certain preconditions. These preconditions are things without which the starting point would itself be impossible. Kant wants to drill down into these foundations and show that these often include the very things the sceptic wants to call into question. Thus, when a sceptic calls these certain things into question, she has in fact relied on those things being the case for the question to be meaningful at all. This type of argument is a ‘transcendental argument’.

There is a charming example of such an argument, given in characteristically aphoristic manner by Wittgenstein in On Certainty:

“383. The argument “I may be dreaming” is senseless for this reason: if I am dreaming, this remark is being dreamed as well – and indeed it is also being dreamed that these words have any meaning.” Wittgenstein, On Certainty.

The idea here seems to be that the sceptic is calling into question the existence of the external world, with the suggestion that one may be dreaming. But, says Wittgenstein, in dreams it can seem like a collection of words has meaning, when in actual fact they don’t; one can dream that a word is meaningful, when in fact it isn’t. So the very meaningfulness of each string of words we encounter also becomes one of the things we cannot be certain about, if we entertain the idea that we are dreaming. Thus, the meaningfulness of the sceptical challenge itself is something we must also call into question! This means that in order for one to suspend doubt over the meaningfulness of the sceptical hypothesis (to take it seriously), one must in effect presuppose that they are not dreaming, an act which itself rules out the sceptical hypothesis from consideration.

1.1 Transcendental arguments in analytic philosophy

Apart from their use by Wittgenstein, in the later half of the 20th century this type of argument enjoyed a period of being in vogue in analytic philosophy, primarily due to the work of Peter Strawson, Hillary Putnam and Donald Davidson.

Consider Putnam’s transcendental argument, which is found in chapter 1 of his 1981 book, Reason, Truth and History (read it here). In a sense, he is developing Wittgenstein’s argument from above. Putnam’s argument purports to refute the sceptical hypothesis that we might be brains in vats, merely  being stimulated to have sensations by some evil scientist. Often, this problem is seen primarily in epistemic terms, in the sense that the challenge is how one could know they weren’t brains in vats. Putnam’s approach, in contrast, is not to look primarily into the notion of knowledge per se, but instead to focus on linguistic issues surrounding what would have to be the case for the sentence ‘I am a brain in a vat’ to be true. His claim is that, once these considerations are taken into account, it becomes evident that the sentence ‘I may be a brain in a vat’ is self-refuting:

“A ‘self-refuting supposition’ is one whose truth implies its own falsiry. For example, consider the thesis that all general statements are false. This is a general statement. So if it is true, then it must be false. Hence, it is false. Sometimes a thesis is called ‘self-refuting’ if it is the supposition that the thesis is entertained or enunciated that implies its falsity. For example, ‘I do not exist’ is self-refuting if thought by me (for any ‘me’). So one can be certain that one’s self exists, if one thinks about it (as Descartes argued).

What I shall show is that the supposition that we are brains in a vat has just this property. If we can consider whether it is true or false, then it is not true (I shall show). Hence it is not true.” (Putnam, Reason, Truth and History, 1981 p. 7-8)

The argument is (as stated in the last two sentences):

  1. If ‘I am a brain in a vat’ could be either true or false, then it is false.
  2. ‘I am a brain in a vat’ could be either true or false.
  3. Therefore, ‘I am a brain in a vat’ is false.

Premise 2 is no more than the sceptic would concede. The burden is to justify the first premise. This premise is supported by semantic considerations, specifically of the reference for the term ‘a vat’ in the proposition ‘I am a brain in a vat’. Putnam’s argument is that there are three general ways that the phrase ‘a vat’, which is a referring term, could get its reference to the object it refers to. Either a referring term:

  1.  has an intrinsic property of referring to the referent (nomenclaturism),
  2. or it refers to the referent via an internal concept on the part of the speaker/hearer (internalism),
  3. or it refers to its referent due to some external relation the speaker/hearer has to the referent (externalism).

Putnam first goes after the notion that words have intrinsic references. On this view, to produce some words, either by speaking or writing them, is to refer to the things that they name. The refutation of this idea is simple. Take an ant crawling in the sand who happens to write out the name ‘Winston Churchill’. The ant has produced those shapes, but it is obvious that the ant has not referred to Winston Churchill. Thus, signs do not intrinsically refer to things.

The underlying thought here is that if signs are ever used to genuinely refer to things, they need to be supplemented by something. Usually, this something additional which is added to the otherwise non-referential sign is a mental act of intention. The words are internally linked to a concept, and it is because of this internal mental association that they are about something (i.e. genuinely refer to things). This is internalism. However, Putnam also rejects this this thesis, on the grounds that that internal mental images also do not intrinsically refer to things. His counter-example is that of two physically identical depictions of a tree, one on Earth and one on a treeless planet. The one on Earth is formed by the usual photographic process. The one on the treeless planet has been formed by pure chance (say, paint dripping onto the bit of paper at random). The photo of the tree is being looked at by a normal person on Earth, while the picture of the tree is found on the treeless planet by a human who has never seen or heard of a tree. Each person has identical mental sensations upon seeing the photo (because the two pictures are qualitatively identical), but only one of the people thereby refers to a tree.

The reason for the difference in this case, says Putnam, is that there is a causal chain which we could in principle trace back from brain of the thinker of the image on Earth, through the light waves hitting his eyes, back into the photo, which was itself caused to have the arrangement of colours it does because of the light that came from the actual tree. In the treeless planet case, there is no causal link backwards from the event of the light entering the person’s eyes to any actual trees. If reference was fixed in the head, then as the internal situation is the same in both cases, they should both refer to the same object. Yet they don’t. The view that Putnam is advocating here is ‘semantic externalism’. Part of what it means to successfully refer to something is for there to be conditions external to the agent reading, writing, hearing or seeing, etc, the referring term. As he says, when it comes to reference it ain’t all in the head.

When we come to the case of the ‘brain in a vat’ proposition, if we apply semantic externalism to it, then we see that the only way that ‘I am a brain in a vat’ could be true is if ‘a vat’ refers to an actual vat. The reference to (in particular) an actual vat can be secured only if there is a causal chain coming from that vat to the brain. While, in a sense, every sensation that the brains-in-vats have is causally related to the vat they are in (and the electronic current being fed through it), their word “vat” is not semantically linked to it in any particular way (at least, no more than every word they use, and it is not the case that every word a brain uses refers to the vat it is sitting in). Rather, when the brains think propositions like ‘that is a tree’, they refer to the objects they take themselves to be in causal relation to in the virtual world they live in; but they fail to refer to anything in the actual world at all:

“How can the fact that, in the case of the brains in a vat, the language is connected by the program with sensory inputs which do not intrinsically or extrinsically represent trees (or anything external) possibly bring it about that the whole system of representations, the language-in-use, does refer to or represent trees or anything external?”

The answer is that it cannot. The whole system of sense-data, motor signals to the efferent endings, and verbally or conceptually mediated thought connected by ‘language entry rules’ to the sense-data (or whatever) as inputs and by ‘language exit rules’ to the motor signals as outputs, has no more connection to trees than the ant’s curve has to Winston Churchill. (ibid, p.13)

While there is certainly more that can be said about Putnam’s argument, this much is clear. Premise 1 of the argument has been given quite a detailed line of supporting argument, which pits the attractive looking causal theory of reference (semantic externalism) against the other alternatives. Could there be a different theory not considered by Putnam? Sure. Could one of the theories considered by Putnam be rescued against his objections. Sure. The point is just that there is a substantive argument here, and it is clear what Putnam thinks is at stake when he says that the sceptic’s proposal is self-defeating.

2. TAG

It is into this tradition that we find Van Til’s transcendental argument for the existence of God (TAG). Van Til never provided a formal version of his argument, but alluded to it frequently, and we find this reinforced throughout the work of Greg Bahnsen. I have always taken it that the form of the argument is as follows:

  1. If God did not exist, human experience would be unintelligible.
  2. Human experience is intelligible.
  3. Therefore, God exists.

However, I think there is reason to doubt that this could really be the form of the argument, given various considerations I will go through below.

Van Til thought that he was providing more than just another argument for God; not just another argument that sits alongside the ontological argument, or cosmological argument, etc. He thought that he was providing a new and more sophisticated way of defending Christianity. His problem with the traditional arguments is that they seemed to concede something to their opponent which gives the game away already from the outset. This was that it was possible to reason at all independently from God. The idea here is that the approach with the traditional arguments is to see if the existence of God follows from premises which are themselves neutral on the question of whether God exists. These arguments thus start from assumption that there are such premises, ones which are neutral. However, it is precisely this that Van Til found objectionable. In contrast, Van Til wanted to say that there are no such premises; no such neutral ground.

This leads to the curious claim by Van Til that his transcendental argument is neither deductive nor inductive:

“Now the only argument for an absolute God that holds water is a transcendental argument. A deductive argument as such leads only from one spot in the universe to another spot in the universe. So also an inductive argument as such can never lead beyond the universe. In either case there is no more than an infinite regression. In both cases it is possible for the smart little girl to ask, “If God made the universe, who made God?” and no answer is forthcoming. This answer is, for instance, a favorite reply of the atheist debater, Clarence Darrow. But if it be said to such opponents of Christianity that, unless there were an absolute God their own questions and doubts would have no meaning at all, there is no argument in return. There lie the issues. It is the firm conviction of every epistemologically self-conscious Christian that no human being can utter a single syllable, whether in negation or in affirmation, unless it were for God’s existence. Thus the transcendental argument seeks to discover what sort of foundations the house of human knowledge must have, in order to be what it is. It does not seek to find whether the house has a foundation, but it presupposes that it has one.” (Van TIl, Survey of Christian Epistemology, Section 11.)

Van Til’s claim here is strange. The version of TAG above is a deductively valid argument. Let p = ‘God exists’ and q = ‘human experience is intelligible’. Then the form of the argument is:

  1. If not-p, then not-q
  2. q
  3. Therefore, p

If this is correct, then the argument is simply a version of modus tollens, which is a textbook example of a deductively valid argument. It is puzzling why Van Til would think that TAG isn’t deductive.

One option, of course, is that I have given it the wrong logical form. However, I have given it the same form as Kantian transcendental arguments (the same sort of form as that of Wittgenstein and Putnam, etc). The Stanford article on transcendental arguments backs up that my phrasing is correct:

“As standardly conceived, transcendental arguments are taken to be distinctive in involving a certain sort of claim, namely that X is a necessary condition for the possibility of Y—where then, given that Y is the case, it logically follows that X must be the case too.”

So, either the Stanford article and I are wrong about what the form of a transcendental argument is, or Van Til was using the term differently, or he was just wrong about whether it was deductive.

What is the correct logical form of Van Til’s TAG?

2.2. The inadequacy of classical implication

There is another issue with what Van Til said, and it is one that adds weight to the thought that his argument does not have the simple form of a modus tollens. Let’s look again at some particular phrases in the quote from him above:

“…unless there were an absolute God their own questions and doubts would have no meaning at all.”

and,

“…no human being can utter a single syllable, whether in negation or in affirmation, unless it were for God’s existence.”

Van Til is saying more than just that if there were no God then the claims about the existence of logic or the possibility of argument would be false; he is saying that without a God these claims ‘would have no meaning at all‘, and that nothing could be said at all ‘whether in negation or affirmation‘. The logic used in the version of TAG we have been discussing here (the Kantian form) doesn’t capture this feature well at all. Rephrased as a logically equivalent modus ponens, it says:

  1. If logic, then God.
  2. Logic.
  3. Therefore, God.

If the consequent of the first premise (‘God’) is false, then the conditional is only true if the antecedent is also false. This means that, if it is true that God is a necessary condition of logic, and if it is false that God exists, then the claim that logic exists is false. But this is exactly where Van Til’s claims from above seem to go further. He doesn’t say that these claims are false, but, as it were, neither true nor false (‘no meaning at all’, ‘whether in negation or in affirmation’). With the classical logic we are using here, this position is not captured. Thus, we have reason to think that this cannot be what Van Til meant when he used the transcendental argument for the existence of God.

3. The logic of  presupposition.

In 1905, Russell published a paper called ‘On Denoting‘. In that paper, he advocated a semantics for descriptions, i.e. phrases like ‘the third planet from the sun’, ‘your favourite ice cream flavour’, and ‘the present king of France’. In particular, he was interested in the latter type of example, as these cases (where there is apparent reference to things that do not exist) had posed problems for previous theories, such as Frege’s. His solution was essentially to say that ‘the present King of France is bald’ has a logical form which is more complex than it appears on the surface; it is in fact a conjunction of two claims:

  1. There is exactly one thing which is the king of France, and
  2. That thing is bald.

Because the first conjunct is false (because there is no king of France), the whole conjunction is false as well. It remains false for the same reason if we change the second conjunct to ‘that thing is not bald’. Thus, ‘the present King of France is bald’ and ‘the present King of France is not bald’ are both false.

In 1953, Peter Strawson proposed an alternative theory to Russell’s. According to Strawson, the sentence ‘the present King of France is bald’ should be considered to be neither true nor false. The reason for this is that it presupposes that there is a king of France. Unlike Russell, who claimed that the sentence implicitly implied there is a king of France, Strawson said it has this as a presupposition.

Presupposition, in Strawson’s sense, differs from implication precisely on the issue of the consequent being possibly neither true nor false. This idea is cashed out by Van Fraassen here. In that we find the standard Strawsonian definition of presupposition:

Presupposition)      (A presupposes B) iff (if A is either true or false, then B is true)

This says that when A presupposes B, A has a truth-value only if B is true; if B is false, then A is neither true nor false.

3.1 TAG with Presupposition instead of Implication

This definition of presupposition does considerably better at capturing the spirit of Van Til’s claims from above. He wanted to ‘up the ante’ by saying that its not just that if what the atheist says is false then God exists, but that if what the atheist says is meaningful at all, then God exists. This is captured by saying:

  1. Whatever an atheist says presupposes that God exists.
  2. Therefore, for whatever an atheist says, if it is either true or false, then God exists.

We are not talking about the specific truth value of what the atheist says, but into the conditions which make it such that it has either truth value.

This also seems to do justice to the following remarks of Van Til:

“Thus the transcendental argument seeks to discover what sort of foundations the house of human knowledge must have, in order to be what it is.”

Thus, we have some reason for thinking that the logical form of Van Til’s argument involves presupposition in this sense. This is the view of the presuppositionalist Don Collett (see this).

3.2 Presuppositional validity

The logic of presupposition, a hot topic in philosophy of language today, has some interesting features. One thing that is particularly relevant here is how far this notion of presupposition differs from classical implication.

The first thing to notice about it is that it is a non-classical logic. This is because there can be formulas which lack a truth value altogether. It is standard to think of the semantics for this sort of logic as the strong Kleene tables.

The fact that some propositions can lack a truth-value makes the notion of validity for presupposition different to that of implication. For instance, while modus ponens is valid for presupposition, modus tollens is not. This means that the following is valid:

  1. A presupposes B
  2. A
  3. Therefore, B.

But the following is not:

  1. A presupposes B
  2. not-B
  3. Therefore, not-A

This is because if A presupposes B, and B is not true, then A is neither true nor false. And in the strong Kleene semantics, if A is neither true nor false, then so is not-A.

It also follows from this that in the logic of presupposition the following form, which is invalid in classical logic, is valid:

  1. A presupposes B
  2. Not-A
  3. Therefore, B

Call this argument form ‘modus presuppans‘. If A presupposes B, then even if not-A is true, B is true. Even the falsity of A entails B, if A presupposes B.

One reason for thinking that this is a more faithful way of rendering Van Til’s idea is how well it fits with other claims he made. In one of his more memorable illustrations, Van Til said that the unbeliever is like a child who can only slap her father in the face because he his supporting her on his knee. The point is supposed to be that even the claim that Christianity is false presupposes that God exists. This result seems to be obtained if we grant that Christianity presupposes that God exists. It is in fact just the argument form from above:

  1. Christianity presupposes God.
  2. Christianity is false.
  3. Therefore, God.

This argument form is valid given Strawson’s logic of presupposition. It seems then that we have a form of TAG that fits well with Van Til’s aims.

4. Problems

The notion of validity for presupposition outlined here might be considered to capture some of the intuitions and ideas of Van Til. However, it also faces some serious problems.

  1. Firstly, it might be completely arbitrary, or even actually inconsistent.
  2. Secondly, there is a disanalogy between the most natural renderings of the first premise of TAG and textbook cases of Strawsonian presupposition, and this suggests that it is a different relation altogether.

4.1 Arbitrariness, or Inconsistency?

It seems quite clear that the central existential claim in Christianity could be cashed out in the following biconditional:

‘Christianity is true if and only if God exists’.

Assume we mean by ‘God’ the Christian God, i.e. the triune God referred to in the Bible, etc. Then this looks fairly watertight. Could Christianity be true if this God does not exist? Could (the Christian) God exist and Christianity not be true? It seems quite clear (to me) that the answer to both questions is ‘no’.

The main claim of the presuppositionalist argument, when cashed out using presupposition rather than implication is that Christianity presupposes that God exists, because every fact is supposed to presuppose that God exists. But this causes a problem with the existential biconditional above. They can’t both be true, or we get a contradiction.

The following argument (the ‘from truth to existence’ argument) is valid:

  1. Christianity is true if and only if God exists
  2. Christianity is true.
  3. Therefore, God exists.

We can also reason the other way (the ‘from falsity to non-existence’ argument):

  1. Christianity is true if and only if God exists
  2. Christianity is false.
  3. Therefore, God does not exist.

But if we also add in that Christianity presupposes that God exists, then ‘from falsity to non-existence’ becomes invalid:

  1. The truth of Christianity presupposes the existence of God.
  2. Christianity is false.
  3. Therefore, God exists.

This is just a version of modus presuppans, and is valid on the Strawson/Kleene semantics. It means that if Christianity presupposes the existence of God, then the falsity of Christianity is compatible with the Christian God existing. And we can also reason the other way as well:

  1. The falsity of Christianity presupposes the non-existence of God.
  2. Christianity is true.
  3. Therefore, God does not exist.

Thus we have an inconsistent set of propositions. If the existential biconditional is true, then the truth of Christianity is incompatible with the non-existence of God. If it is true that the truth of Christianity presupposes that God exists, then it is compatible with the non-existence of God. They are either compatible or incompatible, which means either the existential biconditional has to go or the claim that Christianity presupposes that God exists has to go. I find the biconditional much more obviously fundamental to Christianity, and I find it hard to make sense out of the result that Christianity is true and God does not exist. For me, that is pretty strong evidence that the biconditional is to be kept at the expense of the presuppositional claim.

I want to point to another problem before suggesting why this problem is happening.

4.2 The Disanalogy

We can begin to see a disanalogy between the usual first premise of TAG and standard examples of Strawsonian presupposition. Here are some examples of Strawsonian presupposition:

  1. ‘The King of France is bald’ presupposes that ‘there exists a King of France’.
  2. ‘I have stopped beating my wife’ presupposes that ‘I have a wife’.
  3. ‘Julius is a bachelor’ presupposes that ‘Julius is an unmarried male’.
  4. ‘He set me free’ presupposes that ‘somebody set me free’, etc.

In most of these cases, the relationship between the antecedent and consequent of the presupposition is very obvious:

  • 3 seems to be merely a case of definition (which is linguistic),
  • 4 is just existential generalisation (which is linguistic),
  • and arguably so is 1 (so it is also linguistic),
  • 2 is an example of a leading question (which is linguistic).

On the other hand, it is not so obvious that the existence of logical laws (etc) presupposes that God exists. Part of the reason for this difference is because 1-4 above are all obviously linguistic phenomena; the relationship being brought out in the examples is between elements of language. In contrast, when Van Til states his first premise as “unless there were an absolute God their own questions and doubts would have no meaning at all” and (as I discuss below) this seems more naturally considered to be a metaphysical claim; i.e. not it is not a relation between elements of language, but a relation between things that actually exist.

Here is a way of thinking about it which makes it easier to see why Van Til’s statement seems to be metaphysical and not linguistic. Once we rearrange Van Til’s statement into modus ponens form, we see what the antecedent is, and we can state one of its presuppositions:

1a. The atheist’s own questions and doubts have meaning.

And a presupposition of 1a is claimed to be this:

1b. God exists.

Now compare someone saying 1a with someone saying 2a, along with one of its presuppositions:

2a. I have stopped beating my wife.

2b. I have a wife.

If the Strawsonian account of presupposition, which applies to 2a, is supposed to apply to 1a, then we should expect the way these sentences are related to their respective presuppositions would be quite similar, i.e. the way 1a is related to 1b and the way 2a is related to 2b should be quite similar. But it seems clear to me that the reason that 2b is presupposed by 2a is primarily a linguistic reason. It is a product of the meaning of the words, as used in normal contexts. Most people have the linguistic intuition that 2b is a presupposition of 2a, and this means that we are happy to grant it as true if used as a premise in an argument. There are tricky cases of presupposition, for sure, but 2a-2b isn’t one of those cases. We could even disagree with Strawson, and perhaps agree with Russell, on the details of the semantic relation between 2a and 2b, but it is not seriously disputed that they have some linguistic/semantic relation or other that preserves the rational inference from 2a to 2b.

The relation between 1a and 1b doesn’t seem to be linguistic like that. It doesn’t seem to be part of the meaning of the words “The atheist’s own questions and doubts have meaning” that “God exists”. At the very least, it isn’t a commonplace statement of linguistic meaning, like 2a and 2b. This is why people (other than presuppositionalists) are not happy to concede it as a premise in an argument. It isn’t obvious at all, unlike with 2a and 2b. This utter lack of semantic intuition here is evidence that the claim that ‘“The atheist’s own questions and doubts have meaning” semantically presupposes “God exists”‘ is just false.

4.3 Metaphysical dependence

I would go further and claim that this is intentional. Why is it that 1a implies 1b, on the Van Tilian picture? The answer is essentially that all truths are metaphysically grounded in God, on this view. Van Til often says things which make it clear he has this sort of metaphysical idea in view:

“Man’s ethical alienation plays upon the background of his metaphysical dependence.” (Van Til, Survey of Christian Epistemology, chapter 14, emphasis mine).

It is the fact that man (and everything there is at all) is metaphysically dependent on God that is motivating Van Til. His point is that whatever an atheist might appeal to, anything that exists in any sense, it will end up being something which is metaphysically dependent for its existence on God. This metaphysical dependence is what seems to be driving the idea of presupposition here, and it is not a linguistic phenomenon. The claim isn’t that 1a presupposes 1b in the linguistic Strawsonian sense, but in a stronger metaphysical, we might say ‘Van Tilian’, sense. If this is right, we should really drop the talk of presupposition, and talk explicitly of metaphysical grounding, or metaphysical dependence.

But if we go down this road, we seem to have ended at a destination that is quite far from a transcendental argument, for now the argument is something like this:

  1. For everything there is, if it exists, then God exists (metaphysical dependence claim)
  2. If an atheist questions whether God exists, then the atheist exists (assumption)
  3. If an atheist questions whether God exists, then God exists (1, 2, modus ponens)
  4. An atheist is questioning whether God exists (assumption)
  5. Therefore, God exists.

This argument is valid, and premises 2 & 4 are very likely to be granted by an atheist, and 3 follows from 1 & 2, so all that is required to be supported is 1, which is itself the Van Tilian metaphysical dependence claim. All the Van Tilian needs to do is justify the first premise (their main claim) and they will be able to prove that God exists merely from the presence of an atheist questioning whether God exists. This seems to capture rather well the Van Tilian idea of the child slapping their father in the face.

So it seems that premise 1 is what needs to be justified. But there already is an argument which attempts to get us to this destination, which is the argument from contingency. In fact, the metaphysical dependence argument above is just a special instance of the argument from contingency; we could call it the argument from dependency. If this is correct, then there is no special transcendental method in TAG, and it is just another classical argument for God, alongside the other well-known deductive arguments.

5. Conclusion. 

In conclusion then, the precise form of TAG remains illusive. It seems very hard to square everything that Van Til said into one logical system that doesn’t also give up something seemingly important to how he described it.

Accounting for logic – again

0. Introduction

In this post I will be looking at a blog entry on the BibleThumpingWingnut website, entitled ‘Christianity and Logic’. The entry is written by Tim Shaughnessy, and takes a Clarkian angle. Shaughnessy’s argument is basically that Christianity can provide an ‘epistemological foundation’ for logic, using Scripture as a sort of axiomatic basis for logic, and that ‘the unbeliever’ cannot provide such a foundation, or ‘account’, for logic. If this is the first time you are encountering this Clarkian view, have a look at this article by Clark. I have written on this topic before, and I think that many of those points are directly relevant here.

For instance, here I argue that there is no binary choice between Christianity and non-Christianity; there are different versions of Christianity, different monotheistic religions, different versions of theism, and different versions of atheism. This version of Christianity is just one tiny dot on a huge intellectual landscape. To argue by elimination that this version Christianity is correct, means you have to eliminate a possibly infinite variety of systems. Pitting (this version of) Christianity against ‘the unbelieving worldview’ is already to commit the fallacy of false dichotomy. We might want to call this version of it the ‘Bahnsen fallacy’, in honour of its main witness.

More specifically with regards to the broadly Clarkian idea of deriving logical principles from the Scriptures, I have argued here that this is incoherent. Derivation requires a logical framework, which is constituted in part by logical principles (or axioms); derivation is a logical notion, and thus presupposes logical principles.

There are some new points which seem to be worth raising however, given the particular presentation by Shaughnessy, and so I will be exploring those ideas here.

  1. ‘What is logic?’ 

Shaughnessy’s view of logic seems to be entirely gained from the study of Clark, in that he is the only author cited (rather than, say, Aristotle or Frege) on the topic of what logic is. This is unfortunate, because it seems that  Shaughnessy is unaware of the controversy surrounding the topic. So, we see him state that logic is “the correct process of reasoning which is based on universally fixed rules of thought”. This idea, that logic is about laws of thought, is a historically significant idea, coming to prominence in the 18th and 19th centuries, but it has never been a universal consensus among logicians and philosophers. These days it is not widely represented among practising logicians and philosophers at all (see this for a quick overview). The reason for this is that in the contemporary setting logic has a much broader extension, and can cover systems which deviate wildly from how we might realistically model thought (which is the preserve of logicians and computer scientists working in artificial intelligence). Logic, thought of broadly as concerning valid inference for various types of argument forms, is not considered to be tied in any special manner to how we think. There may be a logic to how we think, but logic is not just how we think. Never-the-less, Shaughnessy makes no mention of this, and simply asserts that logic has this 18th century relation to cognition.

His out-of-date description of logic becomes confounded with outright misunderstandings when he spells out what he considers to be the three laws of thought. It is utterly standard, when going down this non-modern view, to list the three laws of thought as: ‘the law of identity’, ‘the law of non-contradiction’ and ‘the law of excluded middle’. What is odd is the way these are cashed out by Shaughnessy. For instance, the law of non-contradiction is cashed out as “A is not non-A”, and the law of excluded middle is cashed out as “A is either B or non-B”. It seems to me that there is a failure of Shaughnessy to distinguish clearly between different aspects of vocabulary. There is a fundamental difference between logical vocabulary that refers to things directly (like ‘Alex’, ‘London’, ‘your favourite type of ice cream’, etc) and those which express facts (‘Alex is in London’, ‘vanilla is your favourite type of ice cream’, etc). The first are called ‘terms’, and the latter are called ‘propositions’. Propositions can be thought of as made up of terms standing in certain relations to one another. Crucially, propositions are given truth-values, true or false; terms are not. So, ‘Alex’ isn’t true or false; but ‘Alex is in London’ is either true or false. In Shaughnessy’s expression of the law of non-contradiction, we have a letter ‘A’, which seems to be a term, as it is something we are predicating something to, but then the predicate we are ascribing to it is that it is “not non-A”. The problem is that we have a negation fixing to a term, ‘non-A’. As I have pointed out before, negation is a propositional operator, and its function is to switch the truth-value of the proposition is prefixes from true to false (or vice versa). If we prefix it to a referring term, like ‘A’, then (because terms don’t have truth values), the resultant operation is undefined.

The conventional way to express the law of non-contradiction is with a propositional variable, ‘p’, which ranges over all propositions, as follows:

¬(p ∧ ¬p)    (‘it is not the case that both p and not-p’)

If you want to express this using propositions where the relation of terms is explicit (i.e. in a first-order manner), then it would be as follows, where ‘Px’ is a predicate and ‘a’ is a term:

¬(Pa ∧ ¬(Pa))   (‘it is not the case that a both is and is not P’)

The same problem infects “A is either B or non-B”. The correct way to express this is just that for every proposition, either it is true, or it’s negation is true:

p ∨ ¬p     (‘either p or not-p‘)

It is bizarre to say that either ‘A is B or non-B’. There is no predicate ‘non-B’; rather, either B applies or it doesn’t. Take the proposition that I am 6 feet tall. Either I am 6′ or I am not. In the second case I don’t have a property, called non-6′. What would this property be? Every height other than 6′? I am not 6′, but I am also not every height other than 6′. I just am 5’11”. So the way Shaughnessy expresses excluded middle is also confused.

And it’s not like stating non-contradiction and excluded middle is extremely complicated; all it involves is: ‘p or not-p’, and ‘not both p and not-p’. He hasn’t simplified them for a non-specialist audience – he has just misrepresented them.

So we have an out-of-date view of logic, coupled with a technically incorrect presentation of the principles under discussion. It’s not a great start to an article about the nature of logic.

1.1 Logic in the Bible?

Perhaps Shaughnessy’s misrepresentation of the basic laws of thought is more understandable when we see where he is going with all of this. The ultimate point he will be driving at is that these laws are found in the Bible. Various snippets of the Bible are then presented as evidence of this, but because they don’t really fit that well with the laws when expressed properly, he has written them in such a way that the claim that they are found in the Bible becomes (slightly) easier to swallow. Here is what he has to say about it:

“The law of non-contradiction (A is not non–A) is an expression of the eternal character and nature of God, “for he cannot deny [contradict] himself” (2 Tim. 2:13). The law of identity (A is A) is expressed in God’s name, “I AM WHO I AM” (Exodus 3:14), and the law of the excluded middle (A is either B or non-B) is expressed in Christ’s own words, “He who is not with Me is against Me” (Luke 11:23).“

Let’s take these one at a time. It is hard to take them seriously, but I will try.

1.1.1 Non-Contradiction

In the book of Timothy, it is said that God cannot contradict himself. I say that this is completely irrelevant to the principle of non-contradiction. There is a difference between saying things, and things being true (or false). The law of non-contradiction is about the latter, not the former. It isn’t a rule which says ‘thou shalt not contradict thy self’. It says that there is no proposition for which both it and its negation are true. It doesn’t proscribe what you can or cannot say at all.

For example, I can contradict myself, and sometimes do. Does this mean I broke the law of non-contradiction when I did so? No, of course not. Imagine I say ‘It is sunny now, at 14:07’, and then a few minutes later, ‘It was not sunny then, at 14:07’. The two sentences I uttered were expressing (from different times) that it was and was not sunny at 14:07. Obviously, it would be a contradiction if both of these were true, as p and not-p would both be true (exactly what the law of non-contradiction forbids). But were they both true? That would mean that it was both sunny and not sunny at the same time. Conventionally thinking, this is impossible. Therefore, while I contradicted myself, I didn’t break the law of non-contradiction. I expressed a true proposition, and then when I uttered the negation of that proposition what I said was false (or vice versa). Contradicting yourself isn’t a case of breaking the law of non-contradiction.

Back to the Biblical example, God cannot contradict himself. So what? The law of non-contradiction is true even though people can contradict themselves. An example of a being, even an infinite one, who cannot contradict themselves, is not an example of the law of non-contradiction. To think that it is, is to mix up the idea of saying two contradictory things with two contradictory propositions both being true.

1.1.2 Identity

Shaughnessy does manage to state the law of identity correctly, which is that (for all referring terms) A = A. Everything is identical to itself. According to the example given, the law of identity is expressed in “I am who I am”, which is the answer God gives to Moses in the book of Exodus. It has always baffled me as to why this has been seen as a profound thing for God to say here. God tells Moses to go to the Pharaoh and bring the Israelites out of Egypt. Moses basically says, ‘who am I to do that?’ God says that he will be with Moses, but Moses wants a bit more reassurance for some reason:

Moses said to God, “Suppose I go to the Israelites and say to them, ‘The God of your fathers has sent me to you,’ and they ask me, ‘What is his name?’ Then what shall I tell them?”

God said to Moses, “I am who I am. This is what you are to say to the Israelites: ‘I am has sent me to you.’” (Exodus, 3: 13-14)

One of my favourite comedy series ‘Knowing Me, Knowing You’, staring Steve Coogan, features a pathetic TV chat show host, called Alan Partridge. In episode 2, he is interviewing an agony aunt called Dannielle, played by Minnie Driver, who is listing the things she likes in men:

Dannielle: Power is attractive. Sensitivity. Sense of humour. I like a man who knows who he is.

Alan: I’m Alan Partridge.

If you think that the law of identity is expressed by Exodus 3:14, then you should also hold that it is expressed in this little bit of Alan Partridge script.

I’m just going to leave that there.

1.1.3 Excluded Middle

In the last example, Jesus saying “He who is not with Me is against Me” is an example of someone expressing something stronger than the law of excluded middle. The logical law of excluded middle says that for every proposition, p, either it or its negation is true. There are two propositions being considered in the saying above, put together in the form of a disjunction. The two propositions are:

‘x is with Jesus’

‘x is against Jesus’

The combined disjunction is universal, in that it applies to everyone:

For all x: either x is with Jesus or x is against Jesus.

We could write this in first order logic as follows:

∀x (Wx ∨ Ax)

However, this isn’t a logical truth. There is no logical reason to stop someone being neither with nor against Jesus. The following is not a logical contradiction:

∃x (¬Wx ∧ ¬Ax)      (‘there is an x such that it is not with Jesus and it is not against Jesus’)

If Jesus had said ‘Either you are with me or not with me’, then he would have said something which would have been logically true (because of the law of excluded middle). It would have the following form:

∀x (Wx ∨ ¬Wx)

Therefore, when Jesus says that everyone is either with him or against him, something which goes beyond the law of excluded middle, and it is not a logical truth. Why this has been picked to be an instance of this law can only be put down to either the author not understanding what the law actually states, or being so determined to find something that fits the pattern that they wilfully ignore the fact that it doesn’t.

1.2 The problem

If we are thinking of the examples of someone not contradicting themselves, or of everyone being split into the ‘with’ or ‘against’ categories, then we have (at best) particular instantiations of these rules, but not examples of the rules. Consider the difference between:

a) A sign which said ‘do not step on the grass’.

b) Someone walking along the path next to the grass.

With regards to a), we would say that it had the rule, ‘do not step on the grass’, written on it. On the other hand, b) would just be an instance of the someone following the rule.

Finding Jesus saying ‘Either you are with me or you aren’t’ would be like finding someone walking next to the grass. Sure, it instantiates what the law of excluded middle is about, but it isn’t the rule. The rule is general. It says ‘nobody walk on the grass’, not just this guy in particular; excluded middle says ‘for all propositions, either p or not-p‘. The Bible nowhere makes generalised statements about language, reasoning or validity.

So the examples fail in that they aren’t actually instances of the rules (as the laws themselves are muddled by Shaughnessy), but they also fail because (even if we pretend that they do instantiate the rules) they aren’t examples of the rules. The Bible doesn’t have the law of excluded middle stated in it. It instantiates it, in that every proposition expressed in the Bible is either true or false, but that is not important at all. Every proposition expressed in any book is either true or false! Exactly the same goes for non-contradiction. There is nothing special about the Bible such that you can find the three rules of thought in it. If you want to see what a book looks like which explicitly has the rule of non-contradiction in it, read Aristotle’s Metaphysics, book IV, section 3:

“...the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, the same attribute cannot at the same time belong and not belong to the same subject and in the same respect.“

For Aristotle, the basic declarative sentence (the basic proposition) is the ascription of an attribute (or property) to a subject, and this is explored explicitly by him at great length. So ‘Alex is happy’ is this type of sentence. When he says “the same attribute cannot at the same time belong and not belong to the same subject and in the same respect”, this is simply to say that there cannot be any proposition, such as ‘Alex is happy’, for which it is true that ‘Alex is happy’ and it is also true that ‘Alex is not happy’, i.e. we cannot have both p and not-p. In contrast to the Bible then, Aristotle does not just give an instance of a sentence of the same form as the law of non-contradiction, like ‘it is not that Alex is both happy and not happy’ – he reflects on this and states the general proposition in its generalised form. It is explicit. With the case of the Bible, we have shoddy eisegesis going on, where Aristotelian principles are being read into a text that doesn’t have them.

So far, not great. Shaughnessy makes the following claim:

“It is precisely because the laws of logic are embedded in Scripture that the Christian is able to establish from an epistemological standpoint that they are fixed and universal laws. Without this epistemological foundation, we cannot account for the laws of logic“

Well, given what I’ve written above, it should be pretty obvious that I disagree with that. The laws of logic are not in the Bible. Given this, by his own standards, Shaughnessy doesn’t have an ‘epistemological foundation’ and ‘cannot account for’ these laws. Too bad.

2. An epistemological foundation for logic

Shaughnessy then presents the standard presuppositional line, the one we all knew was coming, where they brag about how great their ‘account’ of logic is, and how rubbish ‘the other account’ is.

“The unbeliever cannot account for logic in his own worldview and therefore cannot account for his ability to think rationally. The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered. Never has an adequate response been given. In formal debates, the challenge is often ignored by the unbeliever, yet the challenge demands an answer because debates presuppose logic. The unbeliever is required to use logic in order to make his argument against Christianity consistent and intelligible, but only the Christian worldview can account for logic. He is therefore required to rob the Christian worldview in order to make his argument against Christianity intelligible.”

Ok, well we’ve all seen this over and over again. So I am going to meet the challenge head on, and provide a few different ‘accounts’ of logic, which could be ‘epistemological foundations’ for it.

First of all, what do we mean by and ‘epistemological foundation’ for something? Well, I take it to mean something in virtue of which we can come to know something. So, an epistemological foundation for x could be thought of an an answer to the question, ‘how is it that we are able to know about x?’

Given that, our question is: ‘How is it that we are able to know about logic (and in particular those logical laws)?’. In order to play the game right, I shall not appeal to God in any way, I will just go along with the idea that logical laws are things that have some kind of ontology capable of allowing reference to them, and I will just pretend that the three principles cited by Shaughnessy (identity, non-contradiction and excluded middle) really are ‘logical laws’, even though it is a clumsy and out-dated way to talk about logic. I will play the game anyway, just to be a good sport.

2.1 They are self-evident.

Here is the first way of answering that question: we are able to know about logical laws because they are self-evident truths. This just means that to think about them is to know that they are true. They don’t need anything else to support my knowledge of them, because they are self-evident. This is a really simple answer, and there isn’t much more to be said about it.

The response might be something like: “that’s rationalism! You are saying that all knowledge is rationally determined based on self-evident truths, like Spinoza!” Before we get into the standard disputes about rationalism and empiricism, I want to point out that I don’t need to also say that this is how I get knowledge generally. The question is about logical laws only. Maybe these are the only self-evident truths, and I gain knowledge about other parts of the world through empirical access, or mystical intuition, or because a ghost illuminates the right answer for me. Who cares? The point is that this plainly is an answer to the question ‘how could we know about logical laws?’. It doesn’t require a God of any type, so is available to an atheist (or a theist, or really anyone apart from those people who for some reason are committed to the view that there are no such things as self evident truths). They are pretty good candidates for self-evident truths if you ask me, and I would dispute the claim that there are candidates that are more plausible (is ‘cogito ergo sum’ more plausible as a self-evident truth than non-contradiction? They seem even, if anything). If anything is self evident, its the law of non-contradiction. So this view is plausible, at least on first blush.

If there is a secret cheat-card answer to this that presuppositionalist apologists have, I’ve never heard it. Remember the challenge: “The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered.” Well, that’s one account. Here is another one.

2.2 They are synthetic a priori knowledge

Here is my second proposal: we are able to know about logical laws because they are synthetic a priori truths. In the Critique of Pure Reason, Immanuel Kant summarises his views on this type of knowledge as follows:

“…if we remove our own subject or even only the subjective constitution of the senses in general, then all constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us. What may be the case with objects in themselves and abstracted from all this receptivity of our sensibility remains entirely unknown to us. We are acquainted with nothing except our way of perceiving them, which is peculiar to us, and which therefore does not necessarily pertain to every being, though to be sure it pertains to every human being.”

Synthetic a priori knowledge has the property that it is integral to how we see the world. It is subjective, in the sense that Kant explains above (that is, if we were to remove the subject, then it would also disappear), but it is also universal, in the sense that it applies to “every human being”. So, space and time may be known a priori, yet the knowledge is not simply analytic (i.e. true in virtue of the meaning of the words used), but synthetic (true because of more than just the meaning of the words used). What we know is the form of our intuition, which is a non-trivial fact about the way things are, but is also directly available to us, as subjects, a priori. We are programmed to see the world in a spatio-temporal way.

Kant has his own ways of demonstrating that this is the case, using transcendental arguments which inspired Van Til and should be familiar to all presuppositionalist apologists. Essentially you show that the contrary leads to a contradiction. So we have to see the world in terms of space and time, because the contrary view (where we do not see the world in such a way) leads to complete incoherence. Space and time are necessary presuppositions of the intelligibility of experience (a phrase presuppositionalists love to use). As such, we have transcendental proofs for them. Presuppositionalists, like the gang at BibleThumpingWingnut.com, should welcome this methodology, as it is basically the sophisticated version of the Van Tillian method they endorse themselves, only directed squarely at epistemological issues.

I say that we just point the synthetic a priori machinery at the laws of logic, and there we go, an epistemological foundation for the laws of logic. We know excluded middle, non-contradiction and identity as forms of intuition. Everyone has them (which explains their apparent universal character). If we try to conceive the world without them, we get incoherence (which shows their necessity).

On this view, we are not suggesting that these principles have metaphysical necessity. As good Kantians, we simply say that we cannot know about the numenal realm. But this should be perfectly acceptable to those presuppositionalists who throw the gauntlet of providing an epistemological foundation for the laws of logic. They are the ones, after all, who think that these principles are the ‘laws of thought’. On this reading of what they are, the Kantian line seems perfectly suited.

It would be really hard to imagine a presuppositionalist mounting a successful attack against this view, which didn’t also backfire and undermine their own transcendental arguments. You can’t have it both ways. If you are going to use transcendental arguments for God, I’m going to use them for what I want as well.

2.3 They are indispensable

Here is one last attempt. How do we know about the laws of logic? Well, they are indispensable to our best theories of science, so it is reasonable to believe in them. This is a version of the Quine-Putnam indispensability argument for the existence of mathematical entities. Here is how I see the argument going:

  1. We are justified to believe in all the entities that are indispensable to our best scientific theories.
  2. Laws of logic are indispensable to our best scientific theories.
  3. Therefore, we are justified to believe in the laws of logic.

I’m not personally that convinced by premise 2, but presumably Shaughnessy and all those who throw down the presup gauntlet are. Premise 1 says that we have justification to believe in those things which are indispensable to our best theories, and I think this is going to be accepted by most people. We believe in viruses because our best science tells us that they exist. It is reasonable to hold the belief in viruses on this basis.

This argument doesn’t say that we have conclusively established that the laws of logic exist, but it provides justification. Presuming a broadly fallibilist idea of justification (as most contemporary professional epistemologists do), then even though the indispensability argument doesn’t ensure the laws of logic exist, it provides sufficient support for the belief that they do to be justified. So it allows us to have justified belief in the laws of logic existing. If that belief is also true, then we know that they exist. Thus, this is an explanation of how we come to know (as in ‘justified true belief’) that the laws of logic exist. Thus, it is an answer to how we can have knowledge of them, and ultimately part of an epistemic foundation, and an ‘account’, of them.

3. Conclusion

So, above are three distinct views about the epistemological foundations of logic. None of them required God, or Jesus, or Reformed theology at all. No doubt, they will continue, over at BibleThumpingWingnut.com, to claim that “The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered. Never has an adequate response been given“. In reality though, for those of us who have spent a long time doing philosophy seriously, these claims are easily countered. I’m not saying I have all the answers; I’m saying that they don’t. I don’t know what the ‘right answer’ is about the nature of logic, or how epistemology and logic fit together. It is an incredibly complicated area. As with philosophy, it may be something we will ultimately never answer. It may be that for some reason the question itself doesn’t make sense, but that this realisation doesn’t come for many generations yet. Maybe the answer was given in some obscure scroll, now long forgotten by history. All these possibilities remain. But to claim that there is only one answer to this sort of question is silly. I have thought up the three examples here by referencing well-known ideas in philosophy. I could have easily plundered the great works of philosophy to find dozens more (such as platonism, structuralism, formalism, intuitionism, plenitudinous platonism, etc, etc). Don’t be fooled into thinking that in such a rich and complicated area of philosophy as this, that there are any easy answers.

Creation ex nihilo

0. Introduction

I have recently come across a blog written by Richard Bushey, which has lots of typical apologetical arguments summarised by the author. As such, it is an interesting place to look around to find typical bad arguments to straighten out.

Here I want to look at one in particular, not because there is anything original about it, but really because there is nothing original about it. The post is an example of the sort of regurgitation of arguments made by people like William Lane Craig that one often encounters on the internet. Here is the post, entitled ‘Can a universe emerge from absolutely nothing?‘. In it, Bushey explores the idea of the creation of the universe ex nihilo (or ‘from nothing’), and rehearses some of the common arguments for why this isn’t possible.

  1. Setting

The setting for the topic discussed in the post is ultimately the cosmological argument (probably specifically the kalam cosmological argument popularised by William Lane Craig, on which I have written before). The idea is that one of the arguments put forward to prove the existence of God is that the existence of the universe requires a causal explanation, which could only be God, as a necessarily existing being. The response to this that Bushey is addressing here is to basically call into question whether the universe requires causal explanation. As he explains:

Many people seem to take it for granted that things do not just appear with absolutely no cause. But it would be quite convenient for the atheist if it were the case that this were a possibility. Atheism would then be able to deflect one of the seminal arguments for the existence of God. We need to be able to provide some justification for thinking that universes cannot emerge from absolutely nothing.

Bushey offers five distinct points, and I want to look at three of them (I have nothing to say of any note about quantum vacuums, and am happy to grant that God doesn’t need a cause to exist, at least for now). The three points I will address here are labelled by Bushey as:

a) ‘Nothing’ has no causal powers.

b) What if universes could come from nothing?

c) A good inductive conclusion.

      3. ‘Nothing’ has no causal powers

As the title of this section suggests, Bushey is arguing here that the reason the universe has to be caused by something, such as God, is that nothing is itself not able to cause anything. As an intuition pump to get you in the mood to agree with him, Bushey offers the following examples:

If your co-worker was taking a day off, the boss would naturally ask, “Who is going to cover your shift?” If the coworker said, “Nobody,” the boss would be concerned. ‘Nobody’ has no causal powers. They cannot perform the function of the job because ‘nobody’ designates the absence of somebody. Similarly, if I said that “There is nothing to eat,” my stomach would be empty. If I said that there was nothing that could stop the invasion of a particular army, I would be expressing that the military force would go unchallenged. 

Now we have the idea of what it means to say that ‘nothing’ lacks causal powers. ‘Nothingness’ cannot play the role of a co-worker, satisfy an empty stomach, or impede an oncoming army. Nothingness can’t do anything. Given that primer, here comes the beef:

So when atheists tell us that a universe could emerge from absolutely nothing, or attempt to provide accounts of how nothing could have produced the universe, they are expressing an incoherent thought. If ‘nothing’ designates the absence of anything at all, then it follows that there are no causal powers. If there are no causal powers, then it lacks the capacity to produce universes.

Given that nothingness cannot fill-in for an absent waiter’s shift in a cafe, it seems perfectly reasonable to extend this to think that it cannot manufacture universes either.

So, what is wrong with this? Well, we might already be suspicious of the first example. The boss might be concerned with the fact that nothingness has no causal powers, but I would suggest that it is more likely that he is really concerned about the lack of something to fill in which has the relevant causal powers. And these are not two ways of saying the same thing. It is not like the co-worker said ‘Don’t worry boss – nothingness will fill in for me’, to which the boss replied ‘Oh no, not bloody nothingness again! It’s complete lack of causal powers always ends up causing me grief when it comes time to tidy up at the end of the evening!’ By saying that nothing (or nobody) is going to fill in for you at work, you are saying that there is no thing about which it is true that that thing is going to fill in for you at work; you are not saying that there is this thing called ‘nothing’, about which it is true to say that it is going to fill in for you at work. We must keep these two subtly different understandings entirely distinct when we think about this, or else we are led down a garden path of confusion by Bushey here.

Consider Russell’s treatment of negative existentials in On Denoting. I might want to express the fact that I don’t have a sister by saying ‘my sister does not exist’. On face value, we might think that the best way to think about the semantic value of such a phrase is as a referent about which it is true that she doesn’t exist; as if I refer to a non-existent entity. However, says Russell, far better would be to think about it like this: we are simply saying that for all the things that do exist, none of them are my sister. The propositional function ‘x is my sister’ is false for all existing things.

Let’s apply this to the boss example. Is the boss worried that a) there is a non-existent entity, who has no causal powers, filling in for a shift, or is he worried that b) for all the things that there are with the relevant causal powers, it is false that any of them is filling in for the shift? I see no reason at all to suppose that the best way of reading that situation would be by stipulating a), and every reason to suppose that it would be b). Unless Bushey has some additional argument as to why this reading is not acceptable, we at least seem to have an unproblematic rendering of this example here.

Let’s apply this to the universe example. If an opponent of the cosmological argument (who may or may not be an atheist) suggested that maybe nothing caused the universe to exist, which of the following would be be better to render this as:

a) Before the universe existed, there was nothingness, and that caused the universe to come into being.

b) For all the things that there have ever been (in any sense whatsoever), none of them caused the universe to exist.

Again, I see no reason to think that a) would be the intended meaning of such a suggestion, and every reason to think that it would be b). When someone says that ‘nothing caused the universe to exist’, they just mean the propositional function ‘x caused the universe to exist’ is false for all values of x, not that there is a value of x, called ‘nothing’ about which it is true.

Even saying that ‘nothing lacks causal powers’ is already wrong. ‘Nothing’ isn’t a thing. It is shorthand for ‘it is not the case that there is a thing’, i.e. the negation of an existential quantifier: ¬∃. So, taken literally, the phrase ‘nothing lacks causal powers’, would be rendered as follows (where ‘Cx’ is ‘x has causal powers’):

¬∃x (¬Cx)

Using nothing but the definition of the universal quantifier, we can prove the following equivalence in classical logic:

(¬∃x (¬Cx))  ↔  (∀x (Cx))

This just shows that the phrase ‘nothing lacks causal powers’ logically just means the same as ‘everything has causal powers’. Reifying ‘nothing’ to the status of an abstract object, with no causal powers, is just to misuse language; a crime which is unforgivable when there is a logically straightforward, and existentially unproblematic, analysis available.

4. What if universes could come from nothing?

Bushey has another go at providing some reason for thinking that the universe could not have come from nothing. This time he picks up on another well rehearsed argument from William Lane Craig. The idea this time is that if someone wants to hold that the universe might have come into being out of nothing, then why think that only universes could come into being out of nothingness? Here is how Bushey puts it:

Suppose for a moment that it were true that things could appear without any cause at all. If that were the case, then our rational expectations for the universe would seem to be unjustified. It would become inexplicable why anything, and everything did not emerge without a cause at all. This point was charmingly made by Dr. William Lane Craig in his debate with Dr. Peter Slezek. He pointed out that nobody is concerned that as they are sitting in this debate, a horse may have appeared uncaused out of nothing in their living room and is currently defecating on the carpet as we speak.

The idea seems to be that if we grant special exemption to universes being able to come from nothing, we would be rationally compelled to extend this to cover everything. We should expect random things popping into existence all the time, yet we don’t. We implication is that we don’t have this expectation because we know that things require causes to come into being, and cannot come into being in the absence of causes.

So, should we give a special pass to universes? Isn’t that special pleading if we do so? I say it isn’t, and that again there is a subtle but powerful misunderstanding about nothingness which is driving this line of argument.

Take the idea of a horse just appearing in front of you and defeacting on the floor. We know this isn’t going to happen (setting quantum probabilities to one side). But why do we know this? I say that the reason for this isn’t because we know that things cannot come from nothing. That idea isn’t even relevant. If you are at home in your front room wondering if a horse is about to suddenly appear, that isn’t an example of nothingness! What you know is that the relevant causal properties of what exists around you isn’t sufficient to produce a horse. You know that a horse cannot be produced by this particular type of something.

Let’s turn to the idea of the universe. Given the understanding gained from section 3 above, we do not have to think of ‘nothingness’ as preceding and causing the existence of the universe. We could just say that there is no thing (in any sense) that preceded and caused the universe. The beginning of the universe is the beginning of everything. So, the context which was not conducive to a horse popping up in front of you in the previous example has no counterpart here. There is no ’empty space’ into which the universe pops. There is no ‘nothingness’ waiting to be filled with a universe.

Could an infinite empty void of nothingness suddenly give rise to a universe? I don’t know. Could the universe simply be all that there is? I don’t see why not. Pointing out that horses don’t suddenly appear in front of us randomly is completely irrelevant.

5. A good inductive conclusion.

This last point is quite similar to the previous one, and has a similar root of misunderstanding with it. Here is Bushey again:

Common experience indicates that things have an explanation. They do not just appear, uncaused, out of absolutely nothing. The entire project of science is predicated upon this premise. Science is the search for causes within the natural world. If we were to establish the premise that things appear without a cause, then the project of science would be wholly undermined. Scientists who searched for causes of natural phenomenon would be engaging in a fruitless endeavor. It may just be that their specimen emerged without a cause. Why does a fish have a particular gill? Perhaps it appeared, uncaused, out of nothing.

It is quite easy to spot the error here. Take the fourth sentence in that quote: “Science is the search for causes within the natural world”. I don’t think this is the best definition for science one could find, but it is particularly bad that it is the one Bushey uses in this context. If science is the search for causes within the natural world, then there is no reason to think that it applies to things beyond the natural world. Just because things in the universe behave a certain way, doesn’t mean that the universe itself has to display those behaviours. Say everything in the sea floats, would it follow that the sea floats? If there is no causal explanation for the universe, which simply is all that there is, it would not follow that things that actually exist could not be described by science, or that we would have no reason to think that every particular fact in the universe had a causal explanation.

6. Conclusion.

There is no reason provided in Bushey’s post to think that the universe has to have a cause. One should resist the temptation to reify nothingness into an amorphus blob lacking in certain properties. Don’t slide from a failure of reference to an existent thing, to a successful reference to a non-existent thing. The universe didn’t pop into existence from a pre-existent state of nothingness. It just has a finite past.

At least, maybe it does. I don’t know whether the universe was created or not. Maybe a loving personal god made it in order to teach me about morality. Maybe it popped into existence from a pre-existing state of nothingness. Maybe it is just all there is. My point is that you don’t get to prove the first of these by undermining the second, given that there is a coherent third. That would be a fallacy of false dichotomy.

The problem with Internet atheists

I’ve long been interested in the philosophical problems apparent in much popular Christian apologetics, in particular presuppositional apologetics, but also various other philosophical arguments. Part of the reason for this is simply the presence of bad philosophical arguments, which given my formal philosophical training, I find tempting to expose. But there is also another factor, and that is the smugness, or utter lack of humility, displayed by the people making those bad arguments (Sye Ten, Matt Slick, I’m looking at you). It would be way less inviting to engage with if the proponents of these bad arguments were humble, just playing with an argument or concept to see where it goes, rather than using it like a club to try to hit people over the head with. So it is a mixture of weak arguments and arrogance which annoys me the most.

However, I am increasingly finding this sort of thing on the other side of the divide – on the atheist side of the camp – and this does my head in for precisely the same reasons. Being an atheist (either lacking a belief in a god, or positively believing that there are none) does *not* make you a philosopher, it doesn’t mean you have a good grasp of epistemology, and it does not mean you are correct about anything.  Being able to recite ‘what can be asserted without evidence can be dismissed without evidence’, does *not* make you a philosopher.  Saying that you don’t have a burden of proof just because you are an atheist, is not correct if you have made a claim of any kind. Atheists don’t get a pass. They have to learn the hard way, just like everyone else.

Philosophy, in particular epistemology and logic, are directly relevant to the great debate. It is absolutely fine to talk about these ideas in the absence of formal training. In fact, I think more people should be engaged in precisely these areas and encourage more people to do so. I’m certainly not saying that unless you have a PhD you shouldn’t try to do philosophy. All I’m saying is to remember that philosophy is hard. There is no shallow end of the pool; it’s all deep. Don’t think you are a master Jedi when you barely know one end of a light sabre from the other. Trying to use philosophy like a weapon just to win an argument is going to bite you in the ass if you don’t know what you are doing. Even if you do, it’s still a bad idea.

Philosophy is about exposing the folly of arrogance. Like a grenade, it can go off in your own hands.

There are three ways to avoid this happening: a) don’t bother trying, b) never make a mistake, c) be humble. Always, always, go for the last option.

What is philosophy?

       0. Introduction

There is something strange about philosophy. It questions its own foundations. The nature of philosophy is something that philosophers address as part of their activities as philosophers. It is not something taken for granted as part of the discipline. This makes the question, ‘what is philosophy?’, somewhat paradoxical. One must have some idea of what it is in order to attempt the question (as the attempt to answer it will be an example of philosophical enquiry); yet the extent to which one already knows the answer is also the extent to which the question should be uninteresting, and the answer familiar. It seems like we have enough of an intuitive idea of what philosophy is to know how to go about answering the question, yet are sufficiently in the dark about what the answer will be to to make asking it an interesting and non-trivial exercise.

If one picked up an introduction to philosophy textbook, or walked into a philosophy department in a university and asked the people who worked there what philosophy was, it would not be uncommon to find philosophy characterised as addressing the following three questions:

  1. What is reality?  (Metaphysics)
  2. How should we live? (Ethics
  3. What can we know? (Epistemology) 

The idea behind this traditional view is that there are some special areas of intellectual activity that are reserved for philosophy; there are distinctly philosophical topics, to be addressed by philosophers first and foremost.

This is not an uncontroversial contention however. The idea that there is an area which should be the preserve of the philosopher is contested, from various sides, with some arguing that philosophy really has no right to lay claim to anything, that we don’t need philosophers to tell us about anything at all. Philosophy occupies contested territory. Can it justify its claims to the land it occupies? Or should it give up and hand over the rights to the land to someone else?

I am going to look at two challengers for philosophy in particular, because in seeing their claims to the territory in more detail, we will get a clearer understanding of what philosophy is. The two challengers I will look at are: religion, and science. Each of these disciplines in its own way makes challenges to the legitimacy of philosophy, and claims the territory it sees as philosophy occupying for itself.

  1. Religion

As religion is such a huge and enormously varied area, I will focus on one particular manifestation of it here in order to make my points clear enough; the reformation. On this picture religion sometimes pitted against philosophy. Some say that philosophy requires religion in order to be able to answer the questions it raises, and that philosophy must be subordinate to religion (or theology). It is as if when philosophy tries to address those areas of epistemology, ethics and metaphysics it is trying to lay claim to an area which is properly owned by religion.

Of course, not everything in this example applies to all types of religion, but it conveys a general idea. I will then contrast this with the enlightenment, as this was in many ways a response to the reformation movement that precipitated it.

1.1. The reformation

The reformation marks a point in the history of Christianity where Europe was undergoing huge societal change. Developments in printing and the subsequent spread of Bibles in common vernaculars caused an awareness of the ‘real’ message contained in the text which was seen to have been distorted by the Catholic church. A new (although in many ways traditional) version of Christian religion emerged, which pitted itself against the Roman catholic church – Protestantism, spearheaded by people like Martin Luther and John Calvin. One, admittedly simplified, way of characterising this conflict was in terms of authority. The Catholic position is one in which the ultimate authority lies in the tradition of the church, whereas the Protestants threw this off and replaced it with the authority of the scripture.

This protestant revolution provided a tight combination of ways of addressing all three of the ‘philosophical’ questions from above (perhaps we could call this answer to all three questions together a ‘worldview’). The scriptures constituted first and foremost an epistemological foundation. One could come to know, more or less directly, God’s message as it was written in divinely inspired words. Once this has been granted, the answers to the other questions already seem to be given as well. One can know what to do, because the God’s instructions are found in the scriptures. One can know what reality is like, because the descriptions of the world, and the heavens, are found in the scriptures. Thus, if you wanted to know what you could know, how you should live, and what reality is really like, you would find answers to all of these in the same place; the scripture. What need is there for a philosopher to tell you about these areas, when you already have a hotline to the ultimate authority about all these things?

But things are not so simple. If we pause to look just a little more closely at the picture offered to us by reformation theologians, we may find the all-encompassing worldview set out above to be less than what it seemed. Here is a quote from John Calvin, from his magnum opus, the Institutes of Christian Religion:

“When Paul says that that which may be known of God is manifested by the creation of the world, he does not mean such a manifestation as may be comprehended by the wit of man; on the contrary, he shows that it has no further effect than to render us inexcusable” (Calvin, Institutes of Christian Religion, Chapter 5, Section 14, 1536)

What Calvin is saying here is about ‘general revelation’, where God communicates through his creation. It is indeed possible to find out about God through examination of the natural world, thinks Calvin – only don’t get your hopes up. What you can find out given this route is not much. All that you can really know is that he exists, and that you are therefore ‘inexcusable’. All you can know is that you are guilty. Thus, on this picture, the deepest knowledge to he had through examination of the external world is simply a moral lesson.

In the background here is an implicit recommendation not to try to find out about the world in what we would think of as a scientific manner (i.e. in such a way that can be ‘comprehended by the wit of man’). All you can really know about the world is that God made it, and that as his creature you are morally guilty, and deserving of punishment. Everything else is simply to be accepted as a divine mystery (i.e. something beyond the wit of man). Such a mystery is to be accepted despite lack of comprehension. This type of acceptance without rational foundation is characteristic of faith.

1.2 The enlightenment

The enlightenment is a name that marks a period which followed from the reformation. During this period, large advances were made in science, the americas were settled, and many challenges came to the old traditions in area such as constitutional governance, societal rights and religious tolerance. Key figures in this period include Thomas Jefferson, David Hume, Adam Smith, Thomas Paine, Edward Gibbon, Benjamin Franklin, Voltaire, and Immanuel Kant.

The driving idea that unites most of the work of these figures was that the use of reason was the final authority in all matters. Here is a quote from Kant, in his essay What is enlightenment?:

“This enlightenment requires nothing but freedom … freedom to make public use of one’s reason in all matters. Now I hear the cry from all sides: The officer says: “Do not argue–drill!” The tax collector: “Do not argue–pay!” The pastor: “Do not argue–believe!” … We find restrictions on freedom everywhere. But which restriction is harmful to enlightenment? Which restriction is innocent, and which advances enlightenment? I reply: the public use of one’s reason must be free at all times, and this alone can bring enlightenment to mankind.” (Kant, What is enlightenment?, 1784)

Kant’s point here is that there can be no restriction to the use of reason; no area in which reason is forbidden to go. Compare the use of reason to a weapons inspector, sent into a country to hunt for weapons of mass destruction. If there was an area in which they were not allowed to search, this would undermine every bit of effort they put into searching the remaining area. They could never declare that there were no weapons in the country, as they would likely be stored in the forbidden area. This (somewhat strained) analogy applies to the use of reason. If there is an area in which it is not allowed to go, to question and investigate, then we cannot be sure that the rest of our view on the world is correct, as it may be built on shaky foundations. Yet, there are many who would urge us not to use our reason in their specialist area – the taxman, the drill-seargent, and the pastor. They each want you to accept what they have to say without using your reason to investigate it for yourself. Yet, says Kant, we must resist all such restrictions.

Calvin essentially argued that there are areas, the understanding of the natural world, or the nature of God, to which we cannot hope to apply reason (it is beyond the wit of man). Kant replies that there can be no such injunction. Of course, you may try to use your reason to understand something and fail, but there is no subject where one is forbidden to use reason (nowhere the weapons inspector cannot go). Reason must be utterly free, to be reason at all.

One way of thinking about what philosophy is, is as the unrestrained use of reason. One approaches a topic, any topic, and uses reason to try to understand it. Thus, philosophy doesn’t have a specific subject matter, in the way that biology or history do; but instead, anything can be the subject matter of philosophy – even the nature of philosophy itself.

This means that the idea that religion and philosophy are in conflict is incorrect. Philosophy doesn’t lay claim to religion’s specific subject matter – the nature of God, or ethics, or metaphysics, or whatever. Philosophy lays claim to any and every subject matter, in that there cannot be a restriction on the use of reason.

     2. Science

Another area that is often claimed to be in conflict with philosophy – another area to which it is claimed philosophy should be subordinate and know its proper place – is science. Various popularisers of science, such as Bill Nye, Neil deGrasse Tyson, and Lawrence Krauss make similar points.  Krauss, in particular, voices the idea that philosophy and science compete for the same subject matter:

“…physics has encroached on philosophy. Philosophy used to be a field that had content, but then ‘natural philosophy’ became physics, and physics has only continued to make inroads. Every time there’s a leap in physics, it encroaches on these areas that philosophers have carefully sequestered away to themselves, and so then you have this natural resentment on the part of philosophers.” (Krauss, Has Physics Made Philosophy and Religion Obsolete?, in TheAtlantic.com, 2012).

Another influential proponent of this view is Stephen Hawking, who made the following comments in his 2011 book The Grand Design:

“How can we understand the world in which we find ourselves? How does the universe behave? What is the nature of reality? Where did all this come from? Did the universe need a creator? Most of us do not spend most of our time worrying about these questions, but almost all of us worry about them some of the time. Traditionally these are questions for philosophy, but philosophy is dead. Philosophy has not kept up with modern developments in science, particularly physics. Scientists have become the bearers of the torch of discovery in our quest for knowledge.” (Hawking, The Grand Design, 2011)

It seems that underlying Hawking’s (and by extension the other science populists above) claim is the following two points about philosophy:

  • Philosophy tries to do what science does
  • Philosophy fails to do what science does

What it is that science does, which philosophy apparently tries and fails to do, is discover truths about the world (“Scientists have become the bearers of the torch of discovery in our quest for knowledge”). The idea is that with science we have a tried and tested method which produces reliable models about the world – and this is the best way to find out what the world is like. Science is a tool for finding truths. As such it makes progress – it is cumulative – building on the progress of previous generations. Science is on a journey towards having a better and better understanding, on a journey closer to the truth.

Philosophy is also a tool for finding truths, on this view, only one which lacks the empirical method which is what makes science so reliable. In contrast, philosophy relies on a dubious a priori method, involving nothing but rational reflection, perhaps from the comfort of an armchair. The philosopher, like the palm-reader or astrologer, is making claims about the world, and thus jostling for space with the scientist, who claims to be the only person fit to make such claims. As evidence of how poor the philosophical method is, compare how badly philosophy has done at making progress. The same old issues get brought up again and again, generation after generation. This lack of cumulativity indicates the deficiency of philosophy when compared with science.

This view, which we could call ‘scientism’, is defined as something like the following:

Scientism = The only way to have knowledge about the world is through science

There are two main problems with this view. The first is that it makes the claim, that the only way to have knowledge about the world is through science, itself unknowable as it is not something that can be discovered by the scientific method  (it is not an empirical fact). Secondly, it is a distinctly philosophical claim; it is a non-empirical claim about epistemology, which is the sort of thing that philosophers do, according to this view. Thus, if a scientist endorses scientism, especially as a criticism of philosophy, then they are acting out the thing they are criticising.

In addition to the problems with this type of austere scientism,  I think that the view of philosophy as a truth-finding enterprise can also be questioned. In contrast to this view, I will spend the rest of this post explaining the vision of philosophy associated with Socrates.

      2.2 Socrates

Socrates is in many ways the father of western philosophy. Almost all that we know of him comes through dialogues written by his student Plato, in which Socrates plays the part of the protagonist. The early dialogues are the ones in which it is thought that Plato represented most faithfully Socrates’ actual views, in contrast to the later works in which he becomes a mouthpiece for Plato’s own views. It is on this early period that I want to draw out a view of philosophy which is in contrast to that assumed by the criticisms of Hawking, Krauss, et al. above.

Socrates was an unusual figure. He was a kind of drifter, with no secure income or position in society, who engages people in conversation on the street. He was eventually put to death by the courts of Athens after a trial on trumped up charges – of corrupting the youth, teaching that there are no gods and (my personal favourite) making the weaker argument appear stronger.

His back story, explained in the Apology is that one of his friends once asked the Oracle of Delphi if there was anyone wiser than Socrates. The reply was that there was nobody wiser than Socrates. This was not the answer that Socrates was expecting to hear however:

“Socrates: When I heard the answer, I said to myself, What can the god mean? and what is the interpretation of this riddle? for I know that I have no wisdom, small or great.” (The Apology)

Socrates is puzzled because the Oracle cannot speak untruths, yet it seemed obvious to Socrates that he was nothing special. He decided that if he could find someone who had more wisdom than he did, then he could take them to the Oracle and present the refutation in person. The person he first thinks of is someone with a reputation for wisdom, a politician:

“Socrates: Accordingly I went to one who had the reputation of wisdom, and observed him – his name I need not mention; he was a politician whom I selected for examination – and the result was as follows: When I began to talk with him, I could not help thinking that he was not really wise, although he was thought wise by many, and wiser still by himself; and I went and tried to explain to him that he thought himself wise, but was not really wise; and the consequence was that he hated me, and his enmity was shared by several who were present and heard me. So I left him, saying to myself, as I went away: Well, although I do not suppose that either of us knows anything really beautiful and good, I am better off than he is – for he knows nothing, and thinks that he knows. I neither know nor think that I know. In this latter particular, then, I seem to have slightly the advantage of him.” (The Apology, emphasis mine).

Finding this politician with a reputation for knowledge severely lacking, Socrates became determined to find someone else who could show that the Oracle was wrong. To this end, he went round Athens interrogating people who had other claims to knowledge and wisdom, such as judges, craftsmen, poets, soldiers and scientists. In each case he found that they could speak with authority on the area in which they specialised, but were unable to provide any insight into the foundations on which they rested. When pressed by Socrates to explain what they meant by, say, ‘honour’ or ‘truth’, they would quickly reveal their lack of understanding.

Let’s look in a bit more detail at a particular case in hand. In the Euthyphro Socrates is in line waiting to hear the details of the charges which were being brought against him from the courts. While there, he strikes up a conversation with Euthyphro, who is also waiting in line. Euthyphro is there, not to face charges like Socrates, but to bring charges – against his own father for murder. When he hears this, Socrates becomes excited, believing himself to be in the presence of someone with great wisdom – reasoning that he would not even  contemplate such an action, against their own father, unless he were possessed with a great understanding. Euthyphro even agrees that he is, and that he possesses “exact knowledge of all such matters”.

This leads into a discussion of ‘piety’, and what offends the gods, which is a sort of ancient Greek way of talking about the notions of legally and socially acceptable behaviour – the sort of thing that would be relevant in a court. Socrates asks Euthyphro what piety is, and receives various answers, each of which Socrates points out cannot be correct.

The first answer that Euthyphro offers is basically that piety is what he is doing, i.e. prosecuting religious offenders (such as his father). Socrates points out that while this may be an example of a pious act, it is not the definition, or measure, of piety, because there are other pious acts which do not involve prosecuting people (i.e. Socrates shows that it is sufficient but not necessary for piety).

The second answer Euthyphro offers is that the pious is doing what the gods approve of. Yet, points out Socrates, the gods often quarrel with one another, and so the same thing can be both approved of and disapproved of by the gods. This would mean that something can be both pious and impious.

The third answer Euthyphro offers is that the pious is what all the gods love, and the impious is what all the gods hate. The response to this is the famous dilemma which takes its name from the dialogue (all subsequent quotes are from Euthyphro):

“Socrates: The point which I should first wish to understand is whether the pious or holy is beloved by the gods because it is holy, or holy because it is beloved of the gods.”

Euthyphro is unsure about this, but takes the first horn, and affirms that the gods love what they do because it is holy, which reduces his claim that what is holy is what is loved by all the gods to circularity.

In his final attempt, Euthyphro gives a rather difficult to understand idea, which is as follows:

“Euthyphro: Piety or holiness, Socrates, appears to me to be that part of justice which attends to the gods, as there is the other part of justice which attends to men.”

The idea is something like that piety benefits the gods in the way that justice benefits people. Socrates is quick to point out that the gods need no help from people, so it should make no difference to them if we are pious or not. In the end Socrates has more staying power for the discussion than Euthyphro, who begs off, saying:

“Another time, Socrates; for I am in a hurry, and must go now”

As with many of the dialogues, Euthyphro ends inconclusively. The nature of piety (or justice) is under investigation, and many definitions are interrogated rationally, but we are left at the end no closer to the truth. In some sense then, the exercise seems pointless. We have failed to discover new truths. Just like Hawking complained, philosophy fails to do what science is so good at.

What has happened however, is that Socrates has exposed the folly and arrogance of Euthyphro, who was so cock-sure at the start. Once we scratched beneath the surface, we found that he didn’t really know very much about piety at all. So rather than seeing philosophy as a failed truth-seeking mechanism, we can see it as a sort of successful fallacy-seeking mechanism. We are no closer to knowing what piety is, but we do know something about what it isn’t, and the sorts of mistakes we should avoid when reasoning about things like that. At the foremost of the lessons we should learn from Socrates is humility – intellectual humility. It is easy to over-estimate your own abilities to know things, or to have wisdom. The wise man knows his own limits.

And this is where I see philosophy as being quite different to how Hawking, Krauss, et al. seem to be characterising it. Philosophy is not an enterprise like science, which has a method designed to find out truths about the world. Rather, it is a way of detecting bad arguments, faulty reasoning, and unjustified pretensions. It provides humility by reinforcing our own limitations, and preventing us from thinking that we are more than we really are.

     3. Conclusion

In conclusion then, I see philosophy as a subject with no particular subject matter; it is the use of reason, applied to any area. It is not a method for finding out truths, but a method for finding out falsities and fallacies. This is good when it comes to protecting ourselves from being deceived by others (such as politicians, and dogmatists, etc) It may be that all it really helps us to do is discover our own limitations when it comes to understanding the world.

The “Matt Slick Fallacy Fallacy” Fallacy

Introduction

Recently, a friend of mine sent me a link to a website where a person called A.J. Kitt had written a blog post about my ‘Matt Slick Fallacy’ article. I suggest that if you haven’t read it, then you stop and read it now, as it is important to understand my points (and it is not very long).

In it, Kitt makes some rather scathing remarks, such as:

“…sorry, Malpass. You blew it“

and

“…if Dr. Alex Malpass feels his credibility has been undermined, well… he should. Perhaps next time he’ll check his argument before he puts it out there“.

In this post, I will look at Kitt’s claims and see how they relate to my original post. Kitt explains his general point as follows:

“…his claim only works by severely altering or misunderstanding what should have been the presumed qualities and relationships of Slick’s argument“

While this isn’t specific about what ‘qualities and relationships’ it is that I got wrong, it is clear that the idea has something to to with me representing the spirit of the argument incorrectly. If so, then it would be like saying I argued against a straw-man. Obviously, I don’t want that to be the case, as it would mean that I didn’t address Slick’s actual argument, so let’s look closely at what Kitt has to say about what I said, and how it may have gone wrong.

False substitution fallacy

Kitt says that I make ‘false substitutions’ in my arguments, and it seems that this is the root of my problems, in his view. Kitt doesn’t provide any non-controversial examples of what he means by a ‘false substitution’, but I presume he means something like the following. A ‘false substitution’ fallacy would be where someone claims that an argument, A, is invalid, but the demonstration of that claim addresses a different argument, B, which is arrived at by substituting some term from A for a different term.

For example, imagine your debate partner makes the following argument:

1)    “All A’s are B; x is an A; thus, x is a B”.

You might be determined to argue against this point, and thus try to argue that 1 is invalid. You would commit the ‘false substitution’ fallacy if you then claimed that what your debate partner said was wrong (i.e. that 1 is invalid), but then by way of substantiating this claim proceeded to demonstrate that the following argument is invalid instead of 1:

2)     “Some A’s are B; x is an A; thus, x is a B”.

Correctly showing that 2 is invalid does nothing to show whether 1 is invalid. If you responded by making this type of move, your debate partner might call false substitution fallacy on you. Kitt’s charge is that I am making this sort of fallacy when I argue against Slick.

So I had said that Slick’s argument suffers from the ‘false dilemma’ fallacy (the ‘Matt Slick Fallacy’). Kitt responds that my argument suffers from the ‘false substitution’ fallacy (the ‘Matt Slick Fallacy Fallacy’), and thus that Slick’s argument is rescued. If Kitt is wrong about this, then his argument itself will be fallacious in some way (which would make it the ‘Matt Slick Fallacy Fallacy Fallacy’). Let’s look in more detail at what he says.

Cause and existence

Kitt says about me:

“…he correctly identifies that either God or not-God did it“.

But then, apparently, it all goes wrong when I use my toast example. It is here where I make “the magical substitution”:

“He says, since neither the existence of toast nor the lack of the existence of toast has anything to do with the existence of logic, the God/not-God argument is flawed. Worded that way, did you notice the problem?“

Actually, no, I didn’t. Helpfully, Kitt goes on:

“Malpass substituted existence for cause. With the substitution, he’s right. Whether God exists or not, as well as with whether toast exists or not, doesn’t necessarily say anything about the existence of logic (or anything else).” [emphasis mine]

So, according to Kitt, I was right to point out that ‘Whether God exists or not … doesn’t necessarily say anything about the existence of logic (or anything else)’. Ok, great. To that extent then, it seems we are in agreement! But then comes the following:

“But without that substitution… the toast analogy supports Slick. Toast, or something-other-than-toast, definitely caused logic. In this case, I’m pretty sure logic didn’t happen because toast did it. Therefor, it is logical to assert that something-other-than-toast did. Soooo… sorry, Malpass. You blew it.” [emphasis mine]

Here is where Kitt obviously feels on his strongest ground, where I ‘blew it’. So let’s see what he is saying as clearly as possible. Kitt is saying that I inserted the word ‘existence’ into an argument which originally used the word ’cause’ (“Malpass substituted existence for cause”). When I was addressing the issue in terms of existence, what I said was “right” (“With the substitution, he’s right.”), but if I had addressed the argument in terms of cause, my point would not hold (“But without that substitution… the toast analogy supports Slick. Toast, or something-other-than-toast, definitely caused logic”).

It would be helpful to see both arguments next to each other so we could see clearly the difference between them. Kitt doesn’t provide any quote of mine, or Slick’s, to show the two arguments side-by-side (as I did with the ‘all’ and ‘some’ example above). All he has said directly about the toast analogy so far is this:

“And the analogy could have been accurate – but it wasn’t; just take a look. Simply (according to Malpass): ‘God or not-God accounts for logic’ is the same as: ‘toast or not-toast accounts for logic’“

I don’t see the words ‘existence’ or ’cause’ there, which you would expect to see, given the charge that I fallaciously substituted in one for the other.

And if you think about it, it’s quite hard to come up with a plausible version of how that would go, where one word could be substituted for the other to make two premises which are plausible candidates for what I and Slick said. There are three obvious conditions for the pair of premises to count:

Slick)                  One must be a premise of Matt Slick’s version of his argument.

Malpass)            One must be a premise of my version of Slick’s argument.

Substitution)     The premise from Malpass) must be the premise from Slick), but with ‘existence’ swapped in for ’cause’.

Here is a candidate:

3)    ‘The existence of God accounts for the laws of logic’

4)    ‘The cause of God accounts for the laws of logic’

4 is the result of substituting ‘existence’ for ’cause’, so the Substitution condition is fulfilled. 3 is a fair enough reading of what I said, so the Malpass condition is fulfilled. However, I think 4 would be a very unfair reading of Matt Slick’s argument, so the Slick condition would not be fulfilled. Slick’s view is that God doesn’t have a cause, and certainly not one that itself accounts for logic. He thinks God accounts for logic, not that the cause of God accounts for logic. This candidate fulfils Malpass and Substitution, but not Slick. So this cannot be the substitution that Kitt is talking about. Here is another candidate:

5) ‘God is the cause of logic’

6) ‘God is the existence of logic’

I think 5 would be a slightly different point to what Slick was saying, so it is not clear that it fulfils the Slick condition. But even if it were a perfect characterisation of Slick, it is clear that 6 (i.e. the result of substituting ‘existence’ for ’cause’ in 5) doesn’t even make sense grammatically. When I said there were problems with Slick’s argument, it wasn’t because I pretended that one of the premises of his argument was ‘God is the existence of logic’. It would be a very unfair reading of what I was saying in my original post. Thus, this definitely does not fulfil the Malpass condition.

I am genuinely at a loss for an proposition which is something I said, and is a version of what Matt Slick said but with the word ‘existence’ put in place of the word ’cause’. Even a candidate that just fulfils the Slick and Substitution conditions while remaining grammatically well-formed is difficult to think of, as 6 shows.

If Kitt is trying to argue that I was guilty of the ‘false substitution’ fallacy (by making a straw-man argument out of Matt Slick’s argument that used the word ‘existence’ in place of the word ’cause’), then he needs to substantiate this by providing both of those two arguments. He does not do that, and, for the reasons outlined above, I don’t really see how that specific charge can be substantiated.

Can and does

Kitt makes a further claim that I make a false substitution:

“And then he does it again. Malpass switches out “does” for “can.” “Does” creates a mutually exclusive dichotomy: either God or not-God does account for choose-your-thing. But swapping in “can,” on the other hand, fails. Malpass correctly states that just because not-God cannot do yadda-yadda doesn’t prove that God can. But that’s not what Slick said. Slick still stands. Sooo… sorry, Malpass. You blew it twice.”

Kitt’s claim is that 7 is a dichotomy, but 8 is not:

7) God or not-God does account for x

8) God or not-God can account for x

Kitt gives no reason for thinking that this is true; he must assume that it is so obvious as to not need any argument. No examples from ordinary language are given where swapping ‘does’ for ‘can’ switches between a dichotomy and a normal disjunction. Nothing at all is provided to back up the point. So we have to guess why he thinks it is true.

I say that it is not true. Take any sentence that has the word ‘does’ and which is a dichotomy, substitute in the word ‘can’, and the result will remain a dichotomy. Here is an example:

‘Superman does fly or it is not the case that superman does fly’

This is a dichotomy, as it is of the form ‘A or not-A’. Now substitute in the word ‘can’ for ‘does’:

‘Superman can fly or it is not the case that superman can fly’.

This remains of the form ‘A or not-A’, and thus remains a dichotomy. Substituting in ‘does’ for ‘can’ in a dichotomy doesn’t make any difference to whether it is a dichotomy. So, in fact Kitt blew it.

Kitt’s real mistake, though, is in thinking that either of 7 or 8 is a dichotomy. In reality, neither are (more on this below), and the substitution of ‘does’ for ‘can’ makes no relevant difference to them (or course, it makes a modal difference to talk about what something can do rather than what it does do, but this is not relevant here). The both remain contingent disjunctions.

One last thing on this, before I move on to my main point. He says that when I talk about ‘existence’ rather than ’cause’, and when I talk about ‘can’ instead of ‘does’, I am not talking in the same terms as Slick does, as if I have erected a straw-man and torn that down instead of Slick’s actual argument. Of course, it is possible that I have addressed a different argument to what Slick originally intended, but is it the case that the straw-man I have created is one which uses those substitutions? Did I superimpose ‘existence’, where Slick talked about ’cause’, and did I superimpose ‘can’, where Slick talked about ‘does’?

Here is what I said in my article. In three places I present Slick’s argument. Firstly, and informally, I put it like this:

1. Either God, or not-God.

2. Not-God cannot account for the laws of logic.

3. Therefore God can account for the laws of logic.

Then I make things a bit more clear in ‘reconstruction 1’ (which I say is guilty of false dichotomy):

1. Either God can account for the laws of logic, or not-God can account for the laws of logic.

2. Not-God cannot account for the laws of logic.

3. Therefore, God can.

Finally, I present the argument in such a way that it avoids false dichotomy (‘reconstruction 2’):

1. Either God can account for the laws of logic, or it is not the case that God can account for the laws of logic.

2. It is not the case that (it is not the case that God can account for the laws of logic).

3. Therefore, God can account for the laws of logic.

I don’t actually use the word ‘exists’, but it is not a wild reinterpretation to put it in, such as: ‘Either the existence of God can account for the laws of logic, or it is not the case that the existence of God can account for the laws of logic’. I do use the word ‘can’. So Kitt is correct at least that my version of Slick’s argument uses ‘existence’ and ‘can’. Does Slick use ’cause’ and ‘does’ though?

Here is how Slick puts his TAG argument on his website (https://carm.org/transcendental-argument), and I have highlighted a few key terms:

1.If we have only two possible options by which we can explain something and one of those options is removed, by default the other option is verified since it is impossible to negate both of the only two exist options.

2. God either exists or does not exist.  There is no third option.

3. If the no-god position, atheism, clearly fails to account for Logical Absolutes from its perspective, then it is negated, and the other option is verified.

4. Atheism cannot account for the necessary preconditions for intelligibility, namely, the existence of logical absolutes.  Therefore, it is invalidated as a viable option for accounting for them and the only other option, God exists, is validated.

The word ’cause’ doesn’t appear at all, and the words ‘exist’ and ‘does not exist’ appear in the relevant places. The word ‘does’ doesn’t appear at all, and the words ‘can’ and ‘cannot’ appear in the relevant places. So far, with respect to the use of ’cause/existence’ and ‘can/does’, Slick and my presentation of Slick are in agreement. Kitt’s claim was that I falsely substituted in ‘existence’ for ’cause’, but so far both Slick and I use ‘existence’ and not ’cause’. So far, Kitt’s point seems completely baseless.

In my article that Kitt was responding to, I quoted a short monologue from Slick’s radio show. Just to make sure I didn’t cherry-pick the above presentation of the argument because it suited my point, let’s make sure that the actual version of the argument I used as a foil originally didn’t use ’cause’ or ‘does’. Here is what Slick said on his radio show:

“If you only have two possibilities to account for something … if one of them is negated the other is necessarily validated as being true … So we have ‘God and not-God’, so that’s called a true dichotomy, God either exists, or it is not the case that God exists, we have the thing and the negation of the thing. So now we have a true disjunctive syllogism … We have, for example, the transcendental laws of logic … Can the no-God position account for the transcendental laws of logic? And the ultimate answer is no it cannot. So therefore because it cannot, the other position is automatically necessarily validated as being true. Because, you cannot negate both options out of the only two possibilities; that’s logically impossible.”

Once again, ‘existence’ and ‘can’ are the relevant terms. ‘Cause’ and ‘does’ are not mentioned.  I conclude, given the examination of Slick’s actual arguments, that I have not substituted in terms falsely, but have actually used the terms Slick used. Given that Kitt insists on talking about arguments which use ’cause’ and ‘does’, it is Kitt who has made false substitutions. It is ironic that Kitt has accused me of doing something, when it is himself who is guilty of doing precisely that. Kitt doesn’t directly quote me or Slick in his article, so one could be forgiven if they just read his article for thinking that his assessment was correct. Once we compare what I put with what Slick put, like actually side-by-side comparing them, we see that Kitt’s claims are baseless. This adds a further irony, as Kitt’s explicitly said:

“…if Dr. Alex Malpass feels his credibility has been undermined, well… he should. Perhaps next time he’ll check his argument before he puts it out there.”

It seems that in actual fact, Kitt has been rather sloppy with his claims about my and Slick’s arguments, and failed to check whether the claims were themselves correct before he put it ‘out there’ for other people to critique. Perhaps next time he will check his argument first.

False dichotomy

At the end of all this, there is really only one fallacy, and it is the Matt Slick Fallacy (false dichotomy). Kitt just makes the same fallacy again. Here it is in all it’s glory:

“Toast, or something-other-than-toast, definitely caused logic.“

I say that with this claim, Kitt demonstrates that he does not understand my argument at all, and in fact has just walked straight into the problem that Slick was facing. It may be my fault that he didn’t understand my argument (maybe my words were not sufficiently clear), but it is his own fault for not being able to see this for himself. His reasoning seems to be that the claim that ‘toast or some other thing caused logic’ is logically true. He says as much quite clearly:

“Either:

A. ‘God caused it’ or

B. ‘Something other than God caused it’. 

That – A OR B – is a logically true statement.“

The disjunction (‘A or B’) is not a tautology (i.e. true independently of the content of A and B) – it is not a “logically true statement”. ‘A or not-A’ would be a tautology, but Either: A. ‘God caused it’ or B. ‘Something other than God caused it’ is not an instance of ‘A or not-A’. It isn’t an instance of any other tautology either. Trying to palm it off as a dichotomy is the textbook definition of the false dichotomy fallacy. Sorry, Kitt, but it’s true.

Think about it like this: could the following pair both be true?

9) ‘Either a caused b, or something other than a caused b‘

10) ‘Nothing caused b‘

The answer is: no. If nothing caused b (if 10 is true), then ‘either a caused b, or something other than a caused b‘ (i.e. 9) has to be false. For a Christian (and presumably Kitt is a Christian), this should be obvious. Is it logically true that ‘either a caused God, or something other than a caused God’? The traditional understanding is that God is uncaused. Nothing caused God to exist. But if it were a logical truth that ‘either a caused b, or something other than a caused b‘ then it would entail, logically, that God had a cause. If Kitt is right, then God had a cause.

Causing logic

While that claim of mine (that the proposition ‘something accounts for logic’ is assumed and not argued for) is well rehearsed on this blog, I want to focus on the particular issue Kitt feels is his strongest point; the idea that logic was caused. I think this idea is incoherent. It is quite hard to make this point perfectly clear, but here goes.

Firstly, it is not clear to me that saying ‘logic exists’ is the most helpful way of speaking. There is a wide range of positions on the nature of logic, but straightforwardly ascribing existence to logic is not uncontroversial. Physical objects, like tables and chairs, are the sort of paradigm examples of existing things. Obviously, some philosophers (platonists, etc) have claimed that abstract objects exist. However, these same philosophers also claim that these existing abstract objects are outside the usual causal chains that physical objects are in. The number 17, for example, is generally regarded by platonists to be an eternally existing abstract object, but also causally inert; nothing causes it to exist, and it causes nothing to exist. It has no causal relationships with anything. So this platonistic account of abstract objects, which sanctions the locution ‘abstract object x exists’, doesn’t sanction, ‘y caused abstract object x to exist’. So this cannot be what Kitt means when he says that logic was caused to exist. I think we are owed some sort of explanation of what Kitt has in mind for what he means by logic existing when it is caused to be, but we get nothing of the sort.

Perhaps he may simply want to say that God made the logical principles true, regardless of whether they exist or not as abstract objects. So one might ask ‘why is the law of non-contradiction true’, to which Kitt’s answer would (perhaps) be ‘because God caused it to be true’. This way of talking side-steps the platonistic talk of abstract objects existing. While this is somewhat more attractive as an option therefore, it also suffers from what I consider to be a fundamental incoherence.

The situation is sort of similar to a well-known difficulty for the idea that God caused time to exist. The creation of something is a change. And you cannot have change without time. But the creation of time is a change, specifically the change from time not existing to time existing. This change presupposes that time exists; the time ‘before’ time started to exist, the time and ‘after’ it started to exist. So the creation of time can only take place if time already exists. Thus, there is an incoherence in the idea of the ‘creation of time’. Our notion of creation cannot be applied to the notion of time, without becoming incoherent. In other words, creation presupposes time. You cannot make sense of creation outside of time.

Now consider the claim that God created logic. What was it like before God created logic? You couldn’t use logical inferences, and there would be no logical truths. So it wouldn’t be that ‘Socrates is mortal’ followed from ‘all men are mortal’ and ‘Socrates is a man’. It wouldn’t be that ‘Either Socrates is a man or it is not the case that Socrates is a man’ is true.

One might be tempted to bite the bullet and say ‘well, yeah, before God created logic, stuff was crazy like that’. But I think that even this is not available. If you deny logic altogether, then there is no room for the notion of causation to operate; too much has been taken away for the ascription of causation to mean anything. Here are a few, often admittedly difficult to understand, examples of what it might mean for logic to not exist, and how this makes causation, and indeed everything, impossible.

Trivialism

Maybe you think that when logic didn’t exist all contradictions were true; call this view ‘trivialism’. God existed and didn’t exist; Monday was Tuesday; I was you; up was down, etc. Well, this is equivalent to saying that everything was true and false; every proposition and its negation is true. But now we have an axiom, which we could call the ‘triviality’ axiom:

Triviality)                        ∀p: p & ¬p

(alternatively: ∀p: Tp & Fp)

This says, for all propositions, p, ‘both p and its negation are true’. Alternatively, it says that for all propositions, p, ‘p is both true and false’. It looks like we have a logical principle after all, and we might think that before logic there was in fact a type of logic (a bit like with the time example above). But the logic case is more curious than this. Because, if all contradictions are true, Triviality itself would also be false; the negation of Triviality would be true:

Not-Triviality)             ¬(∀p: p & ¬p)

But, because of Triviality (which says that for every proposition, both it and its negation are true), both Triviality and Not-Triviality are true:

Triviality.2)                    (∀p: p & ¬p) & ¬(∀p: p & ¬p)

But, because of Triviality, Triviality.2 (which says that both Triviality and Not-Triviality are true) would also be false:

Not-triviality.2)        ¬((∀p: p & ¬p) & ¬(∀p: p & ¬p))

But, because of Triviality, both Triviality.2 and Not-Triviality.2 hold:

Triviality.3)                  ((∀p: p & ¬p) & ¬(∀p: p & ¬p)) & (¬(∀p: p & ¬p) & ¬(∀p: p & ¬p))

This is obviously a never ending regress, as from Triviality.3) a Not-triviality.3) could be generated, ad infinitum. If you want to say that what it ‘was like before God had made logic’ is a state where ‘all contradictions were true’ (i.e. trivialism) then you necessarily run into this regress.

The significance of the regress is that it, on trivialism, you cannot talk about what it was like before logic was created, because you would immediately have to contradict yourself, whatever you said. But, making a claim, of any description, is to convey that (at least one) proposition is true and not it’s negation. It is a necessary condition for making a claim, that you convey that (at least one) proposition is true and not it’s negation. For example, if I say ‘It is sunny’, I am communicating the fact that the proposition ‘It is sunny’ is true, and the negation, ‘It is not sunny’, is false. But according to Trivialism, before logic was caused, you could not pick one side out of any pair, p & ¬p, to be true rather than the other, because for every such pair both members are true (and false).

Usually, when something is caused to happen, like when I caused my wine glass to break by knocking it on the floor, a proposition became true (‘the glass is broken’), which was previously not true. So, before God caused logic, when all contradictions were true, it was true that he had ‘not already caused logic’. But if it was true that ‘God has not already caused logic’, then (by Triviality) it was also true that he had already caused logic (because everything is both true and false). So saying that God caused logic, on trivialism, is not to say that he made it true that ‘God caused logic’ (which is how we usually understand causation), because that was already true (and already false). Thus it is impossible to see how, on trivialism, causation as we usually understand it could be employed before logic.

The response might be that: ‘God caused logic’, doesn’t mean that God made something true; rather, that he made something false.  When God caused logic, he didn’t make it true that true that ‘Logic exists’ (because it was already true) – rather, God made it false that ‘Logic does not exist’. Effectively, we mean that he changed one option out of every mutually exclusive disjunction from being true to being false; as if he ‘ironed out’ the contradictoriness from the world. So if ‘p & ¬p’ were true before God caused logic, then by causing logic, he made it false that (say) ‘¬p’. Call this act of making consistency out of inconsistency ‘consistecising’. So ‘God caused logic’ is to say that God ‘consistecised’ all the contradictions, thereby making the principle of non-contradiction true.

It looks like we have we found a way of describing what stuff was like before God caused logic, and what it means to cause logic in such a setting. Before God caused logic, every contradiction was true, but then by causing logic, God made one member from each pair false and not also true (i.e. he consistecised the contradictions).

Well, ask yourself: before God caused logic (i.e. when all contradictions were true) had he already consistecised all the contradictions (i.e. had he already made all the contradictions not contradictory)? The answer, according to Triviality is yes and no; it was true that God had already consistecised all the contradictions, and it was false that he had consistecised all the contradictions. So we cannot say that God causing logic was that he made it false that ‘God has not consistecised all the contradictions’, because this was already false (and already true). We are back to the very same problem of having to state something was made true (‘God consistecised all the contradictions’), which is already true (according to Trivialism); stating that something was made false (‘God has not consistecised all the contradictions’) runs into the same problem, as everything is already false (and true) according to Trivialism.

This makes the idea that ‘all contradictions were true’ an infinitely problematic notion, and an environment in which we can make no sense out of causation.

Nihilism

Trivialism may not be what one means by ‘what it is like before God caused logic’ though. Here is another try:

Nihilism)                        ∀p: ¬(p ∨ ¬p)

(alternatively: ∀p: Fp)

This says that for all propositions, p, ‘neither p nor not-p is true’; or for all propositions, p, ‘p is false’. Nihilism says that nothing is true (in contrast to trivialism which said that everything was true). Perhaps this is what is meant by ‘before God caused logic’.

But could God cause logic to exist if Nihilism were true? Well, if he could, then it would be true that he could. But, by Nihilism, it is false that he could cause logic to exist (because everything is false). So if Nihilism were true, it would be false that God could cause logic. Does God even exist in this situation? No! Otherwise the proposition ‘God exists’ would be true, violating Nihilism! So, if this is what we mean by ‘what it was like before God caused logic’, we would have to say that God couldn’t cause logic, and didn’t even exist, before he caused logic.

But it gets worse. Is Nihilism even true in such an environment? No, it has to be false as well (because every proposition is false). If everything was false, then it would be false that everything was false. Everything wouldn’t be false. So it would be the case that everything was false, and it is false that everything is false. But even that would be false.  It would not be that (everything was false, and everything was not false). Nor would that be the case…

Again we are stuck in a never ending regress. Plus we would have to say that it is false that God could cause logic, and false that God existed, before he caused logic. In what way can we make sense of causation in such a situation? It cannot be normal causation, or anything like it.

It is conceivable that a reply could be made, along the lines of ‘but you are using logic to try to describe what it was like before logic, and you can’t do that’. In response, I say that I am showing that you cannot say anything about what it was like before logic. Specifically, you cannot talk about God, or God causing anything, before logic. The claim, that God caused logic, is precisely the sort of thing you cannot say.

The point is that ‘causing logic to exist’ isn’t like causing a table or a chair to exist. It is not even on the same level as causing the physical universe in total to exist. Saying that there was a point where logic didn’t exist, where logical principles were not true, and that logical inferences were not valid, etc, is just to say something that doesn’t make any sense. Trying to have your cake, by insisting on a time where logic doesn’t apply, but eating it too, by having things coherent enough to have causation remain meaningful, or even for God to exist, is impossible. Saying that God caused logic is incoherent. Saying that it is definitely true that something caused logic, and that this is a logical truth, is just false.

Conclusion

A.J. Kitt tried to defend Matt Slick’s argument against my critique, but his criticisms were hard to make sense of and unsubstantiated, like with the charge that I substituted ‘existence’ for ’cause’. I can see no evidence of Slick using a ‘God caused logic’ argument, and even if he does, I was responding legitimately to an argument where he doesn’t. And if we look at the claim that God, or anything, ’caused’ logic, it seems incoherent. Causation requires logic, just like it requires time. It makes no sense to say of either logic or time that they were caused or created, as causation and creation are temporal notions that are defined in such a way that presupposes that logical notions apply. To put the case in the presuppositional terminology that Slick enjoys; logic is a necessary precondition for the intelligibility of anything, including the idea of causation or the existence of God. Remove logic altogether and everything becomes impossible.

Skepticism, fallibilism, anti-skepticism

    0. Introduction

The following three propositions form an inconsistent triad:

P)   I do not know that I’m not in the matrix*

Q)   I know that X

R)   If I know that X, then I know that I am not in the matrix

 

(X is to be thought of as a proposition with content about the external world, such as ‘it is 3PM’ or ‘I am wearing trousers’, etc, rather than ‘I believe it is 3PM’ or ‘I am receiving sense-data about wearing trousers’, whose content is internal to the subject.)

We can represent the logical form of the propositions as follows, where p = ‘I know I am not in the matrix’, and q = ‘I know that X’:

P)    ~p

Q)     q

R)     q → p

There are three ways that we can formulate an argument using these propositions which generate three positions about knowledge, which I am calling ‘skepticism’, ‘falliblism’ and ‘anti-skepticism’. Each argument is derived by having two of the propositions as premises with the negation of the remaining one as the conclusion.

 

  1. Skepticism

The skeptic formulates her argument as follows:

R)     If I know that X, then I know that I am not in the matrix

P)     I do not know that I am not in the matrix

~Q)     Therefore, I do not know that X

This argument has the form of modus tollens:

q → p

~p

Therefore ~q

 

2. Fallibilism

In contrast, the fallibilist argues from the truth of P and Q to the falsity of R, i.e.:

P)      I do not know that I am not in the matrix

Q)      I do know X

~R)     Not-(if I know that X, then I know that I am not in the matrix)

 

This has the form:

~p

q

Therefore, ~(q → p)

 

What does this rearrangement say? It says that because we do know something, yet we do not know whether we are in the matrix, it follows that knowing that we are not in the matrix it is not a necessary condition for knowledge. Thus one can have knowledge without being able to rule out the skeptical hypothesis.

 

3. Anti-Skepticism

The final combination, the anti-fallibilist (which perhaps represents G.E. Moore?), runs as follows:R)   If I know that X, then I know that I am not in the matrix

Q)   I know that X

~P)   I know that I’m not in the matrix

 

The form of this argument is modus ponens:

q → p

q

Therefore, p

 

On this argument, the requirement of ruling out the matrix as a necessary condition for knowledge is accepted, and the fact of knowledge of X is affirmed, with the consequence that one knows they are not in the matrix. A refutation of the skeptical hypothesis has been achieved (hence the name ‘anti-skepticism’).

 

 

4. How to choose? 

So now we have three rival arguments, each of which picks two of the members of the triad and rejects the third. The question of which argument to pick turns then, not on logic as such, but on the question of which proposition to jettison. Which one seems the least plausible? The problem is that they all seem eminently plausible.

P says that you cannot rule out the matrix, or evil daemon hypothesis. It seems very plausible, at least to anyone who has read Descartes or watched the Matrix. Denying this premise seems to require a refutation of skepticism.

Q says that you know that X. This is obviously going to depend on your choice of X, but why not make X as plausible as you like? Let X be ‘it is now 3PM’ (if it is 3PM), or that you are wearing trousers (if you are wearing trousers), etc. It can be the most run of the mill, ordinary knowledge claim you can think of. By definition, Q should be very plausible, if any knowledge claim at all can be. And P, Q and R are all knowledge claims.

R says that if you know that you are walking down the street, or that it is 3PM, or that you are wearing trousers, or whatever, then you know you are not in the matrix. This is also very difficult to deny. If I know that I am walking down the street, then it is true that I am walking down the street. If it is true that I am walking down the street, then I am not in the matrix. Thus, if I know I am walking down the street then I am not in the matrix. Therefore, it seems that if I know that X, then I know I am not in the matrix.

Where is the weak link here?

 

*for ‘in the matrix’, feel free to substitute in ‘am a brain in a vat’, ‘am being deceived by a Cartesian daemon’, etc.

Craig’s List – Omniscience and actually existing infinities

Introduction

William Lane Craig has famously argued for the ‘Kalam cosmological argument’ (in many places, but for example in Craig & Sinclair [2009]). Here is the argument:

  1. Everything that begins to exist has a cause.
  2. The universe began to exist.
  3. Therefore, the universe had a cause (Craig & Sinclair [2009], p 102).

The argument is clearly valid, as it is a version of modus ponens. Thus, in order to deny the conclusion, one must argue that the first or second premise is not justified.

Most people have argued against premise one, disputing whether all things which begin to exist have causes for their existence, or the fact that a fallacy of composition may be at play with the generalization from all things in the universe to the universe as a whole. I will not be pursuing this line of argument here, but will instead look at premise two.

Premise two seems to be supported by physics, specifically cosmogony, which some say indicates that the spacetime we exist within came into existence at the big bang. People who know more about this than I do tell me that this is actually a misconception of this theory, and that it is not really a theory about the origin of spacetime at all. However, we can avoid delving any further into the details of the physics, because Craig does not rest his argument on the interpretation of the big bang theory. There is a logical argument Craig spends time going into, according to which the universe must have had a beginning – that it is impossible for the universe to have always existed. Here is that argument:

2.1. An actual infinite cannot exist.

2.2. An infinite temporal regress of events is an actual infinite

2.3. Therefore, an infinite temporal regress of events cannot exist. (ibid, p 103)

It is on this supporting argument that I wish to focus. Specifically, it is the first premise of this argument that I will be spending time going into here. If we can knock this premise out, then it undermines the entire supporting argument, and with it the credibility of the main argument. If we can deny 2.1, we can avoid having to assent to 3.

Hilbert’s Hotel

In order to motivate 2.1 (that an actual infinite cannot exist), Craig uses the example of ‘Hilbert’s Hotel’. In this imagined hotel there is an infinite number of rooms. Infinity has a distinctive property, according to which a proper subset of it can be equal in cardinality to the whole, there are various counter-intuitive consequences, which Craig uses to motivate the idea that this could not actually exist. For example, if the hotel is full but a prospective guest arrives asking for a room, the hotel manager can simply ask each occupant to move into the next room, thereby making room number one free. Because there is an infinite number of rooms, there will be room for every occupant, thus making a newly free space for the new guest to stay in, even though the hotel was full. Even if infinite new guests turn up, the hotel manager can make room by getting everyone in the hotel to move into the room with the room number that is twice the number of their current room (so room number two gets room number four, room number four gets room number eight, etc.). This frees up an infinite number of rooms, even though the hotel was full. Craig comments:

“Can anyone believe that such a hotel could exist in reality? Hilbert’s hotel is absurd. But if an actual infinite were metaphysically possible, then such a hotel would be metaphysically possible. It follows that the real existence of an actual infinite is not metaphysically possible” (Craig & Sinclair [2009], p. 109-110).

If this is correct, then because a universe with no first moment would constitute an actually existing infinity, it follows that the universe had a first moment. Thus, the idea is that it is no objection to simply say that maybe the universe always existed. It couldn’t have always existed, says Craig.

However, it is not clear to me that his objection really applies to the universe, and I will spell this out in more detail now.

Pinning down the absurdity

One might wonder what specifically it is about Hilbert’s hotel that Craig finds absurd. It seems that the sheer scale of the hotel, the fact that it has infinite rooms, is not itself absurd to Craig. If it was, then the example would simply have been:

‘Imagine that there is a hotel with infinite rooms in – that’s absurd!’

Given that the example was more complex than this, it seems that just saying that the hotel is infinite is not enough for Craig to bring out the absurdity. Nor does simply adding that the hotel actually exists constitute the absurdity, otherwise the example would have been:

‘Imagine that there is a hotel with infinite rooms in, and that it actually exists – that’s absurd!’

Surely, when picturing Hilbert’s hotel, one pictures it as actually existing. Adding that it actually exists is somewhat empty as a property, and surely not enough on its own to make the difference between not absurd and absurd. So what is it that pushes us over this threshold?

It seems to me, given the examples used to illustrate the absurdity of Hilbert’s hotel, that Craig’s idea is as follows. The factor that gets us across the line is what we might call the behavior of the hotel. With an infinite hotel, given certain conditions obtaining, contradictions can be manifested, and contradictions are absurd. So it took the new guest to arrive, and for everyone to shuffle up one room, for an absurdity to become manifested; namely, the hotel is full, but also has a room available for a new guest. If the guest does not arrive, or arrives but is turned away by the manager, then where is the absurdity? How do we generate a contradiction without interacting with the hotel? It seems like the only way we could imply an absurdity in that case would be simply pointing out that the hotel has infinite rooms. But if this was on its own enough to constitute absurdity, why bother with the example of the guest arriving? Is it just for rhetorical effect? It seems to me that the answer is that without the guest arriving and the creation of the new free room, Craig thinks that nothing absurd is present.

If this right, then we could employ a distinction between active and passive infinities. An active infinity is one that manifests absurd behavior (like being full but also making room for a new guest), whereas a passive infinity is one that does not (like a Hilbert’s hotel which never admits new guests). Now, it should be noted that a passive infinite retains the potential to manifest absurdity; it is passive just so long as it doesn’t actually do so.

This makes the distinction between ‘actually existing’ and ‘not actually existing’ slightly wide of where the beef is here. It seems we could have an actually existing Hilbert’s hotel, which remains passive, and for all Craig has said, this would not be absurd. The absurdity only kicks in when an actually existing infinity becomes active.

The infinite universe is passive

The problem with Craig spelling out the nature of the absurdity associated with actually existing infinities like this, is that it doesn’t apply to the eternally existing universe. There are models where we could make his objection apply, but the most natural way of cashing it out avoids his problem, as I will explain.

Imagine a number line that contains all integers running from minus infinity, through 0 all the way up to positive infinity. Now think of 0 marking out this very moment now. This is a bit like the most natural way of thinking about the eternal universe; each moment has infinitely many earlier moments and infinitely many later moments. If this is how Craig is characterizing the eternally existing universe, then it is a passive infinity. There is no corresponding example to making a free room, or withdrawing a book. One cannot add a moment to time, nor take one away. It is a ‘closed’ infinity. In fact, it is arguably metaphysically impossible to add a time or take one away. Thus, Craig may be correct that active infinities are metaphysically impossible, but because the eternal universe is not one of these, then he has no objection to the eternal universe.

As I said, there are ways of cashing out the eternally existing nature of the universe according to which Craig’s point holds. For example, consider the ‘growing block’ theory of time. According to this theory, the past is a fixed set of facts, which is growing as time moves forwards. We continually add new truths to the stock of settled past truths. If this were the model, then we would have an infinite list of past truths, but we would be able to add to it. In a sense, this would resemble Hilbert’s Hotel and thus make the universe an active infinity.

It should be noted that even on this growing block theory, there is room to doubt whether this really counts as an absurdity. With the hotel example, we can derive a sort of contradiction, in the sense that the hotel was full, but had room for a new guest. If being full means that there is no room, then this is a contradiction. But it is not clear what is the contradictory sentence we are supposed to be able to make out of the growing block theory here. Sure, there are infinite past moments, and then a new one gets added to the pile as time moves forward. The only contradiction I can see here is that the cardinality of the past moments is the same, even after a new one is added to the block. If so, then we have our candidate.

It is a weak candidate, as it seems to me that we ought to simply accept that this is what an infinite block would be like. However, let’s assume that Craig has scored his point here, and that the growing block theory is absurd for that reason. No such account can be leveled at the eternal universe outlined above. It has an infinite number of moments, but there is no possibility of adding new moments or taking them away, so it is passive. It seems like we can block Craig’s argument by simply explaining clearly what an eternal universe looks like, and that while it is infinite in extent, it manifests no absurdity.

In fact, this will form one horn on a dilemma I wish to place Craig in. As we shall see, if there is a problem with the growing block theory, then it also affects Craig’s version of God. The dilemma will be that either the universe is infinite in temporal extension, or God doesn’t exist.

The Infinite God Objection

Craig’s God is omniscient. This means that ‘God knows only and all truths’. Watch him commit to this position here:

It is uncontroversial that there are mathematical truths, like that it is true that 2 + 2 = 4. God knows all these truths as well (Craig explicitly makes this point at 6:20 in the video above). To make the point as simple as possible, God knows the solution to every equation of the form x + y = z, where the variables are natural numbers. As there is an infinite number of such solutions (with a cardinality equal to the smallest infinity, ℵ0), it follows that God’s knowledge is correspondingly at least as infinite as the cardinality of the natural numbers (and obviously greater if he also knows all real number solutions as well).

Let’s consider Craig’s God’s knowledge of these arithmetic solutions as a list of truths, which we could call ‘Craig’s List’. It would be an infinitely long list. So Craig’s God’s knowledge is infinite.

But, according to the Hilbert’s Hotel argument from above, the infinite cannot actually exist. Therefore, an omniscient God cannot actually exist. Craig’s God is omniscient. Therefore, by his own argument, Craig’s God cannot exist.

Call this the ‘Infinite God Objection’.

God’s knowledge is of induction schemas

It could be objected here that God does not need to know every arithmetic truth, such as 2 + 2 = 4, because as long as he knows the base case and all relevant induction schema, he would know enough to deduce the answer to any similar equation. If this were the case, then it would drastically limit the amount of propositions God would need to know, from infinite to a mere handful.

My response to this is that if this were all that were required to know all mathematical truths, then I know all mathematical truths. After all, I know the base case (that 0 is a number) and the relevant induction schema. God and I both have the same resources at hand, and if this is all it takes to know all mathematical truths, then we both know all mathematical truths. This is an awkward consequence, to say the least.

But this consequence is not just awkward. It is intuitively true that there are lots of arithmetical equations that I do not know the answer to, even though I could work them out given my knowledge of the induction schema. It seems more natural to say that I do not know the answers to these questions, but I know how to work out the answers. This makes the response in the God case inadequate though. To concede that God does not know the answer to any mathematical question, but knows how to work out the answer, is just to concede that there are things he does not know. The fact that he could work it out it not a defeater to the claim that he does not know it.

On the other hand, perhaps the similarity is only apparent, and that due to my limited nature, as compared to God’s unlimited all-powerful nature, there is a meaningful difference between the two cases. Perhaps it is the case that I slowly lumber through, applying the schema to the case at hand to derive the answer, and with the possibility that I could always go wrong on the way. In contrast, God applies it at lightening speed, without the possibility of getting it wrong on the way. In this case, there is no arithmetic question you could ask God to which the answer would be ‘I don’t know, but I will work it out for you’; as soon as you have asked the question he has already worked it out. Therefore it is never true that there is something he does not know.

But I could just stipulate an equation, without asking God directly. Even though, were he to think about it he would get the answer immediately, given that he is not currently applying the schema to the case, it is not true that he knows it. So there is something he doesn’t know. So he is not omniscient.

And if we avoid this by saying that he is constantly applying the schema to all cases, then we are right back to the original case, where he knows an infinite number of truths.

Thus this escape route will not help.

God’s knowledge is non-propositional

Craig could say that God’s knowledge is non-propositional, as in the Thomist conception. On this idea, God does not know lots of individual propositions, but rather has one unified knowledge of himself, which is perfectly simple.

To begin with, this contradicts his statements in the video above, where Craig explicitly states that God knows all propositions. Perhaps we can let this slide, as it is him talking somewhat informally.

In a paper entitled ‘A Swift and Simple Refutation of the “Kalam” Cosmological  Argument?‘ (1999), Craig considers a very similar objection, namely that if mathematical truths are just divine ideas, then God’s mind has infinitely many ideas. In defense of the divine conceptualist, Craig offers the following reply:

“[T]he conceptualist may avail himself of the theological tradition that in God there are not, in fact, a plurality of divine ideas; rather God’s knowledge is simple and is merely represented by us finite knowers as broken up into knowledge of discrete propositions and a plurality of divine ideas.” (Craig, (1999), p 61 – 62).

This theological tradition goes back to Thomas Aquinas, and as an explanation of this, Craig cites William Alston’s paper ‘Does God have beliefs?’ (1986). In that paper, Alston says the following:

“[C]onsider the position that God’s knowledge is not propositional. St Thomas Aquinas provides a paradigmatic exposition of this view. According to Aquinas, God is pure act and absolutely simple. Hence there is no real distinction in God between his knowledge and its object. Thus what God knows is simply His knowledge, which itself is not really distinct from Himself. This is not incompatible with God’s knowing everything. Since the divine essence contains the likenesses of all things, God, in knowing Himself perfectly, thereby knows everything. Now since God is absolutely simple, His knowledge cannot involve any diversity. Of course what God knows in creation is diverse, but this diversity is not paralleled in the intrinsic being of His knowledge of it. Therefore ‘God does not understand by composing and dividing’. His knowledge does not involve the complexity involved in propositional structure any more than it involves any other kind of complexity” (Alston, (1986), p. 288).

Thus, if the divine conceptualist can avail himself of this Thomistic tradition of God having non-propositional knowledge, then Craig himself could make the same move to avoid the charge that God knows an infinitely long list of arithmetical truths.

There is a problem of going the Thomist route here, as Aquinas himself is very explicit about whether God knows infinite things:

“Since God knows not only things actual but also things possible to Himself or to created things, as shown above, and as these must be infinite, it must be held that He knows infinite things” (Aquinas, Summae Theologica, Q14, A12).

Alston is perhaps trying to spell out a Thomist inspired view, rather than a Aquinas’ actual views. Even if Aquinas insisted that God knows an infinity of things, perhaps a non-propositional knowledge model can be adopted whereby God knows all mathematical truths without knowing an infinite list of truths. Indeed, Alston turns to F. H. Bradley’s idealism to spell out this possible model. Aston says that on Bradley’s view, the ‘base of our cognition is a condition of pure immediacy’, in which there is no distinction between different objects of knowledge. It is like taking in a painting as a whole, without focusing on any one particular bit of the painting. We can ‘shatter this primeval unity and build up ever more complex systems of propositional knowledge’, which would be like focusing on a particular brush stroke rather than the scene as a whole. This second mode of understanding is more discursively useful, but lacks the ‘felt oneness’ of the primeval apprehension. In contrast to these modes is the nature of the ‘Absolute’ itself – the world beyond our comprehension, which ‘includes all the richness and articulation of the discursive stage in a unity that is as tight and satisfying as the initial stage’. God’s knowledge, says Alston, could be modelled like this.

Wes Morriston, in his paper ‘Craig on the actual infinite’ (2002) considers this move by Craig, and concludes that Alston’s idea is of no help here:

“On Alston’s proposal, then, God’s knowledge is certainly not chopped up into a plurality of propositional states. On the other hand, it is said to have ‘all the richness and articulation’ of discursive thought. Even if this ‘richness and articulation’ does not consist in a multiplicity of propositional beliefs, it must surely involve some sort of distinction and variation and multiplicity within the divine intellect. However ‘tight and satisfying’ the unity of God’s knowledge, it must be thought of as a unity within a multiplicity – a one in a many” (Morriston, (2002), p. 159).

Ultimately, Alston’s idea is just that a God’s knowledge is a sort of synthesis of multiplicity and unity, and Morriston’s reply is that this does not eliminate the multiplicity. So it is not really any help to Craig.

Thus it seems that the non-propositional nature of God’s knowledge is not really a way of getting out of the claim that God is infinite.

Craig’s God is a passive infinity

Given that we now have the distinction between the active and passive infinity at hand, it could be that Craig’s reply would just be that God’s knowledge of arithmetic truths is a ‘closed totality’ of knowledge, and as such is passive. Just as no new moments can be added to the timeline, no new arithmetic truths can be added or subtracted from the totality of mathematical truths. As such it is infinite, but can never manifest absurdities as a result. As such, God can be infinite in this regard and not get chewed up in the teeth of Craig’s argument.

This would be a satisfactory response by Craig, but for one thing. Craig’s God has a very distinctive relationship to time, because Craig has a very particular theory of time. This makes Craig’s God particularly vulnerable to the actively infinite God objection.

Craig’s God and Time

Craig has a fairly nuanced view about God’s relationship to time. Roughly, God existed in an atemporal manner before he created the universe, but then entered into time and became temporal.

“God exists changelessly and timelessly prior to creation and in time after creation” (Craig [1978], p 503).

Craig also believes that the correct theory of time is the ‘A-theory’, according to which the fundamental temporal relations are tensed (like ‘it is now raining’, or ‘it will be sunny’, etc), rather than tenseless (like ‘raining at t1 is earlier than sunny at t2’, etc). For Craig, there is a fact about what is happening now which is metaphysically basic, and continually changing as time rolls forwards. God, being a temporal entity in time, has knowledge of this now, of ‘where he is’ on the timeline so to speak, and consequently what is presently happening:

“As an omniscient being, God cannot be ignorant of tensed facts. He must know not only the tenseless facts about the universe, but He must also know tensed facts about the world. Otherwise, God would be literally ignorant of what is going on now in the universe. He wouldn’t have any idea of what is now happening in the universe because that is a tensed fact. He would be like a movie director who has a knowledge of a movie film lying in the canister; he knows what picture is on every frame of the film lying in the can, but he has no idea of which frame is now being projected on the screen in the theater downtown. Similarly, God would be ignorant of what is now happening in the universe. That is surely incompatible with a robust doctrine of divine omniscience. Therefore I am persuaded that if God is omniscient, He must know tensed facts” (taken from http://www.reasonablefaith.org/god-time-and-eternity, which is a transcript of a paper given in Cambridge in July 23rd 2002)

This makes Craig’s God an ‘temporal epistemic agent’, that is one who is continually updating his knowledge set with new facts about reality as time passes; namely what is presently true. He doesn’t just know that at t1 it is raining – he knows that it is now raining.

Craig’s God is an active actually existing infinity

According to Craig then, God comes to know new things as time moves forwards. But he already knows an infinite number of truths, all the mathematical truths etc, and then he adds to his knowledge as time passes. However, the cardinality of his knowledge, how many truths he knows, stays the same – it is still infinite. So he knows more things, but also the same number of things. This is a manifestation of absurdity, just like Craig complained about with Hilbert’s Hotel, and at least as convincing as the growing block problem. Thus, by his own arguments, Craig’s God cannot exist.

Dilemma

It could be that Craig objects to the distinction between active and passive infinities. Perhaps it was made for rhetorical force only. If so, then his objection should be characterized as:

‘Imagine a hotel with infinite rooms, that’s absurd, therefore it couldn’t actually exist’.

If so, then I find it very implausible. In order to accept it, we would need to have something to justify it, and all Craig offers is that one can derive ‘absurd’ consequences from it, by which he means something contradictory. I agree that if we can derive contradictions from something, then it is to be rejected. However, we have seen that the only way we can get anything absurd from Craig’s examples is if we interact with the infinity, by getting the manager to free up a room for us, etc. Craig has never offered an example of any absurd consequences from thinking of actually existing infinities that are passive. Thus, if he wants to take this option, he still has all his work ahead of him for motivating the first premise of his supporting argument. Until he has provided this motivation, we are free to refrain from assenting to it, and consequently refrain from assenting to the conclusion of the Kalam argument.

But then if Craig accepts the active/passive distinction, then he has a pair of serious problems. Given the eternal universe model, it is infinite but passive. So not absurd. So it can exist. In addition, Craig’s A-theoretic nature of God means that God manifests absurd behavior. Therefore, he cannot exist.

The conclusion, then, is that either Craig has a lot of work to do explaining why actually existing infinities cannot exist, or he has in fact argued himself into a corner where an eternal universe could exist and God cannot. It seems there are big problems for Craig’s God.