How to completely refute ‘How to completely refute atheism’

0. Introduction

Ok. The title is misleading, but I thought it was funny. And it’s not ‘completely’ false. I’m not going to ‘completely’ refute it, but I am going to pick holes in it.

‘How to completely refute atheism‘, if you don’t know, is a video made by Apologia Studios, in which Jeff Durbin tells us how to completely refute atheism. Except he doesn’t. He offers arguments which are demonstrably flawed.

In what follows, I use some snippets from his video (under fair use), but please do check that I am not misrepresenting him by watching his entire video or any of the videos at his YouYube page.

  1. Fake agnosticism

To begin with, I snipped a bit where Durbin blatantly straw-mans agnosticism:

According to Durbin, “agnosticism … says that we can’t know, ultimately, anything propositionally”. His analysis is that the word is made up of the prefix ‘a’, which he says means “negation”, and the word ‘gnosis’, which he says means “knowledge”. He says that the word ‘agnosticism’ means that “We are without knowledge; knowledge cannot be gained or had; we cannot know.” On Durbin’s view, the agnostic says “We can’t know anything”, to which he replies “Do you know that?” He thinks that this shows that agnosticism is self-refuting.

Durbin doesn’t state any arguments formally, but we can see the general outline very easily. The inconsistency he is pointing out is that if the agnostic says “I know that I don’t know anything”, then this entails a contradiction. He knows nothing; but by knowing that, he does know something. So he knows both nothing and something.

     2. Pyrrhonian scepticism

Almost nobody holds that “we cannot know anything”. It is difficult not to think that Durbin was just making agnosticism look worse than it actually is, to make the job of refuting it easier. If he did, then he would clearly be advancing a straw man against agnosticism. And his description of agnosticism obviously unfairly saddles it with the universal rejection of all knowledge. We will come back to this in a moment, but before we do, I want to look at a position which really is the target of Durbin’s attack. Because, even if it is a straw-man, and it doesn’t really address agnosticism, we can still ask how effectively he argues against this straw-man. I argue that it isn’t really a problem even for the straw-man.

There is a position in philosophy which is quite close to the position that Durbin is actually attacking, involving the denial of all knowledge. And that is Pyrrhonian Scepticism. Pyrrho (c. 300BC) is reported to have said:

“…that things are equally indifferent and unstable and indeterminate; for this reason, neither our perceptions nor our beliefs tell the truth or lie. For this reason, then, we should not trust them, but should be without opinions and without inclinations and without wavering, saying about each single thing that it no more is than is not, or both is and is not, or neither is nor is not” (Aristocles, quoted from the Stanford article)

It is not a stretch to say that Pyrrho’s position is that ‘we cannot know anything’. If so, then Pyrrhonian Scepticism is the position that Durbin’s argument was attacking. His idea is that this sort of extreme scepticism refutes itself. And this line of attack certainly has some appeal to it. We derived a contradiction from the assertion that ‘I know that I know nothing’. So imagine that I were to go around saying ‘My view is that Pyrrhonian Scepticism scepticism is true’. This would make me vulnerable to Durbin’s line of attack, as he could ask me whether I know that Pyrrhonian scepticism is true. If I said that I did know it was true, then I would be contradicting the main claim of Pyrrhonian scepticism; but if I said that I didn’t know it, then I would be tacitly conceding that it might not be true after all.

It’s not clear that even this extreme position is vulnerable to Durbin’s attack though. I could say that when I affirm Pyrrhonian scepticism, I am not making a knowledge claim at all; the content of the claim that Pyrrhonian Scepticism is true could plausibly be taken to be: ‘I believe that Pyrrhonian scepticism is true’. If so, I would be saying that ‘I believe that (I can’t know anything)’. If Durbin asked his gotcha question, ‘But do you know that?’, I could reply ‘No, I do not’, quite without self-contradiction. If Durbin asked ‘But do you believe that?’, I could reply ‘Yes, I do’, also quite without contradiction. So a Pyrrhonian sceptic can construe the statement of their own doctrine as merely a belief claim rather than a knowledge claim, and thus avoid Durbin’s accusation of self contradiction.

However, even if we forget this nuance, and insist that anyone who claims to be a Pyrrhonian sceptic is making a knowledge claim, we still have not refuted Pyrrhonian scepticism with this argument. The most we would have demonstrated is an inconsistency between the sceptic’s behaviour and the content of Pyrrhonian scepticism. It doesn’t prove that Pyrrhonian scepticism is wrong; it just shows that the person making the claim isn’t acting like a good Pyrrhonian sceptic. A good Pyrrhonian sceptic should not make knowledge claims. But criticising a claim on the grounds that the person making the claim’s actions are inconsistent with it, is to commit the tu quoque fallacy. So, even if we pretend that Durbin had caught us doing something which was inconsistent with Pyrrhonian Scepticism (like making a knowledge claim), and if he implied that this showed that Pyrrhonian Scepticism was false, then he would have committed the tu quoque fallacy.

But, even if we overlook this informal fallacy, Durbin is still in trouble. Even if Durbin had completely scored his point, and established that it is not possible to say anything as a Pyrrhonian sceptic without immediately contradicting yourself, this still leaves an escape route; you can be a Pyrrhonian sceptic and not make any claims at all. In fact, this response is the one advocated by followers of Pyrrho. When confronted with an argument, the best you can do is wag your finger at it, like Cratylus. If you don’t say anything at all, you cannot contradict yourself!

Presumably, this position would be open to ridicule by Durbin. Being able to avoid the problem only by retreating to complete silence would seem like a capitulation rather than a victory. Despite initial appearances though, this response might actually be thought to have something going for it. The view recommends a sort of spiritual, monk-like silence, which Pyrrhonians thought could be a pathway to enlightenment and happiness:

“…the result for those who are so disposed [to Pyrrhonian scepticism] will be first speechlessness, but then freedom from worry; and Aenesidemus says pleasure.” (ibid.)

Indeed, even if this supposed benefit were not there, a theory is not deemed false merely because it has been arrived at by retreat. Even if the silent Pyrrhonian monk only took his vow of silence reluctantly and after he conceded in a debate that there was no other way to be consistent with Pyrrhonian scepticism, this doesn’t make Pyrrhonian scepticism false. It could still be true for all that. Therefore, even here, when we have been as generous to Durbin as we possibly could, we have not found a refutation of Pyrrhonian scepticism.

So perhaps Durbin has a point against the Pyrrhonian sceptic who goes around making explicit knowledge claims, which is that he is not a ‘good’ Pyrrhonian sceptic. But Durbin does not have a point against one who makes more nuanced belief claims, and certainly not against one who remains in a peaceful silence. So, the argument only even slightly works if you straw-man it so that the opponent has to be an inconsistent Pyrrhonian sceptic (one that makes explicit knowledge claims).

Durbin is not arguing against agnosticism, but against a fake-agnosticism (Pyrrhonian scepticism), and his arguments fail to refute even this weakened opponent.

3. Not-fake agnosticism

Thomas Huxley, who coined the term ‘agnosticism’ in the late 19th century, described the ‘principle of agnosticism’ as follows:

“In matters of the intellect, do not pretend that conclusions are certain which are not demonstrated or demonstrable. That I take to be the agnostic faith, which if a man keep whole and undefiled, he shall not be ashamed to look the universe in the face, whatever the future may have in store for him.” (Huxley, Agnosticism)

The key idea is that in cases where things “are not demonstrated or demonstrable”, we should not “pretend that conclusions are certain”. If we don’t know one way or the other about something, then just be honest about it.

Just in case you thought that this principle was accompanied by a Pyrrhonian denial of the possibility of all knowledge, consider the very next paragraph from Huxley:

“The results of the working out of the agnostic principle will vary according to individual knowledge and capacity, and according to the general condition of science. That which is unproved today may be proved, by the help of new discoveries, tomorrow.” (ibid.)

Huxley is saying that some people will know more than others, depending on the person and the state of science in their day. This clearly presupposes that some people know things, and that things which we do not currently know can become known.

Durbin claims that the agnostic’s position is that ‘We cannot know anything’, yet Huxley (the originator of the term ‘agnosticism’) explicitly claims that ‘the results of the working out of the agnostic principle will vary according to individual knowledge’ But, if nobody knows anything, then the results of applying the agnostic principle will not vary according to individual knowledge; the results would be the same for everyone!

Durbin claims that the agnostic’s position is that “knowledge cannot be gained or had” and that “we cannot know anything”. But Huxley claimed that “that which is unproved today may be proved, by the help of new discoveries, tomorrow”. If knowledge cannot be had, how is it that we could prove things by the help of new discoveries tomorrow?

The answer is that Huxley clearly did not deny the possibility of knowledge per se. Agnosticism is just the idea that when you do not have a demonstration of something, then you should not claim to know it. There are lots of demonstrations Huxley would have accepted, and so things we would have accepted as knowledge, but crucially he thought that there was no such demonstration for God, and that therefore we should just admit that we do not know whether he exists or not.

To be polite, we would have to say that Durbin has not done his research, and that the straw-man is a result of ignorance, rather than outright deception. This interpretation strains credulity though, as a just a cursory internet search pulled up the sources linked in this article. Either way though, he is just plain wrong. Agnostics do not have to affirm that they have no knowledge whatsoever; all an agnostic has to affirm is that they do not know whether God exists. Such a person is not guilty of any charge of self-contradiction, and certainly not because of anything Durbin brought up.

4. Abstract objects

Durbin goes on to make many claims that I could pick at, but I will focus on just one more section, as what I want to say about it is similar to what I was saying about induction in a previous post. In this snippet from the same video, Durbin describes an encounter he had with a maths teacher while he was at Reason Rally. Where we pick it up, he is explaining how if you write an equation in chalk on a blackboard, then the representation is not the maths itself (not the ‘law of math’ itself), but just a representation of it:

The ‘argument’ starts with a familiar idea that the actual law of maths itself “cannot be seen, cannot be touched, cannot be weighed, there is no colour to it, it is a universal, abstract, necessary, invariant, unchanging law”. The atheist maths professor was apparently a believer that the universe is entirely material, and is just “time and chance acting on matter, it is just stuff happening, like Shakespeare says, it is sound and fury signifying nothing“. Because his worldview was entirely materialistic, the maths professor couldn’t account for such a non-material law. Apparently, he conceded all this, and then when Durbin asked him if 2 + 2 = 4, he replied “Maybe not”.

Now, its not entirely clear what is supposed to be going on in this section. Durbin doesn’t really offer an argument to the effect that there is something, a law of maths, which is an existing non-physical thing. He does explain that if you write ‘2’ on a chalk board, and then rub it off, then you have not destroyed “2-ness”. He seems to think that this is sufficient to establish realism about non-material objects. Let’s grant is for the sake of the argument. The problem he is highlighting is that this non-material entity is incompatible with the thesis that there is nothing but matter (i.e. materialism). So the problem is: realism about non-material mathematical objects, along with materialism, is a seemingly incompatible pair. On one view not everything is material, and on the other view everything is material.

Let’s remember that this is a video about (‘completely’) refuting atheism; not about refuting materialism. Is the problem he has outlined a problem for atheism? I don’t see how it is. So far, all Durbin has argued for (using a very elastic conception of the term ‘argued’) is that materialism and realism about non-material objects are incompatible. Of course, the atheist could have conceded his point, renounced his materialism and embraced a realist view about non-material objects, such as platonism. There are various types of platonism contemporary philosophy of mathematics after all. The atheist could have said, ‘Ok then, your chalk example convinced me that platonism is true. Now what?’

Does Durbin have anything that might move us from atheistic platonism to Christianity? Well, sort of.

5. “If you don’t have Jesus, you don’t have math”

His actual thesis is not just that we can’t be materialists, but that we we can’t be atheists:

As we saw above, the idea is that materialism cannot have non-material laws in it. In contrast:

“Christians have a basis for universal, immaterial, invariant laws … the laws of this universe reflect the order that God actually gives to the universe. Our thinking is to be like God’s thinking. God cannot lie. God cannot engage in logical contradictions. All of us are to essentially have our thoughts come into conformity with God’s thoughts.” (video above, 00:07 – 00:40)

Now, there seem to be two distinct ideas being run together here:

Firstly, there is the idea that God maintains order in the universe, preventing the “sound and fury” that would be there otherwise (“the order that God actually gives to the universe”). So God is a maintainer, or giver, of order.

Secondly, there is the idea that the way we think should be like the way that God thinks (“Our thinking is to be like God’s thinking.”). This normative fact (that we ought think like God) restricts the ways we can think about the world. He also says: “God cannot lie. God cannot engage in logical contradictions.” So, because God cannot lie, and our thinking is to be like his, then the logical law of non-contradiction is to be true for us as a result.

So it is clear that these are quite distinct types of things. On the face of it, they are two distinct accounts of the same phenomena. One is that a law is a regularity maintained by God, and the other is that a law is a thought process that God has (coupled with a normative principle). Are they somehow the same thing? Does God maintain the orderliness of the universe through maintaining a regular pattern of thoughts? How does this work? It is all very unclear.

The second idea, where God cannot lie or ‘engage in contradictions’ seems to me to be aimed at explaining a law of logic; specifically, at the law of non-contradiction. But how, we might wonder, is God’s inability to lie related to the mathematical laws that Durbin started off talking about? It seems to have no connection at all. Thus, even if this did justify that God maintained the law of non-contradiction via his pattern of thinking, it wouldn’t establish that the mathematical laws are held in place in the same way. Is there something about the way that God thinks which makes it such that 2 + 2 = 4? That doesn’t seem to make sense.

But it is actually hard to see how God’s inability to lie entails that the law of non-contradiction is true either. A very plausible reading of the phrase ‘God cannot lie’ is that it means ‘God can only speak things which he knows to be true’. What else could not being able to lie mean but having to tell (things that you believe to be) the truth? Let’s also grant that God believes all and only truths. If so, then this entails that he cannot say a contradiction (‘engage in contradictions’) if and only if there are no true contradictions. If, say, the liar sentence is in fact a true contradiction, then God would have to say the conjunctive proposition ‘The liar sentence is true, and it is false’, because that conjunction would be true! If there is a true contradiction, then if God said that it wasn’t true and false, then he would be lying. So saying that God cannot lie only entails that he cannot speak a contradiction if there are no true contradictions. So it only ‘establishes’ that the law of non-contradiction is true if it begs the question by presupposing that there are no true contradictions. It seems to me this consideration completely kills this line of reasoning. God’s honesty cannot entail the law of non-contradiction in any significant sense.

The idea that fact that God does not contradict himself somehow grounds the law of non-contradiction, also suffers from similarly crippling objections. If God uttered a contradictory sentence, “A and not-A“, he would have contradicted himself, but this is not the same as violating the law of non-contradiction. If God contradicted himself (and non-contradiction is true), then he would have simply said two things, one of which was true and the other of which was false. This clearly is not a violation of the law of non-contradiction.

Because it doesn’t relate to the maths stuff, and because it begs the question, let’s leave the second idea, and focus instead only on the first. That was the idea that God maintains the order of the world. The reason that physical objects act in law-like ways is because God imposes such an order on them. Durbin must also think that mathematical laws, like the one he motivated with the chalk example, are also things that God maintains in a similar way. God imposes that 2 + 2 = 4 on the world in much the same way that he imposes e = mc² on the world.

Here is where we run into the same argument as I used in the induction post. Let’s say that God maintains physical and mathematical laws (and while we are at it, let’s throw in logical laws as well). Let’s say that along with maintaining these laws, he has also revealed to us that he maintains these laws. And let’s say that we know this revelation in a such a way that we cannot be wrong about it; that we know it with absolute certainty. I say, even granting all this, we are in no better situation than a sceptic who doubts it.

Take the continuum hypothesis. It says that between the infinity of the natural numbers and the infinity of the real numbers there is no intermediate order of infinity. It is a currently unproven conjecture in mathematics. Does knowing with absolute certainty that God maintains mathematical laws help us figure out if the continuum hypothesis is true? No. It is no help whatsoever. All it does is rephrase the problem. Here is the problem now:

It is currently unknown whether the continuum hypothesis is true.

With the help of Durbin’s worldview, the problem becomes:

It is currently unknown whether the continuum hypothesis is one of the regularities that God maintains.

The simple fact is that, even on this worldview, God has not told us which regularities he has maintained. And the belief (or even knowledge) that God maintains some regularities, gives us no help at all in trying to work out whether the continuum hypothesis is one of those regularities or not.

And it seems Durbin will have to concede this point. It is obvious that the bible doesn’t contain answers to modern day mathematical conjectures. He has to concede that God has not revealed everything to us; he has not revealed exactly which mathematical laws he has maintained. In particular, he has not revealed whether the continuum hypothesis is true or false.

Durbin has to say that God has only revealed that he maintains mathematical laws, not which ones are true, because he doesn’t know via revelation all mathematical laws. But while Durbin doesn’t have answers to particular mathematical problems, he could say that his worldview provides a basis in which we can answer them. On the atheist worldview, where there is no God maintaining order, and “everything is sound and fury”, there is no such basis. Such might be his reply. I will show that this reply has no force to it.

Durbin is clearly in favour of a type of ‘revelational epistemology’, which for our purposes we can say necessarily includes the following condition:

A) The only way one can know that there are regularities (like mathematical laws) is through revelation from God.

It follows from this that an atheist does not know that there are regularities. How could an atheist know such a thing? Could they tell it through their senses? Can they reason to the nature of the universe just by thinking about it? Presuppositionalists, like Durbin, constantly tell atheists that they cannot find out the truth through these means alone, without God. That’s the point of A).

But it follows that the only way to positively know that regularities do not exist could also only be through such a revelation. For reductio, assume that I could determine, without God, that there really were no regularities in nature. It follows that either God does not exist, or A is false. For, if I can determine on my own that there are no regularities, then it couldn’t also be that God had revealed to me that there are regularities. So, on that premise, either he doesn’t exist, or I do not have revelation from him.

So according to revelational epistemology: if the atheist is right about her atheism (and God does not exist), then the she cannot know about whether there are regularities in nature at all. She has to be in the dark about such metaphysical matters. The issue of what reality is like at its deepest core has to be, for an atheist, a mystery. It might be regular, or it might just appear regular. On Durbin’s view, because they lack revelation, an atheist could never know whether there are universal regularities or not. So it is not that on the atheist’s worldview there are no regularities; its that on the atheist’s worldviews one cannot know if there are regularities (assuming Durbin is right about A being true).

So, for the atheist the question is just open, and seemingly impossible to answer definitively. Atheists are forced to do mathematics without knowing whether there really are any mathematical laws or not. This is how the atheist has to deal with mathematical laws in Durbin’s world.

And, say I, in this setting, atheism is no worse off than Durbin’s Christianity, even if we grant him his every claim.

Let’s look at it from Durbin’s point of view. He knows that God exists, and that God has revealed to him that He maintains certain laws of mathematics, logic and physics. This is the opposite position to the atheist in Durbin’s worldview; the atheist has no knowledge about regularities and no revelation, whereas the Christian has both.

Well, even here on his home ground, Durbin is in trouble. Say we are considering a particular mathematical hypothesis, from Durbin’s vantage in his worldview. Say that the hypothesis is geometrical, like:

“‘Parallel lines never meet’ is a universal law”.

Even with all his certain knowledge from God, even granting everything in his worldview, we know that God did not reveal to Durbin (or any Christian) that ‘parallel lines never meet’ is a universal law of geometry, because, as Riemann showed, it is not. And this meant that everyone throughout history, Christian or atheist, who like Kant had been convinced they had certainty about the truth of principles of Euclidian geometry were just wrong. And there is nothing that Durbin has on his worldview that can prevent this from happening in the future. For any purported law that you come across in Durbin’s world, you cannot ever be absolutely sure that it is a genuine universal principle (one of those regularities that God maintains), and not just an apparent one (like with Euclidian geometry). Even if you grant him all of the things that he claims about his own worldview, he could still not know with absolute certainty for any purported law whether it was a law.

This is exactly the same position that the atheist is on, even on Durbin’s worldview. For the atheist, they cannot be sure whether there are any regularities or not. For the atheist, with each purported law, they can never know for absolute certainty whether it is a regularity or not.

Thus, when we stack the deck entirely in favour of Durbin’s worldview (where we grant that God exists, that he maintains the regularities nature, and that he reveals to Durbin with absolute certainty that he maintains the regularities of nature), and where we stack the deck entirely away from the atheist (who has to make do in a world where revelation epistemology was true but where God does not exist to provide revelation) – even when we do that, each position is in exactly the same position with respect to each and every prospective universal law. Neither of them could ever know if it was actually a law or not. As such theist and atheist are indistinguishable with respect to the question of universal regularities.

The discussion between the atheist and theist at this point is where a theist can only say:

I cannot know that [Claim X] is a universal law, but I believe that [Claim X] is a universal law, and I also believe that what makes it true is that it is a regularity that God maintains.

The atheist can reply:

I cannot know that [Claim X] is a universal law, but I believe that [Claim X] is a universal law, and I also believe that what makes it true is that it instantiates an abstract platonic object.

Even granting all of Durbin’s worldview, the theist and the atheist are in precisely the same epistemological situation regarding universal laws. Each of them has a sufficient condition for the regularity, and neither has a necessary condition.

When you grind all the way through to the end, all you come out with is a perfect stalemate. He has taken not one step forward, even if we grant him everything.

5. Conclusion

Jeff Durbin is a one-trick pony. His trick is the straw-man. He will argue against an agnostic by presenting an argument which only (even slightly) works against a different position. Even then, he clearly has no idea about Pyrrhonian scepticism. If you say you are an atheist, he will try to straw-man you with a form of materialism. But don’t fall for it. If he wants to completely refute atheism, he has to actually offer an argument against atheism. So far he has offered an argument against Pyrrhonian scepticism (which fails) and an argument against materialism (which also fails).

Thoughtology

This post is just a note to say that I have started a podcast, called ‘Thoughtology‘. It is a series where I talk to professional philosophers about various interesting things. I have recorded two episodes so far, and plan to get one out every two weeks (schedule permitting).

In the first episode I talk with my friend Arif Ahmed, who is a well-known atheist philosopher, who, among other notable achievements, has debated William Lane Craig on several occasions. We talked about a paper he has recently published in the journal Mind. The topic is David Hume’s argument that it is always irrational to believe in reports of miracles. A well-known response to this is to argue that the combined weight of multiple witnesses could in principle overcome the scepticism one may have on hearing such a report. Arif explains how, when you look at the details of this in a Bayesian framework, the response fails.

In the second episode, I was very lucky to be joined by Graham Priest, who is one of the world’s most notable logicians and philosophers. He is famous for defending a highly controversial position called ‘dialetheism‘, according to which there are some true contradictions. We talked about dialetheism, paradoxes and the metaphysics of logic.

In the coming weeks and months I intend to interview various other professional philosophers, and have about 12 lined up so far. Many of them will be philosophers who are widely known, and many of them will be less established (but equally interesting) people. If you enjoy this blog, you should subscribe to the Thoughtology YouTube channel so that you get the content when it is released.

Thanks.

Induction, God and begging the question

0. Introduction

I recently listened to a discussion during which an apologist advanced a particular argument about the problem of induction. It was being used as part of a dialectic in which an apologist was pinning a sceptic on the topic of induction. The claim being advanced was that inductive inferences are instances of the informal fallacy ‘begging the question’, and thus irrational. This was being said in an attempt to get the sceptic to back down from the claim that induction was justified.

However, the apologist’s claim was a mistake; it was a mistake to call inductive inferences instances of begging the question. Unwrapping the error is instructive in seeing how the argument ends up when repaired. I argue that the apologetic technique used here is unsuccessful, when taken to its logical conclusion.

  1. Induction

Broadly speaking, the problem of induction is how to provide a general justification for inferences of the type:

All observed a’s are F.

Therefore, all a’s are F.

This sort of inference is not deductively valid; there are cases where the conclusion is false even though the premises are true. So, why do we think these are good arguments to use if they are deductively invalid? How do we justify using inductive inferences?

Usually, when we justify a claim, we either present some kind of deductive argument, or we provide some kind of evidential material. These are each provided because they raise the probability of the claim being true. So if I say that lead pipes are dangerous, I could either provide an argument (along the lines of ‘Ingesting lead is dangerous, lead pipes cause people to ingest lead, therefore lead pipes are dangerous’), or I could appeal to some evidence (such as the number of people who die of lead poisoning in houses with lead pipes), etc.

Given this framework, when we are attempting to justify the general use of inductive inferences, we can either provide a deductive justification (i.e. an argument) or an inductive justification (i.e. some evidence).

A deductive justification would be an argument which showed that inductive inference was in some sense reliable. But with any given inductive inference, the premises are always logically compatible with the negation of their conclusion. With any given inference, there is no a priori deductive argument which could ever show that the inference leads from true premises to true conclusion. You cannot tell just by thinking about it a priori that bread will nourish you or that water will drown you, etc. No inductive inference can be known a priori to be truth preserving. Thus, there can be no hope of a deductive justification for induction.

Let’s abandon trying to find a deductive justification. All that is left is an inductive justification. Any inductive inferences in support of inductive inference in general is bound to end up begging the question. Let’s go through the steps.

Imagine you are asked why it is that you think it is that inductive inferences are often rational things to make. You might want to reply that they are justified because they have worked in the past; after all, you might say, inductive inferences got human kind to the moon and back. The idea is that induction’s success is some evidential support for induction.

However, this is not so, and we should not be impressed by induction’s track record. In fact, it is a red herring, for suppose (even though it is an overly generous simplification) that every past instance of any inductive inference made by anyone ever went from true premises to a true conclusion, i.e. that induction had a perfectly truth-preserving track record. Even if the track record of induction was perfect like this, we would still not be able to appeal to this as a justification for my next inductive inference without begging the question. If we did, then we would be making an inductive inference from the set of all past inductions (which we suppose for the sake of argument to be perfectly truth-preserving) to the next future induction (and the claim that it is also truth-preserving). However, moving from the set of past inductive inferences to the next one is just the sort of thing we are trying to justify in the first place, i.e. an inductive inference. It is just a generalisation from a set of observed cases to unobserved cases. To assume that we can make this move is to assume that induction is justified already.

So if someone offers the (even perfect) past success of induction as justification for inductive inferences in general, then this person is assuming that it is justified to use induction when they make their argument. Yet, the justification of this sort of move is what the argument is supposed to be establishing. Thus, the person arguing in this way is assuming the truth of their conclusion in their argument, and this is to beg the question.

Thus, even in the most generous circumstances imaginable, where induction has a perfect track record, there can be no non-question begging inductive justification for future inductive inferences.

2. Does induction beg the question?

We have seen above that when trying to provide a justification for induction, there can be no deductive justification, and no non-question begging inductive justification. Does this mean that inductive inferences themselves beg the question? The answer to that question is quite clearly: no.

Inductive inferences are an instance of an informal fallacy, and that fallacy is called (not surprisingly): the fallacy of induction. The fallacy is in treating inductive arguments like deductive arguments. The irrationality that is being criticised by the fallacy of induction is the irrationality of supposing that because ‘All observed a‘s are F’ is true, this means that ‘All a‘s are F’ is true. Making that move is a fallacy.

Begging the question is when an argument is such that the truth of the conclusion is assumed in the premises. Inductive inferences do not assume the truth of the conclusion in the premises. For example, when you decide to get into a commercial plane and fly off on holiday somewhere, you are making an inductive inference. This is the inference from all the safe flights that have happened in the past, to the fact that this flight will be safe. The premise is that most flights in the past have been safe. Because (as an inductive argument) the premise is logically compatible with the falsity of its conclusion, the premise clearly does not assume that the next flight will be safe, and so the argument does not beg the question.

In fact, this actually shows that no argument can be both a) an inductive argument and  b) guilty of the fallacy of begging the question. So technically, the claim apologists that inductive inferences beg the question is provably false.

Of course, if we tried to justify induction in general by pointing to the past success of induction, that would be begging the question. But to justify the claim that the next flight will be safe by pointing out the previous record of safe flights is not begging the question, it is just an inductive inference.

So the apologist who made the claim that induction begs the question is just wrong about that. He was getting confused by the fact that justifying induction inductively is begging the question. But when we keep the two things clear, it is obvious that inductive inferences themselves do not, and indeed cannot, beg the question.

3. But what if it did?

Induction does not beg the question. That much is pretty clear. But what would be the case if induction was guilty of some other fallacy? Well, if each inductive inference itself was an instance of, say, a fallacy like circular reasoning (like begging the question) then it would mean that people act irrationally when they make inductions, like deciding it is safe to fly on a plane. Yet, it seems like people are not irrational when they make decisions like this. Sure, there are irrational inductive inferences, like that from the fact that the last randomly selected card was red that the next card will be red. But not all inductive inferences are like this, such as the plane example. So the person who wants to claim that inductive inferences are circular has to say something which explains this distinction between the paradigmatic rational inference (like flying) and less rational (or irrational) inductive inferences. Saying that they are all circular would leave no room to distinguish between the good and bad inductive inferences.

So the apologist owes us something about how it is that we can make apparently irrational inductive inferences which seem otherwise perfectly rational. In response to this, they could make the radical move and reject inductive inferences altogether. This would mean that they have doubled down on the claim that induction is circular; ‘Yes, it is circular’, they will say, ‘throw the whole lot out!’.

Yet they are unlikely to make this move. Each day, everyone makes inductive inferences all the time. Every time you take a breath of air, or a drink of water, you are inductively inferring about what will result from the previous experiences you had about those activities. You are inductively inferring that water will quench your thirst because it has done so in the past. So if the apologist wants to reject induction altogether then he must not also rely on it like this, or else be hypocritical.

More likely than outright rejection, they will try to maintain that although induction is irrational in some sense, it can still be done rationally nonetheless. After all, there is a big difference between inferring that the next plane will land safely, or that the next glass of water will nourish, than that the next card will be red. The former are well supported by the evidence, whereas the latter is not. This is what allows us to distinguish between rational and irrational inductive inferences. Not all inductive inferences are on par; some have lots of good evidence backing them up, and some have none.

So, if the apologist wants to maintain that all inductive inferences are guilty of begging the question, then (assuming they don’t deny the rationality of all induction) they would still owe us an account of what makes the difference between a rational inductive inference and an irrational inductive inference. And the account would have to be something along the evidential lines I have just sketched above. How else does one figure out what inductive inferences are rational and which are not, if not by appeal to the evidence? If some new fruit were discovered, you would not want to be the first person to try it for fear of it being poisonous. But if you see 100 people eat of the fruit without dying,  you would begin to feel confident that it wasn’t poisonous. This is perfectly rational. Thus, even if the apologist’s claim were correct, if they do not want to reject induction altogether, they end up in the same situation as the atheists, having to distinguish between good and bad inductive inferences based on the available evidence in support of them.

Even if the charge of irrationality stood (which it does not), it would have to be relegated to the status of not actually playing any role in distinguishing good inductive inferences from bad ones. This strongly discharges any of the real force of the point that was trying to be made.

The claim of the irrationality of induction was not true, but in a sense, it doesn’t make any material difference even if it is true; we still need to distinguish the better inductions from the worse ones.

4. Justifying induction with God

Some theists suggest that they have an answer to this problem which is not available to an atheist. The idea is that through his revelation to us, God has communicated that he will maintain the uniformity of nature. Given this metaphysical guarantee of uniformity, inductive inferences can be deductively justified. When we reason from the set of all observed a‘s being F to all a‘s being F, we are projecting a uniformity from the observed into the unobserved. Yet we were unable to justify making this projection. The theist’s answer is that God guarantees the projection.

We may initially suspect foul play here. After all, how do we know that God will keep his word? It does not seem to be a logical truth that because God has promised to do X, that he will do X. It is logically possible for anyone to promise something and not do it. Thus, it seems like we have just another inductive inference. We are saying that because God has always kept his promise up till now, he will continue to do so in the future. The best we can get out of this is an inductive justification for induction, which is just as question begging as the atheist version of appealing to the past success of induction. I think this objection is decisive. However, let’s suspend this objection for the time being. Even if somehow we could get around this, maybe by saying that it is a necessary truth that God will not break his promise or something, I say that even then we have an insurmountable problem.

5. Why that doesn’t help

The problem now is that while God may have plausibly promised to maintain uniformity of nature, he has not revealed to us precisely which inductive inferences are the right ones; i.e. the ones which are tracking the uniformity he maintains, as opposed to those which are not. God’s maintaining the uniformity of nature does not guarantee that inductive inferences are suddenly truth-preserving. Even if it were true, it did not stop the turkey making the unsuccessful inference that he would get fed tomorrow on Christmas eve, and it did not stop those people who boarded that plane which ended up crashing. Even if God has maintained uniformity of nature, and even if he has revealed that he has done so to us in such a way that we can be certain about it, we are still totally in the dark about which inductive inferences we can successfully make.

So let’s suppose we live in a world where God maintains the uniformity of nature, and that he has told us that he does so. When faced with a prospective inductive inference, and trying to decide whether it is more rational (like the plane ride) or irrational (like the card colour) to make the inference, what could we appeal to in order to help us make the distinction? We cannot appeal to God’s word, as nowhere in the bible is there a comprehensive list of potential inductive inferences which would be guaranteed to be successful if made (which would be tantamount to a full description of the laws of nature). Priests were not able to consult the bible to determine which inductive inferences to make when the plague was sweeping through medieval Europe. They continued to be unaware of what actions of theirs were risky (and would lead to death) and which ones were safe (and would lead to them surviving). The only way to make the distinction between good inductive inferences and less good ones is by looking at the evidence for them out there in the world. Knowing that God has guaranteed some regularity or other is no help if you don’t know which regularity he has guaranteed.

The problem is that we are unable to determine, based only on a limited sample size, whether any inductive generalisation we make is actually catching on to a uniformity of nature, or whether it was just latching on to a coincidence. When Europeans reasoned from the fact that all observed swans were white to the conclusion that all swans were white, they thought that they had discovered a uniformity of nature; namely the colour of swans. They didn’t know that in Australia there were black swans. And this sort of worry is going to be present in each and every inductive inference we can make, even if we postulate that we live in a world where God maintains the uniformity of nature and has revealed that to us. The problem is primarily epistemological; how can we know which inductive inference is truth-preserving? The apologist’s answer is metaphysical; God guarantees that some inductive inferences are truth-preserving (i.e. the ones which track his uniformities). For the apologist’s claim to be of any help, it would have to be God revealing to us not just that he will maintain the uniformity of nature, but which purported set of observations are generalisable (i.e. which ones connect to a genuine uniformity). Unless you know that God has made the whiteness of swans a uniformity of nature, you cannot know if your induction from all the observed cases to all cases is truth-preserving. And God does not reveal to us which inductive inferences are correct (otherwise Christians would be have a full theory of physics).

In short, even if we go all the way down the road laid out by the apologist, they still have all the same issues that atheists (or just people of any persuasion who disagree with the theist’s argument laid out here) do. They have no option but to use the very same evidential tools that atheists (etc) do to make the distinction between the more rational and less rational inductive inferences.

6. Conclusion

The apologist’s claim was that inductive inferences were question begging. I showed that this is not the case (and that in fact it could not be the case). Then I went on to see what would be at stake if the apologist had scored a point. We saw that still the apologist would need to distinguish better and worse inductive inferences, just like the atheist, and would have no other option but to use evidence to make this case. Then we looked at the idea that God guarantees that there would be some uniformity of nature. We saw that this claim does not make any material difference to the status of inductive inferences, and so cannot be seen to be a justification of induction in any real sense.

 

 

 

 

Molinism and Trivial Counterfactuals

0. Introduction

I recently watched a pair of debates (which you can watch here and here) between a Molinist and a Calvinist about the idea of God’s ‘middle knowledge’. The Molinist was Eric Hernandez, and the Calvinist was Tyler Vela. The debate seemed to me to be quite imprecise, and it that both sides would have benefited from a formal framework within which they could precisely pose their various claims and counter-claims. In fairness, Tyler did give a formalised written version of his argument for the second debate (and you can see his slides here). This presented a very clear expression of  (what seems to me to be) an error that both sides were making. I wish to clear up here.

These issues have been investigated by logicians specialising in temporal logic since the late 70’s, and something of a consensus has arisen over the deficiency of the Molinist position. Neither of the participants seemed to be aware of this development. I guess that this is not surprising seeing as it is an obscure area of the literature, and requires a certain amount of technical training to read the logical and semantic details of the papers. Also, and possibly for the same reasons, the lessons do not seem to have made much of an impact on the philosophy of religion scene, never mind the theology scene. Given that I have a good knowledge of this area (having published journal articles on it) I will outline the main issues here with the hope of shedding some light on the debate.

  1. Molina

Luis de Molina was a 16th century Spanish jesuit priest who formulated a position which bears his name in contemporary philosophy of religion. Molina was concerned with how to reconcile human freedom (conceived of as libertarian free will) and God’s sovereignty. However, there is a tension between God’s sovereignty and human freedom. To the extent that humans are free, they are not under the control of God (and that undermines his sovereignty); yet to the extent that God is in control of everything, humans are not perfectly free. The reformed answer to this puzzle is to repackage freedom as a variety of compatibilism. Molina was reacting to this move, and wanted to maintain the strong sense of libertarian freedom as well as the strong sense of sovereignty. It is from this mix that we get Molinism.

2. Future Contingents

The debate that Molina contributes to is one that had been going on for centuries before him. The medievals rediscovered Aristotelian texts that had been lost to western Europe during the dark ages and this contributed to the increasingly sophisticated logical debates that preceded the reformation. In particular, one topic caught the imagination of the medievals, and that was the issue of future contingents. A future contingent is a prediction, like ‘There will be a sea battle tomorrow’ (Aristotle’s example) made in a context where there could be a sea battle and there could be no sea battle. To get a feel of the modal strength of the future contingent, contrast it with an expression of possibility, and an expression of inevitability. So we might say ‘There could be a sea battle tomorrow’. This sentence can be true now even if tomorrow there is no sea battle; for often things don’t happen which were possible (a familiar fact to most people who have ever played the lottery). The modal force of this sentence is very weak. On the other hand, saying ‘There necessarily will be a sea battle tomorrow’ is much stronger. This sentence could be false even if there is a sea battle tomorrow. It may happen by accident, for example, and not of any kind of necessity. A future contingent cuts a line between these two modal extremes. Saying ‘There will be a sea battle’ is stronger than saying that there may be one, but weaker than saying that there must be one.

Aristotle argued (or at least seemed to) in his work On Interpretation (part 9) that purported examples of future contingents, if they were true now, would have to be already impossible or necessary. For if it were already true now that there will be a sea battle tomorrow, then it is going to take place regardless of what you try to do about it; its future truth seems to indicate its present inevitability. Thus, according to Aristotle’s argument, there could be no such thing as a ‘future contingent’ (i.e. a true future-tensed statement which is neither necessary nor impossible). This is a strong form of logical fatalism.

The received view of Aristotle is that his solution this this problem was to advocate that future contingents were neither true nor false, and thus to avoid the fatalism (although not everyone agrees – see this paper by Hintikka). Despite their reverence for Aristotle, the medievals found his solution to be deeply troubling, as it indicated that God could not know the contingent aspects of the future. After all, if God knows all true statements (being omniscient) and believes nothing but true statements (being infallible), then he does not know future contingents (which, being neither true nor false, are not true). Thus, God is seemingly in the dark about whether there will be sea battles tomorrow, or whether certain people will sin, etc. Aristotle’s solution is therefore incompatible with a robust conception of God’s foreknowledge. On the other hand, if God does know the truth-value of future contingent statements, then there is a theological equivalent to the problem of future contingents: God’s knowing true future contingents in advance makes them seem inevitable and thus necessary. If God knows you are going to sin tomorrow, then it is going to take place regardless of what you try to do to prevent it.

Various medieval philosophers, logicians and theologians offered their solutions to this problem, such as Peter Abelard, St. Anselm and William of Ockham. The Anselmian-Ockhamist solution, explained expertly by Peter Øhrstrøm here, was to hold that God knows the truth-values of future contingent statements, but to deny that this entails that the statements themselves become necessary as a result. Ockham diagnosed a ‘modal fallacy’ in the claim that his foreknowledge made them necessary; God knows that p will happen, even though it might not – these are not logically incompatible, and the modal fallacy is supposing that they are. In this sense, there can be genuine true future contingents for Ockham.

Future contingents are logically equivalent to free choices of agents with libertarian free will. A future contingent is a statement of the form ‘it will be that p‘ made in a situation where ‘it is possible that it will be that p‘ and ‘it is possible that it will not be that p‘ are both true. An agent’s choice to do x is free in the libertarian sense only if they could have chosen to do x and have chosen not to do x. So both concepts rely on the prediction being true (or choice being made) in a situation where it’s falsity is possible (where the choice could have not been made). Thus, libertarian free will is really just a special case of a future contingent, where the predicted content is the action of the agent.

Molina essentially accepts the Ockhamist proposal, which was that God knows the future choices of agents without this stopping the possibility of those choices being different (they could be different, but they won’t be). However, he adds to this an additional claim, which is aimed at bolstering the sovereignty consideration. God knows not just which free choices agents will make, but also those free choices they would have made were they to have been faced with different circumstances.

3. Luis

Let’s use an example to make the point clear. Imagine a medieval monk; call him Luis. He lives in a monastery high in the mountains somewhere. In this calm and peaceful environment there are seldom any opportunities for moral temptation (which is part of the point of a monastery after all). Upon entering the monastery, God knows that Luis will not sin for the rest of his life. It is still possible that he could sin (he could decide to leave the monastery and live in the sinful town at the bottom of the mountain). But God knows that though he could do this, he won’t. So far, this is just the Ockhamist picture.

We may wonder about Luis’ moral character in more detail than this though. Sure, he won’t actually sin, but this just seems to be a product of the environment he is living; he won’t be seriously tempted to sin. In a sense then, his moral character is not going to be severely tested in any way. Even though he won’t be, what would have happened if he were to be tempted? Imagine a beautiful maiden were to arrive at Luis’ bedroom one night and beg him to spend the night with her. It won’t happen (given the strict rules of the monastery), but what if it did? Would he have been able to resist, or would he have given in to temptation?

4. Middle Knowledge

Molina thought that God, in his sovereignty, had to know the answer to this sort of question. That is, God has to know the truth-value of every actual future contingent, but also of every counterfactual future contingent. Here is an example of the sort of sentence that Molina claims God would know the answer to:

a) Had it been the case that [Luis is tempted to spend the night with the maiden], then it would have been the case that [Luis will give in to the temptation].

a) is a a conditional (if…, then…), in the subjunctive mood (using the modal modifiers ‘had it been…, it would have been…’) and it has an actually false antecedent (it is not actually the case that Luis is tempted by any maiden). This makes it a counterfactual. It is important to note that the consequent (‘Luis will give in to the temptation’) is a future contingent, specifically one about his libertarian free choice. Molina’s claim is that God knows counterfactuals with future contingents as their consequents, like a).

In addition to him knowing the truth-value of these counterfactuals, the obvious supposition is that some of them are in fact true; it’s not Molinism if all such counterfactuals are false. We will come back to this at the end.

This type of knowledge that Molina claims God has is often referred to as ‘middle knowledge’. Middle knowledge is usually contrasted with two other types of knowledge that God has: natural knowledge and free knowledge. Natural knowledge concerns all the necessary, possible and impossible truths. So that 2 + 2 = 4 is necessary; that it Judas betrayed Jesus is possible; that 2 + 2 = 5 is impossible. In contrast, free knowledge concerns those facts which relate to the creation of the world. So the fact that I exist, or the fact that you are reading this blog post, is part of God’s free knowledge. Middle knowledge is usually contrasted with these two in terms of being between general facts to do with possibility, and particular facts about the contingent world; middle knowledge is supposed to concern counterfactual facts.

5. A Better Distinction Using Possible Worlds

However, this is not the best way of drawing this distinction. With the benefit of possible worlds semantics and a clear understanding of logic, we can make this distinction much more cleanly.

Possible worlds are thought of as just sets of propositions that are maximal and consistent. This just means that for every atomic proposition, p, and every world w: either p is in w or it is not, but not both.

We can then use the usual logical compositional clauses to form more complex propositional forms:

  • if p is not true in w, then ~p is true in w;
  • if p is true in w and q is true in w, then ‘p & q‘ is true in w, etc.

If there is some formula, A, which is true in all worlds, then we say that A is necessary; if it is true in no worlds then A is impossible; if it is true in some worlds but not others, then A is contingent.

All of these propositions would be items of God’s natural knowledge; he knows what is true and what is false at every world, and thus he knows what is necessary, what is contingent and what is impossible. So much for natural knowledge.

Take one world, say w1. We can designate this world as the ‘actual world’, and label it ‘@w‘. Think of it as being the world that God chose to actualise. If a proposition is true at @w, then it is simply true (or ‘true simpliciter’). (Having a special designated actual world is how Kripke originally formulated possible worlds models, though it fell out of favour with most subsequent formal treatments of possible worlds semantics). God’s free knowledge concerns what is true simpliciter (or what is true at @w).

So far, we have used possible worlds semantics to explain the contents of God’s natural and free knowledge. As noted above, the description of God’s middle knowledge is usually cashed out as concerning counterfactuals. And it is, but most counterfactuals actually come under God’s natural knowledge, a claim which we can also spell out clearly now using the benefit of possible worlds. There are two types of counterfactuals that need to be distinguished from Molinist counterfactuals, and this distinction is the counterfactual mirror of the distinction between modally weak predictions, future contingents and expressions of inevitability from above.

On the one hand, God knows ‘might’ counterfactuals of the following type:

b) If I had flipped the (fair) coin, then it might have landed heads.

This type of counterfactual uses the word ‘might’, which is analogous to the word ‘possible’; if I had flipped the coin then landing heads was possible. Equally, landing tails is also possible given the coin flip (assuming a perfectly fair coin, etc). All this means is that at at least one of the worlds which are maximally similar to the actual world at which I flipped the coin, it lands heads.

The point is that ‘might’ counterfactuals are very weak in what they claim. All that is required is that the antecedent condition is compatible with the consequent condition; that there is at least one ‘coin-flip’ world (maximally similar to the actual world) at which the coin lands heads. This just means that the flipping of the coin (in the right sort of circumstance) is compatible with it landing heads. Thus, all ‘might-counterfactuals’ come under natural knowledge. To turn the example to Luis, the following might-counterfactual is true: ‘if Luis had been tempted by the maiden, then he might have given in to the temptation’. Even though that counterfactual is true it doesn’t tell us whether Luis would give in to the temptation or not – it just tells us that he might do. This is why these might-counterfactuals don’t count as middle knowledge.

In contrast, imagine a coin which has heads on both sides (a ‘rigged’ coin). The following counterfactual, which uses ‘would’ instead of ‘might’, would be true for that coin:

c) If I had flipped the (rigged) coin, then it would have landed heads.

Because the coin is rigged, its landing heads is inevitable once it is flipped (assuming of course that it cannot land perfectly on its side, etc). This just means that in every (maximally similar) ‘coin-flip world’, the coin lands heads. And we can immediately see that this is the case, because no matter which way it lands, it will land heads. To make the example relevant to Luis again, we can easily think of consequents which are inevitable given the truth of the antecedent. For example: ‘If Luis had been tempted by the maiden, then he would have been tempted’. The consequent is (in a particularly trivial way) necessitated by the truth of the antecedent. In every (maximally similar) temptation world, Luis is tempted. This sort of example would also not count as middle knowledge, as it does not tell us what free choice Luis would make in the counterfactual situation. This example, like the one above, is also an example of natural knowledge.

So far, we have seen two types of counterfactuals, ‘might-counterfactuals’ and ‘would-counterfactuals’ and neither of them count as middle knowledge (they are both just natural knowledge). What we need to get there is a sort of Goldilocks modality, which is between ‘would’ and ‘might’. There is no natural locution for this in ordinary English, so I will use the somewhat stilted phrase ‘actually-would’. So in contrast to b) and c), the Molinist counterfactual, the real example of middle knowledge, is:

d) If I had flipped the (fair) coin, then it actually-would have landed heads

When we hear d), we need to remember that it doesn’t mean that the coin might land heads, and it doesn’t mean that the flipping of the coin necessitates it landing heads. It means that, though it is possible that it land tails, if it were flipped would in fact happen to land heads. To make the example relevant to Luis, consider the counterfactual: ‘If Luis had been tempted, then he actually-would have given in.

6. Red Line

Now we have clearly and precisely stated the thesis that Molina argues for. He is saying that at least some counterfactuals of type d) are true, and God knows them – they constitute God’s ‘middle knowledge’. The question is how to model this claim. With the previous two types of counterfactuals, we were able to use the standard ideas from the literature on possible worlds semantics (which come from David Lewis, see this and this). Put simply, ‘would’ counterfactuals rely on what is true at every maximally similar antecedent world, whereas ‘might’ counterfactuals rely on what is true at at least one maximally similar antecedent world. These are what grounds these two types of counterfactuals, they are what makes them true, which is to say that they are the semantics for those counterfactuals. But what is it that grounds the truth of the Molinist counterfactual? What is its semantics? There is reason to think that at the moment there is nothing to appeal to – nothing to hang our metaphysical hat on, as it were.

Here is one way of thinking about the situation which makes it clear that as things stand there is no obvious candidate. Consider a simple model, we have three worlds, w1, w2 and w3. Let’s say that w3 is the actual world, @w (which we will draw in red). In @w, Luis is not tempted by the maiden (she does not go to the monastery at all). In w1 and w2 Luis is tempted. He gives in in w1 but not in w2. We can picture this as three worlds which ‘branch’ from one another as follows (worlds ‘overlap’ when they share all the same atomic propositions, and ‘branch’ from one another when they differ over the truth of a proposition):

luis

We can ‘hang our hat’ on a feature of this model to ground the truth of the counterfactual that Luis might have given in: there is at least one of the tempted-worlds in which Luis gives in (i.e. w1). We can also hang our hat on a feature of this model to ground the falsity of the counterfactual that Luis would have given in: it is not the case that he gives in on all of the tempted worlds (i.e. in w2 he does not give in). Each of these types of counterfactual receive a truth-value in a straightforward way. What is unclear is how one could ground the claim that, had he been tempted, Luis actually-would have given in. He gives in on one tempted-world but not the other; w1 and w2 have nothing to distinguish one from the other. Why say that he would give in rather than not give in?

6. Trivial Counterfactuals

It is at this point that I saw both contributors to the podcast making a move which is mistaken. I am quite prepared to believe that Tyler was lead astray by Eric’s lack of clarity at this point (after all, Eric is the Molinist and he should have been able to explain his own position clearly). However, the both made the same move, which obscured the rest of the conversation.

Here is what happened. Tyler was asking Eric if it was possible for God to create the world such that everybody freely chooses to believe in God. They both agreed that it was logically possible for this to happen, in the sense that there was no logical contradiction in the supposition that it happens. However, Eric insisted that though it was logically possible, it was not ‘feasible’ for God to do this. Unfortunately, no definition was given for ‘feasibility’. Tyler wanted to demonstrate that if feasibility has no metaphysical content, then the appeal to it was ad hoc here, being added without any motivation other than avoiding the problem. How he went about framing his argument demonstrated that a clear framework for the semantics for Molinist counterfactuals was lacking. Here is how he presented his argument on the second show:

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Now, the actual details of Tyler’s argument are not important here for my purposes. Just note that the first premises of each of the three arguments are conditionals, and the antecedents talk about worlds being possible and God actualising worlds. They are effectively little counterfactuals about what would be the case had God actualised different worlds.

The implicit idea here is that in a Molinist counterfactual, one changes which world is the actual world; that we move the red line on the picture. Tyler’s whole argument is about what would be the case if a different world were actualised. It is as if this is how the model would look to make the Molinist counterfactual ‘If Luis had been tempted, he would have given in’ true:

luis2

There are two immediate problems with this idea though. Firstly, what we have is no longer really a counterfactual situation. A counterfactual has to have an actually false antecedent, yet on this model the antecedent (Luis is tempted) is actually true (because w1 is now the actual world). Secondly, and more importantly, it is trivial. The problem is that if we move the designation of the actual world to a different place in the ‘tree’, then this change settles the matter of the truth of the consequent of the conditional. And the antecedent of Tyler’s conditionals have the mention of which world is being actualised explicitly as stated in the antecedent. To make this clear, consider the following two questions one may ask:

e) Had God actualised world w1, would Luis have given in to temptation?

f) Had Luis been tempted, would he have given in?

There is a big difference between e) and f). Firstly, nobody would ever say e), outside a contrived philosophy seminar-room example. The reason is partly because in real life possibilities are not labelled neatly like w1 and w2, etc. But let’s suppose that we can get around this somehow (that a magic world-labelling dictionary is available to everyone who introspects hard enough). The problem now is that stating the world by name implicitly includes all the propositions that are true at that world. That’s all a world is! It is like saying:

g) Had God actualised world w1, in which Luis is tempted and gives in, would he give in?

Nobody would ask a question like g) because it contains its own answer, and is thereby trivial. e) is trivial because it is just an elliptical way of asking g). Likewise, the following counterfactual (which is similar to Tyler’s) is trivial:

h) If God had actualised w1, then Luis would have given in to temptation.

This provides us reason to think that h) cannot be any part of the semantics of the Molinist counterfactual d). The reason h) is not equivalent to d) is that h) is trivial, whereas d) is not. Just like the way that e) is trivial and f) is not. What this means is that the correct semantics for the Molinist counterfactual, d), is not just moving the red line in the model for d) to a different place. Tempting though it may be, the analysis of a Molinist counterfactual is not to conceptualise a counterfactual about what would be the case if God had actualised a different world. To do so is to misunderstand Molinism. As I said, I think this mistake was being made by both parties in the debate, although Eric bears the responsibility for articulating his own position correctly.

7. Red Lines

If that is not the answer, then what is? This is where we find the logic literature that I referenced in the introduction to be very helpful. As far as I know, the first systematic logical account of a Molinist branching model was put forward by McKim and Davis in 1976. It was made into a much more elaborate theory by Thomason and Gupta in 1980. A similar theory was also developed by Brauner, Ohrstrom and Hasle in 1999. The way these theories work is to postulate not just one red line, but multiple red lines. In the case of the actual world, what makes a future contingent true is that what it predicts is true in the actual future; the sentence ‘there will be a sea battle’ is true if and only if there is a sea battle in the actual future. The idea of the ‘actual future’ is what breaks the symmetry between all the various possible futures of that moment. In the counterfactual situation, there is no such symmetry breaker, and this is what leaves us only able to ground ‘would’ and ‘might’ counterfactuals, but not Molinist counterfactuals. There is nothing for God to hang his hat on, as it were. What these authors above all have in common is the idea that they need to break the symmetry in the counterfactual situations by adding in actual futures at each counterfactual branching point. At each counterfactual situation where there is a future contingent (like a monk being tempted and deciding whether to give in to it or not) there needs to be an counterfactual ‘actual’ future (a ‘counteractual’ as it were). So our little model would have to be modified to make it a proper Molinist moodel:

luis4

Now we can say that the semantics of a Molinist counterfactual is as follows:

i) ‘Had it been the case that A, then it actually-would have been the case that C’ is true if and only if it is true in the counteractual future future of the most similar A-point that it will be that C’.

So, in the actual world, the Molinist counterfactual ‘had Luis been tempted, he would have resisted’ is true because in the maximally similar tempted situation, the actual future has him resisting the temptation. In the counterfactual situation in which Luis was tempted, he actually resists temptation.

So a technical addition to our models, a specification of counteractual futures at each branching point, provides the required metaphysical feature for us to hang our semantic hat on. God’s middle knowledge is just that he knows where all the red lines are in the overall tree of branching worlds.

8. Problems

Despite its seemingly attractive solution, there are some widely recognised and severe problems for this Molinist semantics. These come in two categories; technical and conceptual.

The technical difficulties are explained in Belnap and Green (1995) and in Belnap et al (2001)  (chapter 6), and also a in chapter of my PhD thesis which is available here (p. 7 – 9). The issue has to do with the semantics of tenses. The problem has to do with iterated tenses, like “It will be that it was that p“, etc. These do not operate properly on the Molinist account, with the result that various tense-logical tautologies are violated by the Molinist logic. Consider the ‘tempted’ point in our Molinist model above. At that time, it is true that Luis is being tempted. Now, it is usually considered a tautology that if something is presently true, then in the past it was going to be true. That ‘you are reading this blog post’ is true now, so before you started reading it the sentence ‘you will read this blog post’ would have been true. This seems to be an elementary fact about how tenses work. Yet, at the ‘tempted’ point in our model, if we go back in the past to the trunk of the tree we find ourselves in a situation where the actual future leads to Luis not being tempted at all.  So even though he is being tempted, it was not the case that he was going to be tempted. In fact, because the actual future of the trunk leads to him not being tempted, we have it that Luis is being tempted, even though in the past it was true that he will never be tempted. This is an odd result. Thomason and Gupta, and Brauner, Ohrstrom and Hasle do make modifications which avoid this issue, but only at a cost. Each time they modify the model it leads to a different intuitive tautology not being true, which led Belnap to describe  the process of constructing ever more complicated Molinist models as ‘mere idle filigree’.

The conceptual problem is just that it is hard to make any sense out of the idea of counteractual futures. Unless one is a full-on modal realist (in the vein of David Lewis), you will think that there is a pretty big ontological difference between what is actual and what is merely possible. What is actual concretely exists, and what is merely possible does not. Yet, when the Molinist posits actual futures of merely possible situations, we find that this intuition gets lost. Are we saying that these situations are sort of concrete and existing? How can something be sort of concrete and existing? If they are fully concrete and existing, then what distinguishes the actual world from them? There is a big metaphysical question mark over this way of conceptualising counterfactuals which makes many think that it is wrong in principle to posit actual futures of counterfactual moments.

9. Alternatives

Instead of going the Molinist route, a more promising proposal is to just abandon the idea of middle knowledge altogether. Molinist counterfactuals are just inherently problematic. What sounds like an initially plausible proposal (that God could know what you would freely do in counterfactual situation) just comes out both technically and conceptually flawed.

Instead, we should embrace the idea that there are only ‘would’ and ‘might’ counterfactuals. In addition, we should be prepared to countenance the prospect that, strictly speaking, most ‘would’ counterfactuals are false. Have a look at these papers (here and here) for some philosophers giving weight to this proposal. When we say ‘Had I flipped the fair coin, then it would have landed heads’, this is just false. So is ‘Had I flipped the fair coin, then it would have landed tails’, although ‘Had I flipped the fair coin, then it would have landed either heads or tails’ is true. Only if the consequent is necessitated by the antecedent is a ‘would’ counterfactual true.

Why think this? Well, I suggest that the most natural way to think about what is grounding counterfactuals (and most metaphysical modality claims) is the natures of actual objects. The reason that this coin could land heads but doesn’t have to is because of the nature of the coin itself. It is because it has heads on one side but not on the other. These facts are what we are hanging our hat on. These facts are what allows us to draw the tree of possibilities in the first place. Nothing about the actual coin picks it landing heads over tails in a counterfactual situation, so there is no metaphysical fact about that. Molinism asks for God to have knowledge about facts which don’t exist.

10. Conclusion

All I wanted to do in this post was explain why a certain way of talking about Molinism is wrong, but to do that as clearly as possible, I have gone through the background of Molinism, explained the basic ideas in the semantics of counterfactuals, and outlined the main thrust of the objections to the Molinist semantics found in the logic literature on this topic. I have also provided a quick sketch of my view, which is a species of Ockhamism.

Is God’s Existence Logically Necessary?

0. Introduction

It is a common platitude in philosophy of religion to hear the claim that the existence of God is necessary, or that God exists ‘in all possible worlds’. However, it seems to me that the existence of God can only really be thought of as (at best) metaphysically necessary, but not logically necessary. Strictly speaking, God doesn’t exist in all possible worlds. In this post, I want to explain a bit about what possible worlds are, from a logical point of view, and explain how God’s existence is not logically necessary in classical propositional logic.

  1. Possible worlds

Perhaps the defining idiom of 20th century analytic philosophy is the term ‘possible worlds’. The traditional story is that this terminology dates back to Saul Kripke’s early logical work on the semantics of modal logic (see here, and here). For an excellent summary of the historical lead-up to this development, see this paper by Jack Copeland. As Copeland notes, the roots of the project can be traced back further, to the development of classical propositional logic in its modern form by people like Frege, Russell and Wittgenstein. As Wittgenstein explains in the Tractatus:

“If an elementary proposition is true, the state of affairs exists: if an elementary proposition is false, the state of affairs does not exist. If all true elementary propositions are given, the result is a complete description of the world. The world is completely described by the specification of all elementary propositions plus the specification, which of them are true and which false.” (4.25-4.26)

In the second line of the Tractatus, Wittgenstein defines the world as ‘the totality of facts’. These facts, or states of affairs that exist, are what makes propositions true or false. So if we specify a truth value to each and every proposition, then this would be a way of specifying what the world is like – it specifies whether the states of affairs that correspond to the propositions exist or not. Let’s use as an example the proposition is ‘Donald Trump is the president of the USA’, which we shall refer to as p. If p is true, then the state of affairs in which corresponds to p exists; i.e. if p is true, then Donald Trump really is the president of the USA.

Once the truth values of the atomic propositions are given, then this generates the truth values of more complex formulas. So if p is true and q is true, then the formula ‘p & q‘ is true as well, etc. In this way, everything that one can say about the world is said just by giving the truth values of all the atomic propositions.

When we are thinking about this process of describing the world via the truth values of the atomic propositions, we need to specify two conditions:

  • We need to ensure that we give each proposition one truth value or other; we cannot ‘forget’ to specify whether p is true or false.
  • We need to ensure that we do not give the same proposition both truth values; we cannot say that p is both true and false.

Let’s call the first condition maximality, because it is saying that our description of the world is maximal in the sense that no proposition is left out. Let’s call the second condition consistency, because it is saying that our application of truth values to propositions is consistent, in the sense that no proposition is given both truth values. This allows us a nice and precise definition of a ‘world’, as used by Wittgenstein:

A world is a maximal and consistent valuation of atomic propositions

On this understanding, a different world is just a rearrangement of truth values to the basic atomic propositions. So, pretending for a moment that there are only 3 atomic propositions (p, q and r), it might be that in the actual world the following combination of propositions is true: (p, q, r). But at some other world, the following combination is true: (p, ~q, ~r).

The number of worlds is a function of the number of elementary (or atomic) propositions we have. If we have just one proposition p, then there are two worlds, because p could be true, and p could be false. If we have two propositions, p and q, then we have four worlds: one in which both are true, one in which both are false, one in which p is true and q is false, and one in which p is false and q is true. In this way, we can construct tables which systematically display all the combinations of truth and falsity to the basic propositions. Here is a picture, from the Tractatus, showing such a ‘truth table’ for three propositions, (p, q, and r):

truth-table

The method of truth tables is used by Wittgenstein in the Tractatus as a method of proving whether complex formulas are true or false independently of the values of their atomic elements, and for whether arguments are valid or invalid. In short, it is a proof theory for propositional logic, and it is both sound and complete. It is taught as an introduction to any logic class.

Given that there are two truth values on this picture, if the number of atomic propositions we have is n, then the number of worlds (i.e. maximal and consistent sets of propositions) is 2 raised to the power of n (which WordPress doesn’t seem to have a symbol for); i.e. the number of  worlds doubles for each additional atomic proposition you have.

It follows very simply from this definition of a world, that a formula of the form ‘p or ~p‘ is going to be true at each and every row of the truth table, which is to say at each world. That’s because each world has the proposition p as either true or false in it due to the maximality constraint. All ‘p or ~p‘ needs to be true is that one or other of its disjuncts is true. So, this formula is considered to be a ‘tautology’ because we do not need to look at the particular variation of truth values in the world we are considering to see if it is true or not. It is true in every world. Similarly, a proposition of the form ‘p & ~p‘ is going to be false regardless of the arrangement of the truth values to the atomic propositions. Because of the consistency condition, each world gives only one truth value to each proposition, and the formula just says that p has both truth values.

Therefore, what we might think of as the ‘law of excluded middle’ is guaranteed by the maximality condition, and the ‘law of non-contradiction’ is guaranteed by the consistency condition. That they are true in every world is a consequence of the definition of a ‘world’.

Also, the notion of validity is just that if the premises of an argument are true, then the conclusion is true. If we plug the argument into a truth table, we can give precise expression to this notion: an argument is valid if there is no row of the truth table on which the premises all come out true but on which the conclusion is also false. This just means that an argument is valid if there is no world in which the premises are true and the conclusion is false.

Although it is often not stated in terms of worlds, the ideas of tautology and validity in classical propositional logic have always made use of the notion of worlds, if construed as maximal consistent sets of propositions.

In essence, all Kripke does to this picture is to add two additional operators to the logic, which say ‘it is possible that…’ (◊p) and ‘it is necessary that…’ (□p). These operators refer, via the semantics (which I will not go into any detail over for ease of reading – though I am more than happy to at a later date) to what is true or false at other worlds, or other ‘possible worlds’. So if ◊p is true, then p is true at some other possible world; and if □p is true, then p is true at every possible world. We can afford to leave out most of the details here because we are primarily focussed on logical possibility, which is handy because it gets somewhat technical otherwise.

If we ask a question about whether a given proposition, p, is logically possible, then we can see if there is a possible world where p is true. There is a world where p is true if and only if there is a maximal and complete assignment of truth-values to the atomic propositions where p is true. So is the following proposition possible?:

a) This glass of beer is full, and I am hungry.

We can formalise a) as follows, where p = ‘this glass of beer is full’ and q = ‘I am hungry’:

b) p & q

Now, as it happens, this glass of beer is half empty (because I have already been drinking from it), and I am not hungry (because I have just eaten dinner), meaning that p is false and so is q. That means that b) (and thus a)) is false. But that doesn’t tell us whether it is possible or not though. What we have to consider to see whether it is logically possible or not is whether there is a contradiction in supposing that it is true. And there is no contradiction in supposing that the truth-values of the propositions are different. Though p and q are both false, they could both be true. As Wittgenstein said when referring to states of affairs,

Any one can either be the case or not be the case, and everything else remain the same. (Wittgenstein, Tractatus, 1.21)

This means that we can vary the truth-values of any of our basic atomic propositions without having to change the others; all the combinations of different truth-values are possible. All that we have to watch out for is that we end up with a proposition to which we have no truth-value, or one that has both truth-values, i.e. as long as we don’t end up with an excluded middle or a contradiction.

Given that there is no contradiction in supposing that ‘This glass of beer is full, and I am hungry’, this means that there is a maximal and consistent set of propositions which contains it, and that means that it is logically possible.

Could the following be true?:

c) This glass of beer is full and the glass of beer is not full.

Now, for c) to be true, both sides of the ‘and’ would have to be true. But these are p and not-p respectively. If both were true, then p would be both true and false. This would be a contradiction, and so (because of the consistency condition) there is no possible world at which this is the case. This means that c) is not logically possible.

Ask yourself this, could the following proposition be true?:

d) This glass of beer is full and God does not exist.

Even if you think that the proposition is in actual fact false (i.e. if you are a theist with a full glass of beer), ask yourself if there is a contradiction which results from supposing that d) is true. It seems that there is not. The logical form of d) seems to just be the following:

e) r & ~g

We can show very easily that this formula is not a contradiction with a truth table:

tt

This shows very explicitly that the formula is false if r and g are both true, and if they are both false, but the formula is true on both middle rows. So it is not always false, i.e. it is not a contradiction. I have just proved that e) is not a contradiction. If someone wants to say that d) is somehow a contradiction, then they need to provide a different logical form for the proposition than e). In propositional logic, this seems to be the only plausible rendering of the form of d), and so it seems that in propositional logic, the formula is not a contradiction. That means that God’s existence is not a logically necessary truth.

3. Conclusion

While the existence of God may be asserted as a metaphysical necessity (however that is cashed out), it cannot be asserted as a logical necessity, if the logic we have in mind is classical propositional logic. I will write a sequel to this paper where we look at the possibilities of cashing out the logical necessity of God’s existence in first order logic, and I will explain how it is not a viable claim there either.

A New Problem for Divine Conceptualism?

0. Introduction

Divine Conceptualism (DC) is an idea about the ontological relationship between God and abstract objects, defended by Greg Welty, in his M.Phil thesis “An Examination of Theistic Conceptual Realism as an Alternative to Theistic Activism“(Welty (2000)), his Philosophia Christi paper “The Lord of Non-Contradiction” (Anderson and Welty (2011)), and his contributions to the book “Beyond the Control of God” edited by Paul Gould (Welty (2016)). Put simply, (DC) identifies abstract objects as something like ideas in the mind of God.

Welty sees his view as being quite close to that of Morris & Menzel‘s (1986) ‘theistic activism’ (TA), according to which:

“…all properties and relations are God’s concepts; the products, or perhaps better, the contents of a divine intellective activity.” (Morris & Menzel (1986), p. 166)

Morris & Menzel’s TA asserts that God created everything which is distinct from God, and that includes the divine concepts themselves. However, as Welty (2000) p.29 observes, TA is vulnerable to ‘bootstrapping’ objections. If God is supposed to be able to create his own properties, then he creates his own omnipotence (because omnipotence is a property); yet it seems that one would already have to have omnipotence in order to be able to create omnipotence. Even more forcefully: God already needs to possess the property of ‘being able to create properties’ in order to create properties. The idea of self-creation is therefore seemingly incoherent.

Welty’s DC can be seen as a modified version of TA; it is TA without the troublesome doctrine of self-creation. On DC:

“…abstract objects … are uncreated ideas in the divine mind; i.e. God’s thoughts.” (Welty, (2000), p. 43

Postulating abstract objects as uncreated divine ideas is designed to avoid the bootstrapping objections from above.

There are of course lots of different types of abstract objects, including propositions, properties, possible worlds, mathematical objects, etc. Here we will only look at propositions. One of the motivations for thinking that propositions in particular are divine thoughts is the argument from intentionality (seen in Anderson and Welty (2011), p 15-18). Propositions are intentional, in that they are about things. So the proposition ‘the cat is on the mat’ is about the cat having a certain relationship to the mat; the proposition is about the cat being in this relation to the mat. In a similar manner, thoughts are also about things. Consciousness is always consciousness of something or other. In Anderson and Welty (2011), it is argued that the laws of logic are propositions, which are necessarily true and really existing things. Given the intrinsic intentionality of propositions, these are argued to be thoughts. However, they cannot be thoughts had by contingently existing entities, like humans, as humans could have failed to exist, whereas laws of logic could not. Thus:

“If the laws of logic are necessarily existent thoughts, they can only be the thoughts of a necessarily existent mind.” (Anderson and Welty, (2011), p.19).

However, I want to point out an objection to this picture, which I have not seen in the literature (a nice summary of existing objections is found here). It is about the definition of the word ‘thought’. (It may be that this problem has been adequately documented in the literature somewhere that I have not seen. Maybe someone can let me know in the comments section.)

  1. Thought

It seems to have gone unnoticed that Welty in particular oscillates between DC being construed in two different and incompatible ways. It has to do with the word ‘thought’. There is no completely standardised usage of this term in the philosophy literature. And it is a term which needs careful definition in a philosophical argument because in natural language the word ‘thought’ is sometimes used to refer to the thinking and sometimes the thought-of; it is either the token of a type of mental activity called ‘thinking’, or it is the content, or object, of the thinking. For example, we may have the intuition that my thought is private, and that it is metaphysically impossible for you to have my thought (which makes thoughts similar to perceptions in this respect). But we may also have the intuition that we can ‘put our thoughts on paper’ or ‘share our thoughts’ with other people. It seems to me that this ambiguity infects Welty’s version of DC due to his not clearly and carefully defining what he means by ‘thought’ so as to disambiguate the term between thinking and thought-of. Welty (2000), for example, doesn’t actually contain a definition of a ‘thought’ anywhere in it, even though it mentions ‘thought’ 135 times in 85 pages.

According to Anderson and Welty (2011), they seem to indicate that a thought is not the content of thinking, but the token of the act of thinking. In a footnote on page 20, they say:

“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).”

The distinction that is being made here is between thoughts, which are individualised occurrences not shareable by multiple thinkers, and the contents of those thoughts, which are generalised and shareable by multiple thinkers. I can have a thought with the same content as you, even though we cannot have the same thought. In Fregean terms, a ‘thought’ (as Anderson and Welty use the term above) is an ‘apprehension’. When one thinks about the Pythagorean theorem, one is apprehending the proposition. In order to be explicit about what I mean, I will disambiguate the term ‘thought’ by referring to the token act of thinking as an ‘apprehension’, and the content of the thought as the ‘proposition’.

2. Blurred Lines

However, in Welty (2000), this distinction is repeatedly blurred. One of the main thrusts of the position defended there is that God’s thoughts function as abstract objects:

“God and I can have the same thought, ‘2+2=4’, in terms of content. But my thought doesn’t function in the same way that God’s thought does. My thought doesn’t determine or delimit anything about the actual world, or about any possible world. But God’s thought does. Thus, it plays a completely different role in the scheme of things, even though God and I have the same thought in terms of content. Thus, God’s thought uniquely functions as an abstract object, because of his role as creator of any possible world. I am not the creator of the actual world (much less, any possible world), and thus my thoughts, though they are in many cases the same thoughts as God’s, don’t function as abstract objects in any relevant sense.” (Welty, (2000), p. 51)

Welty says that God and I can have ‘the same thought in terms of content’, which blatantly smudges the sharp distinction between the apprehension and proposition. We can each apprehend the same proposition. But can I share in God’s apprehension of the proposition? It seems that the answer would have to be: no. God’s apprehension of a proposition is surely private to God, just as my apprehension of a proposition is private to me.

Then Welty ends the passage with “my thoughts, though they are in many cases the same thoughts as God’s, don’t function as abstract objects in any relevant sense”. The only sense in which my thoughts are “the same thoughts as God’s” is in terms of the propositions that I think about being the same as the ones that God thinks about. In that sense they do function as abstract objects, precisely because they are abstract objects, namely propositions! The sense in which ‘my thoughts’ don’t function as abstract objects is in terms of the token act of thinking (the apprehension). That doesn’t function as an abstract object, but then that is not something I share with God. So Welty cannot have it that there is something, x, which is both something I share with God and which doesn’t function as an abstract object. The only reason it seems like this is possible is because of a failure to distinguish clearly between thought as apprehension, and thought as propositional content.

This confusion pops up again and again. Take the argument from intentionality, found in all three Welty publications referenced in this post. Part of the motivation for DC is that propositions are (supposedly) thoughts (because they are intentional) but that they cannot be human thoughts; a non-divine conceptualism, the doctrine that abstract objects like propositions are human thoughts, cannot do the job here. The reason for thinking that they cannot be human thoughts is as follows:

“There aren’t enough human thoughts to go around…, human thoughts don’t necessarily exist, and whose thoughts will serve as the intersubjectively available and mind-independent referents of propositional attitudes (referents that are also named by that-clauses)?”

There are three reasons given against human thoughts being able to play the role of propositions: a) there aren’t enough of them, b) their existence isn’t necessary, c) they aren’t intersubjectively available.

While these considerations look somewhat compelling when trying to think of a human conceptualism without the benefit of the distinction between apprehension and proposition, it quickly loses its force when we apply the distinction. The problem is the combination of two types of properties that propositions need. One type of property is associated with divine apprehensions, and the other type of property is associated with divinely apprehended propositions. Being of sufficient plentitude to play the role of propositions (a), and having necessary existence (b), are of one type, and being ‘intersubjectively available’ (c) is of the other. As I shall show, you cannot have both of these types at the same time, without smudging the distinction between apprehensions and propositions.

Firstly, let’s consider non-divine conceptualism, where thoughts are construed as apprehensions.

There are, of course, only finitely many human apprehensions of propositions; there are only finitely many times people have apprehended propositions. Also, human apprehensions of propositions are contingently existing things, because human minds are themselves only contingently existing things. Human apprehensions are also inherently private, and thus not intersubjectively available. So apprehensions cannot be thought of as ‘doing the job’ of abstract objects for these reasons. That much is quite clear.

On the other hand, there may be infinitely many divine apprehensions, so there would be ‘enough to go round’, and perhaps they each exists necessarily. In this sense, they seem suited to play the role of propositions. However, as apprehensions, they would not be ‘intersubjectively available’. Can I actually share in God’s apprehension of a proposition? Unless I can, they cannot play the role of an abstract object.

Thus, when considering apprehensions, although non-divine conceptualism is not suited to play the job, neither is divine conceptualism. The problem is just that apprehensions are private. So let’s compare non-divine and divine conceptualism, where we construe ‘thought’ as the contents of thoughts.

Right away it is obvious that there is no reason to think that the content of human apprehensions are limited in the same way as their apprehensions were. The contents of human apprehensions just are propositions, so of course they can play the role of propositions!

Equally, if divine thoughts are construed as divinely apprehended propositions, then there will be enough to go round, they will exist necessarily, and they will be intersubjectively available. But in both cases, this is just because propositions themselves are sufficiently plentiful, necessary and intersubjective to play the role of propositions. Obviously, propositions can play the role of propositions. Being apprehended by God, rather than humans, is not what bestows the required properties on them.

3. Begging the question?

But perhaps I have begged the question somehow. Maybe the defender of DC can stipulate that, although my apprehensions are private, God’s apprehensions are somehow intersubjectively available. Call this theory ‘divine accessibility’ (DA). So on DA, propositions are divine apprehensions (which are plentiful, and necessary existing) and crucially also intersubjectively available to humans; they can be the content of humans’ apprehensions.

So, let’s say that I am thinking about the Pythagorean theorem. Let’s say that my apprehension is A. According to DA, the content of my apprehension, what A is about, is a divinely accessible apprehension, D. But the question is, what is the content of the divine apprehension, D? What is it that God is thinking about when he has the thought which is the Pythagorean theorem? There seem to be only a few options:

Either God’s apprehension, D, has content, or it does not. If it has no content, then what is it about D which links it to the Pythagorean theorem, rather than to some other theorem, or to nothing at all? It would be empty and featureless without content.

But, if it does have content, then either the content is that ‘the square of the hypotenuse is equal to the sum of the squares of the other two sides’, or it is something else.

If it does have this as its content, then it seems like the content of D is doing all the work. It seems like the only reason God’s apprehension is linked in any way to the Pythagorean theorem is that it has the theorem as its content. If that is right, then we need to have the proposition itself in the picture for God’s apprehension to be in any way relevant.

Consider what would be the case if the content of God’s apprehension was of something else entirely, like the fact that it all bachelors are unmarried men or something. In that situation, there  would be no reason to say that this apprehension was the Pythagorean theorem. The only divine apprehension that could, even plausibly, look like it is playing the role of the proposition is one which has the proposition as its content.

And if we ask what role God’s apprehension plays here it seems that the answer is that it is just a middle man in between my apprehension and the theorem. It seems to be doing nothing. When I think of the theorem, I have an apprehension, A, and all this is about is one of God’s apprehensions, D, which is itself about the theorem. If p is the Pythagorean therem, and x ⇒ y means ‘x is about y’, then we have:

A ⇒ D ⇒ p

God’s apprehension is just an idle cog which does nothing. Why not just have:

A ⇒ p

Why not just say that I have the theorem as the content of my thought? It would be a much simpler suggestion. Given that for God’s apprehension to be in any way relevant to the proposition in question it has to have the proposition as its content, we seem to require the proposition in the picture anyway. Ockham’s razor should suggest shaving off the unnecessary extra entity in the picture, which is the divine apprehension.

4. Conclusion

Thus, there are really two problems with DC. If construed as the contents of God’s thoughts, divine ‘thoughts’ just are propositions. So for DC to be in any way different from the traditional Fregean picture (where propositions are abstract objects), we have no other option but to construe divine thoughts as divine apprehensions. However, it seems that apprehensions are inherently private, and so they are unsuited to play the role of propositions. Even if we postulate that somehow divine apprehensions are accessible to everyone, they seem to become idle cogs doing nothing.

What is Atheism? II

0. Introduction

Recently I wrote a blog post about different ways of thinking about the definition of the terms ‘atheism’ and ‘atheist’. I was interested in the relation between belief and degrees of belief. Does lacking a belief mean lacking all degree of belief? To me, it seemed like the answer was ‘no’; one can lack a belief that p, yet still have some small degree of belief that p. That was how I describe my own internal doxastic state with regards to the proposition that no gods exist. I don’t feel like it is correct to say that I believe that no gods exist, but I have a small degree of belief that they don’t.

Part of my reasoning behind why I am only slightly in one direction rather than the other is because it is a proposition in metaphysics, and this seems like the most one can ever really have about such propositions. For example, it seems at least conceptually possible that there exists some god who is entirely unverifiable, some sort of deist god who never intervenes in the world and has left no trace of his existence for us to find. How could I ever know if such a god existed? Obviously, I couldn’t. But this type of god would also be the sort of thing that I couldn’t get any information about at all, either for or against. For this type of thing, there couldn’t be any evidence, and so one can never be confident that it doesn’t exist. So while I have an intuition or feeling that they probably don’t exist, it is not strong – after all, I don’t think that I know what the world is like at the most fundamental lever, so I don’t place much weight in what my pre-theoretical intuitions about that sort of thing say. They do lead me in one direction, but only slightly. That’s my view anyway. (An interventionist god who cares about human suffering seems far less likely to me than this epistemologically inaccessible god, and I would have a far lower degree of belief in such a personal god).

So I would say that my degree of belief that there are no gods is more than 0.5, but not much more. It seems to me that this doesn’t qualify as a strong enough belief for saying “I believe that there are no gods”. To me, saying that requires a higher degree of belief than I have. It is a declaration of a certain level of commitment to something to say “I believe that p”, and while it is not saying that you are utterly convinced that p, it is saying more than that you are minimally convinced; belief means something like ‘somewhat convinced’. I’m not sure that there is a precise numerical value which is the cut-off point between non-belief and belief; certainly not for all possible circumstances anyway. However, I just feel like my degree of belief is not strong enough to qualify in this context.

This is just like a situation where you may feel quite sure that a given person has not enough hair to count as hirsute, even though you are not sure whether there really is a precise number of hairs that one has to have in order to count as hirsute, or if so what that number of hairs is. Yet you just feel quite sure that this amount of hair isn’t enough. That’s how I feel about the god proposition.

Before getting to that point though, I spent some time explaining how there is some controversy about the definition of ‘atheist’, and this caused a bit of discussion on the comments below my past blog post on this – quite a lot longer than the actual article itself (and is still continuing as I write this), where people continued to discuss how they saw the right and wrong ways to define ‘atheist’.

My main point in the first section of that post was actually to argue that what seemed like a significant discussion between the atheist and theist is actually just a trivial definitional exercise on which nothing of any significance hangs. By this, I mean that it doesn’t matter if people disagree about whether someone should be called an atheist, a lacktheist or a hard-atheist, etc. The doxastic stance that the person holds, and any burden of evidence that comes with it, is what is actually important, and it remains the same regardless of what definition is used for the terms involved. We should just agree on a definition at the start of the argument and then move on into the interesting stuff.

Here I want to make that point as clearly as possible. So I will visualise a set of related positions – not a comprehensive list, but a reasonably thorough and precise list – so that we can see clearly what the different definitional positions are. I also want to express how this area is actually surprisingly rich from a logical point of view, and the various combinations of positions makes for an interesting enough landscape to categorise as a purely academic exercise. However, once we have a good grasp of the different definitions we could plausibly have in mind (the ‘landscape’), we can see how a particular person’s view gets classified. As we shall see, on some views I am an atheist, on some I am an agnostic atheist. The ability to translate between the different schemes considered provides the potential for more than just an academic classification exercise. It suggests the ability to help people stop talking past one another by providing a precise translation manual. All too often people hold different but not clearly articulated ideas about what it means to be an ‘atheist’ or ‘agnostic’ when they are in discussion and hopefully by setting out the landscape clearly we can be of some help here.

  1. Degree of belief

First, let’s consider the scale of belief about some proposition p (which will remain fixed as ‘some god exists’. The scale ranges from 0 for absolute conviction that p is false, to 1 for absolute conviction that p is true, with 0.5 being the middle point:

atheism1

We can consider, for some agent a which we will keep fixed, that there are various propositions about a‘s beliefs and knowledge claims that we are interested in:

  • Bp      = a believes that p
  • B~p    = a believes that not-p
  • ~Bp    = it is not the case that a believes that p
  • ~B~p  = it is not the case that a believes that not-p
  • Kp       = a knows that p
  • K~p     = a knows that not-p
  • ~Kp     = it is not the case that a knows that p
  • ~K~p   = it is not the case that a knows that not-p

We will track where these propositions go under the belief scale, and then move on to add labels for various positions in as well.

2. Visualisations

Although the pair p and ~p are dichotomous (so that ‘p v ~p‘ is a tautology), this is obviously not the case for Bp and B~p; it is quite possible for neither of them to be true. Our agent might not believe that Kuala Lumpur is the capital of Malaysia, and might not believe that Kuala Lumpur is not the capital of Malaysia. The same goes for Kp and K~p. This leaves room in the middle for a ‘belief-gap’. We will visualise this on our belief scale with a penumbra (or grey area) in which they a neither believes p nor believes that not-p. We could add this to our diagram as a shaded area underneath the section of the range to which it applies:

atheism2

So in the diagram above, the grey area (the penumbra) extends beyond 0.5 degree of belief to some extent in either direction. This reflects that someone could have a degree of belief which is (say) 0.51 that p but that this would not be enough for it to be true that “a believes that p“. For that to be true, a‘s degree of belief has to be greater than this. Precisely how much greater is vague and impossible to give a precise number to. All that we can (or need to) say is that for a to believe that p, their degree of belief has to be greater than the extent of the penumbra.

On either side of the penumbra, we would find the regions in which a holds a positive belief, either that p or that ~p:

atheism3

We can add in knowledge claims here as well, where as we go along the scale towards 1 (or 0), we get to some (vague and impossible to make precise) point at which a doesn’t just believe that p (not-p), but knows that p (not-p):

atheism4

So our fully annotated diagram of the situation looks like this:

atheism5

Given what I outlined in the last post on this topic, I sit just to the left of 0.5 on this scale (where p is ‘some god exists’). The green line is me:

atheism-7

It seems like my degree of belief is such that I don’t believe that p and I don’t believe that not-p. All this is rather uncontroversial*. The controversy, what there is of it, comes in when we decide which labels to apply to which position on the scale. We will do this by adding shaded areas to the top of the diagram. The first proposal we will consider (call it View 1) is where a ‘theist’ is someone who believes that p and an ‘atheist’ is someone who believes that not-p, which makes an ‘atheist’ a ‘hard-atheist’:

atheism8

This has the consequence that theist/atheist is not an exhaustive distinction; it is possible to be in the area not covered by either (which is where I sit on this diagram). I am not an atheist on this picture (I am unclassified on this picture).

We might want to say that there is no such area, and that everyone is either a theist or an atheist. This sort of line has been put to me in the past. The idea is that if you act as if there is no god, then this makes you an atheist. Actions, it might be thought, are binary, in that you either act like you believe in a god (by going to church, praying, etc), or you act as if there is no god (by not going to church, praying, etc). This may make us think that everyone’s actions either make them an atheist or a theist (depending on how plausible we find this reasoning), in which case there should be no gap between the two positions on our scale (call this View 2):

atheism-9

On this view, a theist is not necessarily someone who ‘believes that p‘, but is just someone whose degree of belief that p is greater than their degree of belief that not-p. Similarly for the definition of ‘atheist’. I would count as an atheist on this view, even though I don’t believe that not-p. I count as an atheist just because my degree of belief that p is slightly less than 0.5. The definition of ‘atheist’ on this view is neither the same as ‘hard-atheist’ nor ‘lacktheist’.

As another option (call it View 3), we could think of the theist/atheist distinction as exhaustive, but draw the line between them on the point at which we switch from not believing that p to believing that p. This would make the definition of ‘atheist’ that of the ‘lacktheist’:

atheism-10

On this view, I count as an atheist, and interestingly so would someone whose degree of belief that p was on the positive side of 0.5 but still in the penumbra; the sort of person who would say that they have a very weak degree of belief that some god exists, but not enough for them to say ‘I believe that some god exists’. That person would count as an atheist on this view.

We might think that the term ‘agnostic’ comes in here somewhere, and that it should come in to fill the gap between theist and atheist on View 1, like this (call it View 1.1):

atheist-11

On this picture, an atheist is someone who believes that not-p, a theist is someone who believes that p, and an agnostic is someone who does not believe either of p or not-p. On this picture, I come under the agnostic category, and not the atheist category.

We could add this version of agnostic (i.e. someone who does not believe either p or not-p) to View 2, to make View 2.1, as follows:

atheist-12

On View 2.1, all agnostics are also either atheists or theists; nobody is just an agnostic. On this view, I am an atheist and an agnostic.

Continuing the series, we could include the agnostic in the diagram and have ‘atheist’ pictured as a lacktheist (View 3), resulting in View 3.1, like this:

atheist-13

On this view, I would count as an atheist and an agnostic. On this view all agnostics are also atheists; there are no pure agnostics or agnostic theists.

However, one might think that the term ‘agnostic’ does not relate to a lack of belief but instead to lack of knowledge; it means that you don’t know if p is true, or if not-p is true. If that were the case (View 1.2), we would want to draw the agnostic area as follows:

atheist-14

On this view, there are ‘pure’ agnostics (and I would be one), but there are also agnostic atheists and agnostic theists (in contrast to View 1.1).

If we add this notion of agnosticism to Veiw 2, then we get View 2.2:

atheism-14

In this view, everyone is either an atheist or a theist (there are no pure agnostics) and there can be both agnostic atheists and agnostic theists. This only differs from View 1.1 in that the definition of agnostic is tied to knowledge, not belief.

Lastly, for completeness, I will consider View 3.2, which combines this agnosticism with the lacktheism of View 3:

atheist-15

On this view, an atheist is a lacktheist, and there can be agnostic atheists and agnostic theists. I am an agnostic atheist on this view.

Here are all 9 of the views for comparison:

atheist1atheist2atheist3

3. Logical relationships

We have 9 views outlined above (View 1, 1.1 & 1.2; View 2, 2.1 & 2.3; and View 3, 3.1 & 3.2), but what are the relationships and differences between them? Here is an incomplete table showing some of the various properties of the different views and how they differ from one another:

atheistm

Each view is unique in some respect or another. The difference between View 1.1 and View 1.2 (for example) is just whether agnostic means not believing either way that p or not knowing either way that p. This difference decides whether there are agnostic atheists/theists or not.

According to that summary, I am an there are two views according to which I am antheist, one according to which I am an agnostic, four according to which  I am agnostic atheist, with one where I am not classified. It is noteworthy how many different classifications one and the same doxastic attitude can come under. No wonder there is often confusion as to the usage of the terms involved.

4. Motivations

What we have is a landscape of different definitions and their various combinations. These are just the combinations I could see as being remotely justified. Each combination has something which backs it up conceptually.

  • There seem to be decent reasons for thinking about atheism and theism as being dependent on believing p and on believing not-p, which is the characteristic of View 1, 1.1 and 1.2.
  • However, the idea that belief is tied to action, and is thus binary, gives rise to the motivation for View 2, 2.1 and 2.2.
  • Then again, the definition of atheism as ‘lacktheism’ is clearly very popular among contemporary atheists, and this motivates View 3, 3.1 and 3.2.
  • There also seems to be some intuitive support for the idea that agnosticism simply fills in the space between atheism and theism, such that everyone is either an atheist, and agnostic or a theist (with no overlap), which informs View 1.1.
  • While this view of agnosticism seems fairly intuitive here, there is also something to be said for modelling agnosticism as relating to knowledge. Thomas Huxley, the person who coined the term ‘agnostic’, seems to have this association in mind when he said the following:

Agnosticism is of the essence of science, whether ancient or modern. It simply means that a man shall not say he knows or believes that which he has no scientific grounds for professing to know or believe.

Thus, there is a sort of exigetical support for the idea that agnosticism is epistemic rather than doxastic (i.e. about knowledge rather than just belief). If that is motivational for you, then you may be drawn to thinking of agnosticism as in View 1.2, 2.2 and 3.2.

5. Conclusion

It seems like a simple question, so often gone over, but so rarely gone over methodically:

What does ‘atheist’ mean?

But it has a surprisingly large number of potential, plausible-looking combinations of positions on the table. The benefit of classifying the various possible logical combinations is that we can translate between people’s usages. Here’s how:

First, one needs to assess internally what their level of belief is in the proposition being considered. Decide as best you can what your degree of belief is. Next also try to decide what you think (roughly) the thresholds are for belief and knowledge. Test yourself. For example, if you feel quite confident that you believe that p, do you also feel like you know that p? If not, then you believe without knowledge, and so you are in the middle section, etc.

In this way, we can get a feel for which region in the bottom part of the diagrams you fit into without too much need to quantify your degree of belief precisely. All you have to do is find which region of the belief scale you fit on. Once you have this in place, you can see how you are classified according to the various views. I did this in this post, and showed my results. So if someone asks me if I’m an atheist, I think my reply will now be ‘I’m an agnostic atheist on most definitions of the key terms, but on some of them I am an atheist’. This qualification doesn’t mean that I am changing my mind about what I believe, or trying to dodge any burden of proof for my claim. All the different views indicate is different ways of describing the same thing. 

There is no such thing as the ‘correct’ definition of what an atheist is. There is no such thing as the ‘correct’ definition of anything. Definitions are all arbitrary. One can use a definition in a way that fits the practices of a language using community, but other than ‘fitting in’ there is nothing else to decide whether a definition is correct or not. So there shouldn’t be a debate about what the definitions mean, from a logical point of view. We should only be interested in what people actually believe, and why.

There may be a larger political issue about the definition of ‘atheist’ due to the idea of an ‘atheist community’, but this is an issue I am not interested in. If I don’t classify as atheist enough for the atheist community, then so be it. I’m not going to change my sincerely held views just to be part of a club, and any club which is defined in terms of belief which requires people to adopt beliefs merely for the purposes of joining seems like an inherently contradictory institution.

It may be that people hold that the definitional game is more significant that I think it is for the following reason. It may be that when one joins a religion (or a new church, etc), that one sort of fits their beliefs to the community. As if someone says to themselves, ‘Now I’m part of the Calvinist community, I better figure out what beliefs I have’. This would make the beliefs follow from the belonging to a group. For all I know, this is how people view beliefs, and are happy to let themselves hold beliefs just because they are told that ‘people like us believe in such and such’. To me though, this gets the direction of travel the wrong way. First you have to have certain beliefs, and it is only because you antecedently do (or do not) hold whatever beliefs you do that you qualify for belonging to a club that is defined by beliefs. So one should say something like ‘I believe in the doctrine of predestination and original sin (etc), so I better figure out which group I belong to’. For me, beliefs come first, and labels (such as ‘Calvinist’ or ‘atheist’) follow after.

 

*From here on out, I will assume this basic picture to be correct. One could argue that the penumbra could really just apply to the 0.5 point and extend no distance in either direction. Even if you do so, this would still mean that the grey area has some extension. The reader should feel free to imagine the grey area being larger or smaller if  they so wish if they disagree with the extent I have given it above. It should be agreed by all parties that there is some penumbra, even if it only apples to 0.5 and nowhere else.

Autonomy

0. Introduction

In my recent discussions with Jimmy Stephens (here and here) we discussed his version of presuppositionalism. According to Jimmy, a non-Christian like myself makes a very fundamental assumption which he sees presuppositionalism as challenging. That assumption is about autonomy. When I reason about things, I presuppose that my use of reason is ‘autonomous’. But what does ‘autonomy’ mean?

  1. Kantian Autonomy

One way of thinking about what autonomy means is with reference to Kant’s classic article, What is Enlightenment? In that, Kant describes the opposite of autonomy as ‘nonage’, and defines it as such:

“Nonage is the inability to use one’s own understanding without another’s guidance.”

Given this, we could think about autonomy as the ability to use one’s own understanding without another’s guidance.

Kant is quite explicit about the reasons for nonage:

“Laziness and cowardice are the reasons why such a large part of mankind gladly remain minors all their lives, long after nature has freed them from external guidance. They are the reasons why it is so easy for others to set themselves up as guardians. It is so comfortable to be a minor. If I have a book that thinks for me, a pastor who acts as my conscience, a physician who prescribes my diet, and so on–then I have no need to exert myself. I have no need to think, if only I can pay; others will take care of that disagreeable business for me.”

The idea is that resting your understanding on that of others, and not thinking about something for yourself, makes life easier. One simply does not have to bother with all that ‘disagreeable business’, and can get on with something else more fun.

Despite the obvious attraction of nonage, Kant strongly recommends against it. He considers it to be a kind of intellectual immaturity. This state of immaturity has an intrinsic vulnerability associated with it, as it requires that one is beholden to ‘guardians’, authorities such as ‘books’, ‘pastors’, ‘physicians’, etc, to be making decisions on your behalf. If you do not understand how your diet works, if you have no idea what makes eating one thing better than eating another, then you are entirely dependent on someone else to tell you what to eat. In this way, you are vulnerable to them exploiting you.

Of course, we are all in this position when it comes to many things, and nobody can be an expert in everything. I am dependent on my doctor to tell me which treatment to take, on my mechanic for what to do to my car engine, etc. Kant is not suggesting that everyone becomes entirely dependent on nothing but their own understanding.

What Kant is promoting is the idea that society as a whole should be such that it has no authority too sacred that it cannot be challenged in public. The reason he is making this plea is that the supposed benefit that nonage can have for the ‘minor’ has as a correlate a benefit to the guardian that she defers to. The guardian is given power through the authority they gain when one let’s them make decisions on their behalf. Thus, each guardian of knowledge has an interest in restricting the public use of reason:

“I hear the cry from all sides: “Do not argue!” 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.”

So while it is in the tax collector’s interest if you do not question too much what your taxes are going on, and they will encourage you not to, we must not resign ourselves completely to the position that they cannot be questioned. It is a central pillar of ‘enlightenment society’ that these aspects of the state can be called into question by citizens. In fact, the freedom to be able to do so is constitutive of enlightenment. One must be free to use one’s own reason, to question all authorities, otherwise we are vulnerable to being exploited, like a mechanic who charges you for work that does not need to be done, or a tax collector who takes more money from you than is needed and keeps it for himself. The only way to avoid such things from happening is to remove any restrictions from the public use of reason. It is the only possible check and balance that there is against the pitfalls of nonage.

In the Critique of Pure Reason, Kant makes the following memorable comments on this:

“Reason must be subject, in all its operations, to criticism, which must always be permitted to exercise its functions without restraint; otherwise its interests are imperilled and its influence obnoxious to suspicion. There is nothing, however useful, however sacred it may be, that can claim exemption from the searching examination of this supreme tribunal, which has no respect of persons. The very existence of reason depends upon this freedom; for the voice of reason is not that of a dictatorial and despotic power, it is rather like the vote of the citizens of a free state, every member of which must have the privilege of giving free expression to his doubts, and possess even the right of veto.” (A738/B766)

2. Scientific Authorities

Take an example from our time – scientific authority. Most of us are relatively illiterate when it comes to scientific explanations of complex phenomena, such as climate physics, etc. Most of us do not know what the relevant equations are that govern the climate, and have not looked in any detail as to the data gathered on the topic. So when it comes to questions like climate change, are we not in a position of nonage, where we defer our decision making to authorities outside of ourselves? To some extent, the answer is yes. Climate change could be, as Donald Trump once famously remarked, a conspiracy generated cynically to deprive the United States of economic productivity by the Chinese. For those of us who are not climate scientists, we have to defer our judgement to those who are. Fortunately, there is a very large consensus in the relevant sciences that (unfortunately) man made climate change is not a conspiracy.

This consensus is not inherently suspect only to the degree that the scientific community is such that it is open to challenge its own dogmas. If this science is enlightened, then if someone had a rival model for climate change which could explain all the data just as well which showed it to be not man made, then this would not simply be suppressed due to it calling into question a ‘sacred principle of science’. Rather, it would be given the same treatment as a proposal which is in keeping with the current accepted wisdom in the field. If we are of the opinion that the scientific community allows rival explanations of phenomena to get a fair public hearing, and is subject to the scrutiny of public examination, then we should also be happy to defer to the majority (especially when there is an overwhelming consensus on a subject).

Of course, the conspiracy theorist also calls into question this aspect of the scientific community, as is demonstrated here. The point is though that they need to call this into question in order to avoid the reasonableness of holding to the position of the consensus in the field. If scientists are of one mind about man made climate change, then the only way to avoid going along with them (for us laypeople) is to call into question their public use of reason. In this way, the conspiracy theorist tacitly accepts Kant’s formulation of enlightenment, and the benefits of the public use of reason. All they want to question is whether the relevant science actually is as free and enlightened as it pretends to be. This is why it is part of the conspiracy is that peer review is flawed.

The line of thinking outlined here suggests a distinction between enlightened guardians and unenlightened guardians. The conception of climate change scientists honestly appraising competing theories, publicly critiquing each other’s ideas, and coming to an overwhelming consensus, is an example of a legitimate guardian. If this is the case, then when we defer our understanding to these guardians of knowledge, we do so with the safeguard that this public scrutiny affords. We do not have to have inspected all the arguments personally, because they have been publicly dissected by others. On the other hand, if the guardians are in fact such that they actively suppress any dissenting views, and apply criticism only to those who question the accepted dogmas, then they are unenlightened guardians. Those of us who defer our understanding to them, and transfer them power as a result of doing so, are more at risk of becoming exploited or mislead as a result.

3. Religious Nonage 

Jimmy wants to argue that when I use my reason to try to understand something, I am presupposing that I am autonomous. One scenario that I dogmatically refuse to entertain, according to Jimmy, is one where I am in fact not able to reason at all without God; a sort of necessary nonage.

This phrase ‘without God’ is somewhat ambiguous, and it requires a few words of clarification. One one hand, it could mean a sort of metaphysical dependence. If God exists and created everything, then I would not exist at all without God. If I did not exist, then I would not be able to use my reason. Thus, I could not use my reason at all were it not for God. In this sense, perhaps, my reason cannot be used without God existing.

This doesn’t seem to me to be the type of dependence that reason is supposed to have on God here though. After all, I have this same relationship to my parents. If they had not conceived me together, I would not exist. If I did not exist, I would not be able to reason at all. So I could not reason were it not for my parents existing. My ability to reason is dependent on all sorts of contingent happenings in the past, such as the chance meeting of my great great grandparents, etc. Thus, in this sense I am dependent on many things as well as God for my ability to reason.

I think that when Jimmy says that I am assuming that I am autonomous, that I can reason ‘without God’, he means that I can reason without believing that God exists. What he is saying is that if I do not believe in God then I could not form a coherent view of the world. My way of thinking would be inevitably contaminated with the false starting point and would be doomed to being incoherent somewhere along the lines as a result.

And it is not just the belief in a single proposition, ‘God exists’, that I think Jimmy thinks is required for coherent thought; it is not that some general theism is required. Rather, what is required is Christian theism. I have to believe that God exists, for sure, but I also have to believe that he has revealed himself to me in the bible, etc. It is a God who has shown himself and provided a way of thinking about things that I should accept. Thus, when you believe in God, as Jimmy does, you do not just differ from an atheist on the truth-value of one proposition, but you accept the intellectual guidance provided by God. In addition to believing the core propositions of Christianity, you treat it as an authority, as a guardian and defer your understanding to it. You use your reason only with the guidance of the religion. That is what it means to not be autonomous.

When Jimmy says that I assume that I am autonomous, he is saying that I assume that I do not have to listen to the guidance of God, as offered in the bible, but can make up my own mind about how the world works independently.

4. Do I Assume Autonomy? Should I?

One of the things that is attractive about Kant’s enlightenment vision is that it is utopian. The fully enlightened society is one where everyone is an equal, nobody has any authority which is above the public scrutiny of reason, and as such this mechanism roots out injustice and falsity. Nothing should be beyond question, and everyone should be equally free in this regard. This seems to be the only way to mature intellectually and socially, and to protect ourselves from exploitation by unjust rulers (or even covert conspiracies). I must admit, I find Kant’s utopia very attractive myself (for one thing, it makes me think of Gene Roddenberry’s vision of society depicted in Star Trek).

If we go any distance down this path, then when someone tries to say ‘Do not question – believe!’, we become immediately suspicious. Although I am not accusing him of conscious wrong-doing, Jimmy’s contention seems to have something of the quality of the person trying to restrict reason about it, and for this reason I am suspicious of it. When he suggests that maybe I am not autonomous, it feels like he is saying that I should give up my right to question his doctrine. He is saying that maybe I can’t question his doctrine. If I question whether I can question it or not, he says that I am presupposing that I am autonomous, and therefore begging the question against him.

However, I feel the strong urge to push back here. For one thing, it exposes me as maximally vulnerable to exploitation. The suggestion is that I accept a guardian as having authority over me in precisely my ability to use reason. There cannot be, by definition, any further justification for this, as it is suggesting itself as a standard of justification, or perhaps as a presupposition of justification. So I have to accept the doctrine for no reason. Thus, I am placing myself in a position where I could not know whether I was making the wrong decision, as my usual defence mechanism (thinking about it for myself) is being taken away from me. How would I know if I was being mislead? It seems like I couldn’t.

In addition, the doctrine in question, if it is being suggested as taken for no reason, is on par with every other potential doctrine. It may be that some other religion, or another sect of the same religion, etc, is suggested by someone else to me. Perhaps I meet a Muslim presuppositionalist who argues that I should accept his standard instead. There can be no question of deciding between the two, as to do so would either presuppose that I can make my own assessment of the situation (which is effectively to deny the proposition they are each offering), or to presuppose that one of them is right, and reason from that perspective, which begs the question against the other proposal. Thus, there can be nothing in principle which one could use to distinguish between two different proposed ultimate authorities like this. They have to be accepted without using your reason at all, which means accepted without reason, as a leap of faith.

If a dialetheist tried to argue that there could be true contradictions, then I seem to be faced with similar difficulties. On what grounds could I oppose their suggestion? It would be of no use for me to resort to my usual method of refutation, which is the derivation of a contradiction, as this is exactly what is being proposed to be rejected in the first place. The dialetheist does not just propose a different proposition, but a different standard of evaluation. So much is called into question, one might think, that nothing can be used to arbitrate between the positions. Thus, the decision to accept or reject the proposal cannot be made with the usual kind of justification.

But now, when faced with the proposal on the table in such stark terms, a problem seems to present itself. If I accepted Jimmy’s offer, and shrugged off my autonomous pretensions, and took on his doctrines as authorities, then what would the status of that acceptance be? It would have been an act of volition – I would have acted myself, under my own guidance. If I surrender my autonomy, then this act is my final autonomous act. And it is, in the final analysis, something which I have to do under my own guidance. It is only after I have made the leap that I can be under the guidance of the new guardian. Before hand, when I am do not accept this authority, I must act without it as an authority. Otherwise there would be no transition from one state to the other, as I would already be under the authority of the doctrine. So for the idea of transition to make any sense, it must be from a state of autonomy to a state of nonage. Even if the reply comes that there is no real transition, as we are all under the authority of God whether we choose to acknowledge it or not, it seems that I have to make my own decision to acknowledge it; indeed, all that can be asked of me is to acknowledge it. If I am under the authority of God, then there is nothing I can do about that. The only thing left is to willingly submit to it or not. Yet this is an act which presupposes autonomy. Surrender to the inability to surrender is impossible without the ability to surrender. And this seems to make the proposal paradoxical.

The proposal from Jimmy seems to be to acknowledge that I do not have the ability to acknowledge anything; he wants me to do something which presupposes autonomy, to accept that I could not do anything with autonomy.

5. The Paradox of Love

This reminds me of a paradox which comes from Sartre. The idea is that love is a paradoxical state. It means wanting two incompatible things at the same time. Firstly, it is desired that your lover love you because of some quality that you possess; perhaps your kind heart, or your gentle nature, etc. If your lover loved you without there being any such quality, it would seem like there was nothing they loved about you. This would seem to evacuate the attitude of all content; there would be nothing stopping them falling out of love with you, as nothing motivates it in the first place. The decision seems no better than a random act.

So the lover needs to love you in virtue of something about you; your good qualities, etc. Yet this also faces grave difficulties. If your lover loves you because of your good nature, then if some disaster befalls you and you lose this disposition, then your lover will lose their motivation for loving you. If they loved you in virtue of your lovely appearance, then this may be doomed to be undermined as you age. Thus, the only alternative to loving you for no reason places the love unacceptably at the mercy of your continued possession of various properties. Again, this seems to evacuate the attitude of its content.

What is wanted is a paradoxical combination of being valued for some good quality or other, but also being valued over and above any of these qualities. You want to be valued in virtue of something, yet not in virtue of something. Such is the paradoxical and irrational nature of love, we might think.

Similar paradoxes affect the sexual attitude, according to Sartre. What is desired for the sadist is the objectification of the partner. A resisting partner is one who refuses to be objectified, and defies the basic desire of the sadist. Instead, what the sadist is after is for a willing partner, one who will freely, willingly, subject themselves to the objectification. What is desired is a willing surrender of will. What is desired is an object that it not an object.

While one may simply harbour a irrational desires like this in virtue of being a human with irrational drives and psychology, one cannot be rationally compelled to take on a position such as this. To the robot, or alien, if these human practices are indeed irredeemably paradoxical, then there is no way to rationalise them. They can only be things that make sense to those who are disposed to do them; one has to be built the right way for them to make sense.

It seems to me that the apologist who tries to get you to accept their doctrine, that you are not autonomous, is akin to someone with a romantic or sadistic desire. They want something which is irredeemably paradoxical. They want a willing suspension of will; the autonomous choice to renounce autonomy.

6. Conclusion

There is no real conclusion here. What is left after all of this is the vision of Kant’s utopia, where the use of reason is the only thing that keeps us free, pitted against a suggestion to willingly surrender this protection, without reason or justification. It seems to me to be an intrinsically paradoxical thing to be proposed with – yet this judgement will doubtless be deemed to be a product of my own rebellious perspective. To me it seems a paradoxical and dangerous thing to do; to not do so probably appears just as paradoxical and dangerous to Jimmy.

The Semantics of Nothing

0.   Introduction

The word ‘nothing’ has interesting semantic features. It is a ‘negative existential’, in the sense that it refers to a non-existing thing. This is perplexing, because if ‘nothing’ is a simple referring term, then the semantic role that it plays in contributing to the meaning of a sentence it features in is to point to its referent. As it has no referent, how can it play this role successfully? There are two general strategies for dealing with this puzzle; one is to treat the idea of nothing as a sort of thing, and the other is to treat it as a case of failure to refer at all.

1.   Creation from nothing

The term ‘nothing’ is deployed as part of one of the supports for the Kalam cosmological argument. The first premise of that argument is: ‘whatever begins to exist has a cause’. One of the lines of support for this premise is the familiar dictum ‘nihilo ex nihilo fit’, or ‘nothing comes from nothing’. When pressed on why this is true, a typical line of defense is that ‘nothing has no causal powers’. I say that this sentence is ambiguous, due to the word ‘nothing’. On one account the sentence treats ‘nothing’ as a referring term; something like ‘the complete lack of any object’. On the other account, the term expresses a failure to refer to any thing. The first reading (which I shall call the ‘referential sense’) is the intended sense, but it strikes me as ad hoc (and I will explain this more below). The second sense (which I shall call the ‘denotative sense’) expresses a different proposition altogether – one that fails to support the premise in any way.

2.   A Toy Example

The ambiguity can be brought to the surface if we consider the two semantic accounts of the word in more detail. Before we look at the sentence ‘nothing has no causal powers’, I want to first play with a less controversial example, to get the distinction clear. So my toy sentence is:

1) ‘Nothing will stop me getting to work on time’

First, let’s look at the referential sense of ‘nothing’, as it applies to this sentence. On this account, ‘nothing’ is just another referring term, like ‘John’, or ‘Paris’, or ‘my favourite type of ice cream’, etc. The referent of ‘nothing’ is ‘the complete absence of any things’, or something along those lines. It’s like an empty void with no contents whatsoever.

The sentence is essentially of the form ‘x will stop me getting to work on time’, where ‘x’ is an empty variable waiting to be filled by any constant (or referring term), like ‘John’ or ‘my favourite type of ice cream’, or ‘nothing’ etc. Let ‘Wx’ be a predicate for ‘x will stop be getting to work on time’. If ‘a’ is a constant that refers to my friend Adam, then the proposition ‘Wa’ means that Adam will stop me getting to work on time. I will not get to work on time, because I will be stopped by Adam from doing so. Something that Adam will do, such as physically restraining me, or hiding my keys, or just distracting me with an interesting philosophical discussion, etc, will prevent me from getting to work on time. That’s what Wa is saying.

Let ‘n’ be a constant that refers to ‘the complete absence of anything’. We could put the logical form of 1) as follows:

Ref)   Wn

Ref says that I wont get to work on time because ‘nothing’ is going to stop me. This mirrors the logical form of the sentence above where Adam prevented me from getting to work on time. But this seems wrong, as 1) doesn’t seem to say that I won’t get to work on time because of nothing (i.e. the complete absence of any thing) getting in my way. We don’t seem to be expressing the idea that ‘nothingness’ is going to hide my keys, or engage me in a philosophical discussion, etc. We are not expressing that I will not get to work on time. Rather, we are expressing something close to the opposite of that; the sentiment expressed by ‘nothing is going to stop me getting to work on time’ is that I will be on time to work, come what may. So the referential way of reading the term ‘nothing’ is not appropriate here.

Let’s look at the second account, the denotative account. On this reading 1 gets analysed out as the following (note that we still have the predicate Wx, but use a quantifier and a bound variable and so don’t need the constant ‘n’):

Den)    ~(∃x)(Wx)

On this reading, we are saying that it is not the case that there is a thing such that it will stop me getting to work on time. We could re-write Den as follows:

Den’) (∀x)~(Wx)

Den’ says that for every x, it is not the case that x will stop me getting to work on time. This captures very well the sentiment that come what may we will not let anything prevent us from getting to work on time. We would say that the denotative proposition is true in this situation, and that seems right.

Thus the two analyses are very different. They render propositions with a different logical forms and different truth-values in this case. In the referential case, we are referring to an entity, and saying of that thing that it will succeed in preventing me from getting to work on time. So the logical form of the proposition, when analysed referentially, is wrong. In addition to this semantic or logical issue, we also have a metaphysical or ontological worry. We may feel that the entity referred to in Ref is of dubious ontological status. Nothing doesn’t exist; it isn’t a thing as such. Successful reference seems to have as a presupposition that the referent exists in some sense or other. If that is right, then when we successfully refer to ‘nothing’ then there is something which is the referent for the term ‘nothing’. But if there is some referent, then ‘nothing’ doesn’t mean the complete absence of any thing. It may be that the combination of this model of reference with the insistence of ‘nothing’ meaning the complete absence of any thing is incoherent. So we can feel dissatisfied with Ref here for both ontological and logical reasons.

We may want to avoid this problem by postulating that ‘nothing’ refers to an entity, yet what it refers to is not an existing thing. Nothing is, even though it doesn’t exist. It is a something, just not an existing something. I find this way of talking almost unintelligible. It seems to me as a bedrock metaphysical principle that there are no non-existing things. There is not two types of existence; rather there is only one type of existence. If ‘nothing’ is, then it exists. The terms ‘is’ and ‘exists’ are synonymous. In this regard, I find Russell (On Denoting) and Quine (On What There Is) to be instructive.

Den, on the other hand, does not refer to any thing of dubious ontological status. When recast in the form of Den’ it clearly and explicitly quantifies over all the things that there are and says of those things that none of them are going to stop me getting to work. So it has going for it that it captures the intention behind the sentence, in that it captures that I will not be stopped. Den doesn’t require postulating two types of existence. We don’t have to say that ‘nothing’ is yet does not exist. We do not directly refer to ‘nothing’, we just refer to what there is (and say that it is none of those things).

The difference between Ref and Den could be put like this: the former is a successful reference to something that does not exist, the latter is a failure to refer to anything which does exist.

3.   The Main Case

Let’s apply this to our example of ‘nothing has no causal powers’. Let’s rewrite having no causal powers as being ‘causally inert’, and represent that as a predicate, ‘Ix’. On the referential reading, the sentence has the form:

Ref2)   In

This says ‘nothing is causally inert’. As we have seen, the model of reference used here treats nothing as a referent of the term n, which means it is the thing referred to by n. The proposition is true only if the referent of n, i.e. nothingness, is actually causally inert. And nothingness, as conceived as an empty void with no contents whatsoever, is plausibly causally inert. So the claim seems to capture well the intention behind the apologist’s assertion here. The reason that the universe couldn’t have ‘popped into being from nothing’ is that ‘nothingness’ has no abilities to make things pop into existence. It cannot do anything; it is causally inert.

The denotative reading would be as follows:

Den2) ~(∃x)(Ix)

This says that it is not the case that there is a thing such that it is causally inert. Recast in universal terms, it says:

Den2’) (∀x)~(Ix)

This says that everything is such that it is not causally inert; everything has causal powers. On this reading, we are effectively saying that abstract objects, and similar proposed causally inert entities, do not exist; there are no abstract objects, etc. This is because abstract objects are causally inert, and Den2 says that there is no causally inert thing.

One would suppose, looking at this that in the case of nothing having no causal powers, we should take the referential reading, as this makes sense of the apologist’s claims about how the universe had to have a cause. It is clearly not their intention to assert that causally inert objects don’t exist; they mean to assert that the complete absence of anything cannot itself cause something.

In the toy example, when we distinguish the referential and denotative sense of ‘nothing’, it is clear that the referential sense is incorrect. It entails something which is clearly not intended by the speaker, that I will not get to work on time, when we meant to express that come what may I will get to work on time. In the apologetical example, the analysis seems to go the other way; the denotative sense seems to entail a proposition which clearly isn’t what the apologist intends. So, while the toy example is denotative, the apologetical example is referential.

I have two worries with this conclusion:

a) If we take the referential reading of ‘nothing’ in the phrase ‘nothing has no causal powers’, then we are referring to an entity that is of questionable ontological status. It is the referent of the term n, yet it is the complete absence of any thing. So it is a thing that does not exist. We might want to follow Russell in On Denoting, and Quine in On What There Is and disallow such talk of non-existing things. Indeed, we may consider such talk of nothing as a dubious case of reification. Nothing is not a thing of any type whatsoever.

b) This is my main worry. It seems to me that most cases of the word ‘nothing’ are denotative, and almost none are referential.

Here are a few examples:

  • ‘There is nothing to split the two candidates with only days before the election.’
  • ‘There is nothing I like better than ice cream’
  • ‘Nothing pisses me off more than ice cream’
  • ‘You mean nothing to me’
  • ‘There is nothing in the fridge’

The first four cases are clearly denotative (just plug in the different readings of ‘nothing’ and see for yourself in each case). Possibly in the last example, we may want to use the referential sense, but the denotative sense seems at least as plausible. Are we expressing that there is an absence of any thing in the fridge, or that there is not any existing thing in the fridge? Neither seems preferable.

My question is: can there be an example of a sentence that uses the word ‘nothing’, and isn’t the clearly apologetical ‘nothing has no causal powers’ etc, or some other esoteric metaphysical example, for which the referential reading is clearly the correct one (and not the denotative one)?

Are there ever cases where the referential sense is the correct one, apart from the use in things like supporting the Kalam? If the answer to this question is ‘no’, then the use by the apologist is ad hoc in the support for the Kalam case. This is an open question (feel free to suggest candidate sentences in the comments section). If there is a plausible looking case, then the charge of ad hoc-ness can be deflated.

What is Atheism?

0. Introduction

Atheism may be defined provisionally as the view according to which there are no gods. However, despite this seemingly simple idea, there is a bit of controversy about the more precise meaning of ‘an atheist’. I will spell out some of the issues involved and outline my position.

  1. Atheism and theism

One might like to think of a proposition, p, which is to be understood as follows:

0)           p = ‘Some god exists’

It seems clear that the terms ‘theism’ and ‘atheism’ have some intrinsic relationship to p. One may think that the relationship is of the following sort (where ‘iff’ means ‘if and only if’):

i)            Theism is true      iff     p is true

ii)           Atheism is true    iff     p is false

This means that theism is logically equivalent to the proposition that some god exists, and atheism is logically inequivalent to the proposition that some god exists (it is equivalent to the falsity of ‘some god exists’).

1.1 Atheist and theist

If we accept i) and ii) as the definitions of theism and atheism, then we may move on to the definition of ‘theist‘ and ‘atheist‘. Doing this means bringing the agent, a,  into the definition. The natural way to define these terms is like this:

iii)           a is a theist       iff     a believes that [p is true]

iv)           a is an atheist   iff     a believes that [p is false]

There is a direct symmetry between -ism and -ist on this view. It is a nice and easy to grasp picture. The pattern is that the definiens of iii) and iv) are just those of i) and ii) but with the words ‘a believes that…’ at the start, and that the difference between theism/-ist and atheism/-ist is just that the former has ‘p is true’, and the latter has ‘p is false’. This means that a theist is just someone who believes that theism is true, and an atheist is just someone who believes that atheism is true. Thus, we have the pleasing result that theist is to theism what atheist is to atheism.

Here is a diagram of the logical relations:

slide1

If a is an atheist in the sense of iv) above, call her a ‘hard atheist‘.

2. Lacktheism

There is another way of characterising what it means to be an atheist, and this departs from the pattern we have established above. On this definition, an atheist is someone who does not believe that p is true:

v)        a is an atheist    iff      not-[a believes that p is true]

This definition of atheism is well-represented in public defences of atheism. Atheists commonly claim not to have a positive belief that p is false, i.e. to believe that no god exists, but merely to lack the belief that p is true. When they are doing this, they are advocating v), and someone who does this is a ‘lacktheist’.

3. Does ‘atheist’ mean ‘hard atheist’ or ‘lacktheist’?

There is some controversy about whether ‘atheist’ means ‘hard-atheist’ or ‘lacktheist’. Often, ‘atheists’ self-describe as lacktheists, but this leads to a charge of being ad hoc by the theists. I will explain the controversy and why I think it is logically dissolvable. First, I will outline the argument by theists according to which an ‘atheist’ should be thought of as a ‘hard-atheist’.

It seems like v) (the definition of lacktheist) messes up with the symmetry we had between i) and iii) (theism and theist), and between ii) and iv) (atheism and atheist). The symmetry was that the difference between theism/-ist and atheism/-ist is that the former ascribes truth to p and the latter ascribes falsity to p. With definition v) in place of iv) though, we have switched to talking in terms of the negation of p instead. The diagram would look like this:

slide2

So, the theist is someone who believes that theism is true, but (according to v) the atheist isn’t someone who believes that atheism is true, rather they are someone who does not believe that theism is true. This seeming abnormality may be seen as reason to reject v) (lacktheist) in favour of iv) (hard-atheist). Why, we might think, should we break the symmetry? We might just insist that an atheist is to atheism as a theist is to theism. If so, then an ‘atheist’ is a hard atheist, and a lacktheist isn’t an atheist at all. Changing the definition of ‘atheist’ seems unsystematic. In this situation, it is not that atheist is to atheism what theist is to theism, so we have lost our intuitive looking principle.

Added to the feeling of oddity about breaking the symmetry of the definitions, theists may be cynical about the motives of the atheist who argues for v) rather than iv) (the lacktheist). The reason for this cynicism would be that a consequence of using v) is that the defender of it seems to have less burden of proof in an argument than the defender of iv). And a position with lighter burden is easier to defend. So, the theist may suspect the atheist is choosing definition v) over iv) for the sole reason that  it makes her position easier to defend. If that were the only motivation on behalf of the atheist, we might view her decision to do so as ad hoc. In addition, if the approach treats atheist differently from any other similar position, then there could also be the accusation of special pleading as well.

The theist may insist that the situation should, in fact, be a level playing field, where each side (theist and atheist) has the same justificatory burden. The reasoning for this would be something like the following:

  1. If a says “I am a theist”, then a is implicitly saying that a believes that p is true.
  2. If a (even implicitly) says “I believe that p is true”, then a has the justificatory burden of the claim “p is true”.
  3. Therefore, if a says “I am a theist” then a has the justificatory burden of the claim “p is true”.    (1, 2, hypothetical syllogism)

Thus, claiming to be a theist carries with it the justificatory burden of claiming that it is true that some god exists. These justificatory relations are mirrored with our first definition of an atheist:

  1. If a says “I am an atheist” (and means definition iv), then a is implicitly saying that a believes that p is false.
  2. If a (even implicitly) says “I believe that p is false”, then a has the justificatory burden of the claim “p is false”.
  3. Therefore, if a says “I am an atheist” this means that a has taken on the justificatory burden of the claim “p is false”.   (1, 2, hypothetical syllogism)

Thus, if we use the original definition of ‘atheist’, then the theist and atheist have the same justificatory burden. Surely, to try to change the definition of atheism here would be just to avoid this burden.

And indeed, if a says “I am an atheist”, and means definition v), then a has not made an implicit claim about what a believes. Rather, a has made a claim that a does not have a belief that “p is true”. Thus, premise 1 above would be false if we used definition v) for ‘atheist’. This is why, if a uses the lacktheist definition of ‘atheist’, that a‘s claim “I am an atheist” does not have the justificatory burden of the claim that “p is false”, and why the burden is avoided.

So, the claim could be that the atheist is making an illegitimate switch, from iv) (‘hard atheist’) to v) (‘lacktheist’). It could be seen as illegitimate because definition v) seems to be an otherwise arbitrary breaking of the symmetry of definitions, and seems like it is only justified through the benefit it bestows on the defender of the position (which is the root of the ad hoc complaint). We shouldn’t treat the definition of atheism differently to theism unless there is a good reason to do so  (or it would be special pleading). The atheist seems to have only selfish and illegitimate reasons for identifying as a lacktheist rather than as a hard-atheist.

4. Mirroring

However, one could in fact start the reasoning again slightly differently, and make ‘hard atheist’ look like the deviation from the pattern, and ‘lacktheist’ look like the expected one. This also transfers the charges of ad hoc and special pleading to the theist.

For example, we could stick with definition i), but define atheism as follows:

i)             Theism is true       iff                p is true

vii)           Atheism is true     iff       not-[p is true]

In a classical language, there would be nothing to distinguish between ii) and vii); ‘p is false’ is logically equivalent to ‘not-(p is true)’. Saying that atheism means that “it is not true that there are any gods”, seems just as faithful to the idea of atheism as the claim that it means that “‘there are gods’ is false”. Because they are equivalent, there is nothing one could appeal to logically which could decide in favour of i) rather than vii), and vice versa. Thus, we seem to have no real reason not to start from vii) if we want. And if we do proceed from here, then we can define theism as before, but use v) for the definition of atheism, and it looks like it is obeying the pattern of reasoning employed so far:

iii)           a is a theist       iff                a believes that [p is true]

v)            a is an atheist    iff    not-[a believes that [p is true]]

Now the relations between i) and iii), and vii) and v) are just as neat and tidy as they were earlier. Here is a diagram of the logical relations:

slide3

As before, the relation between -ism and -ist is just that the -ist definition has ‘a believes that…’ added before ‘p is true’. The relation between theism and theist on the one side and atheism and atheist on the other is just that the atheism/ist side has ‘not-…’ prefixing them. On this view, a theist is to theism what an atheist is to atheism. Note that v) is the definition of a lacktheist.

So, an atheist is ‘naturally’ thought of as a lacktheist if we say that atheism means that it is not true that some gods exist. Given that starting point, it isn’t changing the pattern of definitions to get to lacktheism; instead, it looks as if insisting on hard-atheism would be unsystematic here. One can imagine a theist insisting that an atheist should still be a hard-atheist , but this time the accusation of symmetry-breaking could be levelled at the theist for doing so. Who is being unsystematic, it seems, depends on the starting point taken.

And a theist would have a selfish motive for making this demand too. We cannot ignore the fact that insisting that the atheist breaks the symmetry and uses the definition of ‘hard-atheism’ would remove the justificatory advantage that the atheist would otherwise ‘naturally’ have. However, because ii) and vii) are logically equivalent, there can be no reason to pick one over the other, and so the insistence of the theist to use the hard-atheist definition looks to the atheist as being ad hoc – being done merely for the rhetorical benefit it provides to the theist.

Thus, the two positions mirror each other perfectly. Depending on the definition given for atheism, the definition of atheist as hard-atheist or lacktheist seems unwarranted. The theist judges the atheist as trying to illegitimately lighten their own burden; the atheist judges the theist as trying to illegitimately add to the atheist burden. Whether it makes the atheist’s job harder, or the theist’s job easier, depends on whether atheism means that it is false that some gods exist, or whether it is not that some gods exist is true. And there doesn’t seem like there could be any reason for picking one over the other.

There seemed to be an observation that atheist’s were making an illegitimate move when defining atheist as lacktheist, which was being done just to get an advantage over the theist rhetorically. But if we start at another position, it would seem like the theist is the one trying to shift the burden just for their own advantage. This seems to dissolve the accusations of foul play on either side.

5. Post-definitional thinking

I think that the lesson of all this is just that there is nothing purely logical to appeal to which means that ‘atheist’ should be thought of as ‘hard-atheist’ rather than ‘lacktheist’. Either view is equally defensible, and any choice between them can only be ad hoc. In a sense, as it is a discussion about the nature of definitions, it is rather pointless. And this is hardly surprising.

Instead of worrying about the definition of ‘atheist’, we should rather pay more attention to the nature of the beliefs that a holds. In addition to the basic notion of a simply believing that p, we can talk about the ‘degree of belief’ that a has that p. Let’s say that the degree of belief a has that p is the following:

Da(p) = x, where 0 ≤ x ≤ 1.

Degrees of belief are real numbers between 0 and 1, rather like probabilities. They express your feeling of confidence in a proposition. 0 is maximally uncertain, 1 is maximally certain, and 0.5 is absolute indecision.

It seems to me that the proposition p, that there are any gods, is rather hard to evaluate. I find the idea of a personal loving agent quite unlikely indeed, for various reasons (it seems suspiciously like the sort of thing made up by humans, for one). However, the question of whether there are any gods seems a lot more of a difficult thing to evaluate. Perhaps some kind of being created the universe, but remains utterly divorced from the subsequent comings and goings of the world itself, or perhaps one is fascinated by the comings and goings of radically different forms of life on the other side of the universe than us, etc. These sorts of ideas are interesting, but are almost impossible to say anything about, either for or against. I kind of couldn’t have any good reasons to think that any of these sorts of hypotheses were true rather than false. What would count as evidence for or against? In this situation, my degree of belief that p (i.e. the proposition ‘some god exists’) has got to be around 0.5.

Yet, I do have a sneaking suspicion that there probably aren’t any gods like this. If you put a gun to my head and made me decide, I would opt for the no-gods option. That’s what I think is more likely, and so I my degree of belief that p isn’t exactly 0.5. The following is certainly true:

Da(p) < Da(~p)

However, the imbalance seems to me to be very, very slight. I wouldn’t know how to put a precise number on it, but it seems reasonable to think that my degree of belief that ~p is between 0.5 and 0.55.

Now, does this state of mind mean that I believe that p? I certainly believe that there is an almost even probability about whether there are any gods or not, with a very slight imbalance towards no gods. My degree of belief is similarly minimally slanted towards the no-gods position. The question is the relation of these facts to the question of whether I believe that p.

Belief, as opposed to degree of belief, is an all or nothing notion. You either believe p or you don’t. Yet, my degree of belief is a scale. It ranges from 0 (definitely not belief) to 1 (definitely belief), and could be any value in between. How do the two notions relate to one another?

One idea, at one point seemingly advocated by William Lane Craig, is that the relation between belief and degree of belief is as follows:

“If it is more plausible that a premiss is, in light of the evidence, true rather than false, then we should believe the premiss.” (taken from: http://www.reasonablefaith.org/apologetics-arguments#ixzz4Kp11AOyR)

The idea could be put as follows:

a believes that p    iff   Da(p) > 0.5

So long as your degree of belief that p is more than 0.5, then you believe that p is true. On this view, saying that you ‘believe that p‘ just means that your degree of belief is more than 0.5.

One problem with this view is that there seem to be situations in which it sounds wrong to say ‘I believe that p‘, even though they are clearly situations where our degree of belief that p is more than 0.5. Here is one.

Say I have a pack of cards, I thoroughly shuffle it and I take one out. It is the ace of spades. I discard the card, and take another one without looking at it. Let r be the proposition that ‘the card is red’. Do I believe r?

The probability that r is true should be calculated as 26:51 (i.e., the remaining number of red cards:the remaining number of cards), or roughly 0.52. Given that I know this, my degree of belief that r is true should be correspondingly 0.52. Any other number would be perverse.

I think that in this situation, though my degree of belief is clearly in favour of red over black (or not-red), I still don’t think it is correct to say that I believe that the card will be red. I am sufficiently hesitant that the phrase ‘I believe that r is true’ would be misleading. It would indicate a higher degree of belief than that.

Perhaps you are thinking that you do believe that the card is red in this situation. Perhaps tilting the degree of belief 2 percentage points towards r is enough for you. If so, then consider the following version of the previous example:

Say I have a million packs of cards, I thoroughly shuffle it (somehow!) and I take one card out. It is the ace of spades. I discard the card, and take another one without looking at it. Let r be the proposition that ‘the card is red’. Do I believe r?

This situation is exactly like the previous one, except that the chance that the card is red is slightly closer to being exactly 50:50 than before. The probability would be: 0.50000002. Now, the chance that the card is red is only two millionths of a percentage point more likely than that it won’t be. Do you believe that it is red? If so, then your position is probably that of Craig’s above. Any imbalance in one direction entails belief rather than disbelief.

On the other hand, you may be agreeing with my intuition that asserting belief in these situations is incorrect. If so, then this means that there is some value of degree of belief (say 0.45 – 0.55 or something) in which is is not true that you believe p or disbelieve it (or believe ~p). In this penumbra (or indeterminate area) we lack belief that p, even though we possess a positive degree of belief that p. If you think this, then it cannot be true that ‘a believes that p iff Da(p) < 0.5′.

One may ask what the value is, if not 0.5? What does the value of your degree of belief that p have to be in order for it to be true that you believe that p? This, I think, is a complex question. One that is so complex, in fact, that it may be malformed. There may be no answer to it as such. It may be that in certain contexts the threshold is higher than others. Perhaps this varies from person to person, from conversation to conversation, from time to time, etc. Perhaps it varies in a chaotic and untraceable manner. This may be the case, within some sort of range outside of which it doesn’t go. For example, belief is never inappropriate in the case where the agent has a degree of belief which is 0.99, for example. It seems like it also isn’t appropriate in the case where the degree of belief is 0.50000001, etc. When people say ‘I believe that p‘, they are not necessarily reporting to a precise degree of belief (0.65 rather than 0.66, say), but just that they feel that their degree of belief is sufficiently over the threshold (whatever it is). Conversely, when someone says that they believe that ~p, this means that their degree of belief that ~p is sufficiently over the threshold (whatever it is) for ~p. When one is not sufficiently over either threshold, as in the card examples above, one should not say that one believes that p, or that one believes that ~p. One simply lacks beliefs in either direction. This is perfectly compatible with the idea that the degree of belief is believed, and perhaps even known. All that matters is that the degree of belief is extremely close to 0.5.

Thus, I have made a case for my claim to lack belief, which is not ad hoc because it is motivated by a general principle about when to withhold belief either way, and is not special pleading because I apply it to any case that is relevantly similar. I do not believe that any gods exist in the same way as that I do not believe that the card is red. In each case, my degree of belief is very close to 0.5, and that is what makes it inappropriate to affirm in either direction.

5. Conclusion

I think that this characterises my views about theism. I have a degree of belief that theism is false which is marginally over 0.5, but less than enough to indicate positive belief that it is false. Whether that counts as an atheist or not probably depends on your personal choice of definitions. Definitions aside, that is my view.