Logic 101

Sigh.

Two weeks in a row Matt Slick, Andrew Rappaport and the rest on BTWN have tried to save face after I explained my critique of their argument. Seeing as they are still just as confused as before I went on (and possibly more so), I have decided to spell out a few more issues here. They say it is an issue of wording. In reality, it is an issue of logic. As demonstrated already, they don’t get this because they don’t understand logic.

So, the first version of the argument has the first premise as this:

1) ‘Either god or not-god accounts for logic’.

This is how Slick actually said it, word-for-word, at various times on BTWN, in debates with people, on his radio show, etc. It is also a horrible train-wreck of a sentence. So what is wrong with this sentence? The problem is the placement of the ‘not’. Negation is a ‘truth-functional monadic operator’. What this means in more plain terms is just that it prefixes individual formulas (which is what makes it monadic), and the new formula it makes when it has been applied has a truth-value which is a product of the truth-value of the original proposition (which is what makes it truth-functional). So, an example will help. Here is a proposition:

2) Washington was the first president of America.

If we want to negate this proposition, we stick a ‘not’ in front of it as follows:

3) Not-(Washington was the first president of America).

The way negation works is by making the new formula have the opposite truth-value to the original one. Say 2) is true, then 3) (the negation of 2) is false. Also, say 2) is false, then 3) is true. Negation toggles between truth-values.

We can say 3) a little more perspicuously as

4) It is not the case that (Washington was the first president of America).

This means the same as 3).

In English, the grammar is messy and not logically regimented, meaning that we often express the same thing by having the negation in the middle of the sentence rather than at the start, as follows:

5) Washington was not the first president of America.

However, this is just a difference of wording, and 3), 4) and 5) all express exactly the same proposition. In propositional logic, if we set p = ‘Washington was the first president of America’, then we would write all three of these formally as follows:

6) ~(p)

In first-order logic, where we have terms for names and simple properties, we would express it differently. We would have a term for the name ‘Washington’, say ‘w’, and a term for the property ‘…was the first president of America’, say ‘F’. So we would write 2) as follows:

7) Fw

With the negation being:

8) ~(Fw)

Now, to return to Slick’s first premise, the negation does not prefix a proposition, but rather just a term in a proposition. It says that ‘not-god’ accounts for logic. But, as we have just seen, negation prefixes propositions not names. It is as if Slick’s premise would be written in first-order logic as

9) Ag or A~(g)

(where ‘g’ is ‘God’ and ‘A’ is ‘…accounts for logic’).

But because the negation is prefixing not the proposition ‘Ag’ but the name ‘g’ inside the proposition, it makes no sense. It is not a well-formed formula, and so cannot be given a truth-value. It is like the way ‘President first the was America Washington’ is just nonsense, and so neither true nor false. So if we take Slick literally, and phrase the argument exactly as he does, then the first premise isn’t really a premise at all, but a meaningless string of words.

If I said ‘either Bob broke into my house, or not-Bob broke into my house’, you would think I had difficulty talking properly. ‘Not-Bob’ isn’t a person, and obviously he didn’t break into my house. Phrasing it as not-Bob is literally meaningless.

To make it a well-formed formula, the closest thing would be:

10) Ag or ~(Ag)

But now we have a dichotomy as the first premise, and if we use disjunctive syllogism we are going to be inevitably back to triviality (as I literally proved in my original post). Let’s quickly give the argument both ways just in case anyone is still unsure how it goes:

Pr1. Ag or ~(Ag)

Pr2. ~(Ag)                  (i.e. negating the first option)

Con. ~(Ag)                  (i.e. concluding the second option)

 

Pr1. Ag or ~(Ag)

Pr2. ~~(Ag)                  (i.e. negating the second option)

Con. Ag                        (i.e. concluding the first option)

So Slick doesn’t want to repair his train wreck of a sentence, 1), into 10), because it is check-mate for the argument if he does that. No debate. Game over.

So it looks like the choice is between a meaningless first premise (i.e. 9) and a trivial argument (i.e. if we use 10). Well, we can read 1) a little differently, a little more charitably. There is another reading of 1) which is not meaningless. So go back to the example of me saying the following:

11) Either Bob broke into my house, or not-Bob broke into my house.

Instead of reading this as ‘Either Bob broke into my house, or it is not the case that he broke into my house (which would make the subsequent argument trivial again), we could read it as follows:

12) Either Bob broke into my house, or someone else broke into my house.

Now, we can express this perfectly well in first order logic, using quantifiers. These are devices which use variables (rather than names). So one quantifier is called the ‘existential’ quantifier, ‘∃’. To say ‘something is red’, we would use the variable ‘x’ and the predicate ‘R’ for ‘…is red’ and the existential quantifier as follows:

13) ∃x(Rx)

This says ‘There is a thing x such that x is red’, or more colloquially ‘something is red’. So when someone says 12, the implicit assumption is that someone broke into the house, and either it was Bob, or it wasn’t Bob. We can express this as follows:

14) ∃x(Bx) and ((x = b) or ~(x = b))

It says ‘there is a thing x such that x broke into my house, and that thing x is either identical to Bob, or it is not identical to Bob’. More colloquially, ‘either Bob broke into my house or someone else did’. Stating it this way excludes the idea that nobody broke into the house, and presumably you would only say 12) if you knew that someone had broken in.

So we could read Slick’s first premise more charitably along those lines, and build in explicitly the claim that something accounts for logic to the premise, and than say that either that thing is identical to god or it is not identical to god, as follows:

15) ∃x(Ax) and ((x = g) or ~(x = g))

This says ‘there is something that accounts for logic, and that thing is either identical to god, or it is not identical to god’. More colloquially, ‘either  god accounts for logic, or something else does’.

So, it looks like we have made some progress towards finding a more charitable way to cash out the logical form of the first premise. 15) is well-formed, so not meaningless, and it doesn’t lead to triviality the same way as 10) did. So, is this the desired destination for Slick’s argument form? I say no. Here’s why.

There is good reason for thinking that nothing accounts for logic, which would make 15), though elegantly formed, false. Here is Aristotle, in the Metaphysics (book IV, section 4) discussing whether the law of non-contradiction can be demonstrated:

“But we have now posited that it is impossible for anything at the same time to be and not to be, and by this means have shown that this is the most indisputable of all principles.-Some indeed demand that even this shall be demonstrated, but this they do through want of education, for not to know of what things one should demand demonstration, and of what one should not, argues want of education. For it is impossible that there should be demonstration of absolutely everything (there would be an infinite regress, so that there would still be no demonstration); but if there are things of which one should not demand demonstration, these persons could not say what principle they maintain to be more self-evident than the present one.”

This much debated passage seems to be suggesting that non-contradiction cannot be demonstrated from some other foundation, because it is the foundation for demonstration itself. Some things, he suggests, must be the end of demonstration and explanation, lest there be an infinite regress of explanation. If so, then it seems that we may have some reason to suppose that no ‘account’ of this principle of logic can be given. Here is another philosopher, David Lewis, making a similar point:

“Maybe some truths just do have true negations [i.e. maybe non-contradiction doesn’t hold].  … The reason we should reject this proposal is simple. No truth does have, and no truth could have, a true negation. Nothing is, and nothing could be, literally both true and false. This we know for certain, and a priori, and without any exception for especially perplexing subject matters … That may seem dogmatic. And it is: I am affirming the very thesis that Routley and Priest [i.e. philosophers who deny non-contradiction] have called into question and-contrary to the rules of debate-I decline to defend it. Further, I concede that it is indefensible against their challenge. They have called so much into question that I have no foothold on undisputed ground. So much the worse for the demand that philosophers always must be ready to defend their theses under the rules of debate.” (Lewis, Logic for Equivocators, (1998), p 434 – 435).

Lewis, probably the most influential analytic philosopher of the late 20th Century, and no stranger to defending controversial theses adeptly, simply offers no argument in support of non-contradiction. He seems to be implying that the very call to account for it is impossible to answer.

Now, obviously, Aristotle and Lewis can be wrong. I disagree with both about different things (future contingents and realism about possible worlds, respectively), so just citing them as authorities is not a way of establishing the thesis they argue for. However, what this does is highlight the difficulties associated with establishing 15), as it requires explicitly what Aristotle and David Lewis are very insistent cannot be granted; a reason for thinking that non-contradiction holds, or an ‘account’ of non-contradiction.

So this does not say that 15) is false. But it does show that it would be almost impossible to establish it. Matt Slick, an admittedly learned theologian, who has had no training in philosophy or logic, would have to solve a puzzle that has literally been too difficult for the greatest philosophers and logicians in history to solve: how to justify non-contradiction.

With these considerations in mind, we can see how Herculean the task would be to justify the premise. Possibly something accounts for logic, but how do you show that? How do you show that it is not just a brute given foundation?

One thing is clear: Slick’s original way of pumping up the intuition that 1) is true is to cite the fact that either god exists or it is not the case that he exists. But this dichotomy is not the same premise, and could be true even when 15) is false. So it is no help. The fallacy of begging the question, that I accused him of before, was not just that he gave a premise that was a potentially dubitable disjunction instead of a dichotomy; it was that he offered the dichotomy as justification for the premise. That is the essence of the false dichotomy, and now it is clear what the task is for justifying 15), it is obvious that it will not work again.

There is nowhere for this argument to go. It is over, even if they claim that it isn’t. Even if they claim that I was making a point about ‘wording’, or that I was drunk (which I wasn’t), or any other ad hominem. The task is too great to be overcome by Slick, and if it is too difficult for Aristotle or David Lewis, I am not holding my breath that anyone will be able to justify 15) either.

The Infinite Regress for Revelational Epistemology

[This idea is inspired by a very similar regress problem as set out in a draft version of ‘On Knowledge Without God: Van Tillian Presuppositionalism and Divine Deception‘ by Daniel Linford and Jennifer Benjamin.]

Traditionally, it is held that there are two ways of gaining knowledge; either through the senses, or through the use of pure reason. These carry the names of ‘a posteriori’ and ‘a priori’ knowledge respectively. While a priori knowledge can be known with certainty, it is also devoid of any content about the world; one can deduce that the interior angles of a triangle sum to 180º, but not whether any actual triangles exist. In contrast, a posteriori knowledge provides genuine content about the world, but can always be doubted; my senses are telling me that it is daytime, but perhaps I am dreaming. So one has a sort of certainty but no content, one has content but no certainty.

Some presuppositional apologists try to have the best of both worlds, with a third type of epistemological category; revelation. This has the content of a posteriori knowledge, but with the certainty of a priori knowledge; one can know that God exists ‘in such a way that they can be certain’. It is an impressive claim, but one which I think is susceptible to an infinite regress.

There is a simple apologetic mantra, often used by presuppositionalists, about the impossibility of having this type of knowledge unless you are on the right side of the creator of the universe. It says that ‘unless you knew everything, or were told by someone who did, it would be impossible to be certain about any matter of fact’. The obvious implication is that only by being directly revealed something by God can we come to know it for certain. Let’s try to put this clearly:

Revelation)    x can know p for certain if and only if God has revealed to x that p.

I claim that there is a problem for this idea; that it faces an infinite regress. The problem has to do with the possibility of mistaken claims of revelation.

So imagine a person, let’s call him Sye, who thinks that they have had a revelation from God that p is true. In addition, let’s also imagine that some other person, let’s call him Ahmed, thinks that he has had a revelation from God that ~p is true (i.e. that p is false). Now, if we asked him about this, Sye is clearly going to say that only he is correct in this matter. Sye would say that poor old Ahmed mistakenly thinks he has had a revelation when he has not.

But the question would become ‘how can Sye know this?’ Imagine that Sye offers up something about his revelation that he claimed made the difference, and according to which he could tell that his revelation was genuine, and not a mistake. This could only be something relating to the way in which Sye experienced the revelation. But no extra experience could make this difference. If Sye said that in his revelation God told him with a really loud booming voice, or with a golden shimmer around the page, etc, and this is how he knew the message was genuine, we could always postulate that Ahmed’s revelation was delivered in a similar manner. The internal experiences of both agents could be exactly similar in all relevant respects, and it is still conceptually possible for at least one of them to be suffering from a false impression. There cannot be a foolproof experience that confers certainty, or else the empiricists would have had this in the first place, and we would have had no need for revelation at all. Thus, nothing about the experience of the revelation would mark it out as being reliable rather than mistaken.

There could be no a priori explanation for this either, as they are devoid of content, and can never tell us about what is true in the world. They only relate ideas to one another, and so could never say whether, in this actual case, Sye was mistaken or not.

The revelationalist has a natural go-to answer here though, which he will find very tempting, but which I urge is going to lead to the regress. He has a third epistemological route, and he may well be tempted to bring it into action on this question. So Sye may well say that the reason he knows that God’s revelation that p was correct, was that God revealed to him that he had revealed to him that p. Call this a ‘second-order’ revelation; a revelation about a revelation. This would sure-up the worry over whether p had been revealed or not. God has not only told Sye that p, but he also tells Sye that he has told Sye that p.

But then we could run the argument all over again. Imagine now that Ahmed also thinks he has received a similar second-order revelation from God; not only that he has revealed that ~p, but also that he has revealed to him that he has revealed to him that ~p. How can Sye know that he is the correct one, and that Ahmed is incorrect? Again, the only thing he can do is refer once more to the notion of revelation, so that God reveals to him that he had revealed to him that he had revealed to him that p! Thus, Sye would need to appeal to a third-order revelation to sure up the second-order revelation.

But we can run the argument all over again, where Ahmed gets the same third-order revelation, etc, etc. This process clearly goes on forever. At no point in the iterative process can Sye ever lay claim to the type of certain knowledge he is looking for, because at every point there is a possible Ahmed who could have exactly the same experience. The possibility of error over the revelation is a sort of un-holy ghost which can never be banished.

My conclusion from this is that revelational epistemology, as conceived here, is vulnerable to an infinite regress problem, from which it can never escape. It provides no new route to knowledge at all.

The Compatibility of Omniscience and Freedom

I say even if God knows what you are going to do tomorrow, this does not stop you being free to act otherwise. You won’t act otherwise, but you could.

Let’s set out a few definitions. You are free to do an action if it is possible that you do it, and if it is possible that you don’t do it. If either of these options is removed, you are no longer free. So if ‘p’ is ‘you will do x’, then you are free to do x if and only if (iff):

It is possible that p, and it is possible that not-p

Alternatively, we will write this as follows (where ‘◊’ means ‘possibly’):

◊p &  ◊~p

The problem is that this freedom condition seems to be ruled out by the idea of God’s foreknowledge. The reasoning is that if God already knows that p, then it is necessary that p. We can write this as follows, where K = God knows, and □ = necessarily:

If Kp, then □p

And if it is necessary that you are going to do x, then it is not possible that you will not do x. If necessarily p, then it is not possible that not-p:

If □p, then ~◊~p

So let’s put this into an argument that seems to show that freedom and omniscience are incompatible by deriving a logical contradiction:

 

Premise 1) I’m free to do x     (i.e. ‘it is possible that p and it is possible that not-p’)

Conclusion 1) Therefore, it is possible that not-p.

Premise 2) God knows that p.

Premise 3) If god knows p, then p is necessary.

Conclusion 1) Therefore, p is necessary.

Premise 4) If p is necessary, then it is not possible that not-p.

Conclusion 3) Therefore, it is not possible that not-p

Conclusion 4) Therefore, it is possible that not-p, and it is not possible that not-p.

 

We can write exactly the same argument in symbols as follows (in the right I give whether each line is an assumption or how it follows from something previously assumed):

 

Premise 1) ◊p &  ◊~p                         (assumption)

Conclusion 1) ◊~p                              (from pr. 1, and conjunction elimination)

Premise 2) Kp                                      (assumption)

Premise 3) If Kp, then □p                 (assumption)

Conclusion 2) □p                                (from pr.2 and pr.3, and modus ponens)

Premise 4) If □p, then ~◊~p             (definition of □ and ◊)

Conclusion 3) ~◊~p                            (from con.2 and pr.4, and modus ponens)

Conclusion 4) ◊~p & ~◊~p                (from con.1 and con.3, and conjunction introduction)

 

So we have derived a contradiction; it is possible that I will not do x, and it is not possible that I will not do x. This means we have to either reject the truth of one of the premises, or reject the validity of the argument form. Now the validity is easy to address, as it uses nothing but inference rules from classical propositional logic and the duality of necessity and possibility (i.e. □ = ~◊~ and ◊ = ~□~). There is nothing controversial at all here. So we must reject the truth of at least one of premises 1, 2 or 3, on pain of having to accept a contradiction.

Premise 1.

We said that being free to do x requires that it is possible to do both x and to not do x. Not all definitions of freedom require this. In fact this is a strong condition, and ‘compatibilists’ (like Spinoza, or Frankfurt) will contend that one can be free even if only one option is possible, just so long as that option is chosen. So the prisoner is free to stay in the cell, even though it is not possible to leave, for example. So it is possible to reject this premise. I think we can keep it however, and still avoid the consequence. We do not have to be ‘compatibilists’ to argue that God’s foreknowledge is compatible with freedom.

Premise 2.

This says that God knows what will happen tomorrow. To deny this means either giving up on God’s omniscience, or on the fact that there is a truth about the future (i.e. giving up on the principle of bivalence). We could go the second route, and retain omniscience, given that there is no truth about the future for him to not know. It should be noted that if we go this route, we have to also also hold that God is located in time. In this case, he would find out what happens tomorrow with the rest of us. A timeless God cannot ‘find out what happens’, as this would be a temporal activity. Anyway, we do not have to reject bivalence or require God to be in time, as I say we can avoid the contradiction even if premise 2 is true.

Premise 3.

This, as I see it, is where the confusion sets in. It says that ‘If God knows that p, then it is necessary that p’. Why would we think this premise is true? One reason is as follows. If you know something, anything, then it has to be that it is true. After all, you can’t know something false. It’s part of the definition of knowledge that it is of something true. God, who is infallible, only makes this force stronger; he couldn’t be wrong about anything. So if he knows something is going to happen, it is definitely, necessarily, going to happen. How could he be wrong?

Well, we need to be careful about the logical form of what we are saying. It is necessary that God knows p, and truth is a necessary component of knowledge; but this doesn’t mean that what God knows is necessary. Here is the sentence that is doing all the heavy lifting conceptually:

If God knows that you will do x, then it is necessary that you will do x.

I agree that everything God knows is true, i.e. he is infallible, and that everything true is known by God, i.e. that he is omniscient. But this only amounts to the following:

Kp iff p

This says that ‘God knows that p  if and only if p’. I can even go all the way and say that this is a necessary truth:

□(Kp iff p)

Now, we can derive a conditional which is very similar to premise 3 (which I will call 3.1) from this, namely:

3.1) □(If Kp, then p)

But it is important to note that this is as far as we can go. There is no way to go from 3.1 to 3:

□(If Kp, then p), therefore (If Kp, then □p)

So premise 3 does not follow from 3.1. Moreover, I say that 3.1 is actually the correct logical form of: ‘If God knows that you will do x, then it is necessary that you will do x.’

Admittedly, the word ‘necessarily’ is in the consequent in the sentence, and that seems to count against my claim. But then we systematically leave it there when we express both de re (of the thing) and de dicto (of the word) modalities, which should have it in different places. This means we fail to distinguish between the scope of the modality in natural language. Getting the scope of the modality right will solve the problem.

Quine’s example in Word and Object (p120) is that about cyclists being necessarily two-legged (and mathematicians being necessarily rational). To adapt his example, we would say:

If x is a cyclist, then it is necessary that he has two legs.

This sentence also has the word ‘necessary’ in the consequent, when it should be prefixing the whole conditional. It expresses only that under the description of the word cyclist, x has two legs. It is possible that x falls and gets one of his legs somehow cut off, and then x would not have two legs. It is not a necessary truth about x that he has two legs, only a necessary requirement for being a cyclist. So it is necessary de dicto that x has two legs, but not necessary de re. If we speak carefully, we would say:

It is necessary that (if x is a cyclist, then x has two legs)

The above formulation is compatible with the fact that x could fall off his bike and lose a leg, because he would then stop being a cyclist. Neither him being a cyclist nor having two legs is necessary; what is necessary is the connection between being a cyclist and having two legs.

This shows that we regularly fail to state the correct logical form when expressing de dicto modal claims. Sometimes, even though the word ‘necessarily’, etc, is in the consequent, it should be prefixing the whole conditional. And I say that premise 3 is one of these cases.

So if 3.1 was used in place, it would say that it is necessary that if God knows you will do x, then you will do x, just like it is necessary that if x is a cyclist, then he has two legs. Just like with the cyclist example, you do not have to do x (and he could fall off his bike). x doesn’t have to have two-legs, its just that it is necessary that if he is a cyclist then he does. You don’t have to do x, it just that it is necessary that if God knows that you will, then you will. In each case, the conditional is necessary, meaning that the one condition is never true without the other, but the other can be false. If it is false, then the antecedent condition would be false too.

One way of putting this is that it God knows contingent truths, like that you will do x. It is necessary that he knows them, but he only knows them if they are true. It is contingent that you will x, so it is contingent that p is true, and thus God might not know it. All that is necessary is that if it is true, he knows it; and if he knows it, it is true.

If we plug 3.1 in place of 3 in our argument from above, it stops us being able to move from it being true that p, to it being necessary that p. We needed that to get our contradiction, so we have blocked the contradiction. Thus foreknowledge and freedom are compatible.

Conclusion.

So I gave an argument for the incompatibility between divine foreknowledge and freedom, making it as strong as possible, which showed logically that the two concepts lead to a contradiction. However, I suggested the the logical form of the third premise was incorrect, allowing us to keep all the strong assumptions and show that no contradiction is forthcoming.

Thoughts on Jason Petersen’s ‘argument’

At the end of my time on the BibleThumpingWingnut, after a few hours (and about 4 whiskeys, at about 3AM), Tim introduced a new person into the discussion to ‘engage’ with me for a bit. This was Jason Petersen, who advocates a version of Clarkian presuppositionalism. Jason began by laying out an axiomatic demonstration of how you can go from the principle that the bible is the word of god to the conclusion that you can account for the laws of logic. After he explained his ‘axiom of revelation’, which is that the bible is true, he moved to a passage which contains the phrase ‘no lie is of the truth’. We got a bit stuck on this, as I objected that lies can be inadvertently true, as for example when someone intends to deceive, says something they believe is false, but which happens to be correct. I think that this would still count as a lie, but Jason disagreed, urging that we should use the biblical definition instead. I was tired and a bit drunk, so I may have missed what was going on at the time. I thought I should get a more sober reflection down here instead.

As I understand what was going on, Jason was starting with his axiom, and then deriving things from that, part of which included the law of non-contradiction. His point was (I believe), that ‘no lies are of the truth’ is an instance of someone stating the law of non-contradiction, i.e. ~(p & ~p). I think this is an exegetical stretch, and even if interpreted as generously as possible it gives a different law, the semantic principle of bivalence. So I say that ‘no lies are of the truth’ means ‘all lies are false’, which I said was false, due to my understanding of what lying means. But let’s assume that the intentional aspect of lying is not important, and as such lying just means saying a falsehood. This makes the sentence ‘no lies are of the truth’ analytically true (i.e. true by definition). Fair enough. It just means ‘no falsehood is true’. In other words, it means that if something is false, it is not also true. The principle of bivalence says that every proposition takes exactly one truth value: true or false; i.e. that if a sentence is true, it is not false, and vice versa. For some reason, Jason thinks that the sentence actually should be read as meaning ‘it is not the case that both p and not-p’; i.e. it is not the case that p and it is not-p. Notice that this doesn’t use the word truth at all. The difference may seem minor, but it allows that there can be logics where some proposition is neither true nor false (so no bivalence), but where it and its negation are still incompatible (so keeping non-contradiction), etc. Anyway, we can forgive the fact that a) the sentence is false (because I am right about what lying means), b) the sentence at best means something similar to the principle of bivalence, and c) it doesn’t mean the same as the principle of non-contradiction. We can forgive all of those and just assume that he was right. So let’s just say he starts from his revelational axiom, and then ‘derives’ the principle of non-contradiction. That seemed to be what he wanted to do. I say that this is horribly flawed anyway, despite the above.

So he has an axiom: everything in the bible is true (he actually says ‘the bible alone is the word of God written’). This basically just means that every proposition in the bible is true. So think of the bible as a set of propositions, B = {a, b, c, …} and that every member of the set is true. Then he says that he can go to one of those propositions, which is the law of non-contradiction (although he repeatedly dropped the ‘non’ for some reason). Therefore, the law of non-contradiction is true. In this way he derives it from his basic axiom.

So, assuming a = the principle of non-contradiction, the argument so far is:

Premise 1) a & b & c & …       (i.e. all the elements of B)

Therefore, a

However, the inference from B to a (from all the things in the bible, to the one particular thing in the bible), relies on the inference rule called ‘conjunction elimination’; from p & q one can infer p:

Premise 1)  p & q

Therefore, p

Therefore, Jason’s ‘axiom’ needs to be supplemented with, at least, the inference rules of classical logic, if he is to move off his axiomatic starting point to derive anything (even if it is contained as a conjunct in his conjunction). He doesn’t mention inference rules, but he must be assuming them or else he would be stuck with his axiom. So let’s be nice and give them to him. But that means he is assuming classical logic. And that means he is assuming the law of non-contradiction. So he doesn’t need to ‘derive’ the law of non-contradiction, as he would in fact be assuming it at the outset.

But maybe he has in mind a sort of non-classical logic, one that retains the ability to use conjunction elimination, but does not postulate as an axiom that there are no contradictions. But then the problem would be that there would be nothing to stop the paradoxical looking inference rule: ‘negation introduction’, which I have just made up, but would look like this:

Premise 1) p

Therefore ~p

Presumably, Jason would want to object that this rule is not part of his implicit set of inference rules. But the question would then be, why not? It seems to me that the only thing Jason could appeal to would be the fact that there cannot be a contradiction, which just is the principle of non-contradiction. And if he said that he would be admitting that he does presuppose non-contradiction after all, and does not derive it from an axiom.

The results for his logic if he did have negation introduction would be devastating. For a start, from his axiom B, one could derive ~B; from the axiom that the bible is true, one could derive that it is not the case that the bible is true. Even if he derived a from B (the principle of non-contradiction from the bible), one could also derive ~a from B (by deriving a from B, and ~a from a). So the bible would say there could be no contradictions, and it would say that it is not the case that there could be no contradictions.

The point is that negation elimination is to be avoided at all costs. The best way to avoid it is to start with it as an axiom that there are no true contradictions.

 

The Matt Slick Fallacy – Update

On the 10th of January 2016, I went on a YouTube show / podcast, called the BibleThumpingWingnut and talked to Matt Slick for about 2 hours on the subject of his TAG argument, and how it is guilty of the fallacy of begging the question or false dichotomy:

 

The whole discussion with Slick was conducted in a friendly and non-confrontational manner. I enjoyed it, even though it was very late at night (whiskey helped). I think he understood the points I was making, but it was hard going at times to get agreement. This is probably because those guys have no formal training to logic or exposure to analytic philosophy. Even though I was showing that the argument doesn’t work, we left on good terms, and I would happily speak with him again.

Quick note: there were some hints that maybe I was just diagnosing a problem with the ‘wording’ of the argument, which would leave the possibility that a way could be found to repair it. The temptation might be to rephrase it as something logically equivalent; like instead of ‘p or ~p’, the first premise could be reformed as the logically equivalent ‘~(p & ~p)’. That would make the argument of the form ‘It cannot be both this and that, and it is this, so it must not  be that’. But this would fail, as follows:

~(p & ~p)

~p                             (i.e. the second option)

Therefore, ~p        (i.e. not the first option)

Any logically equivalent reformulation like this though will (provably) fall into the same trap; it is just as obvious that the above argument begs the question. The rewording will not help, because fundamentally the same first premise has been entered into the same pattern of reasoning (i.e. we are still using disjunctive syllogism in essence, even though the first premise is now a conjunction). No tactic like this will ever work.

On the other hand, any reformulation which is not-logically equivalent will be a different argument, not a ‘rewording’. Therefore, the argument cannot be ‘reworded’ in such a way to get round the problem. A new argument is needed to get to the conclusion. I’m not holding my breath that one will be forthcoming.

The Matt Slick Fallacy

  1. 0. Introduction. Matt Slick; evangelical Calvinist, radio presenter, apologist. He has made something of a name for himself by promoting a version of the ‘transcendental argument for the existence of God’. His version is one of the easiest to refute that I have come across. However, in all the debates and online discussions I’ve seen Slick engage in, and to be sure he engages in a lot, I have never seen anyone offer what I consider to be the correct refutation. So I will present it here. 

    His argument was given on his radio-show/podcast, on 17th December, 2015, in an episode entitled ‘A Proof of God’. In fact only the last 14 mins of the show are dedicated to this topic, when Slick is prompted by a caller – ‘Hollywood dude’. I will use that version as a foil. Here is the link it on his official ‘CARM’ podcast site: http://carmpodcasting.blogspot.co.uk/2015/12/carm-podcast-1214.html

     

    Admittedly, the argument was given in a rather off-the-cuff manner by Slick in that show, and he could be forgiven for not being clear and careful with his words. On the other hand, his presentation on the show was very similar to many other times he has given the argument in the past, in situations where he had the opportunity to prepare and refer to notes as he spoke, such as:

     

     

     

    The argument is also given in written form on his website, here: https://carm.org/transcendental-argument. The version of the argument I am looking at here is found at the end of the written version (section 9).

     

    1. Disjunctive syllogism and true dichotomy

     

    At 44:15 into our show, Slick explains his argument. He says that he will use the argument form known as ‘disjunctive syllogism’, which is the following inference rule:

     

    Either p or q

    Not-p

    Therefore q.

     

    It says that if either p or q is true, and if it is also true that one of them is not the case (say, p), then the remaining one (q) is true. Disjunctive syllogism is valid in propositional logic, and its validity will not be challenged by me here.

     

    Slick also uses the notion of a ‘true dichotomy’, by which he means a strong type of ‘or’-statement. In propositional logic, ‘or’ is a connective that takes two propositions, e.g. p or q. It’s behavior is entirely logical. ‘p or q’ is true when p is true and q isn’t, when q is true and p isn’t, and when they are both true. It is false when they are both false. That is a disjunction.

     

    Slick’s ‘true dichotomies’ are a strong version of a disjunction; true dichotomies are always true, as by definition one of the options is true in exclusion of the other. The way this is achieved is purely logical; the propositional form of ‘true dichotomies’ is a disjunction between a proposition and its direct negation; ‘p or not-p’.

     

    So here is a normal disjunction:

     

    Either Sam or Alex will come to the party.

     

    If it is true, then one of them will be at the party; but it might be false because perhaps neither Sam nor Alex will come to the party. Consider, in contrast, the following:

     

    Either Sam will come to the party, or she won’t.

     

    In this case it has to be true, because there are no other possible options than Sam being at the party, or her not being at the party. A ‘true dichotomy’ for Slick is like this; it has to be true because it covers all possible options.

     

    1. Slick’s argument

     

    At 44:15, Slick gives the following monologue:

     

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

     

    The argument structure being used is as follows:

     

    1) Either God, or not-God.

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

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

     

    He then proceeds to examine objections to premise 2, such as some of the main ways an atheist (a representative of the not-God camp?) might try to account for the transcendental laws of logic. Are they discovered, measurable features of empirical reality? Slicks says they cannot be. Are they ‘linguistic constructs’? Again, no. Do we vote on them? (Sigh) No. Could they be constructs of human minds? No, no, no. No.

     

    At the end of it, Slick summaries how he speaks to his imaginary interlocutor, the poor atheist, who has had his every attempt at accounting for logic rebutted (this is at 48:22):

     

    “When we go through this with them, I’ll say: ‘See, you can’t account for it. Therefore, the other position is valid’. And then I say: ‘Next!’”

     

    1. Refutation

     

    So, what is my refutation of this argument? Well, it does not involve giving a better account for the transcendental laws of logic than our poor imaginary atheist. Nor does it require pinning Slick down on precisely what it means to have an account of something. Neither does it involve pointing out to Slick that the premise ‘God or not-God’ is not an instance of a true dichotomy because, strictly speaking, it is not a properly formed sentence at all[1]. Anyway, nothing as fancy as the metaphysics of logic is needed here. And we can forgive a badly formed sentence here and there. We can afford to be so magnanimous because there is a logical problem with the argument, and it is very simple. It is a slight of hand, which can go un-noticed, but is easy to spot when spelled out. It is an instance of the fallacy of ‘false dichotomy’.

     

    A true dichotomy, such as:

     

    1. a) ‘Either God exists, or it is not the case that God exists’,

     

    is substituted for the false dichotomy of:

     

    1. b) ‘Either God accounts for the transcendental laws of logic or not-God accounts for the transcendental laws of logic’.

     

    The second is not a genuine dichotomy, because it is quite possible that neither God nor his negation has anything to do with the laws of logic. Here is an example, meant as a reductio of Slick’s argument:

     

    1) Either toast, or not-toast.

    2) The absence of toast cannot account for the laws of logic.

    3) Therefore, toast can account for laws of logic.

     

    Obviously, the absence of toast cannot ‘account’ for anything, especially the notoriously murky metaphysics of logic. Does this mean though that toast itself can? It seems equally obvious that it cannot. Taking one out of the running is not all that is needed to show that the other is the winner by default. Neither toast nor ‘non-toast’ can account for the laws of logic. The unsoundness of the argument is painfully obvious when ‘toast’ is used in place of ‘God’.

     

    To make Slick’s fallacy apparent, let’s spell out the argument a bit more clearly:

     

    1. Reconstruction 1:

     

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

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

    3) Therefore, God can.

     

    As we have seen, the problem with this is that the first premise isn’t a true dichotomy. Slick’s premise says:

     

    Either [x can do y], or [not-x can do y]

     

    This leaves the logical space available, where neither x nor not-x can do y, which stops the argument being sound. Maybe it is the case that nothing can play the role of x; i.e. maybe nothing can account for logic. If this were the case, then we could not prove one of these two options by eliminating the other (which is the whole point of using disjunctive syllogism). So if the first premise is as I have indicated, then we can rule out disjunctive syllogism as a useful argument form; that is, unless some independent reason can be produced for thinking that this form of the premise is true.

     

    The point about the first premise, when spelled out like this, is that it is in need of justification. Slick dangles the true dichotomy of ‘God or not-God’ in order to gain assent (as nobody can deny a tautology), but then switches focus to the false dichotomy above without conceding that he now needs to justify the new premise. This is the heart of the Matt Slick Fallacy; it is a bait and switch from a true dichotomy to a false one.

     

    It is clear that that [not-x can do y] is not the direct negation of [x can do y]. The direct negation of [x can do y] is:

     

    not-[x can do y].

     

    This would make the actual true dichotomy:

     

    Either [x can do y] or not-[x can do y]

     

    To get a feel of the distinction, consider the following:

     

    Either God can account for logic, or not-God can account for logic

     

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

     

    It is a subtle enough point, but makes all the difference. It is a scope distinction about whether the negation should be thought of as ranging over the entire proposition (as in the true dichotomy), or just one element of the proposition (as in Slick’s false dichotomy). Slick’s mistake is rather like supposing that either the present king of France is bald, or the present king of France has hair. In reality, neither is true.

     

    1. Reconstruction 2:

     

    We could get around this problem by making the first premise a true dichotomy:

     

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

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

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

     

    Now the first premise is a true dichotomy (and so definitely true). Also, the form of the argument is definitely that of disjunctive syllogism, so therefore definitely valid.

     

    This is where the good features of this argument end though. All disjunctive syllogisms with true dichotomies as the first premise are doomed to triviality, as is easy to show. This problem is due to the second premise of disjunctive syllogism. In this premise, either of the two options in the first premise (either p or not-p) is negated (it doesn’t matter which one is used). In the example above, it second premise uses not-p rather than p. So it is the negation of not-p, i.e. not-not-p. But this just means we already have our conclusion in our second premise. p is equivalent to not-not-p; the two ‘nots’ cancel each other out. This makes it a case of ‘begging the question’, where the conclusion of the argument is smuggled in as one of the premises.

     

    To make it crystal clear, here is the form of disjunctive syllogism with a true dichotomy as first premise:

     

    p or not-p

    not-not-p

    Therefore, p

     

    If we substitute ‘p’ for ‘not-not-p’ in the second premise (as they mean the same thing), the argument becomes:

     

    p or not-p

    p

    Therefore, p

     

    The first premise is now clearly redundant. We could drop it and the argument would simply be:

     

    p

    Therefore, p

     

    Thus, the argument just boils down to the derivation of p from p. If the argument is formed this way, it becomes entirely trivial. We are left with no reason to think that p is true, other than the simple assertion that p is true in the first place.

     

    1. Conclusion

     

    In conclusion then, Slick has presented an argument which commits the fallacy of false dichotomy, and if repaired so as to avoid that ends up committing the fallacy of begging the question instead. Thus, the argument is either unsound or trivial.

    [1] The sentence has no verb in it. Also, it is dubious that the negation of a noun, such as ‘not-God’, has any meaning whatsoever. In logic, it is propositions that get negated, not names.

The problem with TAG

0. Introduction

In this article, I will discuss the ‘transcendental argument for the existence of God’ (henceforth ‘TAG’). This forms the backbone of the ‘presuppositional’ approach to Christian apologetics, first formulated by Cornelius Van Til (1895 – 1987). At its simplest, it is a radical defense of the Christian position, which boldly tries to dismiss any counter-argument with the claim that the notion of argument itself presupposes the Christian position. If this were true, then the opponent of Christianity would have to assume the truth of the position they oppose when presenting any argument at all. Instead of the Christian being on the back-foot and trying to respond to the attacks of their opponent (say with archeological evidence or biblical contradictions, etc), TAG is an attempt to switch the weight of the attack back at the non-Christian (who has to justify their ability to present an argument of this nature in the first place). While this is an ingenious way of arguing, it is ultimately flawed, as I will show in this paper.

Usually, opponents of the presuppositional apologetic will make one of two mistakes; either they will take the bait of the argument and try to justify how they can ‘account for truth on their worldview’, etc, or they will try to show that the Christian position is unable to account for this itself. Neither of this tactics is advisable, on my view. This is not because I do not think that a non-theistic account of things like argumentation, truth, logic, morality, etc, can be had; on the contrary, I think that coherent non-theistic philosophical positions for all of the above can be formulated. Nor is it that I think that the Christian position is free from internal consistencies; on the contrary, I find the typically given Christian explanations of these things to be lacking in several key aspects (Euthyphro, problem of evil, lack of sufficient justification for biblical claims, etc). However, analysis of the situation reveals that even if one concedes both of these points to the presuppositionalist they have still not made their case. For even if I am unable to account for argumentation (or logic, morality, etc), and even if the Christian position (or ‘worldview’) is able to account for this, we still have not been given a demonstration that the Christian position is a necessary condition for the given feature. What this requires is a general refutation of not just my position, but of every alternative position, leaving Christianity as the only possible account. Absent this argument, TAG has not been justified. Essentially, when the presuppositionalist claims that the Christian worldview is the necessary precondition (or ‘presupposition’) for the intelligibility of human experience generally, the response should be: prove it. They have not provided any such proof so far, and for reasons I discuss below, it seems unlikely any such proof can be forthcoming.

  1. Transcendental Arguments

Transcendental arguments try to establish their conclusion, Y, by showing that it is required for the truth of some other proposition X; one cannot have the X without they without the Y, and we do have the X, so we must also have the Y. Consider the following argument:

  1. One cannot ride a bicycle without having two legs
  2. John is riding a bicycle
  3. Therefore, John must have two legs.

So if this argument is correct, we can say that having two legs is a ‘necessary precondition’ for riding a bicycle.

However, let us suppose that there is a way of riding a bicycle with one leg; perhaps a little-known technique is available whereby the one-legged person can operate a bicycle just as well as a two-legged person. If this were true, then the argument from above becomes unsound, as premise 1) would be false. It would also mean that having two legs is no longer a ‘necessary precondition’ for riding a bicycle; it would be a sufficient precondition, in the sense that having two legs will suffice for being able to ride a bicycle, but it is not necessary if there is a way for a one-legged person to be able to ride a bicycle. The correct argument, adding in the consideration of the one-legged technique, would be as follows:

  1. If one can ride a bicycle, then either they have two legs or they know the one-legged technique.
  2. John is riding a bicycle.
  3. Therefore, John either has two legs or knows the one-legged technique.

This shows that the claim of Y being a ‘necessary precondition’ for X requires that the only way X can be true is if Y is true also. If there is another way that X can be true, say by Z being true instead, then Y is not a necessary precondition for X. So part of showing that Y is a necessary precondition for X means showing that there is no Z which is a different precondition for X.

My point with TAG is that it has not been shown that there is no Z which could account for logic, morality, etc. This holds even if the Christian apologist can account for it, and even if their interlocutor cannot. What must be shown is not just that the interlocutor cannot, but no possible interlocutor can.

  1. TAG Itself

I shall use the words of Prof. Michael Butler as a foil to argue against. Butler is a professor of philosophy at Christ College, Lynchburg, Virginia, and himself a graduate of Westminster Theological Seminary, which Van Til helped to found and taught at for over 40 years. I use his words not because I think Butler is an example of a bad presuppositionalist; on the contrary, he appears to be a very insightful representative of the position. Indeed, the clarity with which he discusses the issue allows a clear formulation of what is wrong with it, and for that I am indebted to him.

According to Butler, TAG runs as follows:

‘It starts with human experience; such things as science, love, rationality and moral duties.  It then asserts that the existence of the Christian God is the necessary precondition of such experiences.  Finally, it proves this indirectly by demonstrating the impossibility of the contrary’.(https://presupp101.wordpress.com/2014/07/14/the-transcendental-argument-for-gods-existence/)

The ‘indirect demonstration’ referred to in the mention of the proof proceeds by showing that the alternative explanations of these experiences are all inconsistent on their own terms:

‘We must point out to them [i.e. atheists] that univocal reasoning [i.e. reasoning independently of God] itself leads to self-contradiction, not only from a theistic point of view, but from a non-theistic point of view as well. It is this that we ought to mean when we say that we must meet our enemy on their own ground. It is this that we ought to mean when we say that we reason from the impossibility of the contrary. The contrary is impossible only if it is self-contradictory when operating on the basis of its own assumptions’. – Van Til, A Survey of Christian Epistemology (Philadelphia: Presbyterian and Reformed, 1969), 204-5

This is the method of ‘internal critique’, where one assumes the interlocutor’s position to show that it leads to internal inconsistencies, as opposed to keeping one’s own assumptions fixed when analyzing the interlocutor’s position.

So two things need to be established:

  1. The Christian worldview can provide a non-self-contradictory account of human experience.
  2. The non-Christian worldview cannot provide a non-self-contradictory account of human experiences.

Talk of ‘the Christian worldview’ and ‘the non-Christian worldview’ is to be taken with a pinch of salt (although this will prove controversial later). Obviously, there are lots of different denominations of Christianity, including reformed Presbyterian, Lutheran, Catholic, Greek Orthodox, etc. Equally, there are many distinct non-Christian positions, including every denomination of every other religious worldview, plus every variation of atheist worldview, etc. If we take this plurality of worldviews into account, then the claim is that at least one Christian worldview can account for the intelligibility of human experience, and that none of the non-Christian worldviews can. This claim has not been demonstrate by presuppositionalists, and I will argue that we have reason to doubt that they can demonstrate this claim.

Although this will be dealt with in much more detail as we go along, here is my argument in a nutshell:

  1. TAG is successful only if every non-Christian worldview necessarily entails a contradiction (or is ‘internally incoherent’).
  2. There is a potentially infinite number of non-Christian worldviews.
  3. Either:
  4. a) There is one way to establish that all the non-Christian worldviews are internally incoherent, or b) One proof is not enough but there is a finite number of ways to establish that they are all incoherent, or c) There is an infinite number of ways required to establish that they are all incoherent.
  5. No proponent of TAG has established a); and it seems easy to prove that b) cannot be established (given a plausible formalization of ‘worldview’ as a set of beliefs); and if c) then it is not possible for a finite being to prove TAG.
  6. Therefore, TAG has not been established, and is likely to be unprovable.

Although this argument may seem complex, my basic point can be easily apprehended. While Greg Bahnsen often presents animated demonstrations that a particular worldview is inconsistent (as with Islam and the way the Koran says that the Bible is a previous message of God etc) there is no attempt to actually prove that every non-Christian worldview is inconsistent. Yet, without this proof, the whole of TAG falls apart.

What we have instead is a rough and ready way of fending off other typically encountered worldviews, the sorts of positions encountered while engaged in disputations with non-Christians. It is like a manual for new apologists to go off into the wider world armed with. But of course, the standards for what might prove useful enough for an apologist to do his job are different than the standards for a philosophical argument such as TAG being successfully proved.

So, how do we establish that every other worldview is internally inconsistent? Fundamentally, that is the problem that must be resolved for TAG and the presuppositional position generally to be viable.

  1. First Try – The Michael Jordan example

Michael Butler first responds to the problem by giving an analogy he attributes to Greg Bahnsen:

‘Suppose a basketball player, say Michael Jordan, beats every worthy opponent in one-on-one basketball games.  He can justifiably claim to be the best individual basketball player in the world.  Suppose further that another jealous (and peevish) basketball player who was previously trounced by Jordan resents that he (Jordan) has titled himself “the best player in the world.”  His comeback is, “just because you have beat every current player does not mean that there is not another one coming who is better than you.”  Jordan’s response can be anticipated; “bring on my next opponent.”  The theoretical possibility that there may be another player better than Jordan is not a concern to him.  In the world of basketball, it is the one who is actually the best player, and not who is possibly be the best player, that is of importance.  In the practice of apologetics, things are similar.  What matters are actual worldviews not possible worldviews’. https://presupp101.wordpress.com/2014/07/14/the-transcendental-argument-for-gods-existence/

Now this ‘comeback’ is demonstrably wide of the mark. In an important sense it is possible worldviews and not just the actual worldviews that matters here, even for the practice of apologetics. There is a logical gap between Jordan’s unbroken record of success and the truth of his being the ‘best’ basketball player. It is not logically impossible for him to win every game he plays and yet not be the best player. Likewise, in the case of worldviews, there is a logical gap between the apologist’s unbroken record of being successful in debate, and the truth of the Christian worldview she defends. It is not logically impossible for someone to win every debate they ever engage in, and yet argue for a false thesis.

The reason the standards are so strict is due to the strength of the claim being made by TAG, point 2) from above. The claim is that the Christian God is a necessary condition on human experience, this means that if there were even one possible non-Christian worldview that could also account for human experience just as well as the Christian one, then the Christian view would lose its status as a necessary condition on the intelligibility of human experience. It might still be able to lay claim to being a ‘sufficient condition’, but it could no longer be claimed to be a necessary condition, which was needed for the proof to go through. This would stop the argument working backwards from the intelligibility of experience to the existence of the Christian God. If, for example, there were an atheist position, Z, which could account for human experience just as well as the Christian one, then one could only work from the intelligibility of experience to the disjunction of the two positions; either the Christian worldview is true or Z is true. This would be no proof of the truth of the Christian worldview then.

If we were to take seriously Butler’s claim that what matters are actual worldviews, then we would have to weaken the argument accordingly. So if we rephrased his articulation of the argument, but made it explicit that we were only talking about actually held worldviews, it would look like the following:

It starts with human experience; such things as science, love, rationality and moral duties.  It then asserts that the existence of the Christian God is the necessary precondition of such experiences.  Finally, it proves this indirectly by demonstrating the impossibility of any of the actually held contraries.

This basically just says: there cannot be a consistent non-Christian worldview because I have not seen one before. It is an elementary inductive fallacy. Even if all of the actually held worldviews were internally contradictory, this would not mean that there wasn’t a possible worldview which wasn’t. So the argument thus stated is invalid.

Stating that we are doing apologetics, where the standards are lower, is not a response. The purpose of apologetics is to provide a ‘reasoned defense of the faith’. An invalid argument is not a reasoned defense of the faith.[1]

To bring out the absurdity of thinking that the Michael Jordan type response is viable consider that if it was actually held worldviews that mattered, rather than merely possible worldviews, then one could prove that God existed by killing everyone who wasn’t a Christian, thus leaving Christianity as the only actually held worldview. This, of course, would not prove it to be correct.

Even though Butler says that Bahnsen’s analogy “hits the mark”, he also sees that it is inadequate, and states the problem clearly:

‘If there are an infinite number of worldviews and TAG only refutes a small slice of them, if one may speak this way, then it has not established that Christianity is the necessary precondition of human intelligibility.  That is, even granting that TAG demonstrates the absurdity of all actual worldviews, it does not follow that all possible worldviews are likewise absurd.’

Butler acknowledges that Bahnsen’s response is unsuccessful, on the basis that “winning the debate and proving that Christianity is the necessary precondition of human experience are two different things”. In this, Butler is quite right.

4. Second Try – Only Two Worldviews

Butler goes on to provide a second response by Bahnsen, and this time one he seems to endorse. Here is the quote in full:

‘But Bahnsen makes the further point is that this criticism misses the thrust of TAG altogether.  TAG argues for the impossibility of the contrary (the non-Christian worldview) and not the impossibility of an infinite number of possible worldviews.  TAG does not establish the necessity of Christianity by inductively refuting each and every possible non-Christian worldview (as finite proponents of TAG, this is an impossible task), but rather contends that the contrary of Christianity (any view that denies the Christian view of God) is shown to be impossible.  And if the negation of Christianity is false, Christianity is proved true.  In other words, the structure of the argument is a disjunctive syllogism.  Either A or ~A, ~~A, therefore, A.

At this point the clever opponent will simply deny the first premise.  He will contend that it should not be construed as a disjunction of a contradiction, but a simple disjunction.  The argument should thus be restated along the following lines: A or B, ~B, therefore, A. And once this move is made he will then contend that while the argument is valid, the first premise involves a false dilemma.  That is, he will grant that given A or B and the negation of B, A does indeed follow, but nevertheless maintain that the argument is unsound because the first premise (A or B) is not true.  The reason being that there are more possibilities than just A and B.  Given a true first premise, A or B or C or D … n, the negation of B merely entails that A along with the disjunction of other propositions besides B (C, D,…n) follows.

In order for this to be successful, it is incumbent upon the opponent of TAG to defend two claims.  First, he must defend the contention that the original first premise is not the disjunction of a contradiction and, second, he must show that there are other possible disjuncts besides B (what we can call the view that is opposed to the Christian worldview).’

The argument seems to be as follows: There is a confusion about what TAG actually claims. In this telling, the argument only says that the negation of the Christian worldview is inconsistent, which means that the options needed to be refuted have gone from seeming to be infinite to actually only being one case. This means the process of performing the demonstration that no non-Christian worldview is consistent should be easy in principle to do, as only one thing needs to be shown to be inconsistent, namely the negation of the Christian worldview.

If the reply comes from the opponent of TAG that it is not a question of refuting only one case but of refuting an infinite number of them, then Butler claims that it is “incumbent upon the opponent of TAG to show that this is the case”, i.e. that “there are other possible disjunctions of other propositions besides B”.

However, this is a shifting of the burden of proof; the proponent of TAG is setting out their premises for the argument, and they have to justify them. It is not incumbent on the opponent of the argument to justify their negation first.

Even though the burden is being fallaciously shifted, it is a burden that is easily met. All that has to be established (in order to show that it is B or C or D… rather than just ~A) is that there is more than one distinct non-Christian worldview. So here are two: the atheist worldview and the Islamic worldview. Each of these are treated separately by Bahnsen, indicating that he thinks of them as separate entities, deserving of distinct refutation. If there was only one alternative worldview there would be no need for separate refutations in these cases. The quote by Kant that Butler puts at the very start of his article explains this very point:

‘If, therefore, we observe the dogmatist coming forward with ten proofs, we can be quite sure that he really has none. For had he one that yielded . . . apodeictic proof, what need would he have of the others?’   –Immanuel Kant

The fact that Bahnsen offers a distinct refutation to the atheist as to the Muslim indicates that he considers them to have separate worldviews, otherwise he would only come with one refutation.

And there is no reason to think that there are only two worldviews, because there are combinations of philosophical positions that can form separate worldviews. An atheist can be a materialist or an idealist, a nominalist or a Platonist, a monist or a dualist, a determinist or an libertarian, an intuitionist or a formalist, etc, etc. So surely, it is quite evident that there is a huge number of potential worldviews, and quite possibly an infinite number. So even though I deny that I had to prove that there is more than one non-Christian worldview (due to the illegitimate shifting of the burden of proof), it is a burden that is trivially easy to meet, so Butler is back facing the issue of having to rule out all of the distinct alternative worldviews.

However, there is an even more pressing issue. And this relates to the other point on which Butler claims that the opponent of TAG has to justify, namely: the original first premise is not the disjunction of a contradiction. In a sense, it doesn’t matter if we take it to be the disjunction of a contradiction. Bahnsen’s claim was that all that needs to be shown is that the negation of the Christian worldview was inconsistent. But what does the ‘negation of a worldview’ actually mean? The usual set-theoretical operation that negation corresponds to is compliment; i.e. the result of removing something from a domain of discourse. So imagine a set, W, which contains all the possible worldviews (including the Christian worldview, WCh) as its elements;

W = {WCh, W1, W2, … Wn}.

If negation is compliment, then the negation of the Christian worldview (‘~A’) would be everything in W that wasn’t the Christian worldview;

‘~A’ = {W – WCh} = {W1, W2, … Wn}.

Therefore, ‘the negation of the Christian worldview’ is just ‘all the worldviews that are not the Christian worldview’; they mean the same thing. To put it in Butler’s terms: ~A = {B, C, D…n}. Therefore it doesn’t matter if we have to refute the negation of the Christian worldview, because this means the same as refuting all the non-Christian worldviews. This would mean that Bahnsen has just restated the objection and not countered it at all. This is a simple logical issue. It indicates a lack of logical sophistication in Bahnsen’s argument, and presuppositionalism in general, that this hasn’t been grasped before.

In fact, it seems easy to prove that there cannot be one method which disproves every non-Christian worldview, because there cannot be one contradiction that they all share. One natural way of understanding worldviews is that a worldview is just a list of propositions that an agent believes to be true. So if I believe that God exists, then the proposition ‘God exists’ is in my worldview set. The set of all possible worldviews is then the set of all sets of propositions. If there are no further restrictions on this then it is logically provable (and trivially so) that the intersection of all the worldviews is empty; i.e. there is no common element, say p, to every set, and thus no contradiction, say p & ~p that they all share.

One could put the point even more simply, as follows. The claim is that every non-Christian worldview is internally incoherent. If by ‘worldview’ we understand a set of propositions believed to be true by an agent, and by ‘internally incoherent’ we mean that the set is inconsistent (i.e. contains a proposition and its negation), then consider the non-Christian worldview that contains only one belief, i.e. {p}. This set is plainly not inconsistent. The retort will likely be that this ultra-simple worldview cannot ‘account for the intelligibility of human experience’. If so, what are the minimal conditions under which a set of beliefs could achieve this? It is not on the opponent of TAG to provide this analysis; all she has to do is point out that without this analysis the proof cannot be claimed to be established. The proponent of TAG needs to provide this analysis as part of the proof itself.

  1. Last Try – Blame Autonomy

There is one final attempt at bridging this gap, which directly focuses on this issue, by which I mean it directly focuses on something that all non-Christian worldviews have in common, and in virtue of which they are necessarily inconsistent.

What, then, is the nature of the non-Christian worldview? Simply put, all non-Christian systems presuppose that experience can be accounted for on autonomous lines. The non-Christian worldviews share the common feature that experience can be made sense of independently of God and his revelatory word. Butler – https://presupp101.wordpress.com/2014/07/14/the-transcendental-argument-for-gods-existence/

Here then, seems to lie the root of the issue for the Van Tillian presuppositionalist. They argue that they can conflate every non-Christian worldview on the basis that they are all ‘autonomous reasoning’ worldviews, as opposed to the Christian one in which independent reasoning is subordinated to the word of God[2]. So the idea is that there is something wrong with the assumption that one can reason ‘autonomously’, which inevitably leads to self-contradiction. Butler continues:

‘From this we can see that Van Til is correct, “We have constantly sought to bring out that all forms of antitheistic thinking can be reduced to one.” Bahnsen elaborates on this important insight:

‘Despite “family squabbles” and secondary deviations among unregenerate men in their thinking, they are united at the basic level in setting aside the Christian conception of God. The indirect manner of proving the Christian position is thus to exhibit the intelligibility of reasoning, science, morality, etc., within the context of biblical presuppositions…and then to make an internal criticism of the presuppositions of autonomous thought (in whatever form it is presently being discussed) in order to show that it destroys the possibility of proving, understanding, or communicating anything.’’

It seems like progress has been made towards addressing how one could prove every alternative worldview is internally inconsistent, namely by positing ‘autonomous reasoning’ as the common element in every non-Christian worldview. However, really nothing has been put forward to get round the basic logical objection. The quote from Bahnsen that Butler cites as ‘elaborating’ on Van Til’s important insight assumes that Van Til’s insight is true, otherwise we are back to the Michael Jordan problem from before, in that refuting the position currently being presented is insufficient to establish that every worldview is inconsistent. This problem remains unless there is some way of establishing that the criticism being leveled also applies to every non-Christian worldview. We have been told that this can be done, and they way of doing it has something to do with autonomous reasoning. But what is it about autonomous reasoning that leads inevitably to internal inconsistency? Nothing in Bahnsen’s quote brings this to the fore. This is what needs to be demonstrated, otherwise an equivalent counterclaim can be made: that there is something inherently inconsistent about non-autonomous reasoning. If we do not have to say what it is about a certain type of reasoning that inevitably leads to inconsistency, then each side can level its own unsupported assertion. There must be more than a simple assertion that autonomous reasoning leads to an internal contradiction, otherwise this is no better than just saying that God somehow guarantees it. So it looked like progress was being made, but without some further argument we are left with unsupported assertion.

At this point, Butler seems to declare that the game has been won already, as the very next paragraph demonstrates:

‘Thus the Christian apologist may boldly assert that without an absolute personal being as the foundation of all things, there is no possibility of ethics. Without the ontological Trinity as the fount of all being, there is no possibility of unifying the particulars of human experience. Without the combined doctrines of the Trinity and man being God’s image bearer there is no possibility of predication and thus language. Without the doctrine of God’s sovereignty and providence there is not ground for inductive logic and science. Without a good and all-powerful God that creates both man and the natural realm there is no reason to believe that our senses are reliable. From these considerations it is clear why TAG is often described as an argument that proves the impossibility of the contrary.’

Each time the words ‘there is no possibility of…’ or ‘there is no ground for…’ occur, this claim has not been supported. At most, there is the Michael Jordan example, where no actually held worldview has managed to account for these issues, but as we saw this is insufficient to prove that there is no other worldview that could.

Thus, as the argument stands, TAG is unproven.

  1. Conclusion

I have offered here an analysis of TAG that appears to show the following: TAG has not been established, and TAG probably cannot be established. Moreover, I offer what I think is the best way to counter the presuppositional apologetic; do not get tempted to respond by showing that your ‘worldview’ is internally consistent, or to show that the Christian worldview is not internally consistent. Merely ask for the proof that no worldview than the Christian one is internally consistent. If the proponent of TAG proceeds to try to undermine your particular worldview, then concede (for the sake of the argument) that your worldview is inconsistent, but still press for the general proof that no other worldview can be consistent. The initial idea with presuppositionalism was to move the burden of the argument from the Christian to the opponent of Christianity; however, for TAG to be established actually has a large burden of responsibility. All I am advocating is that we acknowledge this fact.

The best representatives of the presuppositional apologetic are trying to illicit a ‘Copernican’ shift in the way that the worldview is argued for. The worst representatives are not trying to do this. What they are up to is trying to confuse the non-Christian by demanding philosophical justification for abstract concepts like truth, logic, morality, etc, instead of addressing the actual arguments against Christianity. Any confusion on the part of the interlocutor is then pounced on as evidence that the argument has been won by the Christian. There is a conceit behind such tactics, in that the argument is not being offered honestly. Behind all this is the view that autonomous thought, which is basically thinking for yourself, is the problem; and it is going to be hard to win an argument with someone who thinks that independent thinking is morally wrong. Believing that independent thought is a sin seems to me to be a hallmark of brainwashing, and at the very least a rejection of the enlightenment values that are typical of philosophical argumentation generally. It seems to me that they don’t want to actually win an argument by being right, but instead they want to win an argument by exploiting a sense of philosophical vertigo and then using this vulnerability as an angle to hard-sell religious dogma as the answer.

[1] The essence of the ‘inductive’ fallacy is that an inductive argument is being offered as a deductive argument. However, one could simply construe the unbroken record of success of Michael Jordan as inductive support for the conclusion that he is the best basketball player. If the proponent of TAG wanted to take this move however it would be of no help. It would remove the charge that the argument was invalid, but only by construing it as an inductive argument. If this course was taken then one could never establish that the conclusion was a necessary precondition for human experience; no inductive argument could reach such a strong conclusion.

[2]There are two objections here: 1) autonomy with respect to reasoning is not unique to the Christian worldview (what prevents other monotheisms from claiming that they also subordinate their reasoning to their god?), and 2) there are Christian worldviews where the intellect is not subordinated to the word of God (there are autonomous Christian worldviews; in fact, almost all conceptions of Christianity apart from the Van Tilian presuppositionalist account do not explicitly subordinate the intellect to the word of God). So the equivalence of Christian worldview with non-autonomous reasoning fails in both directions.