How to answer the Sye-clone: Wittgenstein’s transcendental argument

0. Introduction

In a previous post, I have talked about transcendental arguments as used in philosophy. I briefly mentioned one such argument found in an aphoristic comment in Wittgenstein’s book, On Certainty. In this post, I am going explain a plausible argument which can be extracted from Wittgenstein’s aphorism. Specifically, I will say how this works as a sort of strategy for dealing with various radically sceptical challenges that could be posed to you; i.e. for dealing with the types of ‘Sye-Ten Bruggencate challenge’.

  1. Wittgenstein’s Aphorism

On Certainty is the last book that Wittgenstein composed. Really, it is jut the collected papers that he was working on in the final months of his life, which were published posthumously. Here is the quote that I want to focus on:

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

I want to say that there are two distinct arguments in this passage, which I will call the argument from obligation, and the argument from meaning respectively. I will look at the argument from obligation here, and cover the argument from meaning in a subsequent post.

2. The argument from obligation

The key idea behind the argument from obligation is that in a dream one cannot be under any types of obligation.

Imagine a person, Scrooge let’s call him, who is miserly and mean throughout the day, every day. Each time he gets the chance to be mean to someone, he takes it. However, when Scrooge goes to sleep at night, he always has the same dream, in which he is a kind and generous man. In his dreams, whenever Scrooge gets the chance to be nice to someone, he takes it. If we come to make a moral evaluation of Scrooge, I think that we would have to say that he was an entirely miserly and mean individual. His dream-world generosity does not count at all in favour of him being a good person. Dream actions have no moral value whatsoever.

It follows from this that if one is having a dream, then one is not under any moral obligations with regards to the things in the dream. Imagine you have a dream in which you do something morally wrong, like stealing. Upon waking, although you may still feel guilty about what you did in your dream, you have not actually broken any moral obligations, because you didn’t actually do anything, let alone anything wrong. It was only the illusion of doing a morally wrong action.

To press the point, if I dream that I murder someone in cold blood, I do not need to fear going to prison when I wake up, because I have done nothing wrong. Likewise, if I am playing a one-player computer game, like GTA5, and I decide to randomly kill a passer by in the street (we’ve all been there), I have not actually violated any moral proscription against murder. Dreams, like computer games, are not real contexts as such. They are illusory contexts, ones in which moral choices are not evaluated at all. We might say that they are amoral contexts.

The reason these contexts are amoral is that there are no actual agents playing the roles of the injured parties. The utilitarian does not count as harm violent deeds done to a computer sprite, nor to a character in a dream. A deontologist does not include proscriptions about computer sprites or characters in dreams. Each of these two major meta-ethical schools concerns themselves with real agents, not characters in dreams.

What holds for moral obligation, also holds for rational obligation. Imagine someone, let’s call him Scrooge again, who spends all his time constantly debating people in chat rooms online, but constantly failing to live up to his rational obligations. So, he does things like making arguments that have their conclusions explicitly stated as one of the premises. He makes assertions, such as that p is true, but when asked to justify the claim, passes the burden to his interlocutor to prove that p is false, or he provides a deductively invalid or unsound argument, etc. Whenever he has the chance to duck a rational obligation, he takes it. However, every night Scrooge has the same dream where he is constantly debating people online, but now he is the model rational agent and always abides by the rules of rational discourse. Whenever he makes a claim, he backs it up with either a plausible looking deductively valid argument, or he provides some compelling piece of evidence, etc. However, if we come to assess Scrooge’s behaviour in terms of his rationality, we would have to say that he is actually a very irrational interlocutor. All of his actual interactions have him constantly ducking his rational obligations. Just as in the moral case, the fact that he is very well behaved in his dreams doesn’t count for anything.

So, just as dreams are contexts in which there are no moral obligations (amoral contexts), they are also contexts in which there are no rational obligations (arational contexts).

If this preceding line of argument is correct, then we have an interesting result when faced with a radical sceptical doubt, such as the doubt that one is dreaming. The insight comes out if this sceptical challenge is posed as an explicit question, in the form “how do you know you are not dreaming?”

Here it seems that there are really two options: either you are dreaming, or you are not. As we have seen from the above considerations, part of the difference between being awake and dreaming has to do with the presence of obligations, both moral and rational. So when the question is posed, there are two possibilities – either you are dreaming or you are not – and these correspond to either being under obligations (moral and rational) or not. When dreaming, you are not under any obligations. So, if, during a philosophical conversation, the sceptic asks you to to show that you are not dreaming, then on the assumption that you are in fact dreaming, you are not under any rational obligation to provide any kind of answer. It doesn’t matter if offer an invalid argument as your rebuttal, or just walk away and make a sandwich. You are not really having a philosophical conversation at all, and are not really under any rational obligation to justify your claims, or argue consistently, etc. In a dream context, these obligations are just not present. So, if you are dreaming, you do not have to worry about answering the sceptical question.

If you are not dreaming, then you are under all moral and rational obligations. But that means that you need to provide justifications for your positions on things to remain rational, only if you are not dreaming. Thus, being awake is a necessary condition of being under the rational obligation to respond to a potential sceptical challenge.

Here is the argument in premise-conclusion form:

  1. For all rationally obligatory actions x, one is obliged to do x if, and only if, one is awake (i.e. not dreaming).
  2. Answering the sceptic’s question “how do you know you are not dreaming?” is a rational obligation.
  3. Therefore, one is obliged to answer the question “how do you know you are not dreaming?” if, and only if, one is awake (i.e. not dreaming).

It has the form, where O(x) means ‘x is rationally obligatory’, p means ‘you are awake’, and a is ‘answering the sceptic’:

  1. ∀(x), O(x) iff p
  2. O(a)
  3. Therefore, O(a) iff p     (∀-instantiation)

3. Conclusion

What the argument from obligation argument shows is that one is not under the rational obligation to answer a sceptic who wants you to justify that you are not dreaming. If you are dreaming, then you are not under any actual challenge to defend yourself against, on pain of being irrational. In fact, nobody has challenged you at all; there is no sceptic, there is no challenge. The whole context is illusory. On the other hand, if you are in fact under the obligation to make some kind of rational response to the challenge, this must be because you are really in a conversation with someone, and not dreaming the exchange. Thus, being awake is a necessary precondition for the intelligibility of the sceptical challenge itself. We must presuppose that we are awake for the question to be something we are rationally obliged to respond to.

Transcendental arguments and the logic of presupposition.

0. Introduction 

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

1 Transcendental arguments.  

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

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

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

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

1.1 Transcendental arguments in analytic philosophy

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2. TAG

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

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

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

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

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

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

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

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

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

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

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

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

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

2.2. The inadequacy of classical implication

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

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

and,

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

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

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

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

3. The logic of  presupposition.

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

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

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

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

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

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

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

3.1 TAG with Presupposition instead of Implication

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

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

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

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

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

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

3.2 Presuppositional validity

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

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

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

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

But the following is not:

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

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

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

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

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

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

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

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

4. Problems

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

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

4.1 Arbitrariness, or Inconsistency?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

4.2 The Disanalogy

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

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

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

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

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

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

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

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

1b. God exists.

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

2a. I have stopped beating my wife.

2b. I have a wife.

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

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

4.3 Metaphysical dependence

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

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

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

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

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

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

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

5. Conclusion. 

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

Accounting for logic – again

0. Introduction

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

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

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

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

  1. ‘What is logic?’ 

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

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

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

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

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

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

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

p ∨ ¬p     (‘either p or not-p‘)

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

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

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

1.1 Logic in the Bible?

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

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

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

1.1.1 Non-Contradiction

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

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

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

1.1.2 Identity

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

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

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

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

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

Alan: I’m Alan Partridge.

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

I’m just going to leave that there.

1.1.3 Excluded Middle

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

‘x is with Jesus’

‘x is against Jesus’

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

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

We could write this in first order logic as follows:

∀x (Wx ∨ Ax)

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

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

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

∀x (Wx ∨ ¬Wx)

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

1.2 The problem

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

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

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

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

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

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

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

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

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

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

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

2. An epistemological foundation for logic

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

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

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

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

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

2.1 They are self-evident.

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

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

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

2.2 They are synthetic a priori knowledge

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

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

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

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

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

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

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

2.3 They are indispensable

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

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

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

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

3. Conclusion

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

The “Matt Slick Fallacy Fallacy” Fallacy

Introduction

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

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

“…sorry, Malpass. You blew it

and

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

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

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

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

False substitution fallacy

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

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

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

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

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

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

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

Cause and existence

Kitt says about me:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Here is a candidate:

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

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

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

5) ‘God is the cause of logic’

6) ‘God is the existence of logic’

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

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

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

Can and does

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

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

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

7) God or not-God does account for x

8) God or not-God can account for x

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

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

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

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

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

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

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

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

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

1. Either God, or not-God.

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

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

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

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

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

3. Therefore, God can.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

False dichotomy

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

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

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

Either:

A. ‘God caused it’ or

B. ‘Something other than God caused it’. 

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

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

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

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

10) ‘Nothing caused b

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

Causing logic

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

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

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

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

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

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

Trivialism

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

Triviality)                        ∀p: p & ¬p

(alternatively: ∀p: Tp & Fp)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Nihilism

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

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

(alternatively: ∀p: Fp)

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

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

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

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

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

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

Conclusion

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

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 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.