The argument from contingency

0. Introduction

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

  1. The argument

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

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

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

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

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

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

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

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

2. Some Responses 

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

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

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

3. My response

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

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

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

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

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

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

4. Conclusion

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

Problems with ‘The Lord of non-Contradiction’

0. Introduction

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

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

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

  1. The argument

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

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

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

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

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

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

1.1 A more formal version of the argument

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

1.2 Initial problems

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

1.2.1 Polytheism

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

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

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

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

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

1.2.2 False dichotomy

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

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

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

2. The Necessary Truth Hypothesis

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

2.1 Epistemic Modality

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


2.2 Metaphysical Modality

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

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

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

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

And in a footnote they say that they

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

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

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

2.2.1 Metaphysical modality and conceivability

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

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

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

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

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

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

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

2.2.2 Conceivability and non-classical laws

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

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

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

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

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

2.2.3 Excluded middle

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

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

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

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

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

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

2.3 Possible worlds 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2.4 Logical Necessity

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

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

3. Propositions are intentional

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

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

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

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

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

3.1 Intentionality

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

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

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

x is intentional iff x is metnal

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

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

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

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

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

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

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

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

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

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

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

3.1.1 The mark of the mental

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


4. Modal shift

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

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

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

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

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

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

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

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

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

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

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

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

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

Anderson and Welty do anticipate this response:

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

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

They have two responses to such a move:

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

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

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

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

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

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

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

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

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

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

Here is an argument for my claim:

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

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

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


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

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

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

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

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

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

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

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

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

5. Conclusion

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

Transcendental arguments and the logic of presupposition.

0. Introduction 

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

1 Transcendental arguments.  

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

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

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

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

1.1 Transcendental arguments in analytic philosophy

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2. TAG

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

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

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

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

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

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

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

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

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

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

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

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

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

2.2. The inadequacy of classical implication

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

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


“…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.