Logic and God’s Character

0. Introduction

Vern Poytress is professor of New Testament interpretation at Westminster Theological Seminary. He has a handy website, which he runs with John Frame, on which he has put a lot of his published work available for free. In particular, he has a copy of his book Logic: A God Centred Approach to the Foundation of Western ThoughtIn this post, I want to focus on a particular small section of the book, which is Chapter 7 (p. 62 – 68). The chapter is entitled ‘Logic Revealing God’, and in it Poytress addresses the question of whether logic is dependent on God, or if God is dependent on logic. As he says, “We seem to be on the horns of a dilemma” (p. 63).

I will go through the chapter quite closely, and it might be worth reading as it is not long (although I will provide plenty of quotes from the original). It is an instructive chapter because it highlights many of the key themes and ideas that we see presuppositionalists making in their positive arguments. It is also done by a professor in a theological seminary, with a very impressive resume, including a PhD in mathematics from Harvard, and a ThD in New Testament Studies from Stellenbosch, South Africa. Therefore, the presentation of the argument should be pretty strong. And I do think that the book is quite readable, and is packed full of great learning material for anyone wanting to study logic.

However, I think that the sections of the book which deal with the theological and metaphysical underpinnings of his view of logic, such as the one I will explore here, leave a lot to be desired. Hopefully, what I will say will be clear, and my criticisms will be justified.

  1. The Dilemma 

The dilemma that Poytress refers to is not spelled out explicitly, but it seems easily recoverable from what he does say. The opening line in the chapter is: “Is logic independent of God?” To start us off, it is quite natural to see logic as independent from the existence of human beings, as Poytress explains:

“Logic is independent of any particular human being and of humanity as a whole. If all human beings were to die, and Felix the cat were to survive, it would still be the case that Felix is a carnivore. The logic leading to this conclusion would still be valid … This hypothetical situation shows that logic is independent of humanity.” (p. 63)

The example that Poytress gives is slightly confusing, as the truth of the statement “Felix is a carnivore” does not seem to be merely a matter of logic, at least not a paradigmatic one. However, it is clear that the idea of independence that is in play involves the following sort of relation:

Independence X is independent of Y   iff   X would still exist even if Y did not exist

The logical relation he highlights (involving the cat) would hold even if people did not exist, and is thus independent from the existence of people. It follows that X is dependent on Y if and only if the independence condition above fails.

The cat example seems to be mixing up a few different things at the same time. The classification of Felix as a carnivore does not depend on the existence of humans, in that whether people exist or not will not change whether a cat eats meat or not. Yet this fact does not seem to be a purely logical fact, and so the independence that it establishes is not really of logic from the existence of human beings.

It seems to me that an example which makes the point he expresses with “logic is independent of any particular human being and of humanity as a whole,” would be the following. Consider the following inference:

  1. All men are mortal
  2. Socrates is a man
  3. Therefore, Socrates is mortal.

The conclusion follows from the premises, and it does so regardless of whether Socrates exists or not. As it happens, Socrates does not exist (any longer), but this does not make the inference any less valid than when he did exist. Even if Socrates turns out to have been entirely a fictional character who never existed at all, the inference is still valid.

And indeed, the conclusion follows from the premises, regardless of whether anyone exists or not; even if everyone were to die in a nuclear war tomorrow, the above inference would remain valid. Even if there had never been any people at all, the inference would remain valid. At least, that is the thought.

Part of the reason for this thought is that we do not need to refer to the existence of any particular thing when coming to determine whether an inference is valid. We consult what it is that actually determines the validity of the inference, and in doing so we do not have to check to see if any particular thing exists. And what it is that the validity of the inference depends on is something like one of the following candidate considerations:

  • An inference is valid if and only if it is possessing the correct logical form.
  • An inference is valid if and only if it is truth-preserving.

Exactly how we cash this out is contentious of course, but I take it that something like these sorts of example is going to be correct. In Aristotelian logic, for example, the forms Barbara and Celerant are simply given as valid (they are the so-called ‘perfect forms’), and so is any form which is transformable into either of one of the perfect forms via the conversion rules. Different logical systems have different conceptions of what the ‘correct logical form’ is, but one thing that seems obvious is that the existence or not of any particular person, or of humanity in general, is irrelevant to the question of whether a given inference is valid or not. It is a different type of consideration that is relevant.

But if this (or something like this) is what the validity of the inference depends on, then whether it is valid or not isn’t just independent from the existence of human beings, but is independent from the existence of any existing thing – including God.

Here is how Poytress explains this idea:

“Through the ages, philosophers are the ones who have done most of the reflection on logic. And philosophers have mostly thought that logic is just “there.” According to their thinking, it is an impersonal something. Their thinking then says that, if a personal God exists, or if multiple gods exist, as the Greek and Roman polytheists believed, these personal beings are subject to the laws of logic, as is everything else in the world. Logic is a kind of cold, Spockian ideal.” (p. 62)

As I have explained, it is not just that philosophers have postulated logic as being just there, without any motivation. There are reasons, like the independence considerations I outlined, for thinking that any given inference is valid or invalid independently from the existence of any particular thing. It follows from these considerations that logic is not itself dependent on any particular thing, and ‘just is’ (as Poytress puts it).

2. Conflict

As a Christian, such a conclusion brings Poytress into conflict with his core theological doctrines. As he explains:

“This view has the effect of making logic an absolute above God, to which God himself is subjected. This view in fact is radically antagonistic to the biblical idea that God is absolute and that everything else is radically subject to him: ‘The Lord has established his throne in the heavens, and his kingdom rules over all’ (Ps. 103:19).” (p. 62)

Thus, logic seems like it is independent of God, because it seems independent of the existence of anything, yet the doctrine of God being absolute (in Poytress’ sense) requires that everything is dependent on God. I take it that this is the dilemma that he faces:

  • On the one hand, logic is independent from the existence of God (as it seems independent from the existence of any entity whatsoever) but that compromises God’s absoluteness (God seems to be subordinate in some sense to logic).
  • On the other hand, logic is dependent on God, which restores the absoluteness of God, but then we are owed some kind of story about how it is that the validity of an argument depends on the existence of God.

This dilemma can be put as follows:

Is God dependent on logic, or is logic dependent on God?

Poytress takes the second horn, and part of his endeavour in the chapter is to bring out how it is that we see God in logic, how logic ‘reveals God’, as a way of bolstering the claim that logic depends on God.

As a first pass, he says:

“The Bible provides resources for moving beyond this apparent dilemma.” (p. 63)

He provides three examples, which are:

  1. “God is dependable and faithful in his character”
  2. “the Bible teaches the distinction between Creator and creature”
  3. “we as human beings are made in the image of God”

Let’s go through each of these and see what he has to say about each of them.

3. “God is dependable and faithful in his character”

With regards to 1, Poytress points to Exodus 34:6, which mentions that God is faithful, and he then explains:

“The constancy of God’s character provides an absolute basis for us to trust in his faithfulness to us. And this faithfulness includes logical consistency rather than illogicality. God “cannot deny himself” (2 Tim. 2:13). He always acts in accordance with who he is.” (p. 63)

It is not clear to me how this engages with our question, which was whether logic depends on God or God depends on logic. Poytress is identifying the faithfulness, logical consistency and inability to deny himself as three special properties that God has, but to me the possession of these properties is irrelevant to the question at hand. I will try to explain my worry with a thought experiment:

Imagine I were to build a robot. And let’s say that I build the robot in such a way that it could not knowingly lie. This would mean that I program it in such a way that it cannot provide any output which is the contradicts any of the stored data it has in its memory banks (or something like that). If so, then my robot would be analogous in some sense to this description of God. It is, in effect, programmed to be honest. Given that a robot cannot do anything which it is not programmed to do, I would be able to trust in its ‘faithfulness’, in that I could know for sure that any output it generates is consistent with its data banks. Arguably, a robot like this is also logically consistent by definition (assuming the programming is consistent), and because it cannot lie, it cannot deny itself in the relevant sense either. Thus, my robot is perfectly faithful, logically consistent and cannot deny itself. Yet, this would not establish that the validity of any given inference was dependent on the existence of the robot, however. And if not, then it is not clear why these properties being possessed by God would be relevant to establishing anything like the horn of the dilemma that Poytress is going for either.

Perhaps you have some niggling objection here. The robot case isn’t really analogous to God, you might be saying. And that is quite true. For instance, no matter how advanced, my robot wouldn’t be all-knowing. And no matter how reliable its programming is, its programming might become corrupted. Either of these indicate the possibility of some kind of error. Because of the possibility of error like this I shouldn’t trust what it tells me with 100% certainty, and this makes the two cases unalike.

However, seeing as this is just a thought experiment, imagine that (somehow) I were to make a robot which did know everything, and couldn’t have its programming corrupted. Would this mean that logic now became dependent on the existence of the robot? Would the validity of an inference now depend on the existence of this robot? I see no reason for thinking that making these imaginary improvements to my robot could possibly have this effect.

As far as I can understand, an entity’s reliability, faithfulness, or inability to self-deny, etc, can never be relevant for making its existence something upon which the validity of an inference depends. If Poytress has some reason for thinking that the possession of these properties by God makes him the thing whose existence the validity of an argument depends, he spends no time explaining them here.

There are a few options at this point.

  1. By possessing these qualities, my robot becomes a thing that the validity of an inference is dependent on.
  2. The possession of these properties by my robot does not qualify it for being the thing that validity depends on, but they are what qualifies God for this role.
  3. The possession of these properties are not what qualifies anything for this role.

The first option seems prima facie implausible, and at the very least we have been given no reason to think that it is true. The second one leaves unanswered why it is that these qualities make God suitable for the role and not the robot, and implies that there are actually additional criteria for playing the role in question which make the difference (i.e. there must be something about God other than the possession of these qualities which distinguishes him from the robot). The third option is that these qualities are not relevant. Unless there is an additional option I cannot see, it seems like Poytress has to go with option 2, and owes us an explanation of the additional criteria.

4. The Bible teaches the distinction between Creator and creature”

So much for the first point. Let’s move on to the second one, which is about the creator/creature distinction. Poytress says the following:

“God alone is Creator and Sovereign and Absolute. We are not. Everything God created is distinct from him. It is all subject to him. Therefore, logic is not a second absolute, over God or beside him. There is only one Absolute, God himself. Logic is in fact an aspect of his character, because it expresses the consistency of God and the faithfulness of God. Consistency and faithfulness belong to the character of God. We can say that they are attributes of God. God is who he is (Ex. 3:14), and what he is includes his consistency and faithfulness. There is nothing more ultimate than God. So God is the source for logic. The character of God includes his logicality.” (p. 63)

This quote can be split into two sections. The first consists of the first five sentences (ending with “There is only one Absolute, God himself”). The first section really just affirms the doctrine of God being absolute. God alone is absolute; we are not absolute; being absolute, everything is dependent on God, including logic. This much is no help resolving the apparent dilemma we were facing earlier. It is just restating one of the two things we are trying to reconcile, i.e. the absoluteness of God. The question is how to fit this idea, of God being absolute, with the intuitive idea that the validity of an inference seems to have nothing to do with the existence of any particular thing. Simply repeating that God is absolute (in contrast to humans) does not shed any light on this issue.

The second part of the quote wanders back into the issue brought up in the previous point, by talking about the faithful character of God, and thus still seems irrelevant. Even if “[c]onsistency and faithfulness belong to the character of God”, how is the validity of an inference dependent on his existence? We are none the wiser.

Poytress does say that God’s ‘logicality’ is included in his character. And it might be thought that this is relevant somehow. After all, we are talking about logic, and ‘logicality’ is the property of being logical. Surely that is the link.

Well, I think it would be a mistake to think that. In some sense, my robot was already logical. It’s ‘brain’ is just a computer, which processes inputs and produces outputs according to some set of rules (its programming). This is a logical process; computer programming is just applied logic. It seems we are in precisely the same position we were in before. We are still left with no reason to think that if this thing did not exist, that an otherwise valid inference would be invalid. Why does being logical mean that logic depends on you? The answer, it seems, is that it doesn’t.

5. “We as human beings are made in the image of God”

On to point three. Here, Poytress is pointing to the fact that we are made in God’s image:

“God has plans and purposes (Isa. 46:10–11). So do we, on our human level (James 4:13; Prov. 16:1). God has thoughts infinitely above ours (Isa. 55:8–9), but we may also have access to his thoughts when he reveals them: “How precious to me are your thoughts, O God!” (Ps. 139:17). We are privileged to think God’s thoughts after him. Our experience of thinking, reasoning, and forming arguments imitates God and reflects the mind of God. Our logic reflects God’s logic. Logic, then, is an aspect of God’s mind. Logic is universal among all human beings in all cultures, because there is only one God, and we are all made in the image of God.” (p. 64)

The idea seems to be as follows. God makes plans, and so do we, although we only make plans on a ‘human level’. God has thoughts, and so do we, although his thoughts are ‘infinitely above ours’. So in this way, we are similar to God, without being the same as God. We are creatures, whereas he is the creator, and our likeness is only imperfect (or ‘analogical’).

The relevant section is when he explains that “our logic reflects God’s logic”, which is because it is us ‘thinking Gods thoughts after him’, in a process which “reflects the mind of God”. Just like with the planning and thinking examples, our grasp of logic is only analogical, which means that we have an imperfect, creaturely understanding in comparison with God’s perfect understanding. Nevertheless, we imitate of God’s thought processes.

The problem with this view is that it invites a Euthyphro-style dilemma immediately. God thinks in a particular way (a logical way) and we are to think in the same sort of way (to imitate and reflect his way of thinking). But, why does God think in this particular way? More precisely, does God think in this way because it is logical way of thinking, or is it a logical way of thinking merely in virtue of it being the way that God thinks? This is just another way of asking the same question we started with, namely: is God dependent on logic or is logic dependent on God? All we have done here is to rephrase it in terms of God’s thinking; is logic dependent on God’s thinking, or is God’s thinking dependent on logic? And there is no reason to think that rephrasing it in this manner will itself constitute any sort of solution to the initial problem.

What Poytress is actually giving us is a reason for why we (should) think in a logical way. We should think in a logical way because that’s the way that God thinks. And, whatever the merits of this point are, this plainly isn’t relevant to the initial question about the relation between logic and God. The best that can be said about this idea is that it is an answer to a different question altogether.

5. Sidebar – Logical Euthryphro 

But it is also rather hopeless as a solution, when we try to run the argument to its logical conclusion. Remember, the first horn was that God thinks in this particular way because it is (independently from him thinking it) a logical way of thinking. Presumably, Poytress would find just as “radically antagonistic to the biblical idea that God is absolute” as the initial claim that God depends on logic. It really just is the same claim. It just says that logic is independent of God. So, he has to opt for the second horn, which is that this way of thinking is logical merely in virtue of being the way that God thinks.

However, there is a problem with this; it makes God’s decision to think in this way (rather than some other way) inexplicable. To sharpen up the discussion, let’s use some examples. We know that there are lots of different logical systems, including classical logic, extensions of classical logic and non-classical logics, etc. Just to take two examples, there is classical logic and intuitionistic logic. They have different fundamental principles, e.g. intuitionistic logic doesn’t have excluded middle as a general law and classical logic does. God thinks in one of these ways and not the other (presumably). Let’s say he thinks classically, and not intuitionistically. If we were to ask why he thinks in this classical way, as opposed to the intuitionistic way, the one thing we cannot say as an answer is that thinking classically is (independently of God thinking like that) the logical way to think. If we tried to say this, then we would in fact be asserting the first horn of the dilemma, which is “radically antagonistic to the biblical idea that God is absolute”.

But what else could possibly be the answer to this question? God thinks classically rather than intuitionistically because … ? It might be that God has a preference for classical logic rather than intuitionistic logic, but this preference itself cannot be based on the idea that classical logic is (independently of God thinking like that) the logical way to think, or we are right back to the initial horn again. So even if he has a preference for classical logic, it can only be based on some other type of consideration, and not that it is itself the logical way to think. But there is nothing else which could be relevant. He may prefer it because he finds it simpler than intuitionistic logic, or because he likes sound of the word ‘classical’, or because he flipped a coin and it landed heads-up rather than tails-up. But whatever the reason, it can only be something which is irrelevant. His reason can only be arbitrary (which just means that it is a decision made without relevant reason). The one thing which could be relevant is ruled out as being the first horn of the dilemma. And that is what is so pressing about this sort of Euthryphro dilemma.

So let’s say we take this horn. It means that if God thinks classically (rather than intuitionistically), and if we were to imitate the way that God thinks (as Poytress urges), then this would produce some kind of explanation for why we think classically rather than intuitionistically. However, because there is no (non-arbitrary) reason why God thinks classically rather than intuionistically, there is correspondingly no real reason why we do either.

Imagine you find me performing a series of actions, walking to and fro in my house, picking things up and putting them down again seemingly at random. If you ask me why I’m doing this, I might say that I have a reason for doing so. Maybe I say to you that these actions performed together will culminate in an effect which I desire. So, maybe I am building something, but I am in the early stages of doing so, just setting out my tools and clearing a space. To you it looks like a random set of actions, but it has a purpose. I have reasons for doing each of the things that I am doing. Maybe once I have explained my purpose, then the series of actions stops looking so random to you.

Now imagine that you come across me performing a series of actions which again seem random to you. You ask me why I am doing these things, and this time I point to the TV, where you see a figure who is performing the very same sorts of actions. I say that I am acting out this person’s actions after him, and reflecting his actions. ‘Well, why is he doing these particular actions?’, I ask. ‘Oh, no reason’, you reply.

I think that in this second situation, we would have to conclude that you are doing something which is different in type to the first example. There your actions had a reason behind them and were not arbitrary, whereas now, you are just mirroring the random actions of the figure on the TV. Really, your actions are just as random as his; there is no reason why you are doing one thing rather than another, because there is no reason why the figure on the TV is doing one thing rather than another. This is what happens if we follow through on the idea that a) we think logically because we are thinking God’s thoughts after him, and b) if logic is not independent of God. Poytress is committed to b), as the other option would be “radically antagonistic” to his idea of God, and he is also urging that we accept a) in the passage we just looked at. Thus, if we go where Poytress urges, we become like the person imitating the random actions of the figure on the TV.

But, surely, this is where God’s characteristics come into play? God is consistent, and faithful, and cannot deny himself. Surely this is relevant. He couldn’t think in an irrational way, because this would mean being inconsistent. In this way, his consistency grounds the type of logic he opts for.

This may seem like a promising rebuttal. However (no surprise), I don’t think it is. Intuitionism is consistent, and many people have found it to be rational. Michael Dummett, for example, argued strongly for intuitionism. It is not the case that someone who prefers intuitionism to classical logic is committed to any contradictions as a result (intuitionistic logic is not inconsistent). They are not necessarily going to deny themselves, or be irrational, or be ‘illogical’ (partly because they would advocate for intuitionism being the correct logic!). None of the considerations that Poytress presents give us any reason to think that God would have any real reason to prefer classical logic over intuitionism based off the character traits that he has identified.

It might even be the case that God likes paraconsistent, or even dialethic logic. If the principle of explosion really were invalid, then God would be dishonest to say that it was valid. If there really were a true contradiction somewhere (and who knows, maybe God has a morally sufficient reason to create one), then God would deny his own act of creation to say that there was not one. Thus, his honesty, truthfullness and consistency could be made to fit with there being contradictions. His characteristics could be retrofitted to be compatible with pretty much any outlandish logical or metaphysical proposal. And this is because they really just float free from, and are orthogonal to, the issues involved in the debates about non-classical logic.

6. Wrapping up

This post is already quite a lot longer than I had anticipated when I started, so I will finish up by briefly going through the final parts of the chapter we are looking at. Those are called ‘Attributes of God’, ‘Divine Attributes of Law’ and ‘The Power of Logic’. In them, Poytress makes the point that logic and God seem to share various properties:


“If an argument is indeed valid, its validity holds for all times and all places. That is, its validity is omnipresent (in all places) and eternal (for all times). Logical validity has these two attributes that are classically attributed to God.” (p. 65)


“If a law for the validity of a syllogism holds for all times, we presuppose that it is the same law through all times … If a syllogism really does display valid reasoning, does it continue to be valid over time? The law— the law governing reasoning—does not change with time. It is immutable. Validity is unchangeable. Immutability is an attribute of God.” (p. 66)

Immaterial yet effective:

“Logic is essentially immaterial and invisible but is known through its effects. Likewise, God is essentially immaterial and invisible but he is known through his acts in the world.” (ibid)


“If we are talking about the real laws, rather than possibly awed human formulations, the laws of logic are also absolutely, infallibly true. Truthfulness is also an attribute of God.” (ibid)

These properties initially do seem to be drawing a close similarity between logic and God. They seem to share a lot of properties together. And initially, this might seem to be reason to think that their doing so is significant. However, consider that the same case could be made for the rules of chess:

There is nothing in the laws of chess which refer to any times and places. If it is true that, according to the rules of chess, a pawn can move two spaces on its first move, then this is true if you play chess in Bulgaria, or in China, or on the moon. It’s truth is independent on location, which means that that rule, if true anywhere, is equally true everywhere else. But also, if we went back in a time machine to prehistoric times, and if we had taken a chess set with us, we would not have to consult the local tribe to see if they had a different set of rules for chess. It would still be true that a pawn can move two spaces on its first move, regardless of what year we are playing in. And this means that the rule’s applicability is independent of time. If it is true at one time, it is true at all times. The rules of chess, it seems, are omnipresent and atemporal as well.

Chess is also immutable. You might be thinking that chess used to be played differently. In the past, people had different rules for chess, so it isn’t immutable – chess has a history. Quite true, chess does have a history. But so does logic (trust me, I am editing a book about it). People have changed how they have thought about logical laws. For instance, the idea of existential import is present in Aristotelian logic, but not in classical logic. If we can sidestep this issue with logic, by saying that the historical development of logic is not relevant for undermining the claim that logic is immutable, then we can also do the same for chess.

The rules of chess are immaterial. We cannot touch them or measure them, etc. Yet they govern how actual pieces of material get moved about on actual chess boards. So the rules of chess are immaterial yet effective.

The rules of chess are true. It is true that a pawn can move two spaces on its first move. That is a truth.

So the rules of chess are omnipresent, atemporal, immutable, immaterial yet effective and true. Therefore, God thinks ‘chessly’? God’s nature reflects the rules of chess?

We could run the same sorts of considerations for any different (consistent) logical system, like Łukasiewicz’s three valued logic. It also has all the same sorts of properties. But can God think classically and also with three truth-values at the same time? Only an inconsistent God could do that. So if God thinks classically, rather than non-classically, there must be something about non-classical logics which means that their possession of the properties that Poytress identifies is not indicative of anything significant. Again, if there is something which makes this difference, we are not given it.

7. Conclusion

I have no doubt that Poytress is a very smart guy. I don’t have it in me to get a PhD in mathematics from Harvard. And he clearly understands logic very well. It is puzzling then that his discussions on the area I have focussed on in this post are so weak. There is really nothing he has said which helps make the case that logic is dependent on God, rather than being independent from God. I can only conclude that this part of his book was not thought through very well. The only other possibility is that he is so determined to fit together certain doctrines that he is unable to see that his arguments are weak in this area. I may look further at other aspects of the same book in later posts, but from what I have read of it so far, I don’t imagine he will change in any particularly significant way.

Induction, God and begging the question

0. Introduction

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

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

  1. Induction

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

All observed a’s are F.

Therefore, all a’s are F.

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

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

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

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

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

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

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

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

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

2. Does induction beg the question?

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

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

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

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

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

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

3. But what if it did?

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

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

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

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

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

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

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

4. Justifying induction with God

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

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

5. Why that doesn’t help

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

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

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

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

6. Conclusion

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






0. Introduction

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

  1. Kantian Autonomy

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

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

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

Kant is quite explicit about the reasons for nonage:

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

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

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

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

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

I hear the cry from all sides: “Do not argue!” The officer says: “Do not argue–drill!” The tax collector: “Do not argue–pay!” The pastor: “Do not argue–believe!” … We find restrictions on freedom everywhere. But which restriction is harmful to enlightenment? Which restriction is innocent, and which advances enlightenment? I reply: the public use of one’s reason must be free at all times, and this alone can bring enlightenment to mankind.”

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

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

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

2. Scientific Authorities

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

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

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

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

3. Religious Nonage 

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

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

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

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

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

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

4. Do I Assume Autonomy? Should I?

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

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

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

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

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

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

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

5. The Paradox of Love

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

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

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

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

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

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

6. Conclusion

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

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.

Accounting for logic – again

0. Introduction

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

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

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

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

  1. ‘What is logic?’ 

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

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

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

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

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

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

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

p ∨ ¬p     (‘either p or not-p‘)

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

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

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

1.1 Logic in the Bible?

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

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

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

1.1.1 Non-Contradiction

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

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

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

1.1.2 Identity

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

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

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

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

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

Alan: I’m Alan Partridge.

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

I’m just going to leave that there.

1.1.3 Excluded Middle

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

‘x is with Jesus’

‘x is against Jesus’

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

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

We could write this in first order logic as follows:

∀x (Wx ∨ Ax)

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

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

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

∀x (Wx ∨ ¬Wx)

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

1.2 The problem

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

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

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

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

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

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

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

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

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

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

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

2. An epistemological foundation for logic

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

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

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

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

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

2.1 They are self-evident.

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

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

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

2.2 They are synthetic a priori knowledge

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

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

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

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

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

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

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

2.3 They are indispensable

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

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

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

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

3. Conclusion

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

Logic 101


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

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

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

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

2) Washington was the first president of America.

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

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

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

We can say 3) a little more perspicuously as

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

This means the same as 3).

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

5) Washington was not the first president of America.

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

6) ~(p)

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

7) Fw

With the negation being:

8) ~(Fw)

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

9) Ag or A~(g)

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

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

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

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

10) Ag or ~(Ag)

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

Pr1. Ag or ~(Ag)

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

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


Pr1. Ag or ~(Ag)

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

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

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

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

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

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

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

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

13) ∃x(Rx)

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

14) ∃x(Bx) and ((x = b) or ~(x = b))

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

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

15) ∃x(Ax) and ((x = g) or ~(x = g))

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

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

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

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

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

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

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

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

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

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

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

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

The Infinite Regress for Revelational Epistemology

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

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

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

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

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

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

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

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

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

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

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

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

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

Thoughts on Jason Petersen’s ‘argument’

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

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

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

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

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

Therefore, a

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

Premise 1)  p & q

Therefore, p

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

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

Premise 1) p

Therefore ~p

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

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

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


The Matt Slick Fallacy – Update

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


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

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

~(p & ~p)

~p                             (i.e. the second option)

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

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

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