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.

The Compatibility of Omniscience and Freedom

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

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

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

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

◊p &  ◊~p

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

If Kp, then □p

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

If □p, then ~◊~p

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


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

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

Premise 2) God knows that p.

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

Conclusion 1) Therefore, p is necessary.

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

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

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


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


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

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

Premise 2) Kp                                      (assumption)

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

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

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

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

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


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

Premise 1.

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

Premise 2.

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

Premise 3.

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

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

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

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

Kp iff p

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

□(Kp iff p)

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

3.1) □(If Kp, then p)

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

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

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

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

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

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

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

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

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

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

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

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

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


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

Thoughts on Jason Petersen’s ‘argument’

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

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

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

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

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

Therefore, a

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

Premise 1)  p & q

Therefore, p

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

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

Premise 1) p

Therefore ~p

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

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

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


The Matt Slick Fallacy – Update

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


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

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

~(p & ~p)

~p                             (i.e. the second option)

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

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

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