How to completely refute ‘How to completely refute atheism’

0. Introduction

Ok. The title is misleading, but I thought it was funny. And it’s not ‘completely’ false. I’m not going to ‘completely’ refute it, but I am going to pick holes in it.

How to completely refute atheism‘, if you don’t know, is a video made by Apologia Studios, in which Jeff Durbin tells us how to completely refute atheism. Except he doesn’t. He offers arguments which are demonstrably flawed.

In what follows, I use some snippets from his video (under fair use), but please do check that I am not misrepresenting him by watching his entire video or any of the videos at his YouYube page.

  1. Fake agnosticism

To begin with, I snipped a bit where Durbin blatantly straw-mans agnosticism:

According to Durbin, “agnosticism … says that we can’t know, ultimately, anything propositionally”. His analysis is that the word is made up of the prefix ‘a’, which he says means “negation”, and the word ‘gnosis’, which he says means “knowledge”. He says that the word ‘agnosticism’ means that “We are without knowledge; knowledge cannot be gained or had; we cannot know.” On Durbin’s view, the agnostic says “We can’t know anything”, to which he replies “Do you know that?” He thinks that this shows that agnosticism is self-refuting.

Durbin doesn’t state any arguments formally, but we can see the general outline very easily. The inconsistency he is pointing out is that if the agnostic says “I know that I don’t know anything”, then this entails a contradiction. He knows nothing; but by knowing that, he does know something. So he knows both nothing and something.

     2. Pyrrhonian scepticism

Almost nobody holds that “we cannot know anything”. It is difficult not to think that Durbin was just making agnosticism look worse than it actually is, to make the job of refuting it easier. If he did, then he would clearly be advancing a straw man against agnosticism. And his description of agnosticism obviously unfairly saddles it with the universal rejection of all knowledge. We will come back to this in a moment, but before we do, I want to look at a position which really is the target of Durbin’s attack. Because, even if it is a straw-man, and it doesn’t really address agnosticism, we can still ask how effectively he argues against this straw-man. I argue that it isn’t really a problem even for the straw-man.

There is a position in philosophy which is quite close to the position that Durbin is actually attacking, involving the denial of all knowledge. And that is Pyrrhonian Scepticism. Pyrrho (c. 300BC) is reported to have said:

“…that things are equally indifferent and unstable and indeterminate; for this reason, neither our perceptions nor our beliefs tell the truth or lie. For this reason, then, we should not trust them, but should be without opinions and without inclinations and without wavering, saying about each single thing that it no more is than is not, or both is and is not, or neither is nor is not” (Aristocles, quoted from the Stanford article)

It is not a stretch to say that Pyrrho’s position is that ‘we cannot know anything’. If so, then Pyrrhonian Scepticism is the position that Durbin’s argument was attacking. His idea is that this sort of extreme scepticism refutes itself. And this line of attack certainly has some appeal to it. We derived a contradiction from the assertion that ‘I know that I know nothing’. So imagine that I were to go around saying ‘My view is that Pyrrhonian Scepticism scepticism is true’. This would make me vulnerable to Durbin’s line of attack, as he could ask me whether I know that Pyrrhonian scepticism is true. If I said that I did know it was true, then I would be contradicting the main claim of Pyrrhonian scepticism; but if I said that I didn’t know it, then I would be tacitly conceding that it might not be true after all.

It’s not clear that even this extreme position is vulnerable to Durbin’s attack though. I could say that when I affirm Pyrrhonian scepticism, I am not making a knowledge claim at all; the content of the claim that Pyrrhonian Scepticism is true could plausibly be taken to be: ‘I believe that Pyrrhonian scepticism is true’. If so, I would be saying that ‘I believe that (I can’t know anything)’. If Durbin asked his gotcha question, ‘But do you know that?’, I could reply ‘No, I do not’, quite without self-contradiction. If Durbin asked ‘But do you believe that?’, I could reply ‘Yes, I do’, also quite without contradiction. So a Pyrrhonian sceptic can construe the statement of their own doctrine as merely a belief claim rather than a knowledge claim, and thus avoid Durbin’s accusation of self contradiction.

However, even if we forget this nuance, and insist that anyone who claims to be a Pyrrhonian sceptic is making a knowledge claim, we still have not refuted Pyrrhonian scepticism with this argument. The most we would have demonstrated is an inconsistency between the sceptic’s behaviour and the content of Pyrrhonian scepticism. It doesn’t prove that Pyrrhonian scepticism is wrong; it just shows that the person making the claim isn’t acting like a good Pyrrhonian sceptic. A good Pyrrhonian sceptic should not make knowledge claims. But criticising a claim on the grounds that the person making the claim’s actions are inconsistent with it, is to commit the tu quoque fallacy. So, even if we pretend that Durbin had caught us doing something which was inconsistent with Pyrrhonian Scepticism (like making a knowledge claim), and if he implied that this showed that Pyrrhonian Scepticism was false, then he would have committed the tu quoque fallacy.

But, even if we overlook this informal fallacy, Durbin is still in trouble. Even if Durbin had completely scored his point, and established that it is not possible to say anything as a Pyrrhonian sceptic without immediately contradicting yourself, this still leaves an escape route; you can be a Pyrrhonian sceptic and not make any claims at all. In fact, this response is the one advocated by followers of Pyrrho. When confronted with an argument, the best you can do is wag your finger at it, like Cratylus. If you don’t say anything at all, you cannot contradict yourself!

Presumably, this position would be open to ridicule by Durbin. Being able to avoid the problem only by retreating to complete silence would seem like a capitulation rather than a victory. Despite initial appearances though, this response might actually be thought to have something going for it. The view recommends a sort of spiritual, monk-like silence, which Pyrrhonians thought could be a pathway to enlightenment and happiness:

“…the result for those who are so disposed [to Pyrrhonian scepticism] will be first speechlessness, but then freedom from worry; and Aenesidemus says pleasure.” (ibid.)

Indeed, even if this supposed benefit were not there, a theory is not deemed false merely because it has been arrived at by retreat. Even if the silent Pyrrhonian monk only took his vow of silence reluctantly and after he conceded in a debate that there was no other way to be consistent with Pyrrhonian scepticism, this doesn’t make Pyrrhonian scepticism false. It could still be true for all that. Therefore, even here, when we have been as generous to Durbin as we possibly could, we have not found a refutation of Pyrrhonian scepticism.

So perhaps Durbin has a point against the Pyrrhonian sceptic who goes around making explicit knowledge claims, which is that he is not a ‘good’ Pyrrhonian sceptic. But Durbin does not have a point against one who makes more nuanced belief claims, and certainly not against one who remains in a peaceful silence. So, the argument only even slightly works if you straw-man it so that the opponent has to be an inconsistent Pyrrhonian sceptic (one that makes explicit knowledge claims).

Durbin is not arguing against agnosticism, but against a fake-agnosticism (Pyrrhonian scepticism), and his arguments fail to refute even this weakened opponent.

3. Not-fake agnosticism

Thomas Huxley, who coined the term ‘agnosticism’ in the late 19th century, described the ‘principle of agnosticism’ as follows:

“In matters of the intellect, do not pretend that conclusions are certain which are not demonstrated or demonstrable. That I take to be the agnostic faith, which if a man keep whole and undefiled, he shall not be ashamed to look the universe in the face, whatever the future may have in store for him.” (Huxley, Agnosticism)

The key idea is that in cases where things “are not demonstrated or demonstrable”, we should not “pretend that conclusions are certain”. If we don’t know one way or the other about something, then just be honest about it.

Just in case you thought that this principle was accompanied by a Pyrrhonian denial of the possibility of all knowledge, consider the very next paragraph from Huxley:

“The results of the working out of the agnostic principle will vary according to individual knowledge and capacity, and according to the general condition of science. That which is unproved today may be proved, by the help of new discoveries, tomorrow.” (ibid.)

Huxley is saying that some people will know more than others, depending on the person and the state of science in their day. This clearly presupposes that some people know things, and that things which we do not currently know can become known.

Durbin claims that the agnostic’s position is that ‘We cannot know anything’, yet Huxley (the originator of the term ‘agnosticism’) explicitly claims that ‘the results of the working out of the agnostic principle will vary according to individual knowledge’ But, if nobody knows anything, then the results of applying the agnostic principle will not vary according to individual knowledge; the results would be the same for everyone!

Durbin claims that the agnostic’s position is that “knowledge cannot be gained or had” and that “we cannot know anything”. But Huxley claimed that “that which is unproved today may be proved, by the help of new discoveries, tomorrow”. If knowledge cannot be had, how is it that we could prove things by the help of new discoveries tomorrow?

The answer is that Huxley clearly did not deny the possibility of knowledge per se. Agnosticism is just the idea that when you do not have a demonstration of something, then you should not claim to know it. There are lots of demonstrations Huxley would have accepted, and so things we would have accepted as knowledge, but crucially he thought that there was no such demonstration for God, and that therefore we should just admit that we do not know whether he exists or not.

To be polite, we would have to say that Durbin has not done his research, and that the straw-man is a result of ignorance, rather than outright deception. This interpretation strains credulity though, as a just a cursory internet search pulled up the sources linked in this article. Either way though, he is just plain wrong. Agnostics do not have to affirm that they have no knowledge whatsoever; all an agnostic has to affirm is that they do not know whether God exists. Such a person is not guilty of any charge of self-contradiction, and certainly not because of anything Durbin brought up.

4. Abstract objects

Durbin goes on to make many claims that I could pick at, but I will focus on just one more section, as what I want to say about it is similar to what I was saying about induction in a previous post. In this snippet from the same video, Durbin describes an encounter he had with a maths teacher while he was at Reason Rally. Where we pick it up, he is explaining how if you write an equation in chalk on a blackboard, then the representation is not the maths itself (not the ‘law of math’ itself), but just a representation of it:

The ‘argument’ starts with a familiar idea that the actual law of maths itself “cannot be seen, cannot be touched, cannot be weighed, there is no colour to it, it is a universal, abstract, necessary, invariant, unchanging law”. The atheist maths professor was apparently a believer that the universe is entirely material, and is just “time and chance acting on matter, it is just stuff happening, like Shakespeare says, it is sound and fury signifying nothing“. Because his worldview was entirely materialistic, the maths professor couldn’t account for such a non-material law. Apparently, he conceded all this, and then when Durbin asked him if 2 + 2 = 4, he replied “Maybe not”.

Now, its not entirely clear what is supposed to be going on in this section. Durbin doesn’t really offer an argument to the effect that there is something, a law of maths, which is an existing non-physical thing. He does explain that if you write ‘2’ on a chalk board, and then rub it off, then you have not destroyed “2-ness”. He seems to think that this is sufficient to establish realism about non-material objects. Let’s grant is for the sake of the argument. The problem he is highlighting is that this non-material entity is incompatible with the thesis that there is nothing but matter (i.e. materialism). So the problem is: realism about non-material mathematical objects, along with materialism, is a seemingly incompatible pair. On one view not everything is material, and on the other view everything is material.

Let’s remember that this is a video about (‘completely’) refuting atheism; not about refuting materialism. Is the problem he has outlined a problem for atheism? I don’t see how it is. So far, all Durbin has argued for (using a very elastic conception of the term ‘argued’) is that materialism and realism about non-material objects are incompatible. Of course, the atheist could have conceded his point, renounced his materialism and embraced a realist view about non-material objects, such as platonism. There are various types of platonism contemporary philosophy of mathematics after all. The atheist could have said, ‘Ok then, your chalk example convinced me that platonism is true. Now what?’

Does Durbin have anything that might move us from atheistic platonism to Christianity? Well, sort of.

5. “If you don’t have Jesus, you don’t have math”

His actual thesis is not just that we can’t be materialists, but that we we can’t be atheists:

As we saw above, the idea is that materialism cannot have non-material laws in it. In contrast:

Christians have a basis for universal, immaterial, invariant laws … the laws of this universe reflect the order that God actually gives to the universe. Our thinking is to be like God’s thinking. God cannot lie. God cannot engage in logical contradictions. All of us are to essentially have our thoughts come into conformity with God’s thoughts.” (video above, 00:07 – 00:40)

Now, there seem to be two distinct ideas being run together here:

Firstly, there is the idea that God maintains order in the universe, preventing the “sound and fury” that would be there otherwise (“the order that God actually gives to the universe”). So God is a maintainer, or giver, of order.

Secondly, there is the idea that the way we think should be like the way that God thinks (“Our thinking is to be like God’s thinking.”). This normative fact (that we ought think like God) restricts the ways we can think about the world. He also says: “God cannot lie. God cannot engage in logical contradictions.” So, because God cannot lie, and our thinking is to be like his, then the logical law of non-contradiction is to be true for us as a result.

So it is clear that these are quite distinct types of things. On the face of it, they are two distinct accounts of the same phenomena. One is that a law is a regularity maintained by God, and the other is that a law is a thought process that God has (coupled with a normative principle). Are they somehow the same thing? Does God maintain the orderliness of the universe through maintaining a regular pattern of thoughts? How does this work? It is all very unclear.

The second idea, where God cannot lie or ‘engage in contradictions’ seems to me to be aimed at explaining a law of logic; specifically, at the law of non-contradiction. But how, we might wonder, is God’s inability to lie related to the mathematical laws that Durbin started off talking about? It seems to have no connection at all. Thus, even if this did justify that God maintained the law of non-contradiction via his pattern of thinking, it wouldn’t establish that the mathematical laws are held in place in the same way. Is there something about the way that God thinks which makes it such that 2 + 2 = 4? That doesn’t seem to make sense.

But it is actually hard to see how God’s inability to lie entails that the law of non-contradiction is true either. A very plausible reading of the phrase ‘God cannot lie’ is that it means ‘God can only speak things which he knows to be true’. What else could not being able to lie mean but having to tell (things that you believe to be) the truth? Let’s also grant that God believes all and only truths. If so, then this entails that he cannot say a contradiction (‘engage in contradictions’) if and only if there are no true contradictions. If, say, the liar sentence is in fact a true contradiction, then God would have to say the conjunctive proposition ‘The liar sentence is true, and it is false’, because that conjunction would be true! If there is a true contradiction, then if God said that it wasn’t true and false, then he would be lying. So saying that God cannot lie only entails that he cannot speak a contradiction if there are no true contradictions. So it only ‘establishes’ that the law of non-contradiction is true if it begs the question by presupposing that there are no true contradictions. It seems to me this consideration completely kills this line of reasoning. God’s honesty cannot entail the law of non-contradiction in any significant sense.

The idea that fact that God does not contradict himself somehow grounds the law of non-contradiction, also suffers from similarly crippling objections. If God uttered a contradictory sentence, “A and not-A“, he would have contradicted himself, but this is not the same as violating the law of non-contradiction. If God contradicted himself (and non-contradiction is true), then he would have simply said two things, one of which was true and the other of which was false. This clearly is not a violation of the law of non-contradiction.

Because it doesn’t relate to the maths stuff, and because it begs the question, let’s leave the second idea, and focus instead only on the first. That was the idea that God maintains the order of the world. The reason that physical objects act in law-like ways is because God imposes such an order on them. Durbin must also think that mathematical laws, like the one he motivated with the chalk example, are also things that God maintains in a similar way. God imposes that 2 + 2 = 4 on the world in much the same way that he imposes e = mc² on the world.

Here is where we run into the same argument as I used in the induction post. Let’s say that God maintains physical and mathematical laws (and while we are at it, let’s throw in logical laws as well). Let’s say that along with maintaining these laws, he has also revealed to us that he maintains these laws. And let’s say that we know this revelation in a such a way that we cannot be wrong about it; that we know it with absolute certainty. I say, even granting all this, we are in no better situation than a sceptic who doubts it.

Take the continuum hypothesis. It says that between the infinity of the natural numbers and the infinity of the real numbers there is no intermediate order of infinity. It is a currently unproven conjecture in mathematics. Does knowing with absolute certainty that God maintains mathematical laws help us figure out if the continuum hypothesis is true? No. It is no help whatsoever. All it does is rephrase the problem. Here is the problem now:

It is currently unknown whether the continuum hypothesis is true.

With the help of Durbin’s worldview, the problem becomes:

It is currently unknown whether the continuum hypothesis is one of the regularities that God maintains.

The simple fact is that, even on this worldview, God has not told us which regularities he has maintained. And the belief (or even knowledge) that God maintains some regularities, gives us no help at all in trying to work out whether the continuum hypothesis is one of those regularities or not.

And it seems Durbin will have to concede this point. It is obvious that the bible doesn’t contain answers to modern day mathematical conjectures. He has to concede that God has not revealed everything to us; he has not revealed exactly which mathematical laws he has maintained. In particular, he has not revealed whether the continuum hypothesis is true or false.

Durbin has to say that God has only revealed that he maintains mathematical laws, not which ones are true, because he doesn’t know via revelation all mathematical laws. But while Durbin doesn’t have answers to particular mathematical problems, he could say that his worldview provides a basis in which we can answer them. On the atheist worldview, where there is no God maintaining order, and “everything is sound and fury”, there is no such basis. Such might be his reply. I will show that this reply has no force to it.

Durbin is clearly in favour of a type of ‘revelational epistemology’, which for our purposes we can say necessarily includes the following condition:

A) The only way one can know that there are regularities (like mathematical laws) is through revelation from God.

It follows from this that an atheist does not know that there are regularities. How could an atheist know such a thing? Could they tell it through their senses? Can they reason to the nature of the universe just by thinking about it? Presuppositionalists, like Durbin, constantly tell atheists that they cannot find out the truth through these means alone, without God. That’s the point of A).

But it follows that the only way to positively know that regularities do not exist could also only be through such a revelation. For reductio, assume that I could determine, without God, that there really were no regularities in nature. It follows that either God does not exist, or A is false. For, if I can determine on my own that there are no regularities, then it couldn’t also be that God had revealed to me that there are regularities. So, on that premise, either he doesn’t exist, or I do not have revelation from him.

So according to revelational epistemology: if the atheist is right about her atheism (and God does not exist), then the she cannot know about whether there are regularities in nature at all. She has to be in the dark about such metaphysical matters. The issue of what reality is like at its deepest core has to be, for an atheist, a mystery. It might be regular, or it might just appear regular. On Durbin’s view, because they lack revelation, an atheist could never know whether there are universal regularities or not. So it is not that on the atheist’s worldview there are no regularities; its that on the atheist’s worldviews one cannot know if there are regularities (assuming Durbin is right about A being true).

So, for the atheist the question is just open, and seemingly impossible to answer definitively. Atheists are forced to do mathematics without knowing whether there really are any mathematical laws or not. This is how the atheist has to deal with mathematical laws in Durbin’s world.

And, say I, in this setting, atheism is no worse off than Durbin’s Christianity, even if we grant him his every claim.

Let’s look at it from Durbin’s point of view. He knows that God exists, and that God has revealed to him that He maintains certain laws of mathematics, logic and physics. This is the opposite position to the atheist in Durbin’s worldview; the atheist has no knowledge about regularities and no revelation, whereas the Christian has both.

Well, even here on his home ground, Durbin is in trouble. Say we are considering a particular mathematical hypothesis, from Durbin’s vantage in his worldview. Say that the hypothesis is geometrical, like:

“‘Parallel lines never meet’ is a universal law”.

Even with all his certain knowledge from God, even granting everything in his worldview, we know that God did not reveal to Durbin (or any Christian) that ‘parallel lines never meet’ is a universal law of geometry, because, as Riemann showed, it is not. And this meant that everyone throughout history, Christian or atheist, who like Kant had been convinced they had certainty about the truth of principles of Euclidian geometry were just wrong. And there is nothing that Durbin has on his worldview that can prevent this from happening in the future. For any purported law that you come across in Durbin’s world, you cannot ever be absolutely sure that it is a genuine universal principle (one of those regularities that God maintains), and not just an apparent one (like with Euclidian geometry). Even if you grant him all of the things that he claims about his own worldview, he could still not know with absolute certainty for any purported law whether it was a law.

This is exactly the same position that the atheist is on, even on Durbin’s worldview. For the atheist, they cannot be sure whether there are any regularities or not. For the atheist, with each purported law, they can never know for absolute certainty whether it is a regularity or not.

Thus, when we stack the deck entirely in favour of Durbin’s worldview (where we grant that God exists, that he maintains the regularities nature, and that he reveals to Durbin with absolute certainty that he maintains the regularities of nature), and where we stack the deck entirely away from the atheist (who has to make do in a world where revelation epistemology was true but where God does not exist to provide revelation) – even when we do that, each position is in exactly the same position with respect to each and every prospective universal law. Neither of them could ever know if it was actually a law or not. As such theist and atheist are indistinguishable with respect to the question of universal regularities.

The discussion between the atheist and theist at this point is where a theist can only say:

I cannot know that [Claim X] is a universal law, but I believe that [Claim X] is a universal law, and I also believe that what makes it true is that it is a regularity that God maintains.

The atheist can reply:

I cannot know that [Claim X] is a universal law, but I believe that [Claim X] is a universal law, and I also believe that what makes it true is that it instantiates an abstract platonic object.

Even granting all of Durbin’s worldview, the theist and the atheist are in precisely the same epistemological situation regarding universal laws. Each of them has a sufficient condition for the regularity, and neither has a necessary condition.

When you grind all the way through to the end, all you come out with is a perfect stalemate. He has taken not one step forward, even if we grant him everything.

5. Conclusion

Jeff Durbin is a one-trick pony. His trick is the straw-man. He will argue against an agnostic by presenting an argument which only (even slightly) works against a different position. Even then, he clearly has no idea about Pyrrhonian scepticism. If you say you are an atheist, he will try to straw-man you with a form of materialism. But don’t fall for it. If he wants to completely refute atheism, he has to actually offer an argument against atheism. So far he has offered an argument against Pyrrhonian scepticism (which fails) and an argument against materialism (which also fails).


This post is just a note to say that I have started a podcast, called ‘Thoughtology‘. It is a series where I talk to professional philosophers about various interesting things. I have recorded two episodes so far, and plan to get one out every two weeks (schedule permitting).

In the first episode I talk with my friend Arif Ahmed, who is a well-known atheist philosopher, who, among other notable achievements, has debated William Lane Craig on several occasions. We talked about a paper he has recently published in the journal Mind. The topic is David Hume’s argument that it is always irrational to believe in reports of miracles. A well-known response to this is to argue that the combined weight of multiple witnesses could in principle overcome the scepticism one may have on hearing such a report. Arif explains how, when you look at the details of this in a Bayesian framework, the response fails.

In the second episode, I was very lucky to be joined by Graham Priest, who is one of the world’s most notable logicians and philosophers. He is famous for defending a highly controversial position called ‘dialetheism‘, according to which there are some true contradictions. We talked about dialetheism, paradoxes and the metaphysics of logic.

In the coming weeks and months I intend to interview various other professional philosophers, and have about 12 lined up so far. Many of them will be philosophers who are widely known, and many of them will be less established (but equally interesting) people. If you enjoy this blog, you should subscribe to the Thoughtology YouTube channel so that you get the content when it is released.


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.





Molinism and Trivial Counterfactuals

0. Introduction

I recently watched a pair of debates (which you can watch here and here) between a Molinist and a Calvinist about the idea of God’s ‘middle knowledge’. The Molinist was Eric Hernandez, and the Calvinist was Tyler Vela. The debate seemed to me to be quite imprecise, and it that both sides would have benefited from a formal framework within which they could precisely pose their various claims and counter-claims. In fairness, Tyler did give a formalised written version of his argument for the second debate (and you can see his slides here). This presented a very clear expression of  (what seems to me to be) an error that both sides were making. I wish to clear up here.

These issues have been investigated by logicians specialising in temporal logic since the late 70’s, and something of a consensus has arisen over the deficiency of the Molinist position. Neither of the participants seemed to be aware of this development. I guess that this is not surprising seeing as it is an obscure area of the literature, and requires a certain amount of technical training to read the logical and semantic details of the papers. Also, and possibly for the same reasons, the lessons do not seem to have made much of an impact on the philosophy of religion scene, never mind the theology scene. Given that I have a good knowledge of this area (having published journal articles on it) I will outline the main issues here with the hope of shedding some light on the debate.

  1. Molina

Luis de Molina was a 16th century Spanish jesuit priest who formulated a position which bears his name in contemporary philosophy of religion. Molina was concerned with how to reconcile human freedom (conceived of as libertarian free will) and God’s sovereignty. However, there is a tension between God’s sovereignty and human freedom. To the extent that humans are free, they are not under the control of God (and that undermines his sovereignty); yet to the extent that God is in control of everything, humans are not perfectly free. The reformed answer to this puzzle is to repackage freedom as a variety of compatibilism. Molina was reacting to this move, and wanted to maintain the strong sense of libertarian freedom as well as the strong sense of sovereignty. It is from this mix that we get Molinism.

2. Future Contingents

The debate that Molina contributes to is one that had been going on for centuries before him. The medievals rediscovered Aristotelian texts that had been lost to western Europe during the dark ages and this contributed to the increasingly sophisticated logical debates that preceded the reformation. In particular, one topic caught the imagination of the medievals, and that was the issue of future contingents. A future contingent is a prediction, like ‘There will be a sea battle tomorrow’ (Aristotle’s example) made in a context where there could be a sea battle and there could be no sea battle. To get a feel of the modal strength of the future contingent, contrast it with an expression of possibility, and an expression of inevitability. So we might say ‘There could be a sea battle tomorrow’. This sentence can be true now even if tomorrow there is no sea battle; for often things don’t happen which were possible (a familiar fact to most people who have ever played the lottery). The modal force of this sentence is very weak. On the other hand, saying ‘There necessarily will be a sea battle tomorrow’ is much stronger. This sentence could be false even if there is a sea battle tomorrow. It may happen by accident, for example, and not of any kind of necessity. A future contingent cuts a line between these two modal extremes. Saying ‘There will be a sea battle’ is stronger than saying that there may be one, but weaker than saying that there must be one.

Aristotle argued (or at least seemed to) in his work On Interpretation (part 9) that purported examples of future contingents, if they were true now, would have to be already impossible or necessary. For if it were already true now that there will be a sea battle tomorrow, then it is going to take place regardless of what you try to do about it; its future truth seems to indicate its present inevitability. Thus, according to Aristotle’s argument, there could be no such thing as a ‘future contingent’ (i.e. a true future-tensed statement which is neither necessary nor impossible). This is a strong form of logical fatalism.

The received view of Aristotle is that his solution this this problem was to advocate that future contingents were neither true nor false, and thus to avoid the fatalism (although not everyone agrees – see this paper by Hintikka). Despite their reverence for Aristotle, the medievals found his solution to be deeply troubling, as it indicated that God could not know the contingent aspects of the future. After all, if God knows all true statements (being omniscient) and believes nothing but true statements (being infallible), then he does not know future contingents (which, being neither true nor false, are not true). Thus, God is seemingly in the dark about whether there will be sea battles tomorrow, or whether certain people will sin, etc. Aristotle’s solution is therefore incompatible with a robust conception of God’s foreknowledge. On the other hand, if God does know the truth-value of future contingent statements, then there is a theological equivalent to the problem of future contingents: God’s knowing true future contingents in advance makes them seem inevitable and thus necessary. If God knows you are going to sin tomorrow, then it is going to take place regardless of what you try to do to prevent it.

Various medieval philosophers, logicians and theologians offered their solutions to this problem, such as Peter Abelard, St. Anselm and William of Ockham. The Anselmian-Ockhamist solution, explained expertly by Peter Øhrstrøm here, was to hold that God knows the truth-values of future contingent statements, but to deny that this entails that the statements themselves become necessary as a result. Ockham diagnosed a ‘modal fallacy’ in the claim that his foreknowledge made them necessary; God knows that p will happen, even though it might not – these are not logically incompatible, and the modal fallacy is supposing that they are. In this sense, there can be genuine true future contingents for Ockham.

Future contingents are logically equivalent to free choices of agents with libertarian free will. A future contingent is a statement of the form ‘it will be that p‘ made in a situation where ‘it is possible that it will be that p‘ and ‘it is possible that it will not be that p‘ are both true. An agent’s choice to do is free in the libertarian sense only if they could have chosen to do and have chosen not to do x. So both concepts rely on the prediction being true (or choice being made) in a situation where it’s falsity is possible (where the choice could have not been made). Thus, libertarian free will is really just a special case of a future contingent, where the predicted content is the action of the agent.

Molina essentially accepts the Ockhamist proposal, which was that God knows the future choices of agents without this stopping the possibility of those choices being different (they could be different, but they won’t be). However, he adds to this an additional claim, which is aimed at bolstering the sovereignty consideration. God knows not just which free choices agents will make, but also those free choices they would have made were they to have been faced with different circumstances.

3. Luis

Let’s use an example to make the point clear. Imagine a medieval monk; call him Luis. He lives in a monastery high in the mountains somewhere. In this calm and peaceful environment there are seldom any opportunities for moral temptation (which is part of the point of a monastery after all). Upon entering the monastery, God knows that Luis will not sin for the rest of his life. It is still possible that he could sin (he could decide to leave the monastery and live in the sinful town at the bottom of the mountain). But God knows that though he could do this, he won’t. So far, this is just the Ockhamist picture.

We may wonder about Luis’ moral character in more detail than this though. Sure, he won’t actually sin, but this just seems to be a product of the environment he is living; he won’t be seriously tempted to sin. In a sense then, his moral character is not going to be severely tested in any way. Even though he won’t be, what would have happened if he were to be tempted? Imagine a beautiful maiden were to arrive at Luis’ bedroom one night and beg him to spend the night with her. It won’t happen (given the strict rules of the monastery), but what if it did? Would he have been able to resist, or would he have given in to temptation?

4. Middle Knowledge

Molina thought that God, in his sovereignty, had to know the answer to this sort of question. That is, God has to know the truth-value of every actual future contingent, but also of every counterfactual future contingent. Here is an example of the sort of sentence that Molina claims God would know the answer to:

a) Had it been the case that [Luis is tempted to spend the night with the maiden], then it would have been the case that [Luis will give in to the temptation].

a) is a a conditional (if…, then…), in the subjunctive mood (using the modal modifiers ‘had it been…, it would have been…’) and it has an actually false antecedent (it is not actually the case that Luis is tempted by any maiden). This makes it a counterfactual. It is important to note that the consequent (‘Luis will give in to the temptation’) is a future contingent, specifically one about his libertarian free choice. Molina’s claim is that God knows counterfactuals with future contingents as their consequents, like a).

In addition to him knowing the truth-value of these counterfactuals, the obvious supposition is that some of them are in fact true; it’s not Molinism if all such counterfactuals are false. We will come back to this at the end.

This type of knowledge that Molina claims God has is often referred to as ‘middle knowledge’. Middle knowledge is usually contrasted with two other types of knowledge that God has: natural knowledge and free knowledge. Natural knowledge concerns all the necessary, possible and impossible truths. So that 2 + 2 = 4 is necessary; that it Judas betrayed Jesus is possible; that 2 + 2 = 5 is impossible. In contrast, free knowledge concerns those facts which relate to the creation of the world. So the fact that I exist, or the fact that you are reading this blog post, is part of God’s free knowledge. Middle knowledge is usually contrasted with these two in terms of being between general facts to do with possibility, and particular facts about the contingent world; middle knowledge is supposed to concern counterfactual facts.

5. A Better Distinction Using Possible Worlds

However, this is not the best way of drawing this distinction. With the benefit of possible worlds semantics and a clear understanding of logic, we can make this distinction much more cleanly.

Possible worlds are thought of as just sets of propositions that are maximal and consistent. This just means that for every atomic proposition, p, and every world w: either p is in w or it is not, but not both.

We can then use the usual logical compositional clauses to form more complex propositional forms:

  • if p is not true in w, then ~p is true in w;
  • if p is true in w and q is true in w, then ‘q‘ is true in w, etc.

If there is some formula, A, which is true in all worlds, then we say that A is necessary; if it is true in no worlds then A is impossible; if it is true in some worlds but not others, then A is contingent.

All of these propositions would be items of God’s natural knowledge; he knows what is true and what is false at every world, and thus he knows what is necessary, what is contingent and what is impossible. So much for natural knowledge.

Take one world, say w1. We can designate this world as the ‘actual world’, and label it ‘@w‘. Think of it as being the world that God chose to actualise. If a proposition is true at @w, then it is simply true (or ‘true simpliciter’). (Having a special designated actual world is how Kripke originally formulated possible worlds models, though it fell out of favour with most subsequent formal treatments of possible worlds semantics). God’s free knowledge concerns what is true simpliciter (or what is true at @w).

So far, we have used possible worlds semantics to explain the contents of God’s natural and free knowledge. As noted above, the description of God’s middle knowledge is usually cashed out as concerning counterfactuals. And it is, but most counterfactuals actually come under God’s natural knowledge, a claim which we can also spell out clearly now using the benefit of possible worlds. There are two types of counterfactuals that need to be distinguished from Molinist counterfactuals, and this distinction is the counterfactual mirror of the distinction between modally weak predictions, future contingents and expressions of inevitability from above.

On the one hand, God knows ‘might’ counterfactuals of the following type:

b) If I had flipped the (fair) coin, then it might have landed heads.

This type of counterfactual uses the word ‘might’, which is analogous to the word ‘possible’; if I had flipped the coin then landing heads was possible. Equally, landing tails is also possible given the coin flip (assuming a perfectly fair coin, etc). All this means is that at at least one of the worlds which are maximally similar to the actual world at which I flipped the coin, it lands heads.

The point is that ‘might’ counterfactuals are very weak in what they claim. All that is required is that the antecedent condition is compatible with the consequent condition; that there is at least one ‘coin-flip’ world (maximally similar to the actual world) at which the coin lands heads. This just means that the flipping of the coin (in the right sort of circumstance) is compatible with it landing heads. Thus, all ‘might-counterfactuals’ come under natural knowledge. To turn the example to Luis, the following might-counterfactual is true: ‘if Luis had been tempted by the maiden, then he might have given in to the temptation’. Even though that counterfactual is true it doesn’t tell us whether Luis would give in to the temptation or not – it just tells us that he might do. This is why these might-counterfactuals don’t count as middle knowledge.

In contrast, imagine a coin which has heads on both sides (a ‘rigged’ coin). The following counterfactual, which uses ‘would’ instead of ‘might’, would be true for that coin:

c) If I had flipped the (rigged) coin, then it would have landed heads.

Because the coin is rigged, its landing heads is inevitable once it is flipped (assuming of course that it cannot land perfectly on its side, etc). This just means that in every (maximally similar) ‘coin-flip world’, the coin lands heads. And we can immediately see that this is the case, because no matter which way it lands, it will land heads. To make the example relevant to Luis again, we can easily think of consequents which are inevitable given the truth of the antecedent. For example: ‘If Luis had been tempted by the maiden, then he would have been tempted’. The consequent is (in a particularly trivial way) necessitated by the truth of the antecedent. In every (maximally similar) temptation world, Luis is tempted. This sort of example would also not count as middle knowledge, as it does not tell us what free choice Luis would make in the counterfactual situation. This example, like the one above, is also an example of natural knowledge.

So far, we have seen two types of counterfactuals, ‘might-counterfactuals’ and ‘would-counterfactuals’ and neither of them count as middle knowledge (they are both just natural knowledge). What we need to get there is a sort of Goldilocks modality, which is between ‘would’ and ‘might’. There is no natural locution for this in ordinary English, so I will use the somewhat stilted phrase ‘actually-would’. So in contrast to b) and c), the Molinist counterfactual, the real example of middle knowledge, is:

d) If I had flipped the (fair) coin, then it actually-would have landed heads

When we hear d), we need to remember that it doesn’t mean that the coin might land heads, and it doesn’t mean that the flipping of the coin necessitates it landing heads. It means that, though it is possible that it land tails, if it were flipped would in fact happen to land heads. To make the example relevant to Luis, consider the counterfactual: ‘If Luis had been tempted, then he actually-would have given in.

6. Red Line

Now we have clearly and precisely stated the thesis that Molina argues for. He is saying that at least some counterfactuals of type d) are true, and God knows them – they constitute God’s ‘middle knowledge’. The question is how to model this claim. With the previous two types of counterfactuals, we were able to use the standard ideas from the literature on possible worlds semantics (which come from David Lewis, see this and this). Put simply, ‘would’ counterfactuals rely on what is true at every maximally similar antecedent world, whereas ‘might’ counterfactuals rely on what is true at at least one maximally similar antecedent world. These are what grounds these two types of counterfactuals, they are what makes them true, which is to say that they are the semantics for those counterfactuals. But what is it that grounds the truth of the Molinist counterfactual? What is its semantics? There is reason to think that at the moment there is nothing to appeal to – nothing to hang our metaphysical hat on, as it were.

Here is one way of thinking about the situation which makes it clear that as things stand there is no obvious candidate. Consider a simple model, we have three worlds, w1w2 and w3. Let’s say that w3 is the actual world, @w (which we will draw in red). In @w, Luis is not tempted by the maiden (she does not go to the monastery at all). In w1 and w2 Luis is tempted. He gives in in w1 but not in w2. We can picture this as three worlds which ‘branch’ from one another as follows (worlds ‘overlap’ when they share all the same atomic propositions, and ‘branch’ from one another when they differ over the truth of a proposition):


We can ‘hang our hat’ on a feature of this model to ground the truth of the counterfactual that Luis might have given in: there is at least one of the tempted-worlds in which Luis gives in (i.e. w1). We can also hang our hat on a feature of this model to ground the falsity of the counterfactual that Luis would have given in: it is not the case that he gives in on all of the tempted worlds (i.e. in w2 he does not give in). Each of these types of counterfactual receive a truth-value in a straightforward way. What is unclear is how one could ground the claim that, had he been tempted, Luis actually-would have given in. He gives in on one tempted-world but not the other; w1 and w2 have nothing to distinguish one from the other. Why say that he would give in rather than not give in?

6. Trivial Counterfactuals

It is at this point that I saw both contributors to the podcast making a move which is mistaken. I am quite prepared to believe that Tyler was lead astray by Eric’s lack of clarity at this point (after all, Eric is the Molinist and he should have been able to explain his own position clearly). However, the both made the same move, which obscured the rest of the conversation.

Here is what happened. Tyler was asking Eric if it was possible for God to create the world such that everybody freely chooses to believe in God. They both agreed that it was logically possible for this to happen, in the sense that there was no logical contradiction in the supposition that it happens. However, Eric insisted that though it was logically possible, it was not ‘feasible’ for God to do this. Unfortunately, no definition was given for ‘feasibility’. Tyler wanted to demonstrate that if feasibility has no metaphysical content, then the appeal to it was ad hoc here, being added without any motivation other than avoiding the problem. How he went about framing his argument demonstrated that a clear framework for the semantics for Molinist counterfactuals was lacking. Here is how he presented his argument on the second show:


Now, the actual details of Tyler’s argument are not important here for my purposes. Just note that the first premises of each of the three arguments are conditionals, and the antecedents talk about worlds being possible and God actualising worlds. They are effectively little counterfactuals about what would be the case had God actualised different worlds.

The implicit idea here is that in a Molinist counterfactual, one changes which world is the actual world; that we move the red line on the picture. Tyler’s whole argument is about what would be the case if a different world were actualised. It is as if this is how the model would look to make the Molinist counterfactual ‘If Luis had been tempted, he would have given in’ true:


There are two immediate problems with this idea though. Firstly, what we have is no longer really a counterfactual situation. A counterfactual has to have an actually false antecedent, yet on this model the antecedent (Luis is tempted) is actually true (because w1 is now the actual world). Secondly, and more importantly, it is trivial. The problem is that if we move the designation of the actual world to a different place in the ‘tree’, then this change settles the matter of the truth of the consequent of the conditional. And the antecedent of Tyler’s conditionals have the mention of which world is being actualised explicitly as stated in the antecedent. To make this clear, consider the following two questions one may ask:

e) Had God actualised world w1, would Luis have given in to temptation?

f) Had Luis been tempted, would he have given in?

There is a big difference between e) and f). Firstly, nobody would ever say e), outside a contrived philosophy seminar-room example. The reason is partly because in real life possibilities are not labelled neatly like w1 and w2, etc. But let’s suppose that we can get around this somehow (that a magic world-labelling dictionary is available to everyone who introspects hard enough). The problem now is that stating the world by name implicitly includes all the propositions that are true at that world. That’s all a world is! It is like saying:

g) Had God actualised world w1, in which Luis is tempted and gives in, would he give in?

Nobody would ask a question like g) because it contains its own answer, and is thereby trivial. e) is trivial because it is just an elliptical way of asking g). Likewise, the following counterfactual (which is similar to Tyler’s) is trivial:

h) If God had actualised w1, then Luis would have given in to temptation.

This provides us reason to think that h) cannot be any part of the semantics of the Molinist counterfactual d). The reason h) is not equivalent to d) is that h) is trivial, whereas d) is not. Just like the way that e) is trivial and f) is not. What this means is that the correct semantics for the Molinist counterfactual, d), is not just moving the red line in the model for d) to a different place. Tempting though it may be, the analysis of a Molinist counterfactual is not to conceptualise a counterfactual about what would be the case if God had actualised a different world. To do so is to misunderstand Molinism. As I said, I think this mistake was being made by both parties in the debate, although Eric bears the responsibility for articulating his own position correctly.

7. Red Lines

If that is not the answer, then what is? This is where we find the logic literature that I referenced in the introduction to be very helpful. As far as I know, the first systematic logical account of a Molinist branching model was put forward by McKim and Davis in 1976. It was made into a much more elaborate theory by Thomason and Gupta in 1980. A similar theory was also developed by Brauner, Ohrstrom and Hasle in 1999. The way these theories work is to postulate not just one red line, but multiple red lines. In the case of the actual world, what makes a future contingent true is that what it predicts is true in the actual future; the sentence ‘there will be a sea battle’ is true if and only if there is a sea battle in the actual future. The idea of the ‘actual future’ is what breaks the symmetry between all the various possible futures of that moment. In the counterfactual situation, there is no such symmetry breaker, and this is what leaves us only able to ground ‘would’ and ‘might’ counterfactuals, but not Molinist counterfactuals. There is nothing for God to hang his hat on, as it were. What these authors above all have in common is the idea that they need to break the symmetry in the counterfactual situations by adding in actual futures at each counterfactual branching point. At each counterfactual situation where there is a future contingent (like a monk being tempted and deciding whether to give in to it or not) there needs to be an counterfactual ‘actual’ future (a ‘counteractual’ as it were). So our little model would have to be modified to make it a proper Molinist moodel:


Now we can say that the semantics of a Molinist counterfactual is as follows:

i) ‘Had it been the case that A, then it actually-would have been the case that C’ is true if and only if it is true in the counteractual future future of the most similar A-point that it will be that C’.

So, in the actual world, the Molinist counterfactual ‘had Luis been tempted, he would have resisted’ is true because in the maximally similar tempted situation, the actual future has him resisting the temptation. In the counterfactual situation in which Luis was tempted, he actually resists temptation.

So a technical addition to our models, a specification of counteractual futures at each branching point, provides the required metaphysical feature for us to hang our semantic hat on. God’s middle knowledge is just that he knows where all the red lines are in the overall tree of branching worlds.

8. Problems

Despite its seemingly attractive solution, there are some widely recognised and severe problems for this Molinist semantics. These come in two categories; technical and conceptual.

The technical difficulties are explained in Belnap and Green (1995) and in Belnap et al (2001)  (chapter 6), and also a in chapter of my PhD thesis which is available here (p. 7 – 9). The issue has to do with the semantics of tenses. The problem has to do with iterated tenses, like “It will be that it was that p“, etc. These do not operate properly on the Molinist account, with the result that various tense-logical tautologies are violated by the Molinist logic. Consider the ‘tempted’ point in our Molinist model above. At that time, it is true that Luis is being tempted. Now, it is usually considered a tautology that if something is presently true, then in the past it was going to be true. That ‘you are reading this blog post’ is true now, so before you started reading it the sentence ‘you will read this blog post’ would have been true. This seems to be an elementary fact about how tenses work. Yet, at the ‘tempted’ point in our model, if we go back in the past to the trunk of the tree we find ourselves in a situation where the actual future leads to Luis not being tempted at all.  So even though he is being tempted, it was not the case that he was going to be tempted. In fact, because the actual future of the trunk leads to him not being tempted, we have it that Luis is being tempted, even though in the past it was true that he will never be tempted. This is an odd result. Thomason and Gupta, and Brauner, Ohrstrom and Hasle do make modifications which avoid this issue, but only at a cost. Each time they modify the model it leads to a different intuitive tautology not being true, which led Belnap to describe  the process of constructing ever more complicated Molinist models as ‘mere idle filigree’.

The conceptual problem is just that it is hard to make any sense out of the idea of counteractual futures. Unless one is a full-on modal realist (in the vein of David Lewis), you will think that there is a pretty big ontological difference between what is actual and what is merely possible. What is actual concretely exists, and what is merely possible does not. Yet, when the Molinist posits actual futures of merely possible situations, we find that this intuition gets lost. Are we saying that these situations are sort of concrete and existing? How can something be sort of concrete and existing? If they are fully concrete and existing, then what distinguishes the actual world from them? There is a big metaphysical question mark over this way of conceptualising counterfactuals which makes many think that it is wrong in principle to posit actual futures of counterfactual moments.

9. Alternatives

Instead of going the Molinist route, a more promising proposal is to just abandon the idea of middle knowledge altogether. Molinist counterfactuals are just inherently problematic. What sounds like an initially plausible proposal (that God could know what you would freely do in counterfactual situation) just comes out both technically and conceptually flawed.

Instead, we should embrace the idea that there are only ‘would’ and ‘might’ counterfactuals. In addition, we should be prepared to countenance the prospect that, strictly speaking, most ‘would’ counterfactuals are false. Have a look at these papers (here and here) for some philosophers giving weight to this proposal. When we say ‘Had I flipped the fair coin, then it would have landed heads’, this is just false. So is ‘Had I flipped the fair coin, then it would have landed tails’, although ‘Had I flipped the fair coin, then it would have landed either heads or tails’ is true. Only if the consequent is necessitated by the antecedent is a ‘would’ counterfactual true.

Why think this? Well, I suggest that the most natural way to think about what is grounding counterfactuals (and most metaphysical modality claims) is the natures of actual objects. The reason that this coin could land heads but doesn’t have to is because of the nature of the coin itself. It is because it has heads on one side but not on the other. These facts are what we are hanging our hat on. These facts are what allows us to draw the tree of possibilities in the first place. Nothing about the actual coin picks it landing heads over tails in a counterfactual situation, so there is no metaphysical fact about that. Molinism asks for God to have knowledge about facts which don’t exist.

10. Conclusion

All I wanted to do in this post was explain why a certain way of talking about Molinism is wrong, but to do that as clearly as possible, I have gone through the background of Molinism, explained the basic ideas in the semantics of counterfactuals, and outlined the main thrust of the objections to the Molinist semantics found in the logic literature on this topic. I have also provided a quick sketch of my view, which is a species of Ockhamism.