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 x is free in the libertarian sense only if they could have chosen to do x 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 ‘p & 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, w1, w2 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.