An improved paradox about thoughts and worlds

Yesterday, I offered a paradox about possible thoughts and pluralities of worlds. The paradox depends on a kind of recombination principle (premise (2) in the post) about the existence of thoughts, and I realized that the formulation in that post could be objected to if one has a certain combination of views including essentiality of origins and the impossibility of thinking a proposition that involves non-qualitative features (say, names or natural kinds) in a world where these features do not obtain.

So I want to try again, and use two tricks to avoid the above problem. Furthermore, after writing up an initial draft (now deleted), I realized I don’t need pluralities at all, so it’s just a paradox about thoughts and worlds.

The first trick is to restrict ourselves to (purely) qualitative thoughts. Technically, I will do this by supposing a relation Q such that:

1. The relation Q is an equivalence (i.e., reflexive, symmetric, and transitive) on worlds.

We can take this equivalence relation to be qualitative sameness or, if we don’t want to make the qualitative thought move after all, we can take Q to be identity. I don’t know if there are other useful choices.

We then say that a Q-thought is a (possible) thought θ such that for any world there aren’t two worlds w and w′ with Q(w,w′) such that θ is true at one but not the other. If Q is qualitative sameness, then this captures (up to intensional considerations) that θ is qualitative. Furthermore, we say that a Q-plurality is a plurality of worlds ww such that there aren’t two Q-equivalent worlds one of which is in ww and the other isn’t.

The second trick is a way of distinguishing a “special” thought—up to logical equivalence—relative to a world. This is a relation S(w,θ) satisfying these assumptions:

2. If S(w,θ) and S(w,θ′) for Q-thoughts θ and θ′, then the Q-thoughts are logically equivalent.

3. For any Q-thought θ and world w, there is a thought θ′ logically equivalent to θ and a world w such that S(w,θ′).

4. For any Q-thought θ and any Q-related worlds w and w′, if S(w,θ), there is a thought θ′ logically equivalent to θ such that S(w′,θ′).

Assumption (2) says that when a special thought exists at a world, it’s unique up to logical equivalence. Assumption (3) says that every thought is special at some world, up to logical equivalence. In the case where Q is identity, assumption (4) is trivial. In the case where Q is qualitative sameness, assumption (4) says that a thought’s being special is basically (i.e., up to logical equivalence) a qualitative feature.

We get different arguments depending on what specialness is. A candidate for a specialness relation needs to be qualitative. The simplest candidate would be that S(w,θ) iff at w the one and only thought that occurs is θ. But this would be problematic with respect (3), because one might worry that many thoughts are such that they can only occur in worlds where some other thoughts occur.

Here are three better candidates, the first of which I used in my previous post, with the thinkers in all of them implicitly restricted to non-divine thinkers:

1. S(w,θ) iff at w there is a time t at which θ occurs, and no thoughts occur later than t, and any other thought that occurs at t is entailed by θ

2. S(w,θ) iff at w the thought θ is the favorite thought of the greatest number of thinkers up to logical equivalence (i.e., there is a cardinality κ such that for each of κ thinkers θ is the favorite thought up to logical equivalence, and there is no other thought like that)

3. S(w,θ) iff at w the thought θ is the one and only thought that anyone thinks with credence exactly π/4.

On each of these three candidates for the specialness relation S, premises (2)–(4) are quite plausible. And it is likely that if some problem for (2)–(4) is found with a candidate specialness relation, the relation can be tweaked to avoid the relation.

Let L be a first-order language with quantifiers over worlds (Latin letters) and thoughts (Greek letters), and the above predicates Q and S, as well as a T(θ,w) predicate that says that the thought θ is true at w. We now add the following schematic assumption for any formula ϕ = ϕ(w) of L with at most the one free variable w, where we write ϕ(w′) for the formula obtained by replacing free occurrences of w in ϕ with w′:

6. Q-Thought Existence: If ∀w∀w′[Q(w,w′)→(ϕ(w)↔︎ϕ(w′))], there is a thought θ such that ∀w(T(θ,w)↔︎ϕ(w)).

Our argument will only need this for one particular ϕ (dependent on the choice of Q and S), and as a result there is a very simple way to argue for it: just think the thought that a world w such that ϕ(w) is actual. Then the thought will be actual and hence possible. (Entertaining a thought seems to be a way of thinking a thought, no?)

Fact: Premises (1)–(6) are contradictory.

Eeek!!

I am not sure what to deny. I suppose the best candidates for denial are (3) and (6), but both seem pretty plausible for at least some of the above choices of S. Or, maybe, we just need to deny the whole framework of thoughts as entities to be quantified over. Or, maybe, this is just a version of the Liar?

Proof of Fact

Let ϕ(w) say that there is a Q-thought θ such that S(w,θ) and but θ is not true at w.

Note that if this is so, and Q(w,w′), then S(w′,θ′) for some θ′ equivalent to θ by (4). Since θ is a Q-thought it is also not true at w′, and hence θ′ is not true at w′, so we have ϕ(w′).

By Q-Thought Existence (6), there is a Q-thought that is true at all and only the worlds w such that ϕ(w) and by (3) there is a Q-thought ρ logically equivalent to it and a world c such that S(c,ρ). Then ρ is also true at all and only the worlds w such that ϕ(w).

Is ρ true at c?

If yes, then ϕ(c). Hence there is a Q-thought θ such that S(c,θ) but θ is not true at w. Since S(c,ρ), we must have θ and ρ equivalent by (2), so ρ is is not true at c, a contradiction.

If not, then we do not have ϕ(c). Since we have S(c,ρ), in order for ϕ(c) to fail we must have ρ true at c, a contradiction.

Thoughts and pluralities of worlds: A paradox

These premises are plausible if the quantifiers over possible thoughts are restricted to possible non-divine thoughts and the quantifiers over people are restricted to non-divine thinkers:

1. For any plurality of worlds ww, there is a possible thought that is true in all and only the worlds in ww.

2. For any possible thought θ, there is a possible world w at which there is a time t such that

   1. someone thinks a thought equivalent to θ at t,
   2. any other thought that anyone thinks at t is entailed by θ, and
   3. nobody thinks anything after t.

In favor of (1): Take the thought that one of the worlds in ww is actual. That thought is true in all and only the worlds in ww.

In favor of (2): It’s initially plausible that there is a possible world w at which someone thinks θ and nothing else. But there are reasons to be worried about this intuition. First, we might worry that sometimes to think a thought requires that one have earlier thought some other thoughts that build up to it. Thus we don’t require that there is no other thinking than θ in w, but only that at a certain specified t—the last time at which anyone thinks anything—there is a limitation on what one thinks. Second, one might worry that by thinking a thought one also thinks its most obvious entailments. Third, Wittgensteinians may deny that there can be a world with only one thinker. Finally, we might as well allow that instead of someone thinking θ in this world, they think something equivalent. The intuitions that led us to think there is a world where the only thought is θ, once we account for these worries, lead us to (2).

Next we need some technical assumptions:

3. Plurality of Worlds Comprehension: If ϕ(w) is a formula true for at least one world w, then there is a plurality of all the worlds w such that ϕ(w).

4. There are at least two worlds.

5. If two times are such that neither is later than the other, then they are the same.

(It’s a bit tricky how to understand (5) in a relativistic context. We might suppose that times are maximal spacelike hypersurfaces, and a time counts as later than another provided that a part of that time is in the absolute future of a part of the other time. I don’t know how plausible the argument will then be. Or we might restrict our attention to worlds with linear time or with a reference frame that is in some way preferred.)

Fact: (1)–(5) are contradictory.

So what should we do? I myself am inclined to deny (3), though denying (1) is also somewhat attractive.

Proof of Fact

Write T(w,uu) for a plurality of worlds uu and a world w provided that for some possible thought θ true in all and only the worlds of uu at w there is a time t such that (a)–(c) are true.

Claim: If T(w,uu) and T(w,vv) then uu = vv.

Proof: For suppose not. Let θ₁ be true at precisely the worlds of uu and θ₂ at precisely the worlds of vv. Let t_i be such that at t conditions (a)–(c) are satisfied at w for θ = θ_i. Then, using (5), we get t₁ = t₂, since by (c) there are no thoughts after t_i and by (a) there is a thought at t_i for i = 1, 2. It follows by (b) that θ₁ entails θ₂ and conversely, so uu = vv.

It now follows from (1) and (2) that T defines a surjection from some of the worlds to pluralities of worlds, and this violates a version of Cantor’s Theorem using (3). More precisely, let C(w) say that there is a plurality uu of worlds such that T(w,uu) and w is not among the uu.

Suppose first there is no world w such that C(w). Then for every world w, if T(w,uu) then the world w is among the uu. But consider two worlds a and b by (4). Let uu, vv and zz be pluralities consisting of a, b and both a and b respectively. We must then have T(a,uu), T(b,vv) and either T(a,zz) or T(b,zz)—and in either case the Claim will be violated.

So there is a world w such that C(w). Let the uu be all the worlds w such that C(w) (this uses (3)). By the surjectivity observation, there is a world c such that T(c,uu). If c is among the uu, then we cannot have C(c) since then there would be a plurality vv of worlds such that T(c,vv) with c not among the vv, from which we would conclude that c is not among the uu by the Claim, a contradiction. But if c is not among the uu, then we have C(c), and so c is among the uu, a contradiction.

Classical mereology and causal regresses

Assume classical mereology with arbitrary fusions.

Further assume two plausible theses:

1. If each of the ys is caused by at least one of the xs and there is no overlap between any of the xs and ys, then the fusion of the ys is caused by a part of the fusion of the xs.

2. It is impossible to have non-overlapping objects A and B such that A is caused by a part of B and B is caused by a part of A.

It follows that:

3. It is impossible to have an infinite causal regress of non-overlapping items.

For suppose that A₀ is caused by A₋₁ which is caused by A₋₂ and so on. Let E be a fusion of the even-numbered items and O a fusion of the odd-numbered ones. Then by (1), a part of E causes O and a part of O causes E, contrary to (2).

This is rather like explanatory circularity arguments I have used in the past against regresses, but it uses causation and mereology instead.

Persons and temporal parts

On perdurantism, we are four-dimensional beings made of temporal parts, and our actions are fundamentally those of the temporal parts.

This is troubling. Imagine a person with a large number of brains, only one of which is active at any one time, and every millisecond a new brain gets activated. There would be something troubling about the fact that we are always interacting with a different brain person, and only interacting with the person as a whole by virtue of interacting with ever different brains. And this is pretty much what happens on perdurantism.

Maybe it’s not so bad if each brain’s data comes from the previous brain, so that by learning about the new brain we also learn about the old one. And, granted, on any view over time we interact to some degree with different parts of the person—most cells swap out, and we would be untroubled if this turned out to hold for neurons as well. But it seems to me that it is a more attractive picture of interpersonal interactions if there is a fundamental core of the person with which we interact that is numerically the same core in all the interactions, so that the changing cells are just expressions of that same core.

This is not really much of an argument, just an expression of a feeling.

Imposing the duty of gratitude

Normally if Alice did something supererogatory for Bob, Bob has gained a duty to be grateful to me. It is puzzling that we have this normative power to impose a duty on someone else. (Frank Russell’s “And then there were none” story turns on this.)

In some cases the puzzle is solved by actual or presumed consent on the part of Bob.

Here’s the hard case. Bob is in the right mind. Bob doesn’t want the superegatory deed. But his not wanting it, together with the burden to Bob of having to be grateful, is morally outweighed by the benefit to Bob, so Alice’s deed is still good and indeed supererogatory.

I think in this case, Bob indeed acquires the duty of gratitude. We might now say that imposing the burden of gratitude was indeed a reason for Alice not to do the thing—but an insufficient reason. We can also lessen the problem by noting that if being grateful is a burden to Bob, that is because Bob is lacking in virtue—perhaps Bob has an excessive love of independence. To a virtuous person, being grateful is a joy. And often we shouldn’t worry much about imposing on someone something that is only a burden if they are lacking in a relevant virtue.

Disbelief

Suppose Alice believes p. Does it follow that Alice disbelieves not-p? Or would she have to believe not-not-p to disbelieve not-p? (Granted, in both classical and intuitionistic logic, not-not-p follows from p.)

Maybe this is a merely verbal question about “disbelieves”.

Or could it be that disbelief is a primitive mental state on par with belief?

Omniscience and vagueness

Suppose there is metaphysical vagueness, say that it’s metaphysically vague whether Bob is bald. God cannot believe that Bob is bald, since then Bob is bald. God cannot believe that Bob is not bald, since then Bob is not bald. Does God simply suspend judgment?

Here is a neat solution for the classical theist. Classical theists believe in divine simplicity. Divine simplicity requires an extrinsic constitution model of divine belief or knowledge in the case of contingent things. Suppose a belief version. Then, plausibly, God’s beliefs about contingent things are partly constituted by the realities they are about. Hence, it is plausible that when a reality is vague, it is vague whether God believes in this reality.

Here is another solution. If we think of belief as taking-as-true and disbelief as taking-as-false, we should suppose a third state of taking-as-vague. Then we say that for every proposition, God has a belief, disbelief or third state, as the case might be.

Desire, preference, and utilitarianism

Desire-satisfaction utilitarianism (DSU) holds that the right thing to do is what maximizes everyone’s total desire satisfaction.

This requires a view of desire on which desire does not supervene on preferences as in decision theory.

There are two reasons. First, it is essential for DSU that there be a well-defined zero point for desire satisfaction, as according to DSU it’s good to add to the population people whose desire satisfaction is positive and bad to add people whose desire-satisfaction is negative. Preferences are always relative. Adding some fixed amount to all of a person’s utilities will not change their preferences, but can change which states have positive utility and which have negative utility, and hence can change whether the person’s on-the-whole state of desire satisfaction is positive or negative.

Second, preferences cannot be compared across agents, but desires can. Suppose there are only two states, eating brownie and eating ice cream (one can’t have both), and you and I both prefer brownie. In terms of preference comparisons, there is nothing more to be said. Given any mixed pair of options i = 1, 2 with probability p_i of brownie and 1 − p_i of ice cream, I prefer option i to option j if and only if p_i > p_j, and the same is true for you. But this does not capture the possibility that I may prefer brownie by a lot and you only by a little. Without capturing this possibility, the preference data is insufficient for utilitarian decisions (if I prefer brownie by a lot, and you by a little, and there is one brownie and one serving of ice cream, I should get the brownie and you should get the ice cream on a utilitarian calculus).

The technical point here is that preferences are affine-invariant, but desires are not.

But now it is preferences that are captured behavioristically—you prefer A over B provided you choose A over B. The extra information in desires is not captured behavioristically. Instead, it seems, it requires some kind of “mental intensity of desire”.

And while there is reason to think that the preferences of rational agents at least can be captured numerically—the von Neumann–Morgenstern Representation Theorem suggests this—it seems dubious to think that mental intensities of desire can be captured numerically. But they need to be so captured for DSU to have a hope of success.

The same point holds for desire-satisfaction egoism.

Punishment and amnesia

There is an interesting philosophical literature on whether it is appropriate to punish someone who has amnesia with respect to the wrong they have done.

It has just occurred to me (and it would be surprising if it’s not somewhere in that literature) that it is obvious that rewarding someone who has amnesia with respect to the good they have done is appropriate. To make the intuition clear, imagine the extreme case where the amnesia is due to the heroic action that otherwise would cry out for reward.

If amnesia does not automatically wipe out positive desert, it also does not automatically wipe out negative desert.

Fine-tuning of both physical and bridge laws

A correspondent pointed me to a cool paper by Neil Sinhababu arguing that the theist can’t consistently run a fine-tuning argument on which it is claimed that it is unlikely that the constants in the laws of physics permit intelligent life, because if God exists, then for any constants in the physical laws God can make psychophysical bridge laws that make sure that there is intelligent life. By choosing the right bridge laws, God can make a single electron be conscious, after all. Thus any set of constants in laws of physics is compatible with intelligent life.

A quick response is that in the context of the fine-tuning argument, by “intelligent life” we should probably mean “intelligent biological life”. For instance, angels and conscious electrons don’t count, as they aren’t biological. And in fact, I think, in practice the fine-tuning argument is more about biological life than intelligent life as such. This suggests, however, that proponents of the fine-tuning argument should be clearer here. In particular, we (I am one of the proponents) should emphasize that there is a great value in the existence of biological life, and especially intelligent biological life, and this value is not found in intelligent non-biological life. This value is why a perfect being is not unlikely (or at least not extremely unlikely) to fine-tune the universe to for such life.

Second, I think Sinhababu’s argument points to a more subtle way to formulate the fine-tuning thesis. What’s fine-tuned is not the laws of physics alone, but the combination of the laws of physics and the bridge laws, and they are fine-tuned together in such a way as to ensure that there is neither too little nor too much intelligent life. For instance, a set of psychophysical laws where any computation isomorphic to the kinds of computations our brains results in mental functioning like ours would result not just in panpsychism but omnisapientism—everything around us is sapient. For with some cleverness we can find an isomorphism between the states of a single particle and the states of the brain that preserves causation. But omnisapientism isn’t very good: it damages the significance of morality if everything we do creates and destroys vast numbers of sapient beings.

Per se and per accidens multiplication of causes

Can there be an infinite sequence of efficient causes? Famously, Aquinas says both “No” and “Yes”, and makes a distinction between a per se ordering (“No”) and an accidental ordering (“Yes”). But it is difficult to reconstruct how the distinction goes, and whether there is good reason to maintain given modern physics.

Here is the central passage from Summa Theologiae I.46.2 reply 7, in Freddoso’s translation:

It is impossible to proceed to infinity per se among efficient causes, i.e., it is impossible for causes that are required per se for a given effect to be multiplied to infinity—as, for instance, if a rock were being moved with a stick, and the stick were being moved by a hand, and so on ad infinitum.

By contrast, it is not impossible to proceed to infinity per accidens among agent causes, i.e., it is not impossible if all the causes that are multiplied to infinity belong to a single order (ordinem) of causes and if their multiplication is incidental (per accidens)—as, for instance, if a craftsman were to use many hammers incidentally, because one after another kept breaking. In such a case, it is incidental to any given hammer that it acts after the action of a given one of the other hammers. In the same way, it is incidental to this man, insofar as he generates, that he himself was generated by another. For he generates insofar as he is a man and not insofar as he is the son of some other man, since all the men who generate belong to the same order (gradum) of efficient causality, viz., the order of a particular generating cause. In this sense, it is not impossible for man to be generated by man ad infinitum.

However, it would indeed be impossible for the generation of this man to depend upon that man, and upon an elemental body [a corpore elementari], and upon the sun, and so on ad infinitum.

What’s going on here? Re-reading the text (and double-checking against the Latin) I notice that per se and per accidens are introduced not as modifying the causal relations, but the infinite multiplication of causes. No indication is given initially that the causation functions differently in the two cases. Further, it is striking that both of the examples of per accidens multiplication of causes involve causes of the same type: hammers and humans (Freddoso’s “man” translates homo throughout the text).

To a first approximation, it seems then that what is forbidden is a regress of infinitely many types of causes, whereas a regress of infinitely many tokens is permitted. But that is too simple. After all, if an infinite causal sequence of humans generating humans were possible, it would surely also be possible for each of these humans to be qualitatively different from the others—say, in exact shade of eye color—and hence for there to be infinitely many types among them. In other words, not just any type will do.

Let’s focus in on two other ingredients in the text, the observation that the humans all “belong to the same order of efficient causality”, and the sun–elementary body–human example. Both of these rang a bell to me, because I had recently been writing on the Principle of Proportionate Causality. At Summa Theologiae I.4.2, St Thomas makes a different distinction that distinguishes between the human–human and the sun–body–human cases:

whatever perfection exists in an effect must be found in the effective cause: either in the same formality, if it is a univocal agent—as when man reproduces man; or in a more eminent degree [eminentiori modo], if it is an equivocal agent—thus in the sun is the likeness of whatever is generated by the sun’s power.

Here is a suggestion. In distinguishing per se and per accidens infinite multiplication of causes, Aquinas is indeed distinguishing counting types and tokens. But the types he is counting are what one might call “causal types” or “perfections”. The idea is that we have the same causal type when we have univocal agency, “as when man reproduces man”, and different causal type when we have equivocal agency, as when the sun generates something, since on Aquinas’ astronomical theory the sun is sui generis and hence when the sun generates, the sun is quite different from what it generates. In other words, I am tentatively suggesting that we identify the gradus of efficient causality of I.46.2 with the modus of perfection of I.4.2.

The picture of efficient causation that arises from I.4.2 is that in a finite or infinite causal regress we have two types of moves between effect and cause: a lateral move to a cause with the same perfection as the effect and an ascending vertical move to a cause that has the perfection more eminently.

The lateral moves only accidentally multiply the explanations, because the lateral moves do not really explain the perfection. If I got my humanity from another human, there is a sense in which this is not really an explanation of where my humanity comes from. The human I got my humanity from was just passing that humanity on. I need to move upwards, attributing my humanity to a higher cause. On this reading, Aquinas is claiming that there can only be finitely many upwards moves in a causal regress. Why? Maybe because infinite passing-on of more to less eminent perfections is just as unexplanatory as finite passing on of the same perfection. We need an ultimate origin of the perfections, a highest cause.

I like this approach, but it fits better with the sun–elemenatary body–human example than the hand–stick–rock example. It seems, after all, that in the hand–stick–rock example we have the same relevant perfection in all three items—locomotion, which is passed from hand to stick and then from stick to rock. This would thus seem like a per accidens multiplication rather than a per se one. If so, then it is tempting to say that Aquinas’ hand–stick–rock example is inapt. But perhaps we can say this. Hand-motion is probably meant to be a voluntary human activity. Plausibly, this is different in causal type from stick-motion: going from stick to hand is indeed an explanatory ascent. But it’s harder to see the progression from rock to stick as an explanatory ascent. After all, a rock can move a stick just as much as a stick can move a rock. But perhaps we can still think we have an ascent from rock-moving to stick-moved-by-hand, since a stick-moved-by-hand maybe has more of the perfection of the voluntary hand motion to it? That sounds iffy, but it’s the best I can do.

I wish Aquinas discussed a case of stick–stick–stick, where each stick moves the next? Would he make this be a per se multiplication of causes like the hand–stick–rock case? If so, that’s a count against my reading. Or would he say that it’s an accidental multiplication? If so, then my tentative reading might be right.

It’s also possible that Aquinas’ examples of hand–stick–rock and sun–elementary body–human are in fact more unlike than he noticed, and that it is the latter that is a better example of per se multiplication of causes.

Per se and per accidens ordered series

I’ve never been quite clear on Aquinas’ famous distinction between per se and per accidens ordered series, though I really like the clarity of Ed Feser’s explanation. Abridging greatly:

An instrumental cause is one that derives whatever causal power it has from something else. … [A]ll the causes in [a per se] series other than the first are instrumental [and thus] are said to be ordered per se or “essentially,” for their being causes at all depends essentially on the activity of that which uses them as instruments. By contrast, causes ordered per accidens or “accidentally” do not essentially depend for their efficacy on the activity of earlier causes in the series. To use Aquinas’s example, a father possesses the power to generate sons independently of the activity of his own father … .

The problem here is that it’s really hard to think of any examples of purely instrumental causes in this sense. Take Aquinas’s example of a per se series where the hand moves a stick which moves the stone. That may work in his physics, but not in ours. Every stick is basically a stiff spring—there are no rigid bodies. So, for ease of visualization, let’s imagine a hand that pushes one end of a spring, and the other end of the spring pushes the stone. When you push your end of the spring, the spring compresses a little. A compression wave travels down the spring and the tension in the spring equalizes. The spring is now “charged” with elastic potential energy. And it then pushes on both the hand and the stone by means of the elastic potential energy. There is an unavoidable delay between your pushing your end of the spring and the other end pushing the stone (unavoidable, because physical causation doesn’t exceed the speed of light).

Now, once the spring is compressed, its pushing on the stone is its own causal activity. We can see this as follows. Suppose God annihilated your hand. For a very short while, the other end of the spring wouldn’t notice. It would still be pushing against the stone, and the stone would still be moving. Then the spring would decompress in the direction where the hand used to be, and the stone’s movement would stop. But a very short while is still something—it’s enough to show that the spring is acting on its own. The point isn’t that the stone would gradually slow down. The point, rather, is that it takes a while for the stone’s movement to be at all affected, because otherwise we could have faster-than-light communication between the hand and the spring.

What goes for springs goes for sticks. And I don’t know any better examples. Take Feser’s example in his Five Ways book of a cup held up by a desk which is held up by a floor. Feser says the desk “has no power on its own to hold the cup there. The desk too would fall to the earth unless the floor held it aloft”. Yes, it would—but not instantly. If the floor were to disappear, the tension in the desk’s legs—which, again, are just stiff springs—would continue to press upward on the desktop, which would press upward on the cup, counteracting gravity. But then because the bottoms of the legs are unsupported, the tension in the legs would relax, the legs would imperceptibly lengthen, and the whole thing would start to fall. Still, for a short while the top of the desk would have been utterly unaffected by the disappearance of the floor. It would only start accelerating downward once the tension in the legs dissipatated. It takes a time of at least L/c, where L is the length of the legs and c is the speed of light, for that to happen. Again, the legs of the table are charged-up springs whose internal tension is holding up the desktop.

If this is right, then we don’t have any clear examples of the kind of purely instrumental causality that Feser—and, fairly likely, Aquinas—is talking about. Now, it may be that the deep metaphysics of causation is indeed such that indeed all creaturely causation is indeed of this instrumental sort, being the instrument of the first cause. But since Aquinas is using the idea of per se causal series to establish the existence of the first cause, we need an argument here that does not depend on the existence of the first cause.

On Rasmussen and Bailey's "How to build a thought"

[Revised 11/21/2025 to fix a few issues.]

Rasmussen and Bailey prove that under certain assumptions it follows that there are possible thoughts that are not grounded in anything physical.

I want to offer a version of the argument that is slightly improved in a few ways.

Start with the idea that an abstract object x is a “base” for types of thoughts. The bases might be physical properties, types of physical facts, etc. I assume that in all possible worlds exactly the same bases abstractly exist, but of course what bases obtain in a possible world can vary between worlds. I also assume that for objects, like bases, that are invariant between worlds, their pluralities are also invariant between worlds.

Consider these claims:

1. Independence: For any plurality xx of bases, there is a possible world where it is thought that exactly one of the xx obtains and there is no distinct plurality yy of bases such that it is thought that exactly one of the yy obtains.

2. Comprehension: For any formula ϕ(x) with one free variable x that is satisfied by at least one base, there is a plurality yy of all the bases that satisfy ϕ(x).

3. Plurality: There are at least two bases.

4. Basing: Necessarily, if there is a plurality xx of bases and it is thought that exactly one of the xx obtains, then there obtains a base z such that necessarily if z obtains, it is thought that exactly one of the xx obtains.

By the awkward locution “it is thought that p”, I mean that something or some plurality of things thinks that p, or there is a thinkerless thought that p. The reason for all these options is that I want to be friendly to early-Unger style materialists who think that there no thinkers. :-)

Theorem: If Independence, Comprehension, Plurality and S5 are true, Basing is false.

Here is how this slightly improves on Rasmussen and Bailey:

• RB’s proofs use the Axiom of Choice twice. I avoid this. (They could avoid it, too, I expect.)

• I don’t need a separate category of thoughts to run the argument, just a “it is thought that exactly one of the xx exists” predicate. In particular, I don’t need types of thoughts, just abstract bases.

• RB use the concept of a thought that at least one of the xx exists. This makes their Independence axiom a little bit less plausible, because one might think that, say, someone who thinks that at least one of the male dogs exists automatically also thinks that at least one of the dogs exists. One might also reasonably deny this, but it is nice to skirt the issue.

• I replace grounding with mere entailment in Basing.

• I think RB either forgot to assume Plurality or are working with a notion of plurality where empty collections are possible.

Some notes:

• RB don’t explicitly assume Comprehension, but I don’t see how to prove their Cantorian Lemma 2 without it.

• Independence doesn’t fit with the necessary existence of an omniscient being. But we can make the argument fit with theism by replacing “it is thought” with “it is non-divinely thought”.

• I think the materialist could just hold that there are pluralities xx of bases such that no one could think about them.

Proofs

Write G(z,xx) to mean that z is a base, the xx are a plurality of bases, and necessarily if z obtains it is thought that exactly one of the xx obtains.

The Theorem follows from the following lemmas.

Lemma 1: Given Independence, Basing and S5, for every plurality of bases xx there is a z such that G(z,xx) and for every other plurality of bases yy it is not the case that G(z,yy).

Proof: Let w be a possible world like in Independence. By Basing, at w there obtains a base z such that G(z,xx). By S5 and the bases and pluralities thereof being the same at all worlds, we have G(z,xx) at the actual world, too. Suppose now that we actually have G(z,yy) with yy other than xx. Then at w, it is thought that exactly one of yy exists. But that contradicts the choice of w. Thus, actually, we have G(z,xx) but not G(z,yy).

Lemma 2: Assume Comprehension and Plurality. Then there is no formula ϕ(z,xx) open only in z and xx such that for every plurality of bases xx there is a z such that ϕ(z,xx) while for every other plurality of bases yy it is not the case that ϕ(z,yy).

Proof: Suppose we have such a ϕ(z,xx). Say that z is an admissible base provided that there is a unique plurality of bases xx such that ϕ(z,xx). I claim that there is an admissible base z such that z is not among any xx such that ϕ(z,xx). For suppose not. Then for all admissible bases z, z is among all xx such that ϕ(z,xx). Let a and b be distinct bases. Let ff, gg and hh be the pluralities consisting of a, of b, and of both a and b respectively. Then the above assumptions show that we must have ϕ(a,ff), ϕ(b,gg) and either ϕ(a,hh) or ϕ(b,hh), and either of these options violates our assumptions on ϕ. By Comprehension, then, let yy be the plurality of all admissible bases z such that z is not among any xx such that ϕ(z,xx). Let z be an admissible base such that ϕ(z,yy). Is z among the yy? If it is, then it’s not. If it is not, then it is. Contradiction!

Omniscience, timelessness, and A-theory

I’ve been thinking a lot this semester, in connection with my Philosophy of Time seminar, about whether the A-theory of time—the view that there is an objective present—can be made consistent with classical theism. I am now thinking there are two main problems here.

1. God’s vision of reality is a meticulous conscious vision, and hence if reality is different at different times, God’s consciousness is different at different times, contrary to a correct understanding of immutability.

2. One can only know p when p is true; one can only know p when one exists; thus, if p is true only at a time, one can only know p if one is in time. On an A-theory of time, there are propositions that are only true in time (such as that presently I am sitting), and hence an omniscient God has to be in time. Briefly: if all times are the same to God, God can’t know time-variable truths.

I stand by the first argument.

However, there may be a way out of (2).

Start with this. God exists at the actual world. Some classical theists will balk at this, saying that this denies divine transcendence. But there is an argument somewhat parallel to (2) here. If all worlds are the same to God, God can’t know world-variable truths, i.e., contingent truths.

Moreover, we can add something positive about what it is for God to exist at world w: God exists at w just in case God actualizes w. There is clearly nothing contrary to divine transcendence in God’s existing at a world in the sense of actualizing it. And of course it is only the actual world that God actualizes (though it is true at a non-actual world w′ that God actualizes w′; but all sorts of false things are true at non-actual worlds).

But given the A-theory, reality itself includes changing truths, including the truth about what it is now. If worlds are ways that all reality is, then on A-theory worlds are “tensed worlds”. Given a time t, say that a t-world is a world where t is present. Argument (2) requires God to exist at a t-world in order for God to know something that is true only at a t-world (say, to know that t is present).

Now suppose we have an A-theory that isn’t presentism, i.e., we have growing block or moving spotlight. Then one does not need to exist at t in order to exist at a t-world: on both growing block and moving spotlight our 2025-world has dinosaurs existing at it, but not in 2025, of course. But if one does not need to exist at t in order to exist at a t-world, it is not clear that one needs to exist in time at all in order to exist at a t-world. The t-world can have a “locus” (not a place, not a time) that is atemporal, and a being that exists at that atemporal locus can still know that t is present and all the other A-propositions true at that t-world.

Next suppose presentism, perhaps the most popular A-theory. Then everything that exists at a t-world exists at t. But that God exists at the t-world still only consists in God’s actualizing the t-world. This does not seem to threaten divine transcendence, aseity, simplicity, immutability, or anything else the classical theist should care about. It does make God exist at t, and hence makes God in time, but since God’s existing in time consists in God’s actualizing a t-world, this kind of existence in time does not make God dependent on time.

I still have some worries about these models. And we still have (1), which I think is decisive.

A bit of finetuning

Here’s a bit of finetuning in the world’s laws that I just noticed. All the four fundamental forces of nature are conveniently local, in the sense that they drop off to nearly zero with distance. If any one of them weren’t local, the world would not be likely to be predictable to limited knowers like us.

Towards a solution to the "God as author of evil" problem for the Thomistic model of meticulous providence

On the Thomistic primary/secondary causation model of meticulous divine providence, when we act wrongly, God fully determines the positive aspects of the action with primary causation, and we in parallel cause the action with secondary causation.

Like many people, I worry that this makes God the author of sin in an objectionable way.

Alice and Bob are studying together for a calculus exam that will be graded on a curve. In order that she may do terribly on the exam, and thus that he might do better, and hence be more likely to get into his dream PhD program in ethics, Bob lies to Alice, who has missed three weeks of class, that the derivative of the logarithm is the exponential.

What does God cause in Bob’s action on the Thomistic model? It seems that all of the following are positive aspects:

1. The physical movements in Bob’s mouth, throat, and lungs.

2. The sounds in the air.

So far we don’t have a serious theological problem. For (1) and (2) are not intrinsically bad, since Bob could virtuously utter the same sounds while playacting on stage. But let’s add some more aspects:

3. Bob’s intention that the speech constitute an assertion of the proposition that the derivative of the logarithm is the exponential.

4. Bob’s intention that the asserted proposition be a falsehood that Alice comes to believe and that leads to her doing terribly on the exam.

Perhaps one can argue that falsity a negative thing—a lack of conformity with reality. However, intending falsity seems to be a positive thing, a positive (but wicked) act of the will. Thus it seems that (3) and (4) are positive things. But once we put together all of (1)–(4), or even just (3) and (4), then it’s hard to deny that what we have is something wicked, and so if God is intending all of (1)–(4), it’s hard to avoid the idea that this makes God responsible for the sin in a highly problematic way.

There may be a way out, however. In both written and spoken language, meaning is normally not constituted just by the positive aspects of reality but also by negative ones. In spoken language, we can think of the positive aspects as the peaks of the soundwaves (considered as pressure waves in the air). But if you remove the troughs from the soundwaves, you lose the communication. In print, on the other hand, the meaning depends not just on the ink that’s there, but on the ink that’s not there. A page wholly covered with ink means nothing. We only have meaningful letters because the inked regions are surrounded by non-inked regions.

It could well turn out that the language of the mind in discursively thinking beings like us is like that as well, so that a thought or intention is constituted not only by ontologically positive but also by ontologically negative aspects. Now you could be responsible for the ink within the print inscription

5. The derivative of the logarithm is the exponential

without being responsible for the inscription. For instance, you and a friend might have had a plan to draw a black rectangle and you divided up the labor as follows: you inked the region of rectangle covered by the letters of “The derivative of the logarithm is the exponential” and then your friend would ink the rest of the containing rectangle—i.e., everything outside the letters. But your friend didn’t do the job. Similarly, then, if intentions are constituted by both positive and negative features, God could intend the positive features of an intention without being responsible for the intention as such.

This does place constraints on the language of the mind, i.e., on the actual mental accidents that constitutes our thoughts, and specifically our intentions. Note, though, that we don’t need that all intentions have a negative constituent. Only intentions to produce negative things, like falsehood, need to have a negative constituent for us to avert the problem of God willing intentional sin. We could imagine a written language where positive phrases are written in two colors of ink, one for the letters and the other for the surrounding rectangle, and their negations are written by omitting the ink for the letters. In such a language, statements involving positive phrases are purely positive, while those involving negative phrases are partly negative.

I am not very happy with this solution. I still worry that being responsible for the ink in (5) makes one responsible for (5) when one chooses not to have the rest of the rectangle filled in.

Perfect vision

One of the major themes in modern philosophy was concerns about the way that our contact with the world is mediated by our “ideas”. Thus, you are looking at a tree. But are you really seeing the tree, or are you just seeing your sense-impression, which doesn’t have much in common with the tree? Even direct realists like Reid who say you are seeing the cat still think that your conscious experience involves qualia that aren’t like a tree.

Thinking about this gives us the impression that an epistemically better way to relate to the tree would be if the tree itself took the place of our sense-impressions or qualia. Berkeley did that, but at the cost of demoting the tree to a mere figment of our perception. But if we could do that without demoting the tree, then we would be better kinds of perceivers.

However, that on some theory we would be better kinds of perceivers is not a strong reason to think that theory is true! After all, we would be better perceivers if we could see far infrared, but we can’t. It’s not my point to question the orthodoxy about our perceptions of trees.

But now think about beatitude, where the blessed see God. If seeing God is like seeing a tree in the sense that there is something like a mediating supersense-impression in us, then something desirable is lacking in the blessed. And that’s not right. Such a mediated vision of God is not as intimate as we could wish for. Would it not be so much more intimate if it were a direct vision of God in the fullest sense, where God himself takes the place of our qualia? We shouldn’t argue from “it would be better that way” to “it is that way” in our earthly lives, but in beatitude it does not seem such a terrible argument.

But where this kind of argument really comes into its own is when we think of what the epistemic life of a perfect being would be like. The above considerations suggest that when God sees the tree (and it is traditional to compare God’s knowledge of creation to vision), the vision is fully direct and intimate, and the tree itself plays the role of sense-impressions in us. We would expect a perfect being’s vision to be like that.

Now notice, however, that this is an account of God’s vision of the world on which God’s vision is partly extrinsically constituted: the tree partly constitutes God’s conscious experience of the tree. This is the extrinsic constitution model of how a simple God can know. We have thus started with us and with considerations of perfection, and have come to something like this model without any considerations of divine simplicity. Thus the model is not an ad hoc defense of divine simplicity. It is, rather, a model of the perfect way to epistemically relate to the world.

An argument against the Thomistic primary/secondary causation account of strong providence

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed. Some like me think one cannot have circularity in the order of explanation at all. I argued for this thesis in my previous post today. Now I want to draw an interesting application.

On one influential (and I think exegetically correct, pace Eleonore Stump) reading of Aquinas, God decides what our free choices will be. Our free choices cannot be determined by created causes, but they are determined by God. This is because God’s causation is primary causation which is of a different sort from the secondary causation which is creaturely causation. God can primarily cause you to freely secondarily cause something, and this is how providence and free will interact. Often the analogy between an author and a character is given: the author decides what the character will freely do and this does not infringe on the character’s freedom.

But now observe this (which was brought home to me by a paper of one of our grad students). On this picture, God will presumably sometimes providentially make earlier actions happen because of later ones. Thus, God may want you to perform some heroic self-sacrifice in ten years. So, right now God prepares you for this by having you freely engage in small self-sacrifices now. In the “because” corresponding to the explanatory order of providence and primary causation, we thus have:

1. You engage in small self-sacrifices because you will engage in a great self-sacrifice.

However, divine primary causation does not undercut secondary causation, and we have the standard Aristotelian story of habituation at the level of secondary causation in light of which we have:

2. You will engage in a great self-sacrifice because you are engaging in small self-sacrifices.

These explanations form a heterotypic explanatory loop (i.e., we have explanations of two different sorts in opposite directions). But if I am right that no explanatory loop is possible, the above story is not possible. However, there is nothing to rule out the above story if the above Thomistic account of primary and secondary causation’s role in providence is correct. Hence, I think we should reject that account.

If no homotypic circles of explanation, no heterotypic ones either

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed, i.e., there are no homotypic circles of explanation. Some like me think one cannot have circularity in the order of explanation at all. Why? One intuition might be that explanations of all types are still explanations, and so the circularity is still an explanatory circularity. :-) (Yes, that begs the question.) More seriously, heterotypic explanations (namely, explanations of different types) can be combined, sometimes chainwise (A explains B and B explains C, and thereby A explains C) and sometimes in parallel (A explains B and C explains D so A-and-C explains B-and-D). This means that the types of explanation are not quite as separate as they might seem.

Here is an argument building on the second intuition. We need two concepts. First, we can talk of two sets of explanatory relations as independent, namely without any interaction between the explanatory relations in the two sets. Second, given two type of explanation₁ and explanation₂, I will say that explanation_1|2 is a type of explanation where explanation₁ and explanation₂ are combined in parallel.

1. If circularity in explanation is possible, it is possible to have a two-item heterotypic explanatory loop.

2. If it is possible to have a two-item heterotypic explanatory loop, it is possible to have two independent two-item heterotypic explanatory loops where each loop involves the same pair of explanation types as the other loop.

3. Necessarily, if A explains₁ B and C explains₂ D, and the two explanatory relations here are independent, then A-and-C explains_1|2 B-and-D.

4. Necessarily, the relations explains_1|2 and explains_2|1 are the same.

5. It is not possible to have a circle of explanations of the same type.

6. Suppose circularity in explanation is possible. (Assume for reductio)

7. There is a possible world w, such that at w: there are A, B, C and D such that A explains₁ B, B explains₂ A, D explains₁ C and C explains₂ D, and the above explanatory relations between A and B are independent of the above explanatory relations between C and D. (6,1,2)

8. At w: A-and-C explains_1|2 B-and-D. (3,7)

9. At w: B-and-D explains_2|1 A-and-C. (3,7)

10. At w: B-and-D explains_1|2 A-and-C. (4,9)

11. At w: there is a circle of explanations of type 1|2. (8,10)

12. Contradiction! (5,11)

13. So, circularity in explanation is impossible.

I think the most problematic premise in this argument is (4). However, if (4) is not true, we have a vast multiplication in types of explanation.

Symmetric relations and logic

Suppose Alice and Bob are friends, and that friendship is a fundamental relation. Consider the facts expressed by these two sentences:

1. Alice and Bob are friends.

2. Bob and Alice are friends.

It is implausible that these are different facts. For if they were different facts, they would both be fundamental facts (otherwise, which of them would be the fundamental one?), and we would be multiplying fundamental facts beyond necessity—only one of the two is needed in the totality of fundamental facts.

Furthermore, I think that the propositions expressed by (1) and (2) are the same. Here’s one reason to think this. Imagine a three-dimensional written language where plural symmetric predicates like “are friends” are written (say, laser-inscribed inside a piece of glass) with “and are friends” on one horizontal layer, with “Alice” on a layer below the “and” and “Bob” on a layer above it. If (1) and (2) express different propositions, we would have to ask which of them is a better translation of the three-dimensional language. But surely there is no fact about that.

If this is right, then First Order Logic (FOL) fails to accurately represent propositions about fundamental relations, by having two atomic sentences, F(a,b) and F(b,a), where there is only one fundamental fact. Moreover, FOL will end up having non-trivial proofs whose conclusion expresses the same proposition as the premise, since we will presumably have an axiom like ∀x∀y(F(x,y)→F(y,x)) that lets us prove F(b,a) from F(a,b). This is not the only example of this phenomenon. Take the proof that ∀xF(x) follows from ∀yF(y), even though surely the two express the same proposition, namely that everything is F.

In particular, the logic of sentences appears to differ from the logic of propositions, since the proposition that Bob and Alice are friends follows by reiteration from the proposition that Alice and Bob are friends if they are the same proposition, but sentence (2) does not follow from sentence (1) by reiteration (nor is this true for the FOL versions).

If we think there is a One True Logic, it presumably will be a logic of propositions rather than sentences, then. But what it will be like is a difficult question, to answer which we will have to a worked out theory of when we have the same proposition and when we have different ones.

An argument for dualism from Special Relativity and unity of consciousness

Here’s a valid argument:

1. There is always an absolute fact about whether two conscious states are hosted simultaneously.

2. If the mind is physical, there is not always an absolute fact about whether two conscious states are hosted simultaneously.

3. So, the mind is not physical.

Why believe (2)? Well, if the mind is physical, it is a brain—that’s by far and away our best physical theory of the mind. The brain is spatially extended, and it is very plausible that different brain regions are involved in different conscious states. But now we can imagine that one conscious state ends almost when another begins, so that the overlap time between the two conscious states is very, very small—say, a picosecond. If the brain brain regions involved in the two conscious states are sufficiently different (more precisely, if their convex hulls differ sufficiently in comparison to the distance light travels during the overlap time), then there will also be some reference frame in which the two conscious states do not temporally overlap. Hence, it depends on reference frame whether the two conscious states overlap, and there is no fact of the matter about simultaneity of the conscious states.

If I were a physicalist, I think I would attack (1).

Three fixity principles

In debates about free will and foreknowledge as well as about compatibility and incompatibilism, fixity-of-history theses come up. Here is such a thesis:

1. If a decision is causally or logically necessitated by the history behind the decision, then one could not have decided otherwise.

But now we have a crucial question as to what is meant by “the history behind the decision”. There are at least two takes on this. On the temporal version, the history behind the decision is the sum total of what happened temporally prior to the decision. On the causal version, the history is the sum total of what happend causally prior to the decision.

This is not just a nitpicking question. Linda Zagzebski for instance nicely shows that if we go for the causal-history version of (1), then the main argument for the incompatibility of free will and foreknowledge does not get off the ground assuming God’s forebelief is not causally prior to the action. On the other hand, if we go the temporal-history version, then we have a prima facie argument for such incompatibility (though I think it’s blockable).

I am pretty confident that we should go for the causal-history version, and this has to do with the fact that the temporal-history version is not strong enough to capture our fixity intuitions. Suppose that we live in a world with simultaneous causation—say, a Newtonian world with rigid objects such that if you push object A and A pushes B, then B begins to move at exactly the same time as you start pushing (rather than with a delay caused by then need for a compression wave traveling through nonrigid materials at less than the speed of light). Then we could imagine cases where someone’s decision is causally necessitated by something outside the agent that is simultaneous with the decision. Such causal necessitation would just much make it true that one could not have decided otherwise as would causal necessitation by something in the past.

Furthermore, if backwards causation is possible, then a neurosurgeon in the future who used a backwards-causing machine to determine your decision would clearly prevent you from deciding otherwise, even though the neurosurgeon’s action was not in the temporal history. We may not believe backwards causation is possible, but it is clear that if it were possible, then deterministic backwards causation would be just as threatening for free decisions as deterministic forwards causation. This shows that causal determination is indeed a threat.

Of course, my above argument only shows that if we need to choose between the causal and temporal history versions of (1), we should definitely go for the causal one. But perhaps we don’t need to choose. We could accept both versions. But if we think we accept both versions, I think what we really should accept is an even stronger principle, where “history” is causal-cum-temporal (cct). On that stronger principle, event A counts as in the cct history of event E provided that it is either temporally or causally prior to E. The resulting fixity principle is pretty strong principle, but also a bit gerrymandered. And I think accepting this principle not that plausible, because the much simpler causal version captures our intuitions about all the ordinary cases (not involving God, or backwards or simultaneous causation), since in all ordinary cases causal and temporal history coincide, and we should not go for a more complex principle without pretty good reason.

God's forebeliefs are soft facts

The most commonly discussed argument against the compatibility of foreknowledge and free will is based on the “fixity of the past”—that nothing you can do can affect how things were, and hence nothing you can do can affect what God had believed.

However, everyone except the logical fatalist agrees that the “fixity of the past” does not apply to so-called “soft facts”. An example of a soft fact (an expansion of an example of Richard Gale) is to suppose that Alice drank a cup of poison, but hasn’t died yet. Alice would survive if Bob calls 911, but he’s not going to. Then it’s a fact that Alice drank a fatal cup, but this is a soft fact, and there is no difficulty in saying that Bob can make this fact not to have obtained. It is only the hard facts about the past that are supposed to be fixed.

Thus, much of the discussion has focused on the question of whether God’s past forebeliefs could be soft facts. In this post, I want to note that classical theists have very good reason to think that God’s past forebeliefs are soft facts.

Start with the following plausible principle:

1. If a fact F expressed by a past-tense statement is partly grounded in a fact G about the present or future, then F is a soft fact.

Of course, defining a fact “about the present or future” is just as difficult as defining a soft fact, but I am not trying to give a definition of a soft fact, just giving a sufficient condition for being one.

Now, on classical theism, God is simple and hence has no intrinsic accidental features. God’s beliefs about contingent realities then have to be partly constituted by those contingent realities (this is the extrinsic constitution model, and it is unavoidable). Such partial extrinsic constitution is a type of grounding. Thus, God’s belief in a fact is partly grounded in that fact.

Hence, God’s having believed in a fact about the present or future is partly grounded in that fact, and thus by (1) is a soft fact. And everyone except the logical fatalist agrees that soft facts are not subject to the fixity of the past, and hence soft facts about God’s forebeliefs do not threaten free will.

Causal histories and freedom

Linda Zagzebski proposes the plausible principle that one is able to ϕ only if ϕing is compatible with one’s causal history relevant to ϕing.

Suppose Alice is considering whether to rob a bank. While she is doing so, God loudly announces to her nearby friend Bob that Alice will not rob the bank. God’s announcement is in Swahili, which Bob knows and Alice used to know in childhood but completely forgot. But the sound of the language her loving parents spoke to her as a child leads to Alice putting more emphasis on virtue in her deliberation, and she freely decides not to rob the bank.

Since God cannot lie, and since God’s announcement is a part of Alice’s causal history in her deliberation, Alice’s robbing the bank is incompatible with causal history and by Zagzebski’s principle, Alice cannot rob the bank. Yet it is unclear how God’s announcement removes her freedom to rob. After all, had God announced in Swahili that Alice will have breakfast, that would have influenced her deliberation in the same way, and yet obviously she would still have been free to rob the bank. But since Alice doesn’t know Swahili, the content seems causally irrelevant.

I think there are two ways out of this. First, we might cut events very finely. There is (a) God’s saying something or other in Swahili and there is (b) God’s saying in Swahili that Alice will not rob the bank. To determine the causal history, we pare away from the events all that’s causally irrelevant, and so we include (a) but not (b) in the causal history.

Alternately, we might say this. Whether or not Alice knows Swahili, her decision is affected by the detailed facts about the sounds in God’s announcement. Indeed, by essentiality of origins, her deliberation is a numerically different process because of the difference of sounds. And now we can say that God cannot make the announcement, because doing so would result in a circularity in the explanatory order: God would be making the announcement because Alice is not going to rob and Alice is not going to rob because God is making the announcement because she is not going to rob. So it is not so much that the announcement takes away God’s freedom, but that God cannot produce explanatory circularities.

It’s worth noting that Molinism does not seem to help. Sure, the subjunctive conditional of free will

1. Were God to announce in Swahili that Alice won’t rob, Alice wouldn’t rob

is true. But it is necessarily true independently of Molinism!

Two decreases in tension between faith and science

Over the past two hundred years or so, one new tension point arose for the relationship between Christianity and science due to scientific progress—namely, evolution. At the same time, several tension points disappeared due two other instances of scientific progress.

The first instance of this scientific progress was the general abandonment of the Aristotelian eternal world model of the universe with Big Bang cosmology. In the middle ages, Jewish, Islamic and Christian thinkers struggled with the tension between the science/philosophy of the day strongly tending towards a universe that always existed and the theological commitment to a creation a finite amount of time ago. That problem is gone.

The second instance is our scientific understanding of the continuity of organic development from zygote to embryo to infant to adult, which has made quite implausible the old view of discontinuous transition in utero from vegetable to animal to human. This old view was the dominant scientific view of human origins until fairly recently, and it had serious tensions with Christian theology.

The first of these embryological tensions was with Christian moral views about abortion. While traditionally Christians opposed both contraception and abortion, abortion was morally seen as a form of homicide. But on the discontinuous transition view, abortion prior to human ensoulment would only be contraception.

The second embryological tension was a technical problem in Christology. Suppose that in the Incarnation we have the vegetable, mere animal and rational animal sequence. Then Aquinas observes there are two possibilities, neither of which is theologically appealing.

First, it could be that God becomes incarnate as a vegetable or a mere animal. But this seems, as Aquinas says, “unbecoming”. And he seem to be right. The Incarnation reveals to us the person of the Logos, and it would be unbecoming that the Logos become a non-personal being.

Second, it could be that the Incarnation happens only at the beginning of the third stage of development, namely once everything is ready for a rational animal. But then Aquinas says “the whole conception could not be attributed to the Son of God”. Indeed, don’t we even have a tension with the Apostles’ Creed line that Christ “was conceived by the Holy Spirit”? For on this option, Christ was not conceived at all. What was conceived was a vegetable, not Christ. (Indeed, none of us were conceived on this view.) Moreover, one might worry that then there would be a sense in which the flesh of Christ would pre-exist the Incarnation. And that makes it difficult to say that the Word became flesh—for the flesh that Scripture says he “became” would already in a sense have been there, and one can’t become this flesh, since this flesh already has its own identity. (Granted, there may well be some Aristotelian metaphysics one can do to lessen this last worry.)

Aquinas solves the problem by supposing that Christ is conceived fully formed in Mary’s womb, and hence has the rational soul from the first moment of his existence. But this solution is itself problematic. Absent gradual development from a zygote, is this conception at all? If God were to create an adult human either ex nihilo or out of some pre-existing matter, we would not consider that a conception. But neither should we then consider it a conception if God creates a fully-formed fetus, even if he does that out of the pre-existing matter of Mary. So we still have a problem with the Apostles’ creed’s “was conceived by the Holy Spirit”. Moreover, it seems that this deprives Mary of a significant chunk of her motherhood.

But the problem entirely disappears once we think that the human beings begin their existence at conception. Christ is conceived by the Holy Spirit, presumably in that Mary’s ovum is transformed into a zygote by the infinite power of the Holy Spirit, which zygote is the Christ who then grows in utero like we all do.

(Catholics also note that the new scientific understanding of human embryonic development also helps with the doctrine of Mary’s immaculate conception—for only a rational being can be immaculately conceived, since original sin or freedom from it can only apply to a rational being.)

Divine attributes

In previous posts I’ve noted piecemeal that standard definitions of omniscience and omnipotence are incomplete. God’s omnipotence isn’t just that God knows everything—it has to be that he knows it certainly and consciously. We might even say: with maximal certainty and vividness. God’s omnipotence isn’t just that God can do everything—he does it all effortlessly.

It has now occurred to me that both devotionally and philosophically it is fruitful to think about divine attributes by asking what is left out by the rather thin and colorless analytic accounts of them.

Take a flat account of God’s moral perfection as saying that God always does the morally right thing. Well, first, we have to add: and for the right reasons (indeed all the right reasons). Second, we should add that God does this with the perfect attitude—with the appropriate alacrity, without inappropriate regrets, etc.

Or consider the account of God’s being a creator on which God creates everything other than himself. We probably should minimally add that he does this with perfect freedom.

At the moment, this is all I have in the way of clear examples. But I think it’s a worthwhile avenue for exploration and devotion.

Beyond metaphysical immutability

For years I was convinced that the extrinsic constitution model of divine knowledge, which theists who accept divine simplicity must accept, solves the problem of divine immutability in an A-theoretic world where truth changes. The idea was that God’s knowledge of contingent facts is constituted by God’s unchanging essential features (which given simplicity are God himself) together with the changing contingent realities that God knows, that God’s gaze extends to. (This idea is not original to me. Aquinas already had it and probably many contemporary people have independently found it.)

But I now think that this was too quick. For let’s take the idea seriously. The point of the idea is that an unchanging God can have changing knowledge. But now notice that God’s knowledge is conscious. The language of “God’s gaze” that I used above (and which Boethius also uses in his famous discussion of divine knowledge of free actions) itself suggests this—God sees the changing reality. At one time God sees Adam sinless. At another time God sees Adam sinful. This is a difference in conscious state. Granted, this difference in conscious state is entirely metaphysically constituted by the changing reality. But it still means that God’s conscious state changes. It changes in virtue of its extrinsic constituent, but it is still true that God at t₁ is conscious of one thing and God at t₂ is conscious of something else instead. And I submit that that is incompatible with divine immutability.

I think there are two responses the classical theist who believes in changing truths can give. The first is to deny that God is conscious of the changes. I think this is unacceptable. The more vivid and the more vision-like knowledge is, the more perfect it is. The idea that God has merely unconscious knowledge of contingents does not do justice to the perfection of omniscience.

The second response is to bite the bullet and say that God’s conscious state changes but this is compatible with immutability as long as this does not involve an intrinsic change in God. I think this is untenable. That God’s conscious state does not change is, I think, a central part of the content of immutability, regardless of whether this conscious state is intrinsically or extrinsically constituted. For a non-physical being, change of conscious mental state is a paradigmatically central kind of change—regardless of the metaphysics of how that change of conscious state comes about. When God says in Malachi 3:6 that he does not change, it seems very implausible to think that the listener is supposed to say: “Sure, but sometimes God has one conscious state and sometimes another, and because this change is grounded extrinsically, that’s OK.” Malachi isn’t doing heavy-duty scholastic/analytic metaphysics. Similarly, when the early Church Fathers say that God is unchanging I doubt they would tolerate the idea that God’s conscious state changes. The extrinsic constitution story is an explanation of what makes God’s conscious state change, and I expect the Church Fathers wouldn’t have cared what the explanation would be—they would just deny the change.

Jumping from the Church Fathers to the modern period, Calvin says that God “cannot be touched with repentance, and his heart cannot undergo changes. To imagine such a thing would be impiety.” But if God’s conscious states are extrinsically constituted and can change, there would be nothing to prevent the idea of God’s “heart” undergoing changes: when people behave well, God feels pleased; when people behave badly and deserve vengeance, God feels vengeful. The differences in God’s feeling would be, one could imagine, constituted by the differences in human behavior and divine response to it. But it would be implausible to think that Calvin would say “Well, as long as the change is extrinsically constituted, it’s OK.” We then wouldn’t need Calvin’s famous story—itself going back to the Church Fathers—of the accommodation of divine speech to our needs. When Calvin insists that God’s heart cannot undergo changes, he isn’t just concerned about divine metaphysics. He is rightly concerned about a picture of a God with a changing mental life. And here at least, Calvin is with the mainstream of the Christian tradition.

If I am right in the above, there is a disanalogy between how God’s mental state behaves across possible worlds and across times. We have to say that in different possible worlds God has different (extrinsically constituted according to divine simplicity) conscious states. But we cannot say that God has different conscious states at different times.

Some thinkers, especially open theists, want the doctrine of divine immutability not to be about metaphysics but about the constancy of God’s character, purposes and promises. I think they are wrong: the doctrine of immutability really does include what we might call metaphysical immutability, that God has no intrinsic change. But metaphysical immutability is not enough. A mental and especially conscious immutability is also central to how we understand divine immutability.

And this is not compatible with the A-theory of time, given omniscience. Which is too bad. While I myself am a B-theorist, the reasoning in yesterday’s post was giving me the hope that we could detach the A- and B-theoretic debate from theism, so that the theist wouldn’t need to take a stand on it. But, alas, I think a stand needs to be taken.

Could a being in time be eternal in Boethius' sense?

Famously, Boethius says that an eternal being, unlike a merely temporally everlasting being, embraces all of its infinite life at once, “possess[ing] the whole fulness of unending life at once”. What’s that mean?

Our life is strung out across time. Sitting right now I as I am I do not embrace the past and future portions of my life where I am lying down or standing up. If I fully and vividly knew my past and my future, I would be a little closer to being eternal, but it would still not be true that I possess the fullness of that life at once. For it would still be true that I now only possess the property of being seated and not the property of lying down or of standing up. So I think epistemic things are not enough for eternity. And this seems intuitively right—eternity is not an epistemic matter. (Could you have an eternal being that isn’t minded? I don’t see why not.) A necessary condition for being eternal is being unchanging.

But being unchanging is not sufficient. Suppose I were everlastingly frozen sitting in front of my laptop. It would still be true that in addition to the present part of my life there is the future part and the past part, and further subdivisions of these, even if they happen to be boringly all alike. The life of an eternal being does not have temporal divisions, even boring ones. It is all at once.

Here is a weird thought experiment. Imagine you are an everlasting point-sized being with a rich and changing mental life. Suppose all your life is spent at the one spatial location (x₀,y₀,z₀). But now imagine that you get infinitely multilocated across all time, in such a way that your numerically same life occurs at every x-coordinate. Thus, you live your everlasting and rich mental life (x,y₀,z₀) for every possible value of x, and it’s the very same life. Your life isn’t spatially divided. The life at x-coordinate  − 7.0 is not merely qualitatively but numerically the same life as the one at x-coordinate  + 99.4.

Now, one more step. Your life is within a four-dimensional spacetime. Assume that spacetime is Galilean or Minkowskian. Now imagine rotating your life in the four-dimensional spacetime in such a way that what was previously along the x-axis is along the t-axis and vice versa. So now your rich and temporally varied mental life becomes temporally unchanging, but all the variation is now strung out spatially along the x-axis. Furthermore, whereas previously due to multilocation you had your life wholly at every x-coordinate, now you have your life wholly—and the numerically same life—at every t-coordinate. Thus, you have an infinite life all at once at every time for everlasting time. Your life isn’t temporally divided: tomorrow’s life is not simply just like today’s, but it is the numerically same as today’s, because your life is fully multilocated at all the different times.

Here is an interesting thing to note about this. This “sideways life”, varying along the x-axis, satisfies the Boethian definition of eternity even though the life is found in time—indeed at every time. If this is right, then having an eternal life in the Boethian sense is compatible with being in time!

Of course, God is not like you are in my weird story. In my story, your life includes different instances of consciousness strung out along the x-axis, though not along the t-axis. Still this kind of inner division is contrary to the undividedness of the divine mind. An eternal God would not have such divisions either. Nor would he be spatial. Perhaps an argument can be made that if God possesses Boethian eternity, then he has to be timeless. But I think that’s not going to be an easy argument to make.

If this is right, then I have overcome an obstacle to combining classical theism with the A-theory of time. I am convinced that an omniscient being has to be in time if the A-theory is true. But if a being can be in time and yet eternal in the Boethian sense, then a classical theist may be able to accept the A-theory of time. After all, Boethius is paradigmatically a classical theist.

That said, my own view is that the above argument just shows that Boethius has not given us a fully satisfactory characterization of eternity. And I have other reasons to reject the A-theory besides theistic ones.