A test case for explanationism

Here is a test case for explanationist stories about initial priors, on which a more explanatory theory has a higher initial prior. Consider these hypotheses:

1. The universe is not created or governed by reason, has a finite lifetime, and has low initial entropy.

2. The universe is not created or governed by reason, has a finite lifetime, and has low final entropy.

Causation goes from past to future, so absent some kind of foresight involved in the initial conditions, initial conditions are more explanatory than final conditions. Now, presumably there is a nice one-to-one correspondence between worlds where (1) and (2) hold, so absent an explanationist bias in the priors, we shouldn’t have a preference between (1) and (2).

This is just a test case, but I have to confess I don’t have any direct intuition comparing the probabilities of (1) and (2). I like explanationism, so I have a theory-laden reason to assign a higher probability to (1) than to (2).

How has Aquinas not proved the Trinity?

St Thomas holds that we cannot know by natural reason that God is a Trinity. However, he also endorses a version of St Augustine’s account of the Trinity, on which God has a mental Word or concept of himself that he generates mentally, and then there is a Love that is responsive to that Word. Why is this not a proof by natural reason?

On this point, Thomas is sadly brief in the Summa Theologiae: “Again, the similarity with our intellect does not sufficiently prove anything about God, since the intellect is not found univocally in God and in us.”

But Aquinas thinks that we can literally talk about God, even if we do so by means of analogy. He has argued, by reason, that God exists and has all perfections. One of these perfections is knowledge of everything, and thus of himself. Does this not commit Aquinas to being able to say on the basis of natural reason that God generates his self-knowledge, a self-knowledge that, by divine simplicity, must then be God himself rather than a mere creature? And does not God love himself under the description that this knowledge provides?

I think Aquinas would (with perhaps minor cavils) endorse all the claims in my previous paragraph as knowable by natural reason. How is this not a proof of the Trinity? I think the answer is this. Focus on the generation of the Son—the case of the Holy Spirit will presumably be similar. We do not know by reason whether the relation of generating self-knowledge is a real relation in God. If it is a real relation it will individuate the knower from the knowledge, thereby ensuring that there are at least two persons in God. But it needs to be a real relation in God, rather than a merely conceptual one. And here Thomas’s brief remark about univocity seems apposite. Aquinas thinks that what makes our language about God analogical rather than univocal is that the grounding of claims about God is radically different from the grounding of similar claims about creatures. Thus, when we say Socrates is wise, this is grounded by the inherence in Socrates of an accident of wisdom, while when we say God is wise, this is grounded by the identity between God and his wisdom. Because of this, even if it turns out that in us the generation of self-knowledge is a real relation (but not one between persons, since we are not simple, and hence our self-knowledge does not need to be of one essence with us), since the grounding structure of claims about God is radically different, as far as unaided human reason goes, it may not be grounded in a real relation in God—though it might be. We need God’s revelation to know if it is a real relation or not. And indeed God has revealed that it is.

Optimalism and mediocritism

We can think of the optimalist theory of ultimate explanation as the claim:

1. Necessarily, that reality is for the best explains everything.

(I won’t worry in this post about two details. First, whether “reality” in (1) includes the principle of optimality itself—Rescher has suggested that it does, since it’s for the best that everything be for the best. Second, whether “reality” is all the detail of the world, or just the “core” of the world—the aspects not set by indeterministic causation.)

Given that only truths explain, (1) entails:

2. Necessarily, reality is for the best.

Notice that one could accept (2) without accepting (1). One might, for instance, be a Leibnizian and think that there is a two-fold structure to ultimate explanation: first, God’s existence is explained by the ontological argument and, second, God creates the best contingent reality. On this account everything is for the best, but that everything is for the best is not the ultimate explanation, because it does not explain why God exists. Or one might think that reality is necessary and brute, and it brutely has to be like it is. And as a very suprising but non-explanatory matter of fact the way it is is in fact optimal.

I am emphasizing this, because I want to problematize (1). Grant (2). Why should we think that the fact that everything is for the best in fact explains everything?

Suppose that modal fatalism is true, and that it so happens that reality is exactly mid-way between the worst and the best possibility, and is in the only option mid-way between the worst and best. (I assume one can talk of options for reality even given modal fatalism. Otherwise, optimalism falls apart. The “options for reality” may be something like narrowly logically possible worlds.) Then:

3. Necessarily, reality is exactly middling.

Now suppose a “mediocritist” said: “And that reality is necessarily exactly middling explains why reality is what it is.” But why would we buy that? Or suppose that reality is necessarily the only one that is exactly 56.4% of the way up between the worst and the best (where worst would count as 0% of the way up and best as 100%)? Surely we wouldn’t conclude that its being exactly at 56.4% explains why it is the way it is. But if not, then why should its being at 50% explain it, as on mediocritism, or its being at 100% explain it, as on optimalism?

I think what the optimalist ought to say at this point is that analogously to non-Humean pushy laws of nature, there are non-Humean pushy laws of metaphysics. One of these laws is that everything is for the best. It is the pushiness of this metaphysical law that explains reality. But there is something rather odd about pushy laws prior to all beings—they seem really problematically ungrounded.

More on strong open-mindedness

For the last couple of days I have been exploring what I like to call strongly open-minded accuracy scoring rules. It’s well known that every proper scoring rule is open-minded in the sense that it never requires you to reject free information: the expected epistemic utility of updating on the free information is always at least as good as your current expected epistemic utility. It’s strictly open-minded provided that in non-trivial cases (i.e., when the information has a non-zero probability of having statistical relevance to the credences you are scoring) you are required to accept the free information.

Now there are two reasons why one might accept free information about some proposition q. First, you might be wrong about q: your credence may be high while q is false or your credence might be low while q is true. Second, even if you are right about q, the free information may boost your credence in the right direction. I say that a scoring rule is strongly open-minded provided that it licenses you to accept and update on the free information even if you disregard the first consideration. We can then tack on “strictly” if it requires you to do so in non-trivial cases. In the case of a strongly open-minded scoring rule, your acceptance of free information is not a sign of doubt in your propositions—it is not a way of hedging your bets—and thus is arguably compatible with faith in the propositions being evaluated.

A strongly open-minded scoring rule can also be characterized in the following way. There is a more ordinary kind of epistemic paternalism where I might have reason to block another from receiving free information on the grounds that this information could mislead due to the fact that the other has different likelihoods from the ones I think are right. For instance, if too many people have an unjustified mistrust of Dr. Smith such that they are likely to believe the opposite of what Dr. Smith’s experiments reveal, there is reason to give a grant to someone else, because Dr. Smith’s experiments are likely to lead people away from the truth, for no fault of Dr. Smith’s. Call this likelihood-based paternalism. But there is another kind of motivation of the refusal of free information for another, which we might call pure-risk-based paternalism. Even if someone else has the same likelihoods as you do—trusts Dr. Smith just as you do—perhaps the risk that Dr. Smith’s experiments will, by pure chance, provide evidence away from the truth is enough to justify not funding these experiments.

I’ve been collecting results about these issues. Here’s what I seem t have so far, though I have to emphasize that sometimes the proofs are just in my head and I might be wrong. I will specialize on scoring rules for a single proposition, given as a pair of functions T and F, where T(x) is the value of having credence x when the proposition is true and F(x) is the value of having credence x when the proposition is false.

1. A scoring rule sometimes calls for pure-risk-based paternalism if and only if it is not strongly open-minded.

2. A scoring rule that’s strongly open-minded is open-minded.

3. A scoring rule (T,F) is (strictly) strongly open-minded if and only if xT(x) and (1−x)F(1−x) are both (strictly) convex.

4. The logarithmic scoring rule is strictly strongly open-minded. The Brier and spherical rules are not strongly open-minded.

5. If a proper scoring rule is generated by the Schervisch-style integral representation T(x) = T(1/2) + ∫_x^1/2(1−t)b(t)dt and F(x) = F(1/2) + ∫_1/2^xtb(t)dt and b is sufficiently differentiable, then the scoring rule is strongly open-minded if and only if the derivative of log b(x) lies between (3x−2)/[x(1−x)] and (3x−1)/[x(1−x)].

6. A strongly open-minded scoring rule whose logarithm is sufficiently differentiable is unbounded.

7. If your credence in a hypothesis H is at least (at most) 1/2, then a proper scoring rule will not call for purely-risk-based epistemic paternalism with respect to someone whose credence is equal to or higher (lower) than yours.

8. If your credence in a hypothesis H is 1/2, then no proper scoring rule calls for purely-risk-based epistemic paternalism for that hypothesis.

9. For any credences p and r such that 1/2 < r and p < r, there is a strictly proper scoring rule and a situation where the scoring rule calls for the individual with credence r to have purely-risk-based epistemic paternalism for that hypothesis.

Algorithmic priors and human nature

One promising way to define priors is with algorithmic probability, such as Solomonoff priors. The idea is that we have a language L (say, one based on Turing machines), and we imagine generating random descriptions in L in a canonical way. E.g., add an end-of-string symbol to L and randomly and independently generate symbols until you hit the end-of-string symbol, and then conditionalize on the string uniquely describing a situation, and take the probability of a specific situation s to be the probability of that a random description so generated describes s.

These kinds of priors are rather appealing for science, since they appear to be induction-friendly, as they assign high probabilities to compressible—more briefly expressible—situations. Thus, if our situations are distributions of color among ravens, monochromatic distributions get much higher probability as they can be much more briefly described, like ∀x(B(x)) or ∀x(W(x)).

Philosophically, I think the big problem is with the choice of the language. It would be nice if we could let L be a language that cuts nature exactly at the joints. But we don’t know that language. And absent that language, we need something arbitrary.

Here is a particular version of the problem. Take Kuhn’s division of science into ordinary and revolutionary science. One aspect of this division is that in ordinary science, we have a scientific language, and are discovering things within it. In that case, it is reasonable to take L to be that language. However, when we are doing revolutionary science and creating new paradigms, we cannot do that. The new paradigms either cannot be described in the old language or their description is unwieldy in a way that does not do justice to the plausibility of the new paradigm. Indeed, much of the point of revolutionary science is to create a language within which the description of the world is simpler, and then argue that this language is therefore more likely to cut nature at the joints.

Another version of this problem is what language L we choose when we are generating fundamental priors. Practically speaking, we cannot use a scientific language that cuts nature at the joints, because we have not yet discovered it. If this was merely a practical concern, we could try to say that this doesn’t matter: the fundamental priors are ones that we ought to have rather than any that we actually have or could have—perhaps ought does not imply can. But the concern is not merely practical. For one of the main points of our inductive reasoning is to discover what concepts cut nature at the joints, and this is largely an empirical enterprise. If the right fundamental priors were to reflect the joints in nature, then the enterprise wouldn’t make much sense, as we would be obligated to have already completed much of the enterprise before we started it.

So, I think, we have to say L does not always cut nature at the joints, and yet this generating appropriate priors for us. But we still need a constraint on L. After all, we could imagine a language that thwarts our empirical enterprise, such as one where only fairies can be described briefly and anything else requires very long descriptions, so we have very high priors for fairies and very low priors for everything else. What will be the constraint? Practically, we pretty much have to start with some ordinary human language. I think our ideal should not be far from what is practical. Thus, I propose, if we are going to go with algorithmic priors, we should choose L to be a language that fits well with our human nature as communicators. This is an anthropocentric choice, and I think human epistemology is rightly anthropocentric.

But why think that the anthropocentric choice is apt to lead to truth? There are two stories to be told here. First, it may be that human nature requires a measure of trust in human nature. Second, that trust is vindicated if we are created by a good God who loves the truth.

Anselm and Brouwer

I was reading Anselm’s replies to Gaunilo, and was struck by this:

Furthermore: if it can be conceived at all, it must exist. For no one who denies or doubts the existence of a being than which a greater is inconceivable, denies or doubts that if it did exist, its non-existence, either in reality or in the understanding, would be impossible. For otherwise it would not be a being than which a greater cannot be conceived. But as to whatever can be conceived, but does not exist – if there were such a being, its non-existence, either in reality or in the understanding, would be possible. Therefore if a being than which a greater is inconceivable can be even conceived, it cannot be nonexistent.

Let → indicate subjunctive conditionals. Let E!(x) say that x exists.

1. E!(God) → □E!(God).

2. ∀x[if Conceivable(x) and  ∼ E!(x), then: E!(x) → ⋄ ∼ E!(x)].

3. So, not: (Conceivable(God) and  ∼ E!(God)).

4. So, if Conceivable(God), then E!(God).

The ∀x quantifier in (2) is problematic, since it ranges over beings that don’t exist. Perhaps we can read it substitutionally. Let’s suppose we can finesse this issue.

What interests me in (2) is that big conditional in it is most plausibly as seen as a special case of:

5. If C(p) and q, then p → ⋄q,

where C(p) says “conceivably p”, which may or may not be the same as “possibly p”.

We can prove (5) from the Brouwer Axiom

6. If q, then □⋄q,

where L is necessity, and the following principle about subjunctive conditionals:

7. If C(p) and Lr, then p → r,

namely that necessities would still hold no matter what conceivable things happened (to get (5) from (6) and (7), let r be ⋄q). Principle (7) is very plausible if conceivability is possibility: if a possible thing happened, anything necessary would still be true. It’s less plausible if conceivability is not possibility.

And, of course, the Brouwer Axiom is controversial, albeit not quite as much as S5. I initially hoped that the use of the subjunctive conditional in (2) allowed Anselm to get by with something weaker than Brouwer. But not so if the route to (2) goes through (5) and possibility implies conceivability (PIC). For we get Brouwer from (5), PIC and the very plausible principle:

8. If p is possible, then we do not have p → r and p →  ∼ r.

For suppose that contrary to Brouwer we are at a world where q is true, but ⋄q is false at some accessible world. By PIC,  ∼ ⋄q is conceivable. Let p be  ∼ ⋄q. Then C(p) and  ∼ p. But clearly  ∼ ⋄q →  ∼ ⋄q. If we had (5), we would have  ∼ ⋄q → ⋄q, and contradict (8).

So, if Anselm’s argument for (2) goes through (5), we don’t have an improvement over Brouwer. But we can still get (2), given some very plausible assumptions, and the following special case of (5):

9. If C(∼q) and q, then  ∼ q → ⋄q.

And I feel that (9) has some plausibility above (6), at least if conceivability is the same as possibility. For suppose q is true and  ∼ q is possible. Then it seems somewhat plausible that q is possible in the  ∼ q-worlds that are closest to the actual world. Maybe. But maybe there is some way to derive Brouwer from (9) and additional plausible premises.

Does everything in time change?

Over the last two days, I’ve been thinking critically about Aquinas’ First Way. Central to my thinking, and especially yesterday’s post, was the idea that you could have an unmoved mover who is in time but isn’t pure act and who isn’t God. Such an unmoved mover constantly and unchangingly exercises—perhaps mentally—one and the same causal power to make something else move.

But I now wonder if this is possible. Suppose a demiurge that exists in time and has the power to make Bob rotate, and constantly exercises this power. Could this demiurge be unchanging? After all, at noon the demiurge is actively rotating Bob at noon, and at 1 pm the demiurge is actively rotating Bob at 1 pm. We can easily and coherently suppose that the demiurge engages in qualitatively the same activity at 1 pm as at noon. That was the intuition that was driving my thinking about this. But can we coherently add that it is the numerically same activity? For if it’s not numerically the same activity at 1 pm as at noon, then the demiurge has undergone a change, from engaging in activity a₁₂ to engaging in activity a₁₃, even if the two activities are exactly alike.

I am not sure, but I feel a pull to thinking that rotating Bob at 1 pm is a different thing from rotating Bob at noon, assuming that the agent is in time. I don’t just mean that it has different effects—which it does, since spinning-at-noon is a different effect from spinning-at-one—but that the activity of causing rotation is itself different. Maybe the pull comes from this thought. Perdurantists think that substances exist at different times by having different temporal parts at them. Perdurantism is likely false for substances. But whether or not it is true for substanes, it seems very plausible for events and activities. What made World War II exist on each day between September 1, 1939 and September 2, 1945 is that there were hostilities on each day, hostilities that are a part of World War II. Even if on two successive days the hostilities happened to be exactly alike, they would have been numerically different hostilities. If this is right in general, then the activity of rotating Bob at 1 pm is numerically different from that of rotating Bob at noon.

Furthermore, I think existence is a kind of activity. This is most obvious in the case of living things, given the Aristotelian idea that life is the existence of the living and life is an activity, but I think is true in general. Thus a thing that exists in time over a lifetime engages in a sequence of numerically different activities—existing at t₁, existing at t₂, and so on. And hence it changes. And intrinsically so. If so, then everything that exists in time must always change.

If the suggestion that there are no unchanging activities that last over time, then we can escape my worry yesterday that perhaps the sequence of moved movers in the First Way leads to a mover that is unchanging with respect to the activity of moving the next mover in the sequence but is still changing in some other coincidental respect. For the activity of moving the next mover in the sequence would have to change over time, and so the mover would be changing in respect of of its moving the next item in the sequence.

But perhaps not. For we might admit that in all the cases we are familiar with, activity only perdures over time, and there is always something numerically different happening at different times, but say that we could still imagine a being where the numerically same activity is temporally multilocated. And such a being could everlastingly rotate Bob with the activity of spinning Bob being genuinely unchanging.

I don’t know.

Gale's criticism of Stump and Kretzmann's ET-simultaneity

Stump and Kretzmann give three main concepts of simultaneity in their famous paper:

• T-simultaneity between items in time

• E-simultaneity between items in eternity

• ET-simultaneity between items in time and items in eternity.

Stump and Kretzmann observe that ET-simultaneity is not reflexive: a temporal item is not ET-simultaneous with a temporal item and an eternal item is not ET-simultaneous with an eternal item. My mentor Richard Gale in his book on God argues that this is a serious problem: a relation that is’t reflexive just doesn’t have a hope of counting as a simultaneity relation.

But Gale is wrong. For T-simultaneity and E-simultaneity are clearly simultaneity relations, but neither of them is reflexive either! For an eternal item is not T-simultaneous with itself and a temporal item is not E-simultaneous with itself.

Now, granted, when we talk of reflexivity of a relation, it’s within a relevant domain. Thus, we say that being the same color is reflexive, even though St Michael the Archangel is not the same color as himself, because the relevant domain for sameness of color is things that have color, not immaterial intellects.

So we might say that T-simultaneity and E-simultaneity are reflexive because their respective domains are temporal and eternal things, and they are each reflexive in their domains.

We might, but we shouldn’t. Stump and Kretzmann’s investigation is of a domain of items that may or may not be simultaneous in different senses, a domain that includes both eternal and temporal things. And in that domain, none of the relations they consider are reflexive. And that’s OK.

Does it follow from van Inwagen's answer to the Special Composition Question that all complex things are alive?

The view that all objects are either living or simple appears to be a consequence of van Inwagen’s answer to the special composition question, namely that a proper plurality only composes a whole when the parts have a life together, where a proper plurality is a plurality of two or more things.

But this does not follow. Van Inwagen defines:

1. The xs compose y if and only if “the xs are all parts of y and no two of the xs overlap and every part of y overlaps at least one of the xs”.

Now the view that all non-simples are alive follows from van Inwagen’s answer to the special composition question (SCQ) provided that we have to have:

2. Anything that has proper parts is composed of some proper plurality of its proper parts.

3. Whenever something is composed of a plurality of things that have a life together, it is alive.

Indeed, if we have 2 and 3, then anything that has proper parts is composed of proper plurality by 2, which thus have a life together by van Inwagen’s answer to SCQ, and hence the thing composed of them is alive by 3. On the other hand, if there can be something that has proper parts but isn’t composed of a proper plurality of proper parts, then there is no way to use van Inwagen’s answer to SCQ to argue that it’s alive. Furthermore, if there is something that is composed of a proper plurality of proper parts that have a life together but isn’t alive, then we have another counterexample to van Inwagen.

Neither 2 nor 3 is completely obvious. You might, for instance, think that where you are, there is also a heap of atoms shaped just like you. If, further, you are a presentist and a materialist, you will think the atoms compose you and compose the heap. Moreover, the atoms have a life together. But the heap of atoms is not alive, unlike you. So (3) on that view is false.

For a view on which (2) is false, imagine a world consisting of four objects, A, B, C and D. Object A has B, C and D as proper parts. Object B has D as a proper part. Object C has D as a proper part. There are no other instances of proper parthood. This is a world where the company axiom of mereology fails (since B and C have D as a proper part and no other proper parts). It would be interesting to characterize in some non-trivial way the mereological theories where (2) is true. A sufficient condition is to assume atomism (Gemini Pro noted this). We can define this by saying every object has a simple part. For then if an object has a proper part, it is easily seen to be composed by its proper parts. But atomism is not a necessary condition. Consider a gunky mereological model whose domain is infinite sets of natural numbers and parthood is inclusion—then (2) is true.

We could also escape this worry by weakening the definition of composition by dropping the requirement that no two of the xs overlap. That makes van Inwagen’s answer to the SCQ put a more stringer requirement on reality, and it becomes trivial that everything that has proper parts is composed of them, and (2) becomes a matter of logic. We still need an argument for (3), however.

Proper parts and dependence

Consider this initially plausible thesis:

1. If x has a proper part, and all of x’s proper parts depend on y, then x depends on y.

Add:

2. An effect depends on its cause.

3. Nothing depends on itself.

We conclude:

4. Nothing that has proper parts is a cause of all of them.

This has a nice theological application.

5. God is the cause of everything that is not God.

6. Therefore, if God has proper parts, he is the cause of all of them.

7. So, God has no proper parts.

However, I am dubious of premise 1. I think (1) depends on a story about parthood on which a whole is made of its parts. But if we don’t have that story, we could imagine a simple thing that then goes on to produce a proper part for itself. And so we lose the nice argument for divine simplicity. Which is too bad, but there are others.

How do we get to an unmoved mover?

I just realized that there is a difficulty in Aquinas’ First Way that I think hasn’t been noted, which builds on the difficulty noted yesterday.

Put the First Way in the following simpleminded way, which I think captures the central ideas:

1. Causes of change are either passers-on of change or originators of change.

2. It can’t be that the causes of change are all passers-on of change.

3. So there must be an originator of change.

4. And this is an unmoved mover (or, more precisely, unchanged changer).

There is a fair amount of detail one can fill in to argue for (2), but that’s not what I want to focus on. I want to focus on the move from (3) to (4).

What licenses us in thinking that an originator of change is itself unchanging?

The idea seems to be that if a cause of change is itself changing, then it is merely a passer-on of change. But this need not be. In my previous post, I imagined an unchanging and timeless demiurge endowed by God with the power to originate change, and noted that in that scenario the demiurge is an unmoved mover but isn’t God.

But now let’s build up and modify my demiurge story. First, let’s be concrete about what motion the demiurge causes. The demiurge has been gifted by God with the power to directly will Bob to rotate around a fixed axis, and the demiurge changelessly exercises this power. (Maybe Bob is one of the Aristotelian heavenly spheres). Second, let’s specify that the demiurge, albeit unchanging, is in time and has an unchanging body in addition to a mind and will. If we can’t have a changeless thing in space and time, don’t worry about it. The third step will fix that. The third step is this. The demiurge itself is caused by God to slowly orbit the sun in a way that the demiurge does not notice.

Thus, we have a demiurge with a mental power to make Bob rotate, and the demiurge exercises this mental power changelessly. At the same time, and completelessly coincidentally to the demiurge’s exercise of the mental power to make Bob rotate, the demiurge orbits the sun.

The demiurge is thus a moved mover. But it is also an originator rather than passer-on of change. In Aristotelian terminology, the demiurge is a moved mover per accidens: its own movement around the sun is coincidental to its origination of Bob’s axial rotation.

We cannot, thus, assume from the existence of an originator of change that there is an unmoved mover.

Does Aquinas have the resources to fill in the gap? Of course, if the (accidentally) moved originator of change coming out of step (3) of the argument is itself changing, that change has to have a cause, and we can then run the argument again. If we can rule out an ungrounded infinite sequence of accidentally moved originators of change—ones that like our demiurge happen to be moving in one respect but produce change by a coincidental exercise of power—then we can get to a genuinely unmoved mover.

But Aquinas’ main tool for avoiding regresses in cosmological arguments is the idea that there cannot be an infinite regress in a per se causal sequence. And while there are complications in the notion of a per se causal sequence, I think it is pretty clear that the sequence I am imagining is not a per se causal sequence. The demiurge’s moving of Bob is coincidental to the demiurge’s own motion. Suppose that a demiurge makes Bob spin by an unchanging exercise of a mental power, and a tetartourge by an unchanging exercise of a mental power makes the demiurge coincidentally slowly orbit the sun while the tetartourge coincidentally orbits the moon. Then the tetartourge is not a cause of Bob’s motion. But in a per se causal sequence we have transitivity: the earlier items are always causes of the later ones. So this is not a per se causal sequence.

Of course, we might ask what explains the demiurge’s (and tetartourge’s) possession and exercise of the mental power to make something else move. But now we are deviating from the First Way: we are asking for explanations of something other than change. I think one can fill this in, by an argument about causation and regresses rather than change and motion. But if we do that, then the stuff about change and motion that is at the heart of the First Way can simply drop out.

I titled my previous post “An easily patched hole in the First Way”. But I think I was too glib there, too. In that context, too, I think one needs to go beyond the resources of the First Way to patch the hole.

An easily patched hole in the First Way

In his First Way, Aquinas argues that as we trace back the sequence of movers from effect to cause, we get to a first unmoved mover, and this is God.

But need the unmoved mover thus reached in the sequence of movers be God? Imagine this scenario. God creates some material beings, as well as an unchanging, timeless and immaterial demiurge that has the power to make the material beings move—and indeed exercises that power. Then if we were to trace back the sequence of movers, the unmoved mover we would get to would be the demiurge, not God. This demiurge would have potentiality, but not a temporal potentiality, so it would not be itself in motion, and hence it would be an unmoved mover.

This doesn’t deeply affect the argument, since Aquinas could do the same thing as he does in the Third Way, where he traces contingent beings to a necessary being, and then considers the possibility of necessary beings that get their necessity from other beings, and traces it back to an absolutely necessary being, namely God. Similarly, God could say that any unmoved mover that has some potentiality or contingency depends on a prior being and so on, and in the end we would get to God anyway.

Indeed, even in this scenario with a demiurge, we might want to say that it is God and not the demiurge who is the first unmoved mover. For God would still be a mover, albeit working through the demiurge who is a secondary cause, and God would be unmoved, and God would be first. So Aquinas would still be correct that the “first mover” is God—it’s just that the scenario suggests that Aquinas does skip a step.

Explanatory principlism

There are three views about ultimate explanations of reality:

1. Nihilism: There is no ultimate explanation of reality.

2. Onticism: The ultimate explanation of reality involves one or more beings.

3. Principlism: The ultimate explanation of reality involves principles rather than beings.

Nihilism is the standard view among atheists. Onticism is the standard view among theists. The main examples of principlism are axiarchism and optimalism, on which reality is explained by its having the kind of value it does. But other combinations are possible: Rescher was an principlist theist, since he thought that God’s existence could be explained by the fact that it’s for the best that God exists.

I want to say a little about what I think is wrong about principlism. Start with the observation that if truthmaker maximalism is true, principlism cannot get off the ground, because whatever principle helps explain the world is made true by the existence of some being, and if an explanatory proposition is made true by a being, that being is certainly “involved” in the explanation.

Truthmaker maximalism is false. However, I think that a neighboring grounding view is true:

4. Being grounds truth (BGT): All truths are grounded in a combination of what there isn’t, what there is and how what is is.

Given BGT, we have very good reason to reject principlism. For presumably all the principles involved in the explanation of reality are true. If any of them are grounded in what there is or how what is is, then we have onticism rather than principlism: onticism is compatible with principles being involved in explanation, as long as beings are also involved. Thus the only way to defend principlism is to say that what gives the ultimate explanation are principles made true solely by the nonexistence of certain entities. And it is very implausible that the nonexistence of certain entities is the ultimate explanation of our reality, rich in being as it is.

The one version of principlism I can think of that I can reconcile with BGT would be an explanation of our reality in terms of the non-existence of beings that would prevent this reality. (This is kind of like the idea in the Scotus argument that nothing can prevent the existence of God, so God exists.) But this is dubious. Mere lack of preventers of x is not enough to explain the existence of x. One would need some kind of basic principle of plenitude on which everything not prevented must exist.

Punishment and presentism

This seems a bit plausible:

1. It is unjust to punish someone for a feature that is not intrinsic to them.

2. If presentism is true, then having done A is not an intrinsic feature of the agent.

3. Thus, if presentism is true, then punishment for past actions is always unjust.

The presentist may well question (2), insisting that presently having a past-tensed feature that was intrinsic when it was presently had counts as intrinsic. I am a bit unsure of this. It’s a question someone should investigate.

Here is a reason to think that presently having a past-tensed feature should not count as intrinsic. Suppose I am facing a free choice, with the possibilities of doing B and not doing B. Then it seems that no present intrinsic feature of me entails what I will do. But suppose that in fact I will do B. Then just as I have past-tensed properties like having done A, I presently have future-tensed properties like being about to do B. And it seems that if one is intrinsic, so is the other. Thus, if my being about to do B is not a present intrinsic feature of me, my having done A is not a present intrinsic feature of me.

The presentist might respond by embracing an open future and denying that it can be true in the case of a free choice that I will do B. But if this is right, then it seems that in order to defend the justice of punishment for past deeds, the presentist has to do something very controversial—accept an open future. Moreover, this means that a classical Jew, Christian and Muslim can’t be a presentist, since classical monotheists are committed to comprehensive foreknowledge, and hence to the denial of an open future, and the justice of retrospective punishment.

Of course, one might question (1). Here’s how one might start. We can punish Alice for punching Bob. But that’s not an intrinsic feature of Alice. We might respond by saying that Alice is punished for her internal act of will, but that doesn’t seem quite right. Probably a better move is to replace (1) by saying that there must be an intrinsic component to the feature one punishes someone for—say, Alice’s act of will. And the presentist now has trouble with this intrinsic component.

Old Polish Almond Torte

In my family, when someone (including me) has a birthday, they choose a type of cake, and then I bake it, often with the help of one or more kids. A family favorite is the old Polish Chocolate Almond Torte. This is a gluten-free cake, made of almond meal, with leavening provided by a full dozen egg whites (with the twelve yolks going into the cake, too), and a layer of home-made marzipan in the middle. My kids found a version of it in Lemnis and Vitry’s Old Polish Traditions, but the recipe was somewhat confusing and we didn’t like the lemon juice in the marzipan. We found another version online here, which pointed us to the original source as the 1931 Polish cookbook How to Cook by Maria Disslowa. Between the three sources, and experimenting across multiple birthdays, we have the following recipe which I baked for my last birthday.

Old Polish Almond Torte

Note: The recipe takes three days (though perhaps days 2 and 3 could be combined) and is ready to eat on the fourth day, but the only thing done on the first day is freezing the chocolate chips.

Ingredients for Cake

• 284g almond meal (unblanched)

• 227g castor sugar

• 284g powdered sugar

• 12 eggs, separated

• 284g dark chocolate chips (we use Hershey’s Special Dark)

• a couple of tablespoons of unsweetened cocoa

• optional: 1 tsp almond extract (my current opinion: omit to have better taste contrast between layers)

Notes on cake ingredients: Our grocery store doesn’t have unblanched almond meal, so we just buy unblanched (i.e., with skin) unsalted roasted bulk whole almonds and grind them in a coffee grinder. Similarly, we can’t get castor sugar, so we grind granulated sugar in a coffee grinder.

Ingredients for Marzipan Filling

• 250g almond flour (blanched)

• 273g powdered sugar

• 78g (or 78mL) water

• 2.5-3.5 tsp almond extract (use 3.5 if you didn't add the teaspoon to the cake)

Ingredients for Ganache

• 320g dark chocolate chips (Hershey’s Special Dark)

• 43g unsalted butter

• 238g (or 1 cup) heavy whipping cream

Additional Topping Ideas:

• slivered almonds or sweet strawberries

Instructions

Day 1:

Freeze the 284g of chocolate chips for the cake. Do not freeze the chips for the ganache!

Day 2:

Preheat oven to 356F (= 180C). Read over all the instructions for this day.

Grind the pre-measured frozen chocolate chips into a fine powder with a coffee grinder. Since a coffee grinder can’t take all of the chips at once, keep the ones that aren’t ground yet in the freezer.

If you don’t have almond meal, grind the almonds in a coffee grinder as finely as you can.

If you don’t have castor sugar, grind granulated sugar in a coffee grinder. It should be a bit coarser than powdered sugar.

Mix up the chocolate chip powder, sugar and almond meal.

Prepare a 10-inch spring form pan by buttering the bottom and sides, and putting a parchment paper circle on the bottom. Coat the sides with cocoa (this way, the cake remains gluten-free, and it’s better than flour).

Separate the 12 eggs.

Cream the egg yolks with the sugar until a bit fluffy, and while creaming mix in the sugar/meal/chocolate mix.

Stiffly beat the egg whites. Lightly mix them into the yolk-sugar-meal combination. (The egg whites provide all the lift to the cake, so the cake will be too dense if you overmix.)

Pour into the pan. Bake for one hour. Cover and leave overnight. Feel free to refrigerate.

Day 3:

Combine almond flour and powdered sugar for marzipan filling, together with the water and the almond extract. Knead into a homogeneous ball of dough. I start by using a dough hook in a stand mixer, and finish up by hand. Roughly flatten into a thick disc of the same diameter as the cake. It will be about 1 cm thick.

Remove the cake from the pan (I like to use a plastic knife). Cut into two layers and put the disc of marzipan between, making a level layer that reaches the sides.

For the ganache, heat the butter and cream together in the microwave until it is hot, with the butter melted, but before it boils. Add chocolate chips, mixing to ensure they all melt into the ganache. The last couple of grams took more time to dissolve.

Allow the ganache to cool somewhat and become more viscous. (I am usually impatient at this stage, and regret not having enough viscosity.) Pour it a bit at a time on the top of the cake, letting it drip over the sides on a very large plate or other clean platform. Use a spatula to push the drippings up over the sides again, repeating until the cooling ganache stops dripping significantly, and you have nice smooth edges.

Refrigerate overnight.