Thursday, June 30, 2022

Backwards causation, the A-theory and God


  1. There are tensed facts.

  2. If F is a contingent fact solely about physical reality that does not depend on creaturely free choice, then God can effectually will an exact duplicate of F.

Assumption (1) is a central claim of the A-theory of time, in fact form. Assumption (2) is a hedged consequence of omnipotence, formulated to take into account the possibility of uncreatable Platonic entities and the essentiality of origins.


  1. Backwards causation is impossible.

We now have a problem. Let B be the tensed fact that the Big Bang occurred billions of years ago. This is a contingent fact solely about physical reality that does not depend on creaturely free choice. So, by (2), God can effectually will an exact duplicate of B. But an exact duplicate of B would still be a tensed fact about what happened billions of years ago. And to will such a fact about the past would be backwards causation, contrary to (3).

Note how the problem disappears if we don’t have tensed facts. For then all we have is an untensed fact such as that the Big Bang occurs at t0, and God can will that without backwards causation, whether God is in time (e.g., he can then will it at t0) or outside time.

I personally don’t have a problem with backwards causation. But a lot of A-theorists do.

I suppose what the A-theorist should do is to replace (2) with:

  1. If F is a contingent fact solely about physical reality that does not depend on creaturely free choice, then God can effectually will a perhaps re-tensed exact duplicate of F.

Divine temporalism once again

I’m thinking about my recent argument against divine temporalism, the idea that God has no timeless existence but is instead in time, and time extends infinitely pastwards.

Here’s perhaps a simple way to make my argument go (I am grateful to Dean Zimmerman for suggestions that helped in this reformulation). If infinite time is a central feature of reality, as the temporalist says, then one of the most fundamental things for God to decide about the structure of creation is which of these three is to be true:

  1. Nothing gets created.

  2. There is creation going infinitely far back in time.

  3. There is creation but it doesn’t go infinitely far back in time.

But without backwards causation, a temporal God cannot decide between (2) and (3). For at any given time, it’s already settled whether (2) or (3) is the case.

Now, it seems that the temporalist’s best answer is to deny the possibility of (2). We don’t expect God to choose whether to create square circles, and so if we deny the possibility of (2), God only needs to choose between (1) and (3).

But there are two issues with that. First, creation going infinitely far back in time is the temporalist’s best answer to the Augustinian question of why God waited as long as he did before creating—on this answer (admittedly contrary to Christian doctrine), God didn’t wait.

Second, and perhaps more seriously, there is the question of justifying the claim that (2) is impossible. There are four reasons in the literature for thinking that in fact creation has a finite past:

  1. Big Bang cosmology

  2. Arguments against actual infinity

  3. Arguments against traversing an actually infinite time

  4. Causal finitism.

None of these allow the temporalist to justify the impossibility of creation going infinitely far back in time. Big Bang cosmology is contingent, and does not establish impossibility. And if the arguments (ii) and (iii)
are good reasons for rejecting an infinite past of creation, they are also good reasons for rejecting divine temporalism, since divine temporalism would require God to have lived through an actually infinite time. And (iv) also seems to rule out divine temporalism. For suppose that in fact creation follows an infinite number of days without creation. During that infinite number of days without creation, on any day we could ask why nothing exists. And the answer is that God didn’t decide to create anything. So the emptiness of the empty day causally depends on God’s infinitely many decisions in days past not to start creating yet, contrary to causal finitism.

Predictions and Everett

Imagine this unfortunate sequence of events will certainly befall you in a classical universe:

  1. You will be made to fall asleep.

  2. Upon waking up, you will be shown a red square.

  3. You will be made to fall asleep again.

  4. While asleep, your memory will be reset to that which you had in step (1).

  5. Upon waking up, you will be shown a green triangle.

  6. You will be made to fall asleep for a third time.

  7. While asleep, your memory will be reset again to that which you had in step (1).

  8. Upon waking up, you will be shown a green circle.

  9. You will then be permanently annihilated.


  1. How likely is it that you will be shown a green shape?

  2. How likely is it that you will be shown a red shape?

The answers to these questions are obviously: one and one. You will be shown a green shape twice and a red shape one, and that’s certain.

Now consider a variant story where personal identity is not maintained in sleep. Perhaps each time in sleep the person who fell asleep will be annihilated and replaced by something that is in fact an exact duplicate, but that isn’t identical with the original according to the correct metaphysics of diachronic personal identity. (We can make this work on pretty much any metaphysics of diachronic personal identity. For example, we can make it work on a materialist memory theory as follows. We just suppose that before step (1), you happen to have three exact duplicates alive, who are not you. Then during the nth sleep cycle, the sleeper is annihilated, and a fresh brain is prepared and memories will be copied into it from your nth doppelganger. Since these memories don’t come from you, the resulting brain isn’t yours.)

And in the variant story, let’s ask the questions (10) and (11) again. What will the answers be? Again, it’s easy and obvious: zero and zero. You won’t be shown any shapes, because you will be annihilated in your sleep before any shapes are shown.

Now consider Everettian branching quantum mechanics. Suppose there is a quantum process that will result in your going to sleep in an equal superposition of states between having a red square, a green triangle and a green circle in front of your head, so that upon waking up an observation of the shape will be made. Now ask questions (10) and (11) again.

I contend that this is just as easy as in my classical universe story. Either the branching preserves personal identity or not. If it preserves personal identity, the answer to the questions is one and one. If it fails to preserve personal identity, the answer to the questions is zero and zero. The only relevant ontological difference between the quantum and classical stories is that in the quantum stories the wakeups might count as simultaneous while in the classical story the wakeups are sequential. And that really makes no difference.

In none of the four cases—the classical story with or without personal identity and the branching story with or without personal identity—are the answers to the questions 2/3 and 1/3. But those are in fact the right answers in the quantum case, contrary to the Everett model.

Now, one might object that we care more about decisions than predictions. Suppose that you have a choice between playing a game with one of two three-sided fair quantum dice:

  • Die A is marked: red square, green triangle, green circle.

  • Die B is marked: green square, red triangle, red circle.

And suppose pain will be induced if and only if the die comes up red. Which die should you prudentially choose for playing the game? Again, it depends on whether personal identity is preserved. If not, it makes no difference. If yes, clearly you should go for die A on the Everett model—and that is indeed the intuitively correct answer. But the reason for going for die A on the Everett model is different from the reason for going for it on a non-branching quantum mechanics. On the Everett model, the reason for going for die A is that it’s better to get pain once (die A) rather than twice (die B).

So far so good. But now suppose that you’ve additionally been told that if you go for die A, then before you roll A, an irrelevant twenty-sided die will be rolled. (This is a variant of an example Peter van Inwagen sent me years ago, which was due to a student of his.) Then, intuitively, if you go for die A, there will be twenty red branches and forty green branches on Everett. So on die A, you get pain twenty times if personal identity is preserved, and on die B you get pain only twice. And so you should surely go for die B, which is absurd.

One might reasonably object that there are in fact infinitely many branches no matter what. But then on the no-identity version, the choice is still irrelevant to you prudentially, while on the identity version, no matter what you do, you get pain infinitely many times no matter what you choose. And that doesn’t work, either. And if there is no fact about how many branches there will be, then the answer is just that there is no fact about which option is preferable on the identity version, and on the no-identity version, indifference still follows.

This is all basically well-known stuff. But I like the above way of making it vivid by thinking about classically sequentializing the story.

Sunday, June 26, 2022

Against divine temporalism

I stipulate that:

  1. According to pure divine temporalism, God is a being in time without a timeless existence all of whose decisions are made at moments of time.

I will argue that on plausible assumtions divine temporalism is incompatible with divine creative libertarian freedom.

First, we need this:

  1. If pure divine temporalism is true, time has no beginning in the sense that before every moment of time, there was an earlier moment.

This is because everyone agrees that God is eternal. If there were a moment that had no moment before it, then according to pure divine temporalism, that moment would be God’s first moment of existence, without any timeless existence prior to or beyond it, and that is just incompatible with divine eternity. At that first moment it would be correct to say that God has just appeared.

One might object by saying that the first moment has infinite duration, and so it was an infinitely long changeless state. This is difficult to understand. An infinitely long changeless state seems like a timeless state more than anything else. In any case, if the point is pressed, I will simply stipulate that I don’t allow for moments like that.

Now, add this:

  1. Every contingent feature of creation not even partly due to creaturely indeterministic activity was decided on by God with God having had the possibility of deciding otherwise. (Divine creative libertarian freedom)

Next, add some plausible claims:

  1. The fact N that there was a moment of time before which there were no stars obtains.

  2. The fact N is a contingent feature of creation not even partly due to creaturely indeterministic activity.

  3. There is no backwards causation.

  4. Time is linearly ordered: for any distinct moments of time t1 and t2, one is earlier than the other.


  1. For a reductio ad absurdum, assume pure divine temporalism.

What do we have? Well, our assumptions imply that God at some time decided on N while yet having the possibility of deciding to the contrary. But prior to any past time t1, the fact N was already in place. History by time t1 already made it be the case that there was a time before which there were no stars. So if there is no backwards causation, at no past time t1 did God have the possibility of making N not be true. It was always already too late! But divine creative libertarian freedom requires that possibility.

Objection 1: The fact N does not actually obtain. We live in a sequential multiverse and before every time there were already stars in our universe or another.

Response: In that case, let S be the following contingent feature of creation: it was always the case that there already had been at least one star. I.e., for any past time t, there was a time t′ < t at which there had already had been at least one star. And an argument similar to the above goes through with S in place of N. At any past time, it was already too late to make S true, because history at that time was sufficient to make it be the case that prior to every time there was a star.

Objection 2: Fact N is made true by an infinite conjunction of facts such as that in year n there were no stars, in year n − 1 there were no stars, in year n − 2 there were no stars, and God unproblematically makes each of these facts true while having the power not to make it true.

Response: This objection is basically a rejection of (2). It says that some facts (even among the ones that aren’t due to creaturely indeterminism) aren’t freely decided on by God, but are instead consequences of other facts freely decided on by God. This reminds one of the Principle of Double Effect: God need not intend all the consequences of what he intends. He intends Nn, there not being stars in year n, as well as Nn − 1, and Nn − 2, and so on, but doesn’t intend their joint consequence N. I think this is a powerful objection. I don’t want to rule out the possibility of such a thing. But N is a morally unproblematic and structurally central part of the arrangement of reality. It seems very plausible that even if we reject (2) in general, we should accept it in the special case of morally unproblematic and structurally central parts of the arrangement of reality. Otherwise, God isn’t really in charge of creation.

Friday, June 24, 2022

What is a material thing?

Here's a theory: a material thing is something that has or is a causal power that is not a mental causal power. Variant: that is not a rational causal power.

Boltzmann brain blackouts

Some cosmological theories lead to the worrisome conclusion that most people with present brain states like ours are Boltzmann brains—random aggregations of molecules in space that came together to form a brain in a little bubble of oxygen. Usually when people talk about Boltzmann brains, they talk of how this induces a sceptical problem for the theory that generates them. Thinking about Boltzmann brain issues that way leads to messy epistemological questions such as whether we get to simply assume that we have hands, and the like. Moreover, if there is evidence for the cosmological theory, then that becomes evidence for Boltzmann brains, which then undermines the evidence for the cosmological theory, and that’s all a mess.

Here is how I suggest we think about what happens when a cosmological theory T leads to a Boltzmann brain issue. The vast majority of Boltzmann brains—even ones with brain states like ours—are short-lived. Their bubble of oxygen dissipates in the absence of gravity, and after a brief moment of hypoxia they die. So think of the point this way. If a cosmological theory predicts a large ratio of Boltzmann brains to ordinary evolved brains, then the theory makes an empirical prediction: in a moment you are extremely likely to start blacking out. So just do the experiment: wait a moment and see if you’re blacking out. If you’re not, then you’ve got very strong disconfirmation of the cosmological theory, and you’re done with it. You don’t have to worry about self-defeat, Moorean questions about whether you have two hands, or anything deep like that. (And if you are blacking out, then if it’s a Boltzmann brain related blockout, you’ll be dead in a moment. If you do come back to, and not in the afterlife, that’s massive evidence against the theory again, but now you should see a doctor about your blackout problem.)

In fact, you don’t even have to wait: on cosmological theories that generate too many Boltzmann brains, you should expect to already be starting to black out—because most of the Boltzmann brains will be extremely short-lived.

Objection: There will be long-lived Boltzmann brains, too.

Response: Sure. But for entropic reasons they will be much less common than the short-lived ones. You might, of course, worry that in many of these cosmological scenarios there are infinitely many Boltzmann brains, and infinitely many are short-lived and infinitely many are long-lived, and you can’t say that the short-lived ones are more common. The short-lived ones will be more common in a “typical” large finite region, but overall we just have infinity. Now, if you are worried about this—and I think you should be—then that worry already applied at the beginning of the story when you looked at the ratio of ordinary to Boltzmann brains, because there will be infinitely many of each on such a cosmological theory, and the formulation of the problem that I gave at the beginning, namely that Boltzmann brains greatly outnumber ordinary brains, is inaccurate. (I think if you do have this worry, then the theory has another problem, namely that probabilistic reasoning makes no sense in a world described by the theory. That is a kind of sceptical and self-defeat problem, but of a different nature.)

My point in this post is modest: if you want to say that Boltzmann brains greatly outnumber ordinary brains, then instead of thinking deep stuff about self-defeat of theories and scepticism, you should just think of the theory that generates this prediction as falsified by future observation.

Thursday, June 23, 2022

What I think is wrong with Everettian quantum mechanics

One can think of Everettian multiverse quantum mechanics as beginning by proposing two theses:

  1. The global wavefunction evolves according to the Schroedinger equation.

  2. Superpositions in the global wavefunction can be correctly interpreted as equally real branches in a multiverse.

But prima facie, these two theses don’t fit with observation. If one prepares a quantum system in a (3/5)|↑⟩+(4/5)|↓⟩ spin state, and then observes the spin, one will will observe spin up in |3/5|^2=9/25 cases and spin down in |4/5|^2=16/25 cases. But (roughly speaking) there will be two equally real branches corresponding to this result, and so prima facie one would expect equally likely observations, which doesn't fit observation. But the Everettian adds a third thesis:

  1. One ought to make predictions as to which branch one will observe proportionately to the square of the modulus of the coefficients that the branch has in the global wavefunction.

Since Aristotelian science has been abandoned, there has been a fruitful division of labor between natural science and philosophy, where investigation of normative phenomena has been relegated to philosophy while science concerned itself with the non-normative. From that point of view, while (1) and (less clearly but arguably) (2) belong to the domain of science, (3) does not. Instead, (3) belongs to epistemology, which is study of the norms of thought.

This point is not a criticism. Just as a doctor who has spent much time dealing sensitively with complex cases will have unique insights into bioethics, a scientist who has spent much time dealing sensitively with evidence will have unique insights into scientific epistemology. But it is useful, because the division of intellectual labor is useful, to remember that (3) is not a scientific claim in the modern sense. And there is nothing wrong with that as such, since many non-scientific claims, such as that one shouldn’t lie and that one should update by conditionalization, are true and important to the practice of the scientific enterprise.

But (3) is a non-scientific claim that is absurd. Imagine that a biologist came up with a theory that predicted, on the basis of their genetics and environment, that:

  1. There are equal numbers of male and female infant spider monkeys.

You might have thought that this theory is empirically disproved by observations of a lot more female than male infant spider monkeys. But our biologist is clever, and comes up with this epistemological theory:

  1. One ought to make predictions as to the sex of an infant spider monkey one will observe in inverse proportion to the ninth power of the average weight of that sex of spider monkeys.

And now, because male spider monkeys are slightly larger than females, we will make predictions that roughly fit our observations.

Here’s what went wrong in our silly biological example. The biologist’s epistemological claim (5) was not fitted to the actual ontology of the biologist’s theory. Instead, basically, the biologist said: when making predictions of future observations, make them in the way that you should if you thought the sex ratios were inversely proportional to the ninth power of the average weights, even though they aren’t.

This is silly. But exactly the same thing is going on in the Everett case. We are being told to make predictions in the way you should if the modulus squares of the weights in the superposition were chances of collapse. But they are not.

It is notorious that any scientific theory can be saved from empirical disconfirmation by adding enough auxiliary scientific hypotheses. But one can also save any scientific theory from empirical disconfirmation by adding an auxiliary philosophical hypothesis as to how confirmation or disconfirmation ought to proceed. And doing that may be worse than obstinately adding auxiliary scientific hypotheses. For auxiliary scientific hypotheses can often be tested and disproved. But an auxiliary epistemological hypothesis may simply close the door to refutation.

To put it positively, we want a certain degree of independence between epistemological principles and the ontology of a theory so that the ontology of the theory can be judged by the principles.

Tuesday, June 21, 2022

The cogito and time-delay

I’ve been thinking about how well Descartes’ cogito argument works given the following plausisble thesis:

  1. Every perception, including introspection, has a time delay.


  1. I am in pain.

  2. If I am in pain, then I exist.

  3. So, I exist.

Supposedly, (2) is clear and distinct. But wait (!). By (1), I only introspect premise (2) with a time delay. In other words, by the time I introspect premise (2), the pain is over. It is one thing to be in pain—obviously, when I am in pain, I am in pain—but it is another to be aware that I am in pain.

In other words, at the present moment, if I am to stick to the indubitable, all I get to say is:

  1. I was in pain.

  2. If I was in pain, then I existed.

  3. So, I existed.

Now, if eternalism or growing block is true, I still get to conclude that I exist simpliciter, but not indubitably so (since I need to rely on the arguments for eternalism or growing block).

But there is an even more serious problem. Once we accept the time delay thesis (1), we no longer have indubitability in our introspection of pain. For suppose the time delay from being in pain to being aware that one is in pain is a microsecond. But now consider the half-microsecond hypothesis that the universe came into existence, fully formed, half a microsecond ago. If so, I would still have the introspective awareness of being in pain—without having had a pain! The half-microsecond hypothesis is crazy, but no crazier than the evil demon hypothesis that Descartes cares so much about. So now we don’t have indubitability about (2) or (5).

And what goes for pain goes for any other conscious state, i.e., for anything that Descartes calls “thought”.

We might now want to deny the time-delay thesis (1), and say that:

  1. Whenever I have a conscious state Q, I am immediately thereby aware of having state Q.

But a bit of introspection shows that (8) is false. For being aware is itself a conscious state, and so if (8) were true, then whenever I have a conscious state, I have an infinite sequence of conscious states of meta-awareness. And I clearly do not.

Indeed, introspectively reflecting on the states of meta-awareness shows that sometimes the time-delay thesis is true. Let’s say that I am aware that I am in pain. It takes reflection, and hence time, to become aware that I am aware that I am in pain. So the time-delay thesis is at least sometimes true.

Now it might be that we are lucky and the time-delay thesis is false for introspection of first-order conscious states, like being in pain. I am a little sceptical of that, because I suspect a lot of non-human animals are in pain but don’t even have the first meta-step to perceiving that they are in pain.

So let’s grant that the time-delay thesis is false for introspection of first-order conscious states. Now it is no longer true that, as Descartes thought, his cogito could be run from any conscious states. It can only be run from the ones for which the time-delay thesis is false. But it’s worse than that. Even if the time-delay thesis is false for some introspective perceptions, it is not indubitable that it is false for them. The claim that these introspections lack time-delay is far from indubitable.

Yet all that said, isn’t it true that even in the half-microsecond world, I exist? Even if I didn’t have the pain that I think I had, surely to think that I had it requires that I am! Yes, but I only become aware that I think I had a pain with a time-delay from my thinking that I had a pain, because the time-delay thesis is empirically true at all the meta-levels.

This is all very strange. Maybe one can save something by supposing that awareness of a conscious state Q is always partly constituted by Q, and even with a time-delay we have indubitability. Maybe in the half-microsecond world, I couldn’t be aware of having had a pain when I didn’t have the pain, because the second-order awareness is partly constituted by the occurrence of the first-order awareness, be that occurrence past or present. Maybe, but the partial constitution thesis seems dubitable. And once we get to some meta-levels it seems implausible. Couldn’t I be mistaken in thinking that I aware that I am aware that I am aware that I am aware of Q, while in reality I only had two meta-levels?

I am feeling disoriented and confused now.

Monday, June 20, 2022

Why isn't a timeless being evanescent?

I think God is timeless. For a long time I’ve been vaguely worried by the thought that on a B-theory of time, a timeless being is like a being that exists at only one instant of time. But the latter being is really evanescent, while a timeless being is the opposite of evanescent. What’s the difference?

We can say: well, a being that exists at only one instant will cease to be when a new instant comes, but a timeless being won’t cease to be. But now imagine a being that exists at only one instant, but that instant is the very last instant of time. It’s no longer true that that being will cease to be, because to cease to be there has to be a future time at which one does not exist, and at the last instant of time there is no future at all. Yet the being that exists at the last instant of time is still evanescent.

If one believes in a “flow of time”, one can say that a timeless being is like a being at an instant of “time” in a “time” sequence that doesn’t flow (so it’s not really time, but only “time”). But a “flow of time” is hard to make sense of.

Here are two alternative stories. First, we might suppose that instants of time can have a “duration weight”. Thus, while one might think that the duration of n instants of time is always (in the most natural units) precisely n, one might think that instants have a duration which measures how long they endure. It’s not that they are exactly intervals. It’s still going to be the case that no change is possible during an instant. But perhaps duration is possible. Then on a discrete theory of time, a sequence of instants has a duration equal to the sum of the durations of the instants. And on a continuous theory of time, the temporal length of a segment of intervals is equal to the integral of the durations.

We can then say that a timeless being is like one that exists on an instant of infinite duration, an instant that has nothing before it or after it. On a discrete theory, this is straightforwardly just an infinite duration. On a continuous theory, it would be like a Dirac delta.

Second, we might hypothesize that what yields the subjective experience of “moving on” from one instant to another is the poverty of our experiences contained in the instant. But mystics talks of being caught up to eternity in their experiences of the infinite: time appears to slow down for them. But the experiences of mystics do not, after all, comprehend the infinite. However, perhaps, an experience that did comprehend the infinite would slow one down to the point that an instant would literally last subjectively for eternity. And this subjective time could then be an accurate reflection of the internal time of the being. If so, then only a being that comprehends the infinite, like an infinite God contemplating himself, could be timeless.

(Note that there may be some difficulty in fitting the above to the common observation that time flies when you’re having fun. But it has been hypothesized that the latter is due to the fact that when you’re having fun, you fail to notice every tick of your internal clock. Thus the fact that time flies when you’re having fun isn’t merely due to the richness of the experience when you’re having fun. It may be that what we have is a kind of phenomenon where modest finite fun makes subjective time go by faster, but then once we transcend fun into a mystical experience, the opposite happens.)

Life, simulations and AI

  1. An amoeba is alive but an accurate simulation of an amoeba wouldn’t be alive.

  2. If (1), then an accurate simulation of a human wouldn’t be alive.

  3. So, an accurate simulation of a human wouldn’t be alive.

  4. Something that isn’t alive wouldn’t think.

  5. So, an accurate simulation of a human wouldn’t think.

  6. If an accurate simulation of a human wouldn’t think, Strong AI is false.

  7. Strong AI is false.

Behind (2) is the idea that the best explanation of (1) is that computer simulations of living things aren’t alive. I think (4) is perhaps the most controversial of the premises.

Friday, June 17, 2022

Yet another formulation of my argument against a theistic multiverse

Here’s yet another way to formulate my omniscience argument against a theistic multiverse, a theory on which God creates infinitely concretely real worlds, and yet where we have a Lewisian analysis of modality in terms of truth at worlds.

  1. Premise schema: For any first order sentence ϕ: Necessarily, ϕ if and only if God believes that ϕ.

  2. Premise schema: For any sentence ϕ: Possibly ϕ if and only if w(at w: ϕ).

  3. Premise: Possibly there are unicorns.

  4. Premise: Possible there are no unicorns.

  5. Necessarily, there are unicorns if and only if God believes that there are unicorns. (Instance of 1)

  6. Possibly, God believes that there are unicorns. (3 and 5)

  7. Possibly God believes that there are unicorns if and only if w(at w: God believes that there are unicorns). (Instance of 2)

  8. w(at w: God believes that there are unicorns). (6 and 7)

  9. w(at w: God believes that there are no unicorns). (from 1, 2, 4 in the same way 8 was derived from 1, 2, 3)

So, either there is a world at which it is the case that God both believes there are unicorns and believes that there are no unicorns, or what God believes varies between worlds. The former makes God contradict himself. The content of God’s beliefs varying across worlds is unproblematic if the worlds are abstract. But if they are concrete, then it implies a real disunity in the mind of God.

Premise schema (1) is restricted to first order sentences to avoid liar paradoxes.

Tuesday, June 14, 2022

There could still be a persistence-based cosmological argument even if there were existential inertia

Suppose that today at noon, Felix the cat enters a time machine and travels back to the time of the dinosaurs, where he spends the rest of his life hunting small reptiles. According to the doctrine of existential inertia, objects have a blockable tendency to continue existing.

Question: If Felix has existential inertia, was his inertial tendency to continue existing blocked at noon when he time-traveled to the past, and hence failed to exist past today’s noon?

My intuition is that the answer is negative. Existential inertia seems to me to be about “having a future” and today at noon, Felix does have a future, even if that future is in the distant past. In other words, if there is such a thing as existential inertia, it concerns what I call “internal” rather than “external” time.

Beyond mere intuition, here is a reason for a defender of existential inertia to agree with me. If existential inertia concerns external time, then in a relativistic world it is a doctrine that says that an object that exists at point z of spacetime has a tendency to exist somewhere or other in the forwards lightcone centered on z. But there is something odd about a metaphysical principle, like existential inertia is supposed to be, that impels an object to continue to exist in some location or other in some infinite set of locations (say, the infinite number of locations in the forward lightcone one second away from the present in some reference frame), without impelling the object to exist in any particular location, or even imposing any kind of probability distribution on where it is to exist. Moreover, it is not clear why the forward lightcone would be so metaphysically special that a fundamental metaphysical principle would coordinate with lightcones so neatly.

Perhaps this is not completely convincing. But it has some legs. There is thus some reason to think that existential inertia applies to internal rather than external time. But if so, then existential inertia has not removed all that needs to be explained about persistence. For a normal cat not only tends to continue to exist in its internal-time future, but also tends to continue to exist in its external-time future, since normally there is no time travel. And this external-time persistence is not explained by existential inertia, if existential inertia concerns the external-time future. So there is a persistence to explain, and theism offers an explanation. There is still room for an argument for theism from persistence.

Here is a closely related explanatory problem: Why is it that internal and external time tend to be correlated, so that internal-time persistence tends to imply external-time persistence?

Suppose that, contrary to my relativity theory intuitions, one insists that existential inertia concerns external-time persistence rather than internal-time persistence? Then there is still something to be explained: the correlation between internal and external time.

Thursday, June 9, 2022

The mind-world similarity thesis

Eventually, the modern tradition becomes very suspicious the idea that there can be a similarity between the contents of the mind and characteristics of things in the external world. First, we have Locke denying the possibility of the similarity thesis for secondary qualities like red and sweet, and then we have others, like Berkeley and Reid, denying the possibility of the similarity thesis for primary qualities, like triangularity. In the case of primary qualities, it just seems absurd to think that the mind should hold something like a triangle.

This denial of the possibility of the similarity thesis seems to me to be a massive failure of the philosophical imagination, and a neglect of a sympathy to the history of philosophy. The allegation of the absurdity of thinking that triangularity should be present in the mind and in the world seems to come from thinking that the only way triangularity can be present in an entity is by the entity’s having triangularity. But why should having be the only possible relation by which triangularity could be present in a thing?

Here are some ways in which a property could be in a thing without the thing having the property.

  • Let S be the set of the polygonality properties. Thus, the members of S are triangularity, quadrilaterality, etc. Triangularity is then in S qua member of S, but S is not a triangle—it does not have triangularity.

  • On divine simplicity, God is identical with his divinity. But God can be present in Francis without Francis having God’s divinity—i.e., without Francis being divine.

  • Suppose that I have a wood triangle in a steel box. The triangle’s triangularity is in the triangle, and the triangle is in the box, so the triangularity is in the box.

  • Say that my fingernail is pointy. The properties of a thing are parts of a thing. So, the fingernail has its pointiness as a part. But the fingernail is a part of me, and parthood is transitive. So the pointiness of the fingernail is a part of me. But I am not pointy, even though I have a pointiness in me.

There is nothing absurd, then, about there being triangularity in the mind without the mind being itself triangular.

Moreover, having triangularity in the mind is not even a necessary condition for there to be a relevant similarity between the mind and a wooden triangle outside of me. It could be that the triangularity in the triangle is not a simple entity, but is composed of two components, T and P, where the P component is common (either as type or as token) between all properties, and the T component distinguishes triangularity from other properties. Thus, squareness might consist of S and P, and redness might consist of R and P. Well, then, we can suppose that when I think of or perceive a triangle as a triangle, then T comes to be in my mind without P doing so. Perhaps T comes to be “elementally” present in my mind, or perhaps it comes to be compounded with something else. (Here is a Thomistic version: triangularity has an essence T and a natural esse P; when present in the mind, the essence is there, but instead comes to have a different thing from the natural esse, say an intentional esse.) In either case, we have something importantly in common between the mind and the triangle qua triangular, namely T, without having triangularity in the mind, but only a component of triangularity.

There is no paucity of options. Indeed, we have an embarrassment of riches—many, many ways of making the similarity thesis true.

The variety of virtue ethical systems

One thinks of virtue ethics as a unified family of ethical systems. But it is interesting to note just how different virtue ethical systems can be depending on how one answers the question of what it is that makes a stable character trait T be a virtue? Consider, after all, these very varied possible answers to that question, any one of which could be plugged into a virtue ethical account of rightness as what accords with virtue.

  • having T is partly constitutive of eudaimonia (Aristotelian virtue ethics)

  • having T is required by one’s nature or by the nature of one’s will (natural law virtue ethics)

  • a typical human being is expected to gain utility by having T (egoist virtue ethics)

  • a typical human being is expected to contribute to total utility by having T (utilitarian virtue ethics)

  • it is pleasant to think of oneself as having T (hedonistic virtue ethics)

  • it is pleasant to think of another as having T (Humean sentimentalist virtue ethics)

  • God requires one to have T (divine command virtue ethics).

The resulting ethical systems are all interesting, but fundamentally very different.

Tuesday, June 7, 2022

The incoherence of Spinoza's mode ontology

According to Spinoza, I am a mode and God is the only substance. But I am not directly a mode of God. I am a mode of a mode of a mode of … a mode of God, with infinitely many “a mode of” links in between.

This is incoherent. It is an infinite chain with two ends, one being me and the other being God. But any infinite chain made of direct links has at most one end: it would have to be of the form 1:2:3:4:…, with one endpoint, namely zero. We can stick on another chain running in the other direction, like …:iv:iii:ii:i, and get the two ended sequence 1:2:3:4:…:iv:iii:ii:i. But this two-ended sequence is not a chain, because there is no connection between any of the arabic numbered nodes and any of the roman numbered nodes.

Ways out of the closure argument for physicalism

One of the main arguments for physicalism is based on the closure principle:

  1. Any physical event that has a cause has a physical cause.

It is widely thought that it follows from (1) that:

  1. If a physical event has a nonphysical cause, the event is overdetermined.

And hence in the absence of systematic overdetermination, mental causes must be physical.

But (2) doesn’t follow from (1). There are at least three ways for an event E to have two sufficient causes A and B:

  • overdetermination

  • chaining: A causes B which causes E or B causes A which causes E

  • parthood: A causes E by having B as a part which causes E, or B causes E by having a part A which causes E.

Let’s think a bit about how the chaining and parthood options might avoid physicalism in the case of mental causation and yet allow for closure.

Option I: Nonphysical-physical-physical chaining: A nonphysical event M causes a physical event P which causes a physical event E. This can’t be the whole story for how we respect closure. For by closure, P will need a physical cause P2, and so it is looking like P is going to be overdetermined, by M and P2. But that does not follow without further assumptions. For we could have the following scenario:

  • E is caused by an infinite chain of physical causes which chain is causally preceded by M, namely: P ← P2 ← P3 ← ... ← M, with infinitely many physical events in the “…”.

This scenario requires the possibility of an infinite sequence of causal means, contrary to causal finitism, and hence is unacceptable to me. But those who are less worried about infinite chains of causes should take this option seriously. Note that this option is reminiscent of Kant’s view on which our noumenal selves collectively cause the physical universe as a whole.

Option II: Physical-nonphysical-physical chaining: Here, the physical event P causes E by having a mental event as an intermediate cause. This option exploits a loophole in the closure principle as it is normally formulated: nothing in the closure principle says that the physical cause can’t operate by means of a nonphysical intermediary. Granted, that’s not how we normally think of physical causes as operating. But there is nothing incoherent about the story.

Option III: Physical parts of larger events: A physical event E is caused by a physical event P, and the physical event P is itself a part of a larger event M which is only partly physical. One might object that in this case it’s only P and not the larger event that counts as the cause. But that’s not right. If someone dies in the battle of Borodino, then at least three causes of death can be given: a shot being fired, the battle of Borodino, and the War of 1812. The shot is a part of the battle, and the battle is a part of the war. One particular way to have Option III is this: a quale Q is constituted by two components, a brain state B (say, a state of the visual cortex) and a soul state S of paying attention to the brain system that exhibits B, with B being the causally efficacious part of the Q. So a physical event—say, an agent’s making an exclamation at what they saw—counts as caused by the physical event B and the event Q which is not physical, or at least not completely physical.

One might object, however, that by “nonphysical”, one means entirely nonphysical, so Q’s having a nonphysical part S does not make Q nonphysical. If so, then we have one last option.

Option IV: Some or all physical causes cause their effects by having a nonphysical part that causes the event. That nonphysical part could, for instance, be an Aristotelian accidental or substantial form. Thus, here a physical event E is caused by a physical event by means of its nonphysical part M.

What if one objects that “physical” and “nonphysical” denote things that are purely physical and nonphysical, and neither can have a part that is the other? In that case, we have two difficulties. First, the closure principle is now stronger: it requires that a physical event that has a cause always has a purely physical cause. And we have a serious gap at the end of the argument. From closure at most we can conclude that a physical event doesn’t have a purely nonphysical cause. But what if it has a partly physical and partly nonphysical cause? That would be enough to contradict physicalism.

Wednesday, May 25, 2022

Anti-Bayesian update and scoring rules in infinite spaces

Bayesian update on evidence E is transitioning from a credence function P to the credence function P(⋅∣E). Anti-Bayesian update on E is moving from P to P(⋅∣Ec) (where Ec is the complement of E). Whether one thinks that Bayesian update is rationally required, it is clear that Bayesian update is better than anti-Bayesian update.

But here is a fun fact (assuming the Axiom of Choice). For any scoring rule on an infinite space, there is a finitely additive probability function P and an event E such that 0 < P(E) < 1 where P(⋅∣E) and P(⋅∣Ec) get exactly the same score everywhere in the probability space. It follows that when dealing with finitely additive probabilities on infinite spaces, a scoring rule will not always be able to distinguish Bayesian update from anti-Bayesian update. This is a severe limitation of scoring rules as a tool for evaluating the accuracy of a credence function in infinite cases.

Here’s a proof of the fun fact. Let s be a scoring rule. Say that two credence functions are maximally opinionated provided that they assign 0 or 1 to every event. It is known that then there are two different maximally opinionated finitely additive probability functions p and q such that s(p) = s(q) everywhere. Let P = (p+q)/2 be their average. Let E be an event such that p(E) = 1 and q(E) = 0 (such an event exists because p and q are maximally opinionated and yet different). Then P(⋅∣E) = p and P(⋅∣Ec) = q while P(E) = 1/2. Hence conditionalization on E and Ec has exactly the same score.

One might take this as some evidence that finite additivity is not good enough.

Tuesday, May 24, 2022

Physicalism and the progress of science

People sometimes use the progress of science to argue for physicalism about the mind. But it seems to me that Dostoevskii made more progress in understanding the human mind by existential reflection than anybody has by studying the brain directly. More generally, if we want to understand human minds, we should turn to literature and the spiritual masters rather than to neuroscience.

Thus, any argument for physicalism about the mind from the progress of science is seriously flawed. And perhaps we even have some evidence against physicalism. For it is a surprising fact that we learn more about the mind by the methods of the humanities than by study of the brain if the mind is the brain.


I'm trying to thin the herd of old computers at home. I realized that the only real reason I had a 20-year-old Linux box at home was if I ever wanted to use a 3.5" drive in it to deal with floppies for various systems, especially my HP 1653B oscilloscope (I could get a USB floppy drive for one of the laptops at home, but they aren't usually compatible with non-DOS disk formats). 

Moreover, the 3.5" drive in the computer wasn't even working. Aligning the heads on the drive solved that problem, and then I assembled a GreaseWeazle using one of the blue pill microcontroller boards I have lying around. Then I made a 3D printable case for the messy assembly.

And now I can read and copy floppies for my oscilloscope on my laptop. :-)

Wednesday, May 18, 2022

Dog whistles

From time to time I’ve had occasion to make use of examples where someone says different things to two different interlocutors in a single utterance. My favorite examples were pointing to a bottle and saying “Gift!”, which would mean a very different thing to a German speaker and to an English speaker, or using coded language while speaking to someone while knowing a spy is overhearing. Such examples illustrate the interesting fact that we cannot identify propositions with equivalence classes of utterance tokens, because a single utterance token can express different propositions.

But arguments based on such contrived cases have a tendency to be less than convincing. However, it has just occurred to me that dog whistles in politics are a real-life example of the same phenomenon, and one technically within a single language.

By the way, if we’re looking for equivalence classes that function like propositions, I guess instead of looking at equivalence classes of tokens utterances, we should look at equivalence classes of context-token pairs, where a context includes the language and dialect as well as the (actual? intended?) audience.

Tuesday, May 17, 2022

A near lie

Alice knows that her friend Bob has no pets and no experience with birds. While recommending Bob for a birdkeeping job at a zoo and having discovered or to be surprisingly ignorant about birds, she says:

  1. Bob has a fine collection of Southern yellow-beaked triggles.

It seems that Alice is lying. Yet it seems that to lie one must assert, and to assert one must express a proposition. But Alice’s sentence does not express a proposition since “triggle” is meaningless.

Sentence (1) seems to entail the falsehood:

  1. Bob owns some birds.

But entailment is a relation between propositions, and (1) neither is nor expresses a proposition. We might want to say that if it did express a proposition, it would express a proposition entailing (2). But even that isn’t so clear. After all, maybe a world where “triggle” denotes a science-fictional beaked reptile is closer than a world where it denotes a kind of bird (imagine that some science-fiction writer almost wrote Southern yellow-beaked triggles as reptiles into a story but stopped themselves at the last moment).

Here is what I think I want to say about what Alice did. According to Jorge Garcia, what makes lying bad one linguistically solicits trust that what one is saying is true, while at the same time betraying that trust. Alice did exactly that, but without asserting. So, while Alice did not lie, she did something that is wrong for the same reason that lying is.

Wednesday, May 11, 2022

Chinese Room thought experiments

Thought experiments like Searle’s Chinese Room are supposed to show that understanding and consciousness are not reducible to computation. For if they are, then a bored monolingual English-speaking clerk who moves around pieces of paper with Chinese letters letters—or photographic memories of them in his head—according to a fixed set of rules counts as understanding Chinese and having the consciousness that goes with that.

I used to find this an extremely convincing argument. But I am finding it less so over time. Anybody who thinks that computers could have understanding and consciousness will think that a computer can run two different simultaneous processes of understanding and consciousness sandboxed apart from one another. Neither process will have the understanding and consciousness of what is going on in the other process. And that’s very much what the functionalist should say about the Chinese Room. We have two processes running in the clerk’s head. One process is English-based and the other is a Chinese-based process running in an emulation layer. There is limited communication between the two, and hence understanding and consciousness do not leak between them.

If we accept the possibility of strong Artificial Intelligence, we have two choices of what to say about sandboxed intelligent processes running on the same hardware. We can say that there is one person with two centers of consciousness/understanding or that there are two persons each with one center. On the one person with two mental centers view, we can say that the clerk does understand Chinese and does have the corresponding consciousness, but that understanding is sandboxed away from the English-based processing, and in particular the clerk will not talk about it (much as in the computer case, we could imagine the two processes communicating with a user through different on-screen windows). On the two person view, we would say that the clerk does not understand Chinese, but that a new person comes into existence who does understand Chinese.

I am not saying that the proponent of strong AI is home free. I think both the one-person-two-centers and two-person views have problems. But these are problems that arise purely in the computer case, without any Chinese room kind of stuff going on.

The one-person-two-centers view of multiple intelligent processes running on one piece of hardware gives rise to insoluble questions of the unity of a piece of hardware. (If each process runs on a different processor core, do we count as having one piece of hardware or not? If not, what if they are constantly switching between cores? If yes, what if the separate the cores to separate pieces of silicon that are glued along an edge?) The two-persons view, on the other hand, is incompatible with animalism in our own case. Moreover, it ends up identifying persons with software processes, which leads to the unfortunate conclusion that when the processes are put to sleep, the persons temporarily cease to exist—and hence that we do not exist when sufficiently deeply asleep.

These are real problems, but no additional difficulty comes from the Chinese room case that I can see.

Tuesday, May 10, 2022

Towards a static solution to Wordle

A static solution to Wordle would be a sequence of five guess words which would distinguish all the answer words. I've run C-based parallel nearly-brute force (with some time-saving heuristics) code to try to see if there is a static solution. No luck so far. The closest I have is flitt dawds vughy kerel combo paean, which leaves two pairs undistinguished (spine/snipe and gauge/gauze). There may be a full solution, but I don't have it. (Note: I am working with the original answer list, not the modified New York Times one.)

Friday, May 6, 2022

Punishment and the law

Here’s a valid argument:

  1. It is only permissible to punish a person for doing what is morally wrong.

  2. It is permissible for the state to punish a person for disobeying law.

  3. Therefore, disobeying law is morally wrong.

This is already an interesting and somewahat controversial conclusion. It pushes us to the view that when the law forbids something that is innately morally permissible—such as driving on the left side of the road—that thing becomes morally impermissible.

We can then continue arguing to another controversial conclusion:

  1. It is not morally wrong to disobey unjust requirements.

  2. Therefore, no unjust requirement is law.

I suppose all this focuses one’s attention on (1). The opposing view would be that it is permissible to punish a person for doing things that are legally wrong even when they are merely legally wrong. But this seems mistaken. A person who fulfills all moral imperatives is perfectly innocent. But it is wrong to punish a perfectly innocent person.

Note that the first argument implies that taking literally the idea of what some Catholic authors called “purely penal laws”, where there is no moral obligation to obey, just an obligation to pay the penalty if one is caught disobeying, is highly problematic. For if it’s penal, it imposes a punishment, and it’s wrong to impose a punishment for what isn’t wrong to do. That said, it may be that the idea of “purely penal laws” is just a misuse of the word “penal”. We can think of them as laws that simply impose a special fee applicable if one is caught disobeying, but that fee is not a punishment. We can imagine, for instance, a setup where there is a set fee for traveling by bus with a ticket and a larger fee for traveling without a ticket which is levied at random, namely when a ticket checker is present. (I remember that once in Poland buses had a sign detailing a with-ticket price and a without-ticket price, the second being an order of magnitude higher.) But it is a difficult question when something is a fee and when it is a punishment. This question famously came up for Obamacare.

Wednesday, May 4, 2022

Evils that are evidence for theism

It’s mildly interesting to note, when evaluating the evidential impact of evil, that there can be evil events that would be evidence for the existence of God. For instance, suppose that three Roman soldiers who witnessed Christ’s resurrection conspired to lie that he didn’t see Christ get resurrected. That they lied that they didn’t see Christ get resurrected entails that they thought they witnessed the resurrection, and that would be strong evidence for the existence of God, even after factoring in the counterevidence coming from the evil of the lie. (After all, we already knew that there are lots of lies in the world, so learning of one more won’t make much of a difference.)

In fact, this is true even for horrendous and apparently gratuitous evils. We could imagine that the three soldiers’ lies crush someone’s hopes for the coming of the Messiah, and that could be a horrendous evil. And it could also be the case that we can’t see any possible good from the lie, and hence the lie is apparently gratuitous.

Monday, May 2, 2022

An argument for probabilism without assuming strict propriety

Suppose that s is a proper scoring rule on a finite space Ω continuous on probabilities and suppose that for no probability p is the expectation Eps(p) infinitely bad (i.e., no probability is infinitely bad by its own lights). Suppose that s is probability distinguishing: there isn’t a non-probability c and probability p such that s(c) = s(p) everywhere. Then any non-probability credence c is weakly s-dominated by some probability p: i.e., s(p)(ω) is at least as good as s(c)(ω) for all ω, and strictly better for at least one ω. (This follows from the fact that Lemma 1 of this short piece holds with the same proof when q is a non-probability.)

If one thinks that one should always switch to a weakly dominating option, then this conclusion provides an argument for probabilism.

One might, however, reasonably think that it is only required to switch to a weakly dominating option when one assigns non-zero probability of the weakly dominating option being better. If so, then we get a weaker conclusion: your credences should either be irregular (i.e., assign zero to some non-empty set) or probabilistic. But a view that permits violations of the axioms of probability but only when one has irregular credences seems really implausible. So your credences should be probabilistic.

The big question is whether probability distinguishing is any more plausible as a condition on a scoring rule than strictness of propriety. I think it has some plausibility, but I am not quite sure how to argue for it.

Truth-directedness and propriety of scoring rules does not imply strict propriety

A scoring rule assigns a score to a credence assignment (which can but need not satisfy the axioms of probability), where a score is a random variable measuring how close the credence assignment is to the truth.

A scoring rule is strictly truth-directed provided that if c is a credence assignment that is closer to the truth than c is at ω, then c gets a better a score at ω. A scoring rule is proper provided that for all probabilities p, the p-expected value of the score of a probability p is at least as good as the p-expected value of the score of any other credence, and is strictly proper.

Propriety for a scoring rule is a pretty plausible condition, but it’s a bit harder to argue philosophically for strict propriety. But scoring-rule based philosophical arguments for probabilism—the doctrine that credences ought to be probabilities—require strict propriety.

In a clever move, Campbell-Moore and Levinstein showed that propriety plus strict truth-directedness and additivity (the idea that the score can be decomposed into a sum of single-event scores) implies strict propriety.

Here’s an interesting fact I will show: propriety plus strict truth-directedness do not imply strict propriety in the absence of additivity. Further, my counterexample will be bounded, infinitely differentiable and strictly proper on the probabilities. Personally don’t find additivity all that plausible, so I conclude the Campbell-Moore and Levinstein move does not the discussion of strict propriety and probabilism ahead much.

Let Ω = {0, 1}. Given a credence function c (with values in [0,1]) on the powerset of Ω, define the credence function c* which has the same value as c on the empty set and on Ω, but where c*({0}) is the number z in [0,1] that minimizes (c({0})−z)2 + (c({1})−(1−z))2, and where c*({1}) = 1 − c*({0}). In other words, c* is the credence function closest to c in the Euclidean metric such that c*({0}) + c*({1}) = 1.

Now let b*(c) = b(c*). Then b* agrees with b score on the probabilities, and hence is strictly proper on them. Further, every value of b* is a Brier score of some credence, and hence b* is proper.

We now check that it is strictly truth-directed. Brier scores are strictly truth-directed. Thus, replacing a credence function with one that is closer to the truth on Ω or on the empty set will improve the b* score. Moreover, it is easy to check that c*({0}) = (1+c({0})−c({1}))/2. It’s easy to check that if we tweak c({0}) to move us closer to the truth at some fixed ω ∈ {0, 1}, then c* will be closer to the truth at ω as well, and similarly if we tweak c({1}) to be closer to the truth at ω, and in both cases we will improve the score by the strict truth-directedness of Brier scores.

Finally, however, note that b* is not strictly proper and does not have a domination theorem of the sort used in arguments for probabilism, since the b*-score of any credence c that fails to be a probability due to its being the case c({0}) + c({1}) ≠ 1 but that gets the right values on the empty set and Ω (zero and one, respectively) is equal to the b*-score of c*, and c* will be a probability in that case.

Note that in the example above we don't have quasi-strict propriety either.

Friday, April 29, 2022

Generating quasi-strictly proper scoring rules

A scoring rule s assigns to a credence c on a space Ω a score s(c) measuring the inaccuracy of c. The score is itself a function from Ω to [−∞,M] (for some fixed M), so that s(c)(ω) measures the inaccuracy of c if the truth of the matter is that we are at ω ∈ Ω. A scoring rule is proper provided that Eps(p) ≤ Eps(c) for any probability p and any other credence c: i.e., provided that the p-expected value of the score of p is at least as good as (no more inaccurate than) as the p-expected value of any other score. It is strictly proper if the inequality is strict. It is quasi-strictly proper if the inequality is strict whenever p is a probability and c is not.

Here’s a fun fact about scoring rules.

Theorem: Let s be any continuous bounded proper scoring rule that is defined only on the probabilities. Then s can be extended to a continuous bounded quasi-strictly proper scoring rule defined on all credences.

This result works in the finite-dimensional case with standard Euclidean topologies on the space of credences (considered as elements of [0,1]PΩ) and on the scores (considered as values in [−∞,M]Ω). But it also works in countably-infinite-dimensional contexts in the right topologies ((PΩ) on the side of the credences and the product topology on the side of the scores), regardless of whether by “probabilities” we mean finitely or countably additive ones.

The proof uses three steps.

First, show that the probabilities are a closed subset of the space of credences.

Second, apply the Dugundji extension theorem to extend the score s from the probabilities to all credences while maintaining continuity and ensuring that the range of the extension is a subset of the convex hull of the range of the original score. Let s0 be the extended score. The convex hull condition and the propriety of the original score on the probabilities implies that s0 is proper, though not necessarily quasi-strictly so.

Third, let s1(c) = d(c,P) + s0(c), where Q is the set of credences that are probabilities and d(c,Q) is the distance from c to Q in the (PΩ) norm. This equals s0(c) and hence s(c) for a credence c.

I don’t know if there is much of a philosophical upshot of this. Maybe a kind of interesting upshot is that it illustrates that quasi-strict propriety is easy to generate?

Wednesday, April 27, 2022

Theism and emotional attitudes to adversity

Here are two three possible emotional attitudes towards great adversity:

  1. Judaeo-Christian: hope

  2. Stoic: calm

  3. Russellian: anger/despair.

Now consider this argument:

  1. The appropriate attitude towards great adversity is Judaeo-Christian or Stoic.

  2. If naturalism is true, the appropriate attitude towards great adversity is Russellian.

  3. So, naturalism is false.

The reason for (1) is the obvious attractiveness of the hopeful-to-calm part of the emotional spectrum as a way of dealing with diversity.

The reason for (2) is that emotions should fit with reality. But as Russell argues, a naturalist reality does not care about us: we came from the nebula and we will go back to the nebula, and the darkness of our life makes Greek tragedy the supreme form of human art. The most we can do shake our fist at the injustice of it all.

Monday, April 25, 2022

Rowe-style inductive arguments from evil

The examples, like Rowe’s, of evils in the inductive argument from evil are chosen to make them have a certain epistemic feature F. And the claim is that P(E has F | God) < P(E has F | no God), with the background information containing the occurrence of E (i.e., the evidence isn’t that the evil has occurred, but that the evil has F). Exactly what F is differs from paper to paper, but roughly the feature is that after investigation we don’t have a plausible candidate theodicy.

But not every evil has F. If every evil had F, then the examples in the literature wouldn’t run as heavily as they do to lethal harm to children and animals. The examples used by the atheological arguers are chosen to be particularly compelling and what makes them compelling is that they have F—nobody runs an inductive argument from evil based on robber barons getting stomachaches from too much caviar, because such evils do not have F.

So there are evils that don’t have F. And then P(E has F | God) > P(E has F | no God) by Bayesianism. So checking whether an evil has F sometimes yields an argument against the existence of God (namely when the evil does have F) and sometimes yields an argument for the existence of God (when the evil doesn’t have F).

And we do not know (as far as I know, Tooley is the only one to have made a serious attempt to figure it out, and his account fails for technical reasons) what the result is once the evidence is consolidated.

Friday, April 22, 2022

Arguing for divine simplicity

I want to defend this argument:

  1. If God is not simple, then some of God’s parts are creatures.

  2. If some of the parts of x are creatures, then x is partly a creature.

  3. God is not even partly a creature.

  4. So, God is simple.

I think (2) is very plausible. Premise (3) follows from the transcedence of God.

That leaves premise (1) to argue for. Here is one argument:

  1. If God is not simple, then God has a part that is not God.

  2. Anything that is not God is a creature.

  3. So, if God is not simple, then God has a part that is a creature.

Premise (5) is true by definition of “simple”. Premise (6) follows from the doctrine of creation: God creates everything other than God.

But perhaps one doesn’t believe the full doctrine of creation, but only thinks that contingent things are created. I think we can still argue as follows:

  1. If God is not simple, then God has contingent parts that are not God.

  2. Anything contingent that is not God is a creature.

  3. So, if God is not simple, then God has a part that is not God.

Why think (8) is true? Well, let’s think about the motivations for denying divine simplicity. The best reasons to deny divine simplicity are considerations about God’s contingent intentions or God’s contingent knowledge, and the idea that these have to constitute proper parts of God. But that yields contingent parts of God.

Now, what if one rejects even the weaker doctrine of creation in (9)? Then I can argue as follows:

  1. If God is not simple, then God’s contingent thoughts are proper parts of God.

  2. God is contingently the cause of each of his contingent thoughts.

  3. Anything that God is contingently the cause of is a creature of God.

  4. So, if God is not simple, then God has a part that is not God.

Again, the idea behind (11) is that it flows from the best motivations for denying divine simplicity.

Thursday, April 21, 2022

What do we learn about God's existence from the clear failures to find justification for evils?

Suppose we know of some evil e1, and careful further investigation clearly fails to turn up justification that God would have to allow that evil. Let F1 be that clear failure.

Now, those who defend the inductive argument from evil claim that F1 is evidence against the existence of God. But now presumably sometimes after investigation of some other evil, say e2, we do not clearly fail to turn up justification for an evil (i.e., we either find a justification or it is unclear whether we have done so). Presumably, in that case the clear failure F2 to turn up a justification would have been evidence against the existence of God. But now it is a basic Bayesian result that the absence of F2 is evidence for the existence of God.

In practice, the results of investigation vary from evil to evil. Sometimes we clearly fail to find a justification and sometimes we don’t clearly fail. When we clearly fail, that is Bayesian evidence against theism. When we don’t clearly fail, that is Bayesian evidence for theism. What does the totality of the evidence say?

We don’t know. We just don’t have the numbers. We don’t have good numbers as to how many investigations resulted in a clear failure to turn up a justification and how many have not. Nor do we have any really good estimates of the crucially important conditional probabilities for any particular evil, namely how likely we are to clearly fail to find a justification assuming God exists and how likely we are to clearly fail to find a justification assuming God doesn’t exist.

The answer to the question in the title of the post, then, is: Not much.

One might object that I stacked the deck by talking of clear failures to find a justification. Perhaps I should instead have talked of failures to clearly find a justification. Failures will then be much more common, and there will be very few cases of clear finding of a justification. However, at the same time, our expectation that we be able to clearly find a justification given God’s existence will not be that strong. For these are controversial matters, where clarity is hard to have, and we would expect them to be such. Indeed, it is not clear that assuming the existence of God we would ever expect to clearly have found a justification, because there could always be further evil consequences down the road that we did not take into account.

Learning of secret wickedness

When people learn that some apparently really decent person was a hypocrite who secretly practiced execrable vices, that tends to shake people’s faith in God. We can explain this by noting that the case provides one with a vivid case of moral evil, which provides evidence against the existence of God.

But we already knew that there was a lot of moral evil out there. So the effect on belief in God should not be very significant. And it is worth noting that learning of cases like the above can actually help with the problem of evil. In our time, we are very hesitant to use the punishment theodicy for evils that happen to people. But learning that there are more people with terrible hidden vices than we thought increases the probability that any particular evil befalling an apparently decent adult might actually be a well-deserved punishment.

Of course, a punishment theodicy will only go so far. It doesn’t apply to animals or small children. And the Book of Job teaches that it doesn’t apply to all cases of adults either. But realizing the dark truth that people who appear to be exemplars of virtue can be quite wicked should open us to the possibility that the punishment theodicy applies to a lot more cases than we thought.

Of course, the more cases we have to which the punishment theodicy applies, the more moral evils we have that need a theodicy as well. But free will considerations can help a lot with moral evils.

So it may well be that learning of someone’s secret evils is a wash in terms of the evidential import of the evil for God’s existence.

Friday, April 15, 2022

Towards a great chain of being

Here is one way to generate a great chain of agency: y is a greater agent than x if for every major type of good that x pursues, y pursues it, too, but not vice versa.

Take for instance the cat and the human. The cat pursues major types of good such as nutrition, reproduction, play, comfort, health, life, truth, and (to a limited degree) social interaction. The human pursues all of these, but additionally pursues virtue, beauty, and union with God. Thus the human is a greater agent than the cat.

Is it the case that humans are at the top of the great chain of agency on earth?

This is a difficult question to answer for at least two reasons. The first reason is that it is difficult to identify the relevant level of generality in my weaselly phrase “major type of good”. The oak pursues photosynthetic nutrition, the dung beetle does its thing, while we pursue other forms of nutrition. Do the three count as pursuing different “major types” of good? I want to say that all these are one major type of good, but I don’t know how to characterize it. Maybe we can say something like this: Good itself is not a genus but there are highest genera of good, and by “major type” we mean these highest genera. (I am not completely sure that all the examples in my second paragraph are of highest genera.)

The second reason the question is difficult is this. The cat is unable to grasp virtue as a type of good. A cat who had a bit more scientific skill might be able to see an instrumental value in the human virtue—could see the ways that it helps members of communities gain cat-intelligible goods like nutrition, reproduction, health, life, etc. But the cat wouldn’t see the distinctive way virtue in itself is good. Indeed, it is not clear that the cat would be able to figure out that virtue is itself a major type of good, no matter how much scientific skill the cat had. Similarly, it is very plausible that there are major types of good that are beyond human knowledge. If we saw beings pursuing those types of good, we would likely notice various instrumental benefits of the pursuit—for the pursuit of various kinds of good seems interwoven in the kinds of evolved beings we find on earth (pursuing one good often helps with getting others)—but we just wouldn’t see the behavior as the pursuit of a major type of good. Like the cat scientist observing our pursuit of virtue, we would reduce the good being pursued to the goods intelligible to us.

Thus, if octopi pursue goods beyond our ken, we wouldn’t know it unless we could talk to octopi and they told us that what they were pursuing in some behavior was a major type of good other than the ones we grasp—though of course, we would still be unable to grasp what was good in it. And as it happens the only beings on earth we can talk to are humans.

All that said, it still seems a reasonable hypothesis that any major type of good that is pursued by non-human organisms on earth are pursued by us.

Thursday, April 14, 2022

Some possible progress on continuous scoring rules and dominance in an infinite case

On finite sample spaces, we have the Pettigrew-Nielsen-Pruss domination theorem for strictly proper scoring rules that are continuous when restricted to the probabilities that shows that the score of any non-probability is dominated by the score of a probability. Last year, I showed that for a reasonable sense of “continuous”, this is not true on countably infinite sample spaces (when we take probabilities to be countably additive; for if we take probabilities to be finitely additive, there are no strictly proper scoring rules).

In the comments, Ian then suggested that we want our scoring rule to be continuous on all credences, not just the probabilities.

Here are two preliminary responses, though not all the details of the proof of the second have yet been checked, so I could just be wrong.

First, what happens seems to depend on the topology on the space of credences. Credences can be thought of as functions from PΩ to [0,1]. One possibility is to take the space of credences to get the product topology on [0,1]PΩ. In that case, there is no continuous strictly proper (or even quasi-strictly proper) scoring rule. This follows from the uncountability of PΩ which shows that any countable intersection of neighborhoods of a probability function will contain infinitely many non-probability functions, so that any continuous score will have the property that for every probability there is a non-probability that gets the same score.

But, second, another reasonable topology on [0,1]PΩ is the ℓ(PΩ) topology. This topology is easily seen to be equivalent on the probabilities to the 1(Ω) topology (where a probability p on PΩ corresponds to a function p* ∈ ℓ1(Ω) defined by p*(x) = p({x})). The example in my earlier post was a score s that was equal to the spherical score on all the probabilities and s(c)(n) = 1/2(n+1) for any non-probability credence, where we identify Ω with the natural numbers.

Let Q be the space of probability functions on PΩ. Let d(c) = infp ∈ Qc − p be the distance from c to Q. We can prove that d(c) = 0 iff c is a probability, and d is continuous in our topology. Let ϕ(c) = 0 if d(c) ≥ 1/4 and ϕ(c) = 4d(c) if d(c) < 1/4. This will be a continuous function. Now define s(c)(n) = ϕ(c)/2(n+1) + (1−ϕ(c))c*(n)/∥c*2, where c*(n) = c({n}), and where the second summand is deemed to be zero if ϕ(c) = 1 (regardless of the denominator). I haven’t checked all the details yet, but this s looks continuous to me in the relevant norm, but the domination result is false for any non-probability c. The important point is that the function c ↦ ∥c*2 is continuous and non-zero for c such that d(c) < 1/4, and that’s one of the points I might yet have an error in.

Tuesday, April 12, 2022

Transworld depravity is false

Plantinga’s transworld depravity thesis holds that in every world that God is contingently capable of actualizing (i.e., every “feasible” world), either there is no significant freedom or there is at least one free wrong choice. I will argue that transworld depravity is in fact false, assuming Molinism.

But consider a possible situation A where the first significantly free choice runs as follows. Eve has a choice whether to eat a delicious apple or not, while knowing that God has forbidden her from eating the apple. Eve comes into the choice with a pretty decent character. In particular, she is so constructed that she is unable to take God’s prohibitions to be anything but reasons against an action and God’s commands to be anything but reasons for an action. Nonetheless, she is free: she can choose to eat the apple on account of its deliciousness, despite God’s prohibiting it.

By Molinism, if enough detail is built into the situation, either:

  1. in A, Eve would eat the apple, or

  2. in A, Eve would not eat the apple.

If (2) is true, then transworld depravity is false, because God could simply take away freedom after Eve’s first choice, and so we have a feasible world where there is exactly one significantly free choice, and it’s right.

Suppose then (1) is true. Now imagine a situation A* where just before Eve is deliberating whether to eat the apple, God announces that the prohibition on eating the apple is now changed into a command to eat the apple. If in A, Eve would eat the apple on account of its deliciousness despite its being forbidden, she would a fortiori eat the apple if God were to command her to do so. Thus:

  1. in A*, Eve would eat the apple.

But then transworld depravity is false, because again God could take freedom away after Eve’s first choice.

The argument as it stands does not show that transworld depravity is necessarily false. I try to do that here with a similar but perhaps less compelling argument.

Wednesday, April 6, 2022

Consequentialism and probability

Classic utilitarianism holds that the right thing to do is what actually maximizes utility. But:

  1. If the best science says that drug A is better for the patient than drug B, then a doctor does the right thing by prescribing drug A, even if due to unknowable idiosyncracies of the patient, drug B is actually better for the patient.

  2. Unless generalized Molinism is true, in indeterministic situations there is often no fact of the matter of what would really have happened had you acted otherwise than you did.

  3. In typical cases what maximizes utility is saying what is true, but the right thing to do is to say what one actually thinks, even if that is not the truth.

These suggest that perhaps the right thing to do is the one that is more likely to maximize utility. But that’s mistaken, too. In the following case getting coffee from the machine is more likely to maximize utility.

  1. You know that one of the three coffee machines in the breakroom has been wired to a bomb by a terrorist, but don’t know which one, and you get your morning coffee fix by using one of the three machines at random.

Clearly that is the wrong thing to do, even though there is a 2/3 probability that this coffee machine is just fine and utility is maximized (we suppose) by your drinking coffee.

This, in turn, suggests that the right thing to do is what has the highest expected utility.

But this, too, has a counterexample:

  1. The inquisitor tortures heretics while confident that this maximizes their and others’ chance of getting into heaven.

Whatever we may wish to say about the inquisitor’s culpability, it is clear that he is not doing the right thing.

Perhaps, though, we can say that the inquisitor’s credences are irrational given his evidence, and the expected utilities in determining what is right and wrong need to be calculated according to the credences of the ideal agent who has the same evidence.

This also doesn’t work. First, it could be that a particular inquisitor’s evidence does yield the credences that they actually have—perhaps they have formed their relevant beliefs on the basis of the most reliable testimony they could find, and they were just really epistemically unlucky. Second, suppose that you know that all the coffee machines with serial numbers whose last digit is the same as the quadrilionth digit of π have been rigged to explode. You’ve looked at the coffee machine’s serial number’s last digit, but of course you have no idea what the quadrilionth digit of π is. In fact, the two digits are different. You did the wrong thing by using the coffee machine, even though the ideal agent’s expected utilities given your evidence would say that you did the right thing—for the ideal agent would know a priori what the quadrilionth digit of π is.

So it seems that there really isn’t a good thing for the consequentialist to say about this stuff.

The classic consequentialist might try to dig in their heels and distinguish the right from the praiseworthy, and the wrong from the blameworthy. Perhaps maximizing expected utility is praiseworthy, but is right if and only if it actually maximizes utility. This this still has problems with (2), and it still gets the inquisitor wrong, because it implies that the inquisitor is praiseworthy, which is also absurd.

The more I think about it, the more I think that if I were a consequentialist I might want to bite the bullet on the inquisitor cases and say that either the inquisitor is acting rightly or is praiseworthy. But as the non-consequentialist that I am, I think this is a horrible conclusion.