Backwards causation, the A-theory and God

Suppose:

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.

Add:

3. 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:

4. 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.

Questions:

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

11. 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.

Against divine temporalism

I stipulate that:

0. 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:

2. 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:

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

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

5. There is no backwards causation.

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

Finally:

7. 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 N_n, there not being stars in year n, as well as N_n − 1, and N_n − 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.

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.

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:

3. 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:

4. 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:

5. 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.

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.

Consider:

2. I am in pain.

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

4. 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:

5. I was in pain.

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

7. 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:

8. 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.

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.

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.

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.

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.

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.