Beyond metaphysical immutability

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

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

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

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

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

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

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

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

Two kinds of change

I ran across this old post of mine and it made me think that there is an interesting distinction between two kinds of change which one might label as objectual and factual change. Objectual change is change in objects, including both an object’s acquiring or losing properties and an object’s coming or ceasing to be. Factual change is change in reality itself—the facts of reality themselves change, with future facts coming to be present (and on open future views getting filled out) and present facts coming to be past. We can put this in terms of change of facts, change of truth value of (“fully closed”) propositions, or change of reality as a whole.

When A-theorists accuse B-theorists of having a static picture of the universe and B-theorists respond with the at-at theory of change (change is a thing’s having a property at one time and lacking it at another), they are talking past each other to some degree. The A-theorist is talking of factual change. The B-theorist is talking of objectual change. The A-theorist is simply right that on the B-theory there is no factual change: the facts about reality were, are and will ever be the same. That there is objectual change on the B-theory does not contradict this. But at the same time, the A-theorist’s accusation of static factuality is something the B-theorist should proudly admit as a feature and not a bug: truth does not change.

That there is objectual change is a part of our uncontroversial data about the world. That there is factual change is the A-theory in a nutshell, and hence begs the question against the B-theorist.

At this point it seems we have an impasse. Where should the debate go? I think one thing to figure out is whether one of the kinds of change depends on the other. Suppose it turns out that objectual change would need to depend on factual change. Then the A-theorist has won: the B-theory has no change at all. Note that the at-at theory of change is not a sufficient response to a claim that objectual change depends on factual change. For the at-at theory depends on the concept of time (change is having different properties at different times), and if time itself requires factual change, then the at-at theory itself requires the A-theory. This suggests that if the at-at theory is going to be the B-theorist’s response, the B-theorist owes the A-theorist an account of what makes time be time (McTaggart insisted on the latter point).

What about the other direction? That one is kind of interesting, too. One might think that factual change would need to arise from objectual change. Aristotle apparently did. It’s not clear, however, how one gets the A-theorist’s change of reality, where future facts become present and present facts become past, out of changes in objects. Perhaps one can read McTaggart’s infamous argument against the coherence of the A-theory as an attempt to show that this task can’t be done, at least in the special case where the objects are events.

Can we offer such an argument? Maybe. We aren’t going to be able to get factual change simply from the fact that objects have different ordinary properties at different times, say a light being green at t₁, orange at t₂, and red at t₃. For there is no way to use such facts to ground which of these times are past, present or future. So it seems that if we’re to get factual change from objectual change, we’re going to have go the route McTaggart suggests, and try to ground it in terms of objects’ temporal A-properties, say this light’s being past, present, or future. But that seems problematic. For the change between past, present and future does not happen in the lifetime of the light. During the lifetime of the light, the light is always present—it is only past after its existence and it is only future before its existence! But a change that does not happen during an object’s lifetime is, of course, a Cambridge change, like a horse’s becoming posthumously famous. And Cambridge change must always be relative to something else changing really. But then it is in the latter change that we should be grounding our factual change. And now we are off on a vicious regress, much as McTaggart (perhaps for somewhat different reasons) thought.

This suggests to me that just as the B-theorist denies that objectual change depends on factual change, the A-theorist should deny that factual change arises from objectual change. As more than one philosopher has noted, the A-theorist should respond to McTaggart by taking A-temporality, understood as factual change, as primitive.

Presentism and B-theory

It’s common to say that presentism entails the A-theory. But that’s not so clear. Suppose that time can pass in the absence of change. Now imagine a world of with a beginning or an end of time, objects, but no change, no temporal parts, and no events except ones that last for all time. In that world, we automatically have a kind of presentism: all the objects and events that exist always exist presently. Yet a B-theorist could accept the possibility of such a world, too: the world need not have a distinguished present moment of time. Thus, a B-theorist could say that A-theory is impossible (say, because of McTaggart’s dubious arguments) but presentism is possible—though contingently false.

We obviously don’t live in such a world. Though Parmenides may have thought he did.

Appearances of atemporality

Here’s a way to think about presentism. We have a three-dimensional reality and temporal modal operators, such as Prior’s P, F, H and G (pastly, futurely, always-pastly and always-futurely), with appropriate logical rules.

But now imagine this scenario: Reality consists of an eternally frozen time slice from a complex two-way-deterministic Newtonian world resembling our world—“frozen Newtonian world” for short. There are particles at various positions with various momenta (I assume that q = mdx/dt is a law of nature rather than a definition of momentum, and momentum is fundamental), but they are ever still, unchanging in their Newtonian properties. Now if Q is one of the operators P, F, H and G, define the operator Q′ as follows:

• Q′p if and only if either (a) reality consists of an eternally frozen Newtonian world and in an unfrozen Newtonian world that agrees with reality on its present slice we would have Qp or (b) we have Qp and reality does not consist of an eternally frozen Newtonian world and we have Qp.

Then the primed operators behave logically just like the unprimed ones. But according to the primed operators, “there is change and motion”. For instance, for a typical particle z eternally frozen at location x, it will be the case that P′(z is not at x) and F′(z is not at x), since in an unfrozen Newtonian world whose present slice is just like our world’s, there will be past and future times at which z is not at x.

So what? Well, the presentist’s big intuition is that on a B-theory of time there is no change: there is just a four-dimensional block, where one dimension just happens to be called “time” and things are different at different locations along that dimension, but simply calling a dimension “time” doesn’t make it any different from the spatial ones.

But the B-theorist can respond in kind. On presentism there is no change: there is just a three-dimensional world related to other three-dimensional worlds via certain modal operators that are called “pastly”, etc., but simply calling a modal operator P “pastly” doesn’t make it any different from deviant operators like P′.

The presentist will, presumably, say that it’s not just a matter of calling the operator P “pastly”, but rather the operator is the primitive pastly operator, so that if something pastly is different from how it’s now, it has changed. But now the B-theorist can just respond in the same way. It’s not just a matter of calling one of the four dimensions “time”, but rather the dimension is the primitive time dimension, so that if something is different at a different time from how it is now, it has changed or will change.

(Granted, a B-theorist does not need to think that the distinction between space and time is primitive. I am inclined not to, and hence I cannot make the above response.)

Presumably, even after this dialogue, the B-theorist’s alleged reality will look static to the presentist. But I think the presentist’s alleged reality can look atemporal to the B-theorist—it’s just a three-dimensional world with no time dimension and some modal operators relating it to other three-dimensional worlds.

On two knowledge arguments

There is a structural similarity between the main reasons for adopting the A-theory of time and the knowledge argument against physicalism. In both cases, it is claimed that there is some information that we know but which is left out of the reductive theory:

1. I know that Alice is sitting now

and

2. I know what it feels like to be sitting.

The first piece of knowledge cannot be derived from data about tenseless reality and the second cannot be derived from data about physical reality, or so it is claimed.

The similarity between the two arguments suggests that there should be a correlation between dualism and adherence to the A-theory of time: for if one is convinced by one argument, one is more likely to be convinced by the other, and if one is unconvinced by one, one is less likely to be convinced by the other. Speaking for myself, I am a B-theorist dualist, and while I am unconvinced by the time argument, I go back and forth on the mind one.

It is interesting, though, to see if we can go beyond superficial similarity. One way to do that is to see if the best responses to one of the arguments can generate plausible responses to the other.

The best response to the time argument seems to be the Kaplan story that “now” is a mere indexical, and that the content of “Alice is sitting now” is the proposition that Alice sitting is at t₁ (if t₁ is now), though the character or linguistic meaning of “Alice is sitting now” is something different from the character of “Alice is sitting at t₁” (specifically, a character is a function from world-utterance pairs to propositions, and this character assigns to an utterance of “Alice is sitting now” at t in w the proposition that Alice is sitting at t).

Is there a similar story about mind argument? It’s not so clear to me. Perhaps a start would be to say that what makes me it true that I know what it feels like to be sitting is that:

3. I know that sitting feels like this.

The physicalist analogue to the Kaplan story would then be that “Sitting feels like this” expresses the proposition that sitting feels like ϕ where ϕ is some physical state of affairs, but the character or linguistic meaning of “Sitting feels like this” and “Sitting feels like ϕ” are different. I don’t think this works, however. There are two ways of taking this approach:

1. ϕ is a specific neural state that I have when I feel like I’m sitting (say, S-fibers firing)

or

2. ϕ is a complex functional state that anything has when it feels like it’s sitting, a state implemented by different neural or other physical states in different beings.

On (a), we have an analogy to the time case, for we can take the character of “Sitting feels like this” to be a function that assigns to world-utterance pair the proposition that sitting feels like ϕ where ϕ is the physical state that is the feeling for the utterer in that world. But there is also a serious disanalogy: for in the time case, the B-theorist knows (or can claim to know) the character, since the B-theorist knows a priori the specific rule by which a referent is assigned to “now” at a world-utterance pair. But the physicalist does not know a priori the specific functional story which assigns a referent to “like this” at a world-utterance pair.

On (b), we have a disanalogy, since the character is constant: at every world-utterance pair, the same proposition is assigned as the content of “Sitting feels like this.”

Still, maybe there is still a fundamental analogy, in that the time case teaches us (if we accept the Kaplan story) that one proposition can be expressed by two sentences s₁ and s₂ such that it is correct to say “I know s₁” but not correct to say “I know s₂”. Thus, I know that I am sitting now but I don’t know that I am sitting at t₁. And similarly, maybe, I know that sitting feels like this but I don’t know that sitting feels like ϕ.

What if we go the other way around, and see if the best answer to the mind argument helps with the time argument?

I guess what is generally thought to be the best answer to the mind argument is something like this: there is a conceptual difference between the “like this” of the feeling and the physical or functional state ϕ, but ontologically they are the same. And this seems very close to Michelle Beer’s defense of the B-theory.

Another prominent answer to the mind argument is to deny that the knowledge claim expresses factual knowledge, as opposed to something like know-how or imaginative mirroring. It seems to me that a know-how story could be told about the time argument: to know that Alice is sitting now is to have certain kinds of know-how concerning dealing with Alice’s sitting. The “imaginative mirroring” case might be harder.

Theories of time and truth-supervenes-on-being

Truth supervenes on being is the thesis that if two worlds have the same entities, they are otherwise the same. I just realized something that should be pretty obvious. One cannot hold on to all three of the following:

• A-theory

• eternalism

• truth supervenes on being.

For according to eternalism, at any two different times, the facts about what exists are the same. So if truth supervenes on being, at any two different times, all facts are the same—and in particular the facts about what time is objectively present will be the same, which contradicts A-theory.

In other words, just as the best version of presentism (that of Trenton Merricks) rejects that truth supervenes on being, so does the best version of the moving spotlight theory. Moreover, closed-future growing blockers—and, in particular, classical theist growing blockers—will also want to reject that truth supervenes on being since substantive truths about the future won’t supervene on being given growing block.

All this suggests that we are left with only two major theories of time available to those who accept that truth supervenes on being:

• B-theoretic eternalism

• growing block with an open future.

More on bilocation and movement

It is often said that the four-dimensionalist doesn’t have a good theory of movement beyond the at-at theory which holds that

1. to move is to be at x₁ at one time and at x₂ at a different time, where x₂ ≠ x₁.

However, I am inclined to think the at-at theory is false due to an argument that my son came up with: if an object is bilocated at both x₁ and x₂ at one time and stays unmoved in both locations until a later time, then it is true that the object is at x₁ at one time and at x₂ at another time, and yet has not moved.

It is interesting that this argument also works against the most natural tensed theory of movement, namely that:

2. an object has moved provided that it was at x₁ and is at x₂, where x₂ ≠ x₁.

For imagine that an object was and still is bilocated between x₁ and x₂ and has remained entirely unmoving. Nonetheless, it was at x₁ and is now at x₂, and x₂ ≠ x₁, so according to (2) it has moved.

Thus, my son’s argument against the at-at theory does not seem to confer an advantage on the A-theory of time.

It is tempting to tweak (2) to something like this:

3. an object has moved provided that the set of locations at which it is now present is different from a set of locations at which it was present.

But that fails. For cessation of bilocation is not movement. If an object was bilocated between two locations x₁ and x₂, and then ceased to exist at x₂, while remaining at x₁, the object nonetheless did not move, even though (3) says it did.

Furthermore, space at least could be discrete. So imagine a point particle that was bilocated at two neighboring points x₁ and x₂ in space. The particle then simultaneously moved from x₁ to x₂ and from x₂ to x₁. Yet the set of points occupied by the particle was the same as it is now. So (3) says it did not move, but it did move, twice over.

I suppose one can deny the possibility of bilocation. But that is a big price to pay, I think.

I suspect that any theory of change that the A-theorist comes up with that solves this problem will also solve the problem for the four-dimensionalist.

God and the B-theory of time

1. All reality is such that it can be known perfectly from the point of view of God.

2. The point of view of God is eternal and timeless.

3. Thus, all reality is such that it can be known perfectly from an eternal and timeless point of view.

4. If all reality is such that it can be known perfectly from an eternal and timeless point of view, then the B-theory of time is true.

5. So, the B-theory of time is true.

I am not sure of premise (4), however.

My experience of temporality

This morning I find myself feeling the force of presentism. I am finding it hard to see my four-dimensional worm theory as adequately explaining why my experience only includes what I am experiencing now, instead of the whole richness of my four-dimensional life. I am also finding it difficult to satisfactorily explain the sequentiality of my experiences: that I will have different experiences from those that I have now, some of which I dread and some of which I anticipate eagerly.

When I try to write down the thoughts that make me feel the force of presentism, the force of the thoughts is largely drained. After all, to be fair, when I wrote that I have am having trouble “explaining why my experience only includes what I am experiencing now”, shouldn’t I have written: “explaining why my present experience only includes what I am experiencing now”, a triviality? And that mysterious sequentiality, is that anything beyond the fact that some of my experiences are in the future of my present experience?

The first part of the mystery is due to the chopped up nature of my consciousness on a four-dimensional view. Instead of seeing my life as a whole, as God sees it, I see it in very short (but probably not instantaneous) pieces. It is puzzling how my consciousness can be so chopped up, and yet be all mine. But we have good reason to think that this phenomenon occurs outside of temporality. Split brain patients seem to have such chopped up consciousnesses. And if consciousness is an operation of the mind’s, then on orthodox Christology, the incarnate Christ, while one person, had (and still has) two consciousnesses.

Unfortunately, both the split brains and the Incarnation are mysterious phenomena, so they don’t do much to take away the feeling of mystery about the temporal chopping up of the consciousness of my four-dimensional life. But they do make me feel that there is no good argument for presentism here.

The second part of the mystery is due to the sequentiality of the experiences. As the split brain and Incarnation cases show, the sequentiality of experiences in different spheres of consciousness is not universal. The split brain patient has two non-sequential, simultaneous spheres of consciousness. Christ has his temporal sphere (or spheres, if we take the four-dimensional view) of consciousness and his divine atemporal sphere of consciousness. But seeing the contingency of the sequentiality does not remove the mystery in the sequentiality.

It makes me feel a little better when I recall that the presentist story about the sequentiality has its own problems. If my future experiences aren’t real—on presentism they are nothing but stuff in the scope of a modal “will” operator that doesn’t satisfy the T axiom—then what am I anticipating or dreading? It seems I am just here in the present, and when I think about this, it feels just as mysterious as on four-dimensionalism what makes the future impend. Of course, the presentist can give a reductive or non-reductive account of the asymmetry between past and future, but so can the four-dimensionalist.

So what remains of this morning’s presentist feelings? Mostly this worry: Time is mysterious and our theories of time—whether eternalist or presentist—do not do justice to its mysteriousness. This is like the thought that qualia are mysterious, but when we give particular theories of them—whether materialist or dualist—it feels like something is left out.

But what if I forget about standard four-dimensionalism and presentism, and just try to see what theory of time fits with my experiences? I then find myself pulled towards a view of time I had when I was around ten years old. Reality is four-dimensional, but we travel through it. Future sufferings I dread are there, ahead of me. But I am not just a temporal part among many: there is no future self suffering future pains and enjoying future pleasures. The past and future have physical reality but it’s all zombies. As for me, I am wholly here and now. And you are wholly here and now. We travel together through the four-dimensional reality.

But these future pains and pleasures, how can they be if they are not had by me or anyone else? They are like the persisting smile of the Cheshire cat. (I wasn’t worried about this when I was ten, because I was mainly imagining myself as traveling through events, and not philosophically thinking about my changing mental states. It wasn’t a theory, but a way of thinking.) Put that way, maybe it’s not so crazy. After all, the standard Catholic view of the Eucharist is that the accidents of bread and wine exist without anything having them. So perhaps my future and past pains and pleasures exist without anyone having them—but one day I will have them.

Even this strange theory, though, does not do justice to sequentiality. What makes it be the case that I am traveling towards the future rather than towards the past?

And what about Relativity Theory? Why don’t we get out of sync with one another if we travel fast enough relative to one another? Perhaps the twin who travels at near light speed comes back to earth and meets only zombies, not real selves? That seems absurd. Maybe though the internal flow of time doesn’t work like that.

I do not think this is an attractive theory. It is the theory that best fits most of my experience of temporality, and that is a real consideration in favor of it. But it doesn’t solve the puzzle of sequentiality. I think I will stick with four-dimensionalism. For now. (!)

Asymmetric temporal attitudes and time travel

Philosophers sometimes use thought experiments concerning the asymmetry of attitudes towards future and past events as arguments for a metaphysical asymmetry between past and future. For instance, the fact that I would prefer a much larger pain in my past to a smaller pain in the future is puzzling if the past and future are metaphysically on par.

Here’s a thesis I want to offer and briefly defend:

• It is not rationally consistent to give use thought experiments in this way and to accept the possibility of backwards time travel.

The reason is quite simple: if backwards time travel is possible, our asymmetric attitudes track personal time, not objective time. If I am going to travel 100 million years back in six minutes, I will prefer a smaller pain in five minutes to a much larger pain 100 million years ago, since both of these pains will be in my personal future and only a minute of personal time apart. But the metaphysical asymmetry between past and future tracks external time, not personal time.

Times that never become present

Could there be times that are never present? At first sight, this seems a contradiction: surely, each time t is present at itself. Given the B-theory of time, this indeed is automatically true.

Not so, however, for A-theories. There is no contradiction in the growing block growing by leaps and bounds. Imagine that suddenly a whole minute is added to the growing block. The times in the middle of that minute never got to be at the leading edge of reality, and hence never got to be present, since to be present is to be at the leading edge of reality, given growing block. Or consider the moving spotlight: the spotlight could jump ahead in the spacetime manifold by a minute or an hour or a year, skipping over the intervening bits of the manifold. It's less clear whether it is possible to have times that aren't ever present given presentism. Still, Dean Zimmerman has considered an eccentric version of presentism on which there still is a four-dimensional spacetime manifold. On such a view, times could be identified with hypersurfaces in some preferred foliation, and there might be some such hypersurfaces that never become present.

So, apart from the B-theory and many versions of presentism, we have a possibility of times that are never present. Why would we want to countenance such a nutty option, though?

I can think of two reasons. The first would be to reconcile Aristotle's theory of time with many physical theories. According to Aristotle, times are endpoints of changes, and any interval of time contains at most finitely many changes, so that time is discrete. (Causal finitism might be a reason to adopt such a theory.) But in many modern physical theories, from Newton at least through Einstein, time is a continuous coordinate. One can try to reconcile the two views by supposing that time is continuous, as Newton and Einstein suppose, but that only those times which are the endpoints of changes are ever present. Aristotle then may be right that times are discrete, as long as we understand him to be speaking only about the times that matter, namely those that ever become present. The second motivation would be to have a flash ontology--an ontology on which physical things exist only during the discrete moments of quantum collapse--while softening the counterintuitive consequence that at most times the universe is empty. For we could identify the times that ever become present with the times at which a flash occurs. Then even if at most times, in the broad sense of the word "times", the universe is empty, still the universe is non-empty at all the times that matter, namely at all the times that become present.

Neither a B-theorist nor a standard presentist can suppose times that are never present. But she might still suppose something that plays a similar functional role. She could think of abstract times as numbers or as hypersurfaces in an abstract continuous manifold. Then real time could be discrete, while abstract time is continuous.

Presentism and theoretical simplicity

It's oft stated that Ockham's razor favors the B-theory over the A-theory, other things being equal. But the theoretical gain here is small: the A-theorist need only add one more thing to her ideology over what the A-theorist has, namely an absolute "now", and it wouldn't be hard to offset this loss of parsimony by explanatory gains. But I want to argue that the gain in theoretical simplicity by adopting B-theoretic eternalism over presentism is much, much larger than that. In fact, it could be one of the larger gains in theoretical simplicity in human history.

Why? Well, when we consider the simplicity of a proposed law of nature, we need to look at the law as formulated in joint-carving terms. Any law can be formulated very simply if we allow gerrymandered predicates. (Think of "grue" and "bleen".) Now, if presentism is true, then a transtemporally universally quantified statement like:

1. All electrons (ever) are negatively charged

should be seen as a conjunction of three statements:

2. All electrons have always been negatively charged, all electrons are negatively charged and all electrons will always be positively charged.

But every fundamental law of nature is transtemporally universally quantified, and even many non-fundamental laws, like the laws of chemistry and astronomy, are transtemporally universally quantified. The fundamental laws of nature, and many of the non-fundamental ones as well, look much simpler on B-theoretic eternalism. This escapes us, because we have compact formulations like (1). But if presentism is true, such compact formulations are mere shorthand for the complex formulations, and having convenient shorthand does not escape a charge of theoretical complexity.

In fact, the above story seems to give us an account of how it is that we have scientifically discovered that eternalist B-theory is true. It's not relativity theory, as some think. Rather it is that we have discovered that there are transtemporally quantified fundamental laws of nature, which are insensitive to the distinction between past, present and future and hence capable of a great theoretical simplification on the hypothesis that eternalist B-theory is true. It is the opposite of what happened with jade, where we discovered that in fact we achieve simplification by splitting jade into two natural kinds, jadeite and nephrite.

Technical notes: My paraphrase (2) fits best with something like Prior's temporal logic. A competitor to this are ersatz times, as in Crisp's theory. Ersatz time theories allow a paraphrase of (1) that seems very eternalist:

3. For all times t, at t every electron is negatively charged.

However, first, the machinery of ersatz times is complex and so while (3) looks relatively simple (it just has one extra quantifier beyond (1)), if we expand out what "times" means for the ersatzist, it becomes very complex. Moreover on standard ersatzist views, the laws of nature become disjunctive in form, and that is quite objectionable. For a standard approach is to take abstract times to be maximal consistent tensed propositions, and then to distinguish actual times as times that were, are or will be true.

Change and presentism

This post is an illustration of how widely intuitions can differ. It is widely felt by presentists that presentism is needed for there to be "real change", that the B-theory is a "static" theory. But I have the intuition that presentism endangers real change. Real change requires real difference between the past states and present states, and real difference requires the reality of the differing states. But if there are no past states, there are no real differences between past and present states, and hence no change.

Of course, a presentist can say that although a past state is unreal, there can nonetheless be a real difference between it and a real present state, just as there can be a real difference between the world of Harry Potter and our world, even though the world of Harry Potter isn't real. In a sense of "real difference" that's true, I agree. But not in the relevant sense. Change is a relation between realities.

The presentist can also insist that my line of thought is simply a case of the grounding problem for presentism, and can be resolved in a similar way. Supposing a window has just changed from being whole to being broken. Then while the past unbroken state doesn't exist, there does exist a present state of the window having been whole. I am happy to grant this present state to the presentist, but it doesn't affect the argument. For the relevant difference isn't between the window having been whole and the window being broken. For if no one broke the window, there would still have been a difference between the state of the window having been whole and the window being broken. There is always a difference between a state of something having been so and a state of its being so, but this difference isn't the difference that constitutes change.

(Incredible as it may seem to the presentist, when I try to imagine the presentist's world, I imagine an evanescent instantaneous world that therefore doesn't exist long enough for any change to take place. I am well aware that this world includes states like it was the case that the window was whole, but given presentism, these states seem to me to be modal in nature, and akin to the state of it is the case in the Harry Potter universe that magic works, and hence are not appropriate to make the world non-evanescent.)

Probably the presentist's best bet is simply to deny that real difference in my sense is needed for change. All that's needed is that something wasn't so and now is so. But if something's having been not so and its being so doesn't imply a real difference, it's not change, I feel.

Of course, the presentist feels very similarly about the B-theorist's typical at-at theory of change (change is a matter of something's being one way at one time and another way at another time): she feels that what is described isn't really change.

And this, finally, gives us the real upshot of this post. There are interesting disagreements where one side's account of a phenomenon just doesn't seem to be a description of the relevant concept to the other side--it seems to be a change of topic. These disagreements are particularly difficult to make progress in. Compare how the compatibilist's account of freedom just doesn't seem to be a description of freedom to the libertarian.

I don't have a general theory on how to make progress past such disagreement. I do have one thing I do in such cases: I try to find as many things connected with the concept in other areas of philosophy, like epistemology, philosophy of science, ethics and natural theology. And then I see which account does better more generally.

Reality of change and change of reality

B-theorists are often accused of destroying the reality of change. That's a false accusation. B-theorists may have a reductive theory of change (to change is nothing but to have a property at one time and lack it at another), but they no more deny the reality of change than people who have a reductive theory of bachelorhood (to be a bachelor is nothing but to be a never-married marriageable man) deny the reality of bachelorhood.

However, there is a charge in the vicinity that does stick. While we B-theorists believe in the reality of change, there is an important sense in which we don't believe reality changes, since what is true simpliciter is always true simpliciter. Events don't become real or cease to be real. So we can say that we believe in the reality of change but not the change of reality.

Internal time, external time, probability and disagreement

Suppose that Jim lives a normal human life from the year 2000 to the year 2100. Without looking at a clock, what probability should Jim attach to the hypothesis that an even number of minutes has elapsed from the year 2000? Surely, probability 1/2.

Sally, on the other hand, lives a somewhat odd human life from the year 2000 to the year 2066. During every even-numbered minute of her life, her mental and physical functioning is accelerated by a factor of two. She can normally notice this, because the world around her, including the second hands of clocks, seems to slow down by a factor of two. She has won many races by taking advantage of this. An even-numbered external minute subjectively takes two minutes. Suppose that Sally is now in a room where there is nothing in motion other than herself, so she can't tell whether this was a sped-up minute or not. What probability should Sally attach to the hypothesis that an even number of minutes has elapsed from the year 2000?

If we set our probabilities by objective time, then the answer is 1/2, as in Jim's case. But this seems mistaken. If we're going to assign probabilities in cases like this—and that's not clear to me—then I think we should assign 2/3. After all, subjectively speaking, 2/3 of Sally's life occurs during the even-numbered minutes.

There are a number of ways of defending the 2/3 judgment. One way would be to consider relativity theory. We could mimic the Jim-Sally situation by exploiting the twin paradox (granted, the accelerations over a period of a minute would be deadly, so we'd have to suppose that Sally has superpowers), and in that case surely the probabilities that Sally should assign should be looked at from Sally's reference frame.

Another way to defend the judgment would be to imagine a third person, Frank, who lives all the time twice as fast as normal, but during odd-numbered minutes, he is frozen unconscious for half of each second. For Frank, an even numbered minute has 60 seconds' worth of being conscious and moving, while an odd numbered minute has 30 seconds' worth of it, and external reality stutters. If Frank is in a sensory deprivation chamber where he can't tell if external reality is stuttering, then it seems better for him to assign 2/3 to its being an even-numbered minute, since he's unconscious for half of each odd-numbered one. But Frank's case doesn't seem significantly different from Sally's. (Just imagine taking the limit as the unconscious/conscious intervals get shorter and shorter.)

A third way is to think about time travel. Suppose you're on what is subjectively a long trip in a time machine, a trip that's days internal time long. And now you're asked if it's an even-numbered minute by your internal time (the time shown by your wristwatch, but not by the big clock on the time machine console, which shows external years that flick by in internal minutes). It doesn't matter how the time machine moves relative to external time. Maybe it accelerates during every even-numbered minute. Surely this doesn't matter. It's your internal time that matters.

Alright, that's enough arguing for this. So Sally should assign 2/3. But here's a funny thing. Jim and Sally then disagree on how likely it is that it's an even-numbered minute, even though it seems we can set up the case so they have the same relevant evidence as to what time it. There is something paradoxical here.

A couple of responses come to mind:

• They really have different evidence. In some way yet to be explained, their different prior life experiences are relevant evidence.
• The thesis that there cannot be rational disagreement in the face of the same evidence is true when restricted to disagreement about objective matters. But what time it is now is not an objective matter. Thus, the A-theory of time is false.
• There can be rational disagreement in the face of the same evidence.
• There are no meaningful temporally self-locating probabilities.

A Metaphysicality Index

A grad student was thinking that Platonism isn't dominant in philosophy, so I looked at the PhilPapers survey and indeed a plurality of the target faculty (39%) accepts or leans towards Platonism. Then I got to looking at how this works across various specializations: General Philosophy of Science, Philosophy of Mind, Normative Ethics, Metaethics, Philosophy of Religion, Epistemology, Metaphysics, Logic / Philosophy of Logic and Philosophy of Mathematics. And I looked at some other views: libertarianism (about free will), theism, non-physicalism about mind, and the A-theory of time.

Loosely, the five views I looked at are "metaphysical" in nature and their denials tend to be deflationary of metaphysics. I will say that someone is "metaphysical" to the extent that she answers all five questions in the positive (either outright or leaning). We can then compute a Metaphysicality Index for an individual, as the percentage of "metaphysical" answers, and then an average Metaphysicality Index per discipline.

Here's what I found. (The spreadsheet is here.) I sorted my selected M&E specialities from least to most metaphysical in the graph.

On each of the five questions, the Philosophers of Science were the least metaphysical. This is quite a remarkably un-metaphysical approach.

With the exception of Platonism, the Philosophers of Religion were the most metaphysical. (A lot of Philosophers of Religion are theists and may worry about the fit between theism and Platonism, and may think that God's ideas can do the work that Platonism is meant to do.)

Unsurprisingly, the Metaphysicians came out pretty metaphysical, though not as metaphysical as the Philosophers of Religion. (And this isn't just because the Philosophers of Religion believe in God by a large majority: even if one drops theism from the Metaphysicality Index, the Philosophers of Religion are at the top.

Interestingly, the Philosophers of Mathematics were almost as metaphysical as the Metaphysicians (average Metaphysicality Index 29.2 vs. 29.8). They were far more Platonic than anybody else. I wonder if Platonism is to Philosophy of Mathematics like Theism is to Philosophy of Religion. The Philosophers of Mathematics were also more theistic and more non-physicalistic than any group other than the Philosophers of Religion.

It's looking to me like the two fields where Platonism is most prevalent are Logic (and Philosophy of Logic) and Philosophy of Mathematics. This is interesting and significant. It suggests that on the whole people do not think one can do mathematics and logic in a nominalist setting.

For the record, here's where I stand: Platonism: no; Libertarianism: yes; God: yes; Non-physicalism: yes; A-theory: no. So my Metaphysicality Index is 60%.

The flow of time

Famously, D. C. Williams ridiculed the deep-seated intuition (at the heart of Bergson's thought, of course) that there is a flow of time, asking how fast time is flowing, if it's flowing. Some wits have tried to respond: "Always at a second per second." But there is a much better and less trivial answer. And interestingly it is an answer that has a home in the B-theory of time.

The Twin Paradox suggests that we should distinguish the internal time of an individual from something like the generally shared external time of the human community. Thinking about time travel suggests a similar distinction, as Lewis has noted. But once we have a distinction between internal and external time, then we can give a non-trivial answer to Williams' question. The flow of time is measured in terms of external units of time per internal units of time. If external time is defined by the shared life of the human community (that's one among a number of options—we should probably understand "external time" in a context-sensitive way), normally time flows at one external second per second. But if I were to engage in travel at relativistic speeds, it could be that in a month of internal time, eight years of external time would elapse. And if I were to engage in gradual backwards time travel, then I would have a negative rate of time's flow: maybe I would be moving at −1 external century per internal second. (In non-gradual time travel, the rate would be undefined.)

The distinction between internal and external time fits best with the B-theory. So the notion of time's flow, surprisingly, seems to have its home in the B-theory.

Can A-theorists believe in time travel?

I used to think that A-theorists cannot consistently believe in time travel. I think I was mistaken. As best as I can reconstruct my line of thought it was this. Time travel requires a distinction between external and internal time. If I go into a time machine, then maybe in five minutes I'll be a thousand years ago. That's a contradiction given non-circular time unless one distinguishes as follows: internally in five minutes I'll be a thousand years ago externally. But now I think that what I must have been thinking was that in five internal minutes my internal present will no longer line up with the world's objective present, since in five internal minutes my internal present will be about thousand years behind the world's external present. I don't know for sure if that's the thought I had, but if it was, it would have been a howler. For on the view, internally in five minutes, I will be at the time at which the world's external present was about a thousand years ago. Or, to put it from the external point of view, a thousand years ago I was five minutes older than I am now (age is measured internally). Even presentists can say that.

To see that this is coherent, consider a theory that takes external time to governed by the A-theory but internal time to be entirely governed by the B-theory. Thus, superimposed on the external A-series of past, present and future, there is an indexical B-series of earlier-for-me and later-for-me, where these relations are perhaps defined by internal causal relations (earlier states causing later ones). There is no more need for these two series to line up than there would be a need for the two series to line up if the external series were a B-series.

However, while this is coherent, maybe it undercuts one of the main motivations for the A-theory. For if there is a distinction between internal and external time, as there must be for time travel to be possible, all the changes we actually experience are changes with respect to internal time. In other words, they are B-type changes. But the typical A-theorist thinks B-type changes--it (internally) earlier being one way, and (internally) later another--are not what we experience when we experience "real change". Indeed, if time travel is possible, it is possible to live all of one's life at one external time, but moving through external space. Basically, just imagine that at each moment you travel to some external time t₀, but to a different spatial location in it. Maybe you have a backpack time-machine which is permanently stuck on t₀, but with the spatial locations changing. You'd experience change, because your state at internally earlier times will be different from your state at internally later times. But it would be mere B-type change, since it would all be happening at one and the same objective time.

I suppose one could say that in time-travel scenarios, especially the preceding one of living all of one's life at one external time, our experiences of change become non-veridical, for a condition on the veridicality of our experiences of change is that our internal clock lines up correctly with external time, and time-travel causes a misalignment. Maybe.

But in any case, now that we have the possibility of living all of one's life--a life that presumably could have rich causal interconnections--at one objective external time, just moving "sideways" to new spatial locations, I do think that the motivations for the A-theory decrease. For we see that what matters for the diachronic richness of our lives is that our lives be stretched over internal time, not over external time. It also matters that other people's internal times be sufficiently lined up with ours. But that doesn't call for the A-theory, either.

So, all in all, while A-theorists can believe in time travel, thinking time travel through would undercut much of the motivation for the A-theory.

McTaggart on the unreality of time

One version of McTaggart's argument for the unreality of time is:

1. If time is real, there is change.
2. If there is change, there is fundamental change, and it is the change of events or instants from future, to present, to past.
3. There is no fundamental change of events or instants from future, to present, to past.
4. So there is no change.
5. So time is not real.

(Here, "past", "present" and "future" are understood as incompatible. Thus, "past" and "future" mean wholly past and wholly future.) I am dubious of (2). But I think (3) can be defended in the following way, inspired by C. D. Broad (I think).

We need three principles:

6. If something undergoes non-Cambridge change from being F to being non-F, then at some time it exists and is F and at some time it exists and is non-F.
7. Cambridge change is never fundamental.
8. Everything that exists is present, and neither past nor future, when it exists.

Thus:

9. Nothing exhibits a non-Cambridge change from being future to being present, or from being present to being past, or from being future to being past. (6 and 8)
10. Hence nothing fundamentally changes from future, to present, to past. (7 and 9)

I think the contemporary A-theorist should deny (2). And most do.

Becoming

A-theorists talk of something called "becoming" which they say B-theorists have no room for. I don't really understand what this is. I am inclined to say that

1. x becomes F if and only if there is a time at which x is non-F and a later time at which x is F.

If so, then there is becoming—-indeed, objective becoming—-on the B-theory. Now, I think most A-theorists will agree that (1) is a necessary truth. So where's the disagreement on becoming?

Maybe, the disagreement lies in this. Although (1) is a necessary truth, nonetheless becoming is something more than just being non-F and later being F. This "something more" is necessarily there whenever something is earlier non-F and later F, but it is nonetheless something extra. (Just as God's knowing that the sky is blue is something more than just the sky being blue, but that "something more" is always there whenever the sky is blue, since God knows that the sky is blue necessarily if and only if the sky is blue.) But I really don't know what this "something more" is. I feel here like van Inwagen on substitutional quantification.

Well, that's not quite right. For it may be that (1) isn't exactly right. Suppose x has gappy existence. It exists from morning until noon and then from dinner until midnight. From morning until noon x is non-F and from dinner until midnight x is F. Does x become F? I could imagine someone saying "No" (and indeed a colleague did say just that). If not, then (1) may not be right.

Maybe one thinks gappy existence is impossible. (But why not? It seems no harder than being a spatially scattered individual, and if we're made of precisely located particles, which sure seems comprehensible, we're that.) But then consider this case. At every time that (in some unit system) is an irrational number, x is non-F and at every time that is a rational number, x is F. Then x satisfies (1). But does x ever become F? If so, when? At any time at which it is F, it also was F at an infinite number of earlier but arbitrarily close times. (This argument requires time to be a continuum, which I fear it's not.)

So one might question (1), though I am happy to bite the bullet in both cases. Maybe one should insist that to become F, you need to be non-F over an interval of times and be F over a succeeding interval of times, or something like that. But such modifications are neutral between the A- and B-theories.

Perhaps, though, the A-theorist's insistence on becoming is not so much about objects becoming a certain way, as about truths changing. The B-theorist is committed to propositions not changing in truth value. Many (but not all) A-theorists think propositions change in truth value. Thus,

2. There is becoming if and only if there is a proposition p that is true at one time and not true at another.

The B-theorist will then reject that there is becoming in this way. But notice that no it no longer seems appropriate to speak, as some A-theorists do, of doing justice to our "experience of becoming." For while we may experience the sky turning from blue to purple, we do not experience, except in a very theory-dependent way, the proposition <The sky is blue> turning from true to false. That's a change (though presumably a Cambridge one) in a Platonic entity.