Internal space

As David Lewis taught us, time travel calls for something like a notion of internal time. If I am about to travel to the time of the dinosaurs, then maybe in an hour I will meet a dinosaur. But that's an internal time hour. If I am going to spend the rest of my life in the Mesozoic, then—assuming nothing kills me—I will grow old before I am born, but this "before" is tied to external time, since of course in internal time, I grow old after being born.

Perhaps ordinary travel calls for a notion of internal space. Let's say today I am in room 304 of the hospital, and yesterday I was in room 200. The doctor comes and asks: "Does it still hurt in the same place as it did yesterday?" I tell her: "No, because yesterday it hurt in room 200, and today it hurts in room 304." But that's external place, and the doctor was asking about internal place.

Internal place is moved relative to external place while the body as a whole is locomating. But it can also be moved when only parts of the body are moving. If my hands are hurting, and I clasp my hands to each other, I thereby make the internal places where it hurts be very close externally, but they are still as distant internally as they would be were I to hold my arms wide. If, on the other hand, my two hands grew together into a new super-hand, the two places would come to be close together.

I wonder: If I grow, does my head come to be internally further from my feet? I think so: There are more cells in between, for instance.

Rob Koons has suggested to me that the notion of internal place can help with Brentano's notion of "coincident boundaries": Suppose we have two perfect cubes, with the red one on top of the green one. Then it seems that the red cube's bottom boundary is in the same place as the green cube's top boundary. (Sextus Empiricus used basically this as an argument against rigid objects.) Question: But how can there two boundaries in the same place? Answer: There are two internal places in one external place here.

Van Inwagen on the Rate of Time’s Passage

This post is co-authored by Hud Hudson, Ned Markosian, Ryan Wasserman, and Dennis Whitcomb. It is based on an unpublished paper by the four of us that is available online here.

In the 2^nd edition of his book, Metaphysics (Boulder, CO: Westview Press, 2002), Peter van Inwagen offers a new argument against the passage of time. In the 3^rd edition of the book (Westview Press, 2009) the same argument appears, and it also appears in a recent Analysis paper by Eric Olson (“The Rate of Time’s Passage,” Analysis 61: pp. 3-9). Here’s a quote from van Inwagen.

Does the apparent “movement” of time… raise a problem? Yes, indeed… the problem is raised by a simple question. If time is moving (or if the present is moving, or if we are moving in time) how fast is whatever it is that is moving moving? No answer to this question is possible. “Sixty seconds per minute” is not an answer to this question, for sixty seconds is one minute, and – if x is not 0 – x/x is always equal to 1 (and ‘per’ is simply a special way of writing a division sign). And ‘1’ is not, and cannot ever be, an answer to a question of the form, ‘How fast is such-and-such moving?’ – no matter what “such-and-such” may be… ‘One’, ‘one’ “all by itself,” ‘one’ period, ‘one’ full stop, can be an answer only to a question that asks for a number; typically these will be questions that start ‘How many…’… ‘one’ can never be an answer, not even a wrong one, to any other sort of question – including those questions that ask ‘how fast?’ or ‘at what rate?’. Therefore, if time is moving, it is not moving at any rate or speed. And isn’t it essential to the idea of motion that anything moving be moving at some speed…? (2002: 59)

Here’s the gist of van Inwagen’s argument. If time passes, then it has to pass at some rate. And even if that rate is expressible in a number of different ways (e.g., 60 minutes per hour, 24 hours per day, etc.), it must also be true (if time passes at all) that time passes at a rate of one minute per minute. But one minute per minute is equivalent to one minute divided by one minute. And when you divide one minute by one minute, you get one (since, van Inwagen says, “if x is not 0 – x/x is always equal to 1”). But ‘one’ (not ‘one’ of anything, but just plain old ‘one’) is the wrong kind of answer to any question of the form “How fast…?” So it must be that time does not pass after all. QED.

We can put the reductio part of van Inwagen’s argument a bit more carefully as follows.

(1) The rate of time’s passage = 1 minute per minute.

(2) 1 minute per minute = 1 minute ÷ 1 minute.

(3) 1 minute ÷ 1 minute = 1.

--------------------

(4) The rate of time’s passage = 1.

We have several problems with this argument, but will discuss only two of them here. (We discuss some other problems, and the two problems raised here in more detail, in the paper linked to above.)

First problem: It’s not true that for any x distinct from 0, x ÷ x = 1. Take for example the Eiffel Towel. If you divide the Eiffel Tower by itself, you don’t get 1. You don’t get anything, because division is not defined for national landmarks. Division is an operation on numbers, and a minute – like a meter or a tower or a car – is not a number. So 1 minute ÷ 1 minute is undefined, and thus (3) is false.

(One can, of course, say things like: 10kg divided by 5 kg is 2 kg. But we take this to be loose talk – it is the numbers, not the quantities, that are being divided. Similarly, one can show that a rate of one kilometer per minute is equal to sixty kilometers per hour by multiplying fractions and canceling out units: 1k/1m x 60m/1hour = 60k/1hour. Once again, we take this to be a loose way of speaking – it is the fractions, not the rates, that are being multiplied.)

Second problem: (2) is also false. Van Inwagen supports it by saying that “…‘per’ is simply a special way of writing the division sign.” (2002: 59) We disagree. The forward-slash (‘/’) can be used to abbreviate both ‘per’ (i.e., ‘for every’) and ‘divided by’, but it is a mistake to treat ‘per’ as synonymous with ‘divided by’. To see this, consider the claim that time passes at a rate of one minute per minute. This may be uninformative, but that doesn’t make it untrue. A minute does pass every time a minute passes, just as a car passes every time a car passes. So ‘1 minute per minute’ expresses a genuine rate. But now consider the claim that time passes at a rate of 1 minute ÷ 1 minute. This is worse than uninformative – it is nonsensical. That is because 1 minute ÷ 1 minute is a division problem (without a defined answer) and a division problem is not a rate of change. One might as well say that time passes at a rate of orange x banana. So ‘1 minute ÷ 1 minute’, unlike ‘1 minute per minute’, does not express a rate.

We conclude that van Inwagen’s anti-passage argument fails, for (2) and (3) are both false.

Presentism, causation and truthmakers for the past

I’m working on both causation and the truthmaker objection to presentism, and it seems to me that it might be possible to kill two birds with one stone. What follows is the basic idea, and I’d love to hear your thoughts.

Suppose that presentism is true. What is the nature of causation? It’s the relation between what and what? Or, more relevantly, between when and when? Since, according to presentism, the past does not exist, either causation is a relation between nothing and something in the present, or causation is simultaneous, or causation is not a relation at all. The first option seems dubius. A two place relation (I’m ignoring contrastivism, for the moment) has two relata, after all, not one.

What, then, about the second option? C. B. Martin defends this view in The Mind in Nature—or, at any rate, that’s my understanding of what Martin defends. But it’s not clear how to make sense of causal processes on this view. (Persistence intuitively has causal constraints; how are we to make sense of these constraints if all causation is simultaneous?)

The third option seems to me the route to go. Here’s an initial proposal: Causation is a fact about presently existing (Armstrongian) states of affairs, or tropes if you have them. It is a fact about e, say, that c brought it about. Suppose, however, that existentialism is true, so that if x does not exist, there are no singular propositions about x. If c is a state of affairs and the particular that is a non-merelogical constitutent of c no longer exists, then the fact that c caused e is the fact about e that something c-like brought it about. If c is a trope no longer instantiated and the instantiation condition is true, so that uninstantiated properties do not exist, then too causation is the fact that something c-like brought about e.

How are we to understand “something c-like”? Here’s one proposal: Properties are or of necessity confer causal powers, so we can understand “something c-like” as “something with the following causal powers profile...” (Of course the Neo-Humeans can’t really accept this view, but how many Neo-Humeans are presentists?)

What should we say about the fact in question, that e was brought about by something c-like? It might be a property of the world, as in Bigelow’s “Presentism and Properties.” It might be a property of e. Or it might not be a property, but a fact grounded in something else. Or a primitive fact about e.

Whatever answer one gives here seems also to be an answer to the objection to presentism from truthmakers about the past. Hence the presentist, so long as they can offer a theory about the nature of the fact that e was brought about by something c-like, can kill two birds with one stone, a theory of causation and a response to the truthmaker objection.

Here’s an initial proposal. Take property instances to be tropes. Then, with certain other assumptions about tropes, events can be understood as tropes. So trope c caused trope e. That turns out to be a fact about e: that it was brought about by c. Since I’m inclined to accept both existentialism and the instantiation condition, this will turn out to be the fact, about e, that it was brought about by something c-like. The fact is a basic truth, and e alone is its truthmaker. This is analagous to e’s also being, in virtue of either being or of necessity conferring causal powers, (part of) the truthmaker for counterfactuals describing what objects with e would do in various circumstances. It is a truthmaker for future truths and for the past truth about c.

One further claim, and we have a theory of truthmakers for the past. These basic causal facts about tropes are cumulative. So the fact that e was brought about by c is the fact that e was brought about by something c-like which was brought about by something...., which was brought about by something..., and so on. As long as there is a causal chain from some present state of affairs to every past state of affairs, there is a present truthmaker for every past state of affairs.

Tropes carry with them their entire causal history and their entire power profile, and so are truthmakers for past and future truths. Present property instances do a lot of work on this view, but that’s about what we should have expected given presentism.

Proxy "Presentism"

Proxy “actualism,” as defined by Karen Bennett in her article by that name, is roughly the view that while everything that exists is actual, everything—even what could exist but doesn’t—has proxies that do exist. Every possible thing has a proxy that actually exists. (For Plantinga, my essence is my proxy; for Linsky and Zalta, I, when I am nonconcrete, am my proxy.)

Bennett argues that proxy “actualism” is not actualism. In drawing a sharp distinction between two sorts of things that actually exist, the proxies and the objects for which they are proxies, the proxy “actualist” introduced two domains of quantification, just as the possibilist does. The proxy “actualist” has simply moved the distinction between merely possible and actual individuals into the actual world.

Let proxy “presentism” be roughly the view that, while everything that exists is present, everything—even merely past and future objects—has a proxy that presently exists. While I’m not certain, I’m inclined to think Crisp’s view and the view offered to the presentist by Merricks in Truth and Ontology are each a version of proxy “presentism”.

Question: Isn’t proxy “presentism” just as presentist as proxy “actualism” is actualist? That is, if proxy “actualism” is not actualism, then isn’t proxy “presentism” not presentism?