Say that an entity E has age T at t if and only if E began to exist exactly at t-T[note 1] Observe that the age of an entity can be positive, zero, or negative. What kind of property of E is the having of a particular age?
Here is the problem. An entity continues to change in respect of age even when it no longer exists. But when an entity does not exist, the only change it can engage in is pure Cambridge change—the sort of "change" that Napoleon "experiences" when he changes from not being thought about by the Duke of Wellington or Bill Clinton to being thought about. I will assume that the age is the same kind of property during a substance's lifetime as afterwards.[note 2]
Now, Cambridge change is in the end grounded in something else undergoing non-Cambridge change. The Duke of Wellington or Bill Clinton change from not thinking to thinking about Napoleon, and thus Napoleon "changes" from being not thought about by them to being thought about by them. So the change in the age of an entity must be grounded in an something else's undergoing a genuine, non-Cambridge change. But what is that something else? And what does that something else change in respect of?
One intuitive thing to say is that "the time changes". E comes to have age T when the time changes from not being equal to t0+T, where t0 is the time E first came to exist, to being equal to t0+T. But what kind of a change is that? Time surely isn't literally some enduring entity that has a succession of temporal properties like "being noon", "being 3pm", etc. Maybe what we want to say is that reality itself or the cosmos changes in respect of time: it changes from being such that it is not t0+T to its being such that it is t0+T.
Suppose that our ontology includes moments of time, and that if t is a moment of time, then t exists at t and only at t. We can then say that the age of E changes to T precisely when reality changes so as to include the moment t0+T. If our ontology does not include moments of time, but, say, is relational, we may need to do some more work, but I do not see any obvious in-principle bar to defining the time.
We now have a seemingly well-defined property of age, defined in terms of reality's inclusion of a particular moment of time. Now, here is an oddity. This property of age can be equally well defined on a B-theory as on an A-theory. Indeed, I alluded to nothing A-theoretical in the account. A first consequence—Dean Zimmerman has a paper that among many other interesting things says something like this—is that it won't do to define the difference between the A- and B-theories in terms of the objective futurity, presentness and pastness of events, since such properties can be defined in terms of age, and both the A- and B-theories can define the property of age, and the definition seems mind-independent. Nor will it do to define the distinction between the A-theory and the B-theory in terms of an A-theorist's being committed to age being a non-Cambridge property. For the above argument shows that age is a Cambridge property (and by the same token, so are futurity, presentness and pastness), so it would be grossly unfair to the A-theorist thus to define the A-theory. A third consequence is that a reductio, like McTaggart's, of the very idea of futurity, presentness and pastness properties is apt to equally attack the B-theory as the A-theory, since both the B-theory and the A-theory can define such properties.
How, then, to define the A-theory, if not in terms of objective futurity, presentness and pastness of events? I see only one way at present: in terms of the idea that propositions change in truth value. The A-theorist, then, is one who gives up on the eternity of truth: p can be true at t0 but false at t1. This Aristotelian theory of propositions is, I think, false (on this theory, tomorrow I will no longer believe the same things as I believed today about my actions from today, even in cases where I have not forgotten these actions), but it is not clearly absurd.
6 comments:
...is that it won't do to define the difference between the A- and B-theories in terms of the objective futurity, presentness and pastness of events, since such properties can be defined in terms of age, and both the A- and B-theories can define the property of age, and the definition seems mind-independent.
On the A-theory presentness cannot be defined in terms of age. It is primitive, right?
The A-theorist, then, is one who gives up on the eternity of truth: p can be true at t0 but false at t1.
I can't see how this follows. A-theorists can accept both tenselessly true propositions and tensedly true propositions (see Tooley) but use tensed properties to explain why states of affairs are in time.
-Christian
The difficulty with primitive tensed properties is that unless they are Cambridge properties, they fall afoul of the McTaggart-style argument I give in favor of age being a Cambridge property.
Take the simplest case. Suppose a moment of time (one can also do this with events) has primitive, non-Cambridge properties of being past, present or future. Then we have a violation of the following plausible principle: An entity can only change from having to not having some non-Cambridge property if it exists at more than one time. But moments of time exist only at themselves.
Moreover, it is a mistake to think there is just a triad of tensed properties: past, present or future. There is in fact a continuum: past by 17 days, past by 5 hours, present, future by 7 minutes, future by 18 minutes, etc. Events change in respect of these properties just as handily when they don't exist as when they do exist, which shows that the properties are Cambridge ones.
(Which Tooley piece are you thinking of here? I've read little of him.)
Let me step back.
An entity continues to change in respect of age even when it no longer exists.
I don't understand how any x can undergo anything at all if it does not exist. Do you mean presently exists? And by 'age' you don't mean temporal duration, but how past or how future something is, i.e., it's first temporal part if it's past, or last temporal part if it is future. Is that right? And I'm not sure that anything has an age at a time, but let's suppose it.
The idea is that n years past and n years future, for example, are extrinsic. I think this is right. So, x is n years past at t iff t is present and x is n years before t. What grounds this? That t is present and x is n years before t. We have an intrinsic property and an intrinsic relation that grounds the fact that x is n years past. What does it change in respect of? In respect of which time is present. I don't see this view running afoul of a McTaggartian objection.
I don't see how the B-theory is going to ground the claim that x is n years past at t. Perhaps they can say x is n years before this utterance where this utterance is simultaneous with t. But utterance reflexive views are implausible.
You wrote: An entity can only change from having to not having some non-Cambridge property if it exists at more than one time. But moments of time exist only at themselves.
This might be a problem for Presentists. But Moving Spotlight theorists don't have it. Entities can be present at one time and not at those times later than, or earlier than, the present. Thus, if t is present, e is present at t and past at all times later than t.
"Moreover, it is a mistake to think there is just a triad of tensed properties: past, present or future."
I want to say an entity e is past at t iff t is present and for some n > 1, e is n moments earlier than t. We thus get one property of pastness and spectrum of earlier than and later than relations.
-Christian
Oh, Tooley's book "Time, Tense, and Causation" is what I had in mind.
Christian:
1. The age of an entity is how long ago it began to exist. Thus, the age of WW2 is how long it is since the beginning of WW2.
2. I don't see why the problem is not a problem for moving spotlight views. Let me put it this way: On that view, a moment of time, say t7, changes from being future, to being present, to being past. But it seems to me that if something changes from having P to having an incompatible Q, then either the change is a Cambridge change, or else there are two times, at one of which the entity exists having P and at the other of which the entity exists having Q. But t7 exists only at t7, so the change from future, to present, to past must be a Cambridge change. (This is basically C. D. Broad's argument against understanding temporality in terms of temporal properties of events.)
3. There does not seem to be a difficulty in defining a property of age on the B-theory. We say that x has age T at time t iff t is such that x first came into existence at t-T. This seems prima facie a perfectly fine definition of a property, and makes no reference to utterances or anything like that. Now maybe you will say: "The task wasn't to define what it means to say that x has age T at time t. The task was to define what it means to say that x has age T simpliciter." But the B-theorist rejects the notion of having a changing property simpliciter.
But it seems to me that if something changes from having P to having an incompatible Q, then either the change is a Cambridge change, or else there are two times, at one of which the entity exists having P and at the other of which the entity exists having Q.
Okay, we take some time, t7, that goes from being present to be being past. t7 is present at t7, and past at times later than t7.
But t7 exists only at t7, so the change from future, to present, to past must be a Cambridge change.
Why do you say this? A-theorists won't. Times can exist when they are not present. Thus, t7 can exist at times other than t7. WWII exists, but it is past. Perhaps, WWIII exists, but it is future.
So there is t7, it has the property of presentness at t7, then at t8 it loses it. It is present as of t7, past as of t8.
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