Yesterday I rambled on about the problem of indexical terms in sentences. (Words like I, now, here, and so forth) I noted that many philosophers seem to treat temporal indexes differently than spatial indexes. I question that distinction. Now I should add that this really isn't an argument. It's just an observation about something taken for granted that I don't think should be. I want to talk a little more about it.
Sider, whom I've blogged about before, has a great little book that touches upon this. (ยง4.5 on page 87) The main objection to this objection comes from Chrisholm who argues there is a disanalogy between space and time. He alleges the following.
It is possible that there exists an x such that every part x has exists at more than one time at the same place.
It is not possible that there exists an x such that every part x ever has exists at more than one place at the same time.
Now four dimensionalists, like Sider, simply deny the first statement. (Yeah it's a convoluted way of phrasing, but I didn't want to "improve it" too much lest I screw it up) That is to exist at at multiple times require distinct parts at those times. The three dimensionalist, who things things persist through time, would accept Chisholm. However if the analogy only works depending upon whether we're already a four dimensionalist (entities are composed of temporal and spatial parts) or a three dimensionalist (entities are composed of spatial parts that persist through time) then the appeal to analogy is quite weak. Nearly circular in fact.
There are three related arguments which Sider gives. The first is the meaning of extension. Those committed to entities persisting through time argue that they have extension in space. (Not all do, of course, such as Cartesian minds or Thomist souls - but even then we have material related to these things, which is what is at question) Why does the concept of extension only apply to space? Should it? i.e. get to the very concept of spatiality. This is still fairly weak though.
The second part goes back to Leibniz' Law. We say an entity has different parts because as we proceed spatially the properties change. Thus my hair is a part because it has different properties from my skin. Yet under temporal conceptions myself 10 years ago has different properties from myself now. Why not by the same reasoning say I have temporal parts?
The third argument is a modal one, which is a tad more complex. Consider the left half of the space occupied by some object. The region of space occupied by this object (R) "and its material contents might have been, intrinsically, exactly as they actually are even if the rest of the world had been eliminated. In that case an object exactly occupying R would have existed. But then we should postulate an object in actuality that exactly occupies R. For surely the elimination oft he rest of the world outside of region R would not bring a new object into existence; but what other object could this object be, other than a part of the [object] that actually occupies region R?" (89) By the exact same argument we can replace talk of spatial region to temporal regions (or spans).
Now I fully agree all these arguments (and closely related ones) are fairly week. However that doesn't mean that they aren't correct. Those rejecting them though face a bigger problem. How do their objections not also carry over to the spatial forms? That is, can one argue against these appeals to temporal parts without also calling into question spatial parts?
Now some might not have problems with that. (Certain idealists, for instance) But overall I think it a compelling argument. The arguments against temporal parts along these lines simply rests on the intuition that time is sufficiently different from space so as to not consider the arguments reasonable, even if we can't argue consistently against one without the other. But this just shows our biases (IMO) rather than a good reason to treat them differently. (As many know, I don't trust intuitions too much)
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