Tuesday, June 12, 2012
Postdocs: Philosophy of Cosmology (Rutgers)
Thursday, May 31, 2012
Ruth Marcus Memorial Event (Yale, Sept 2012)
CELEBRATION OF THE LIFE OF RUTH BARCAN MARCUS
Saturday afternoon, September 29th, 2012
Yale University Campus
New Haven, CT
Details of venue, time and program will be settled soon, and a more formal announcement will then be distributed.
Tuesday, April 24, 2012
Dispositions and Interferences: the Paper
Thanks again to all of you who commented on my original posts and, if you have any last-minute comments and suggestions, please do let me know as I haven't submitted the final version yet.
Saturday, April 14, 2012
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.
Sunday, February 12, 2012
Podcasts: Power Structuralism in Ancient Ontologies Project
Jon Jacobs: "Is Causation a Relation?"
I look forward to listening to all of them!
Tuesday, February 7, 2012
Metaphysical Mayhem 2012!!!
Metaphysical Mayhem is back!!! Rutgers University will be hosting a 5-day summer school for graduate students May 14-18, 2012. John Hawthorne, Katherine Hawley, Ted Sider, Jonathan Schaffer, and Dean Zimmerman will lead the seminars on a variety of topics in metaphysics, including: natural properties, composition as identity, grounding, metaphysical explanation, and stuff like that...
For more information, see:
http://fas-philosophy.rutgers.edu/mbenton/mayhem.html
Thursday, January 19, 2012
Presentist counting
In a posthumous paper, David Lewis shows that one can find a presentist paraphrase of sentences like "There have ever been, are or ever will be n Fs" for any finite n. But his method doesn't work for infinite counting.
It turns out that there is a solution that works for finite and infinite counts, using a bit of set theory. For any set S of times, say that an object x exactly occupies S provided that at every time in S it was, is or will be the case that x exists and at no time outside of S it was, is or will be the case that x exists. For any non-empty set S of times, let nF(S) be a cardinality such that at every time t in S it was, is or will be the case that there are exactly nF(S) objects exactly occupying S. This is a presentist-friendly definition. Let N be any set of abstracta with cardinality nF(S) (e.g., if we have the Axiom of Choice, we should have an ordinal of that cardinality) and let eF(S) be the set of ordered pairs { <S,x> : x∈N }. We can think of the members of eF(S) as the ersatz Fs exactly occupying S. Let eF be the union of all the eF(S) as S ranges over all subsets of times. (It's quite possible that I'm using the Axiom of Choice in the above constructions.) Then "There have ever been, are or ever will be n Fs" can be given the truth condition |eF|=n.
This ersatzist construction suggests a general way in which presentists can talk of ersatz past, present or future objects. For instance, "There were, are or ever will be more Fs than Gs" gets the truth condition: |eG|≤|eF|. "Most Fs that have ever been, are or will be were, are or will be Gs" gets the truth condition |eFG|>(1/2)|eF|, where FG is the conjunction of F with G. I don't know just how much can be paraphrased in such ways, but I think quite a lot. Consequently, just as I think the B-theory can't be rejected on linguistic grounds, it's going to be hard to reject presentism on linguistic grounds.