Sunday, February 12, 2012

Podcasts: Power Structuralism in Ancient Ontologies Project

I think that Anna Marmodoro's Power Structuralism in Ancient Ontologies project is one of the most interesting metaphysics projects around at the moment. And it got even more interesting now that they have added to their website links to a series of podcasts, which include:


Jon Jacobs: "Is Causation a Relation?"
Peter Van Inwagen: "Relational vs. Constituent Ontologies"

I look forward to listening to all of them!

Tuesday, February 7, 2012

Metaphysical Mayhem 2012!!!

This makes me wish I was still a grad student :-)
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> : xN }. 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.

Saturday, October 8, 2011

Another Philosophy Jobs Site: PhilJobs

We had none, now we have two and they are both amazing!!! Open-access philosophy job listings, that is. Alongside Phylo Jobs (check out the new features, btw!), now we have PhilJobs (courtesy of David Bourget and David Chalmers).
The next step now is to replace first-round interviews at the Eastern with either Skype interviews or straight on campus interviews and the dysfunctional APA will have be made completely irrelevant.

Monday, September 19, 2011

New Philosophy Jobs Site!

Wonderful news for job seekers and search committees via The Philosophy Smoker:
Chris Sula and [David Morrow] have revamped the Phylo site to create an actual jobs board to (ahem) supplement the JFP. The URL is the same as the old wiki: http://phylo.info/jobs. As of today, we’ll start accepting job postings in that space from departmental representatives only. Following Harry Brighouse’s advice, we’ll also require a link to an external site (e.g., an announcement on the department’s web site) to verify each post’s authenticity. We’re moving the job wiki to http://phylo.info/jobs/wiki. People will still be able to post unofficial updates there. We’re still in the process of updating the wiki software to play nicely with the jobs board, but it will be up well before anyone needs to post status updates. In the meantime, watch the main jobs board to find out about job openings.

Monday, August 22, 2011

A paradox concerning propositions

Propositions generally seem to be about things. The proposition that Tibbles is on the mat is about Tibbles and a mat. The proposition that 2+2=4 is about some numbers. The proposition that chips are on the counter is about chips and a counter. And so on.

Some propositions (statements, sentences, beliefs, etc.) are intuitively about themselves. For example, the proposition that all propositions merit investigation is intuitively about itself.

Now for a paradox. Consider the following proposition P: every proposition that is not about itself is mundane.

P is paradoxical because it seems to be about itself if and only if it is not. Let me draw this out. Suppose first that P is about itself. Then we can show that P is not about itself as follows. P is about all and only those propositions that are not about themselves, for it says that each is mundane. So, P is not about any proposition that is about itself. Therefore, P is not about P if P is indeed a proposition that is about itself. Therefore, P is not about itself if it is about itself. Suppose, on the other hand, that P is not about itself. We have already observed that P is about those propositions that are not about themselves (because P reports that each is mundane). Therefore, if P is one of those propositions that aren't about themselves, then P is about P. So, either way, we fall into contradiction.

We can make the paradox more acute by stipulating that 'x is about y' means 'x quantifies over instances of a kind of which y is an instance'. We can then ask whether or not P is about P in that precise sense. (If you think you see a way out of the paradox, ask yourself if there's a way to re-write the paradox that avoids your solution, and I'm guessing you'll see that there is.)

This paradox will remind you of Russell's paradox concerning the set of all sets that aren't members of themselves. But I believe the paradox of propositions is much harder to solve. Concerning sets, we can, if we like, treat "set" talk as plural reference talk (thereby eliminating the existence of sets altogether), or else we may carefully craft axioms of sethood (such as ZFC) that preclude the existence of sets that are members of themselves.

But such solutions are not nearly as promising when it comes to propositions. If you think we can simply eliminate propositions, then run the paradox in terms of sentence tokens: the sentence token represented by P surely exists (or at least there are things arranged P-wise...). We might try to craft axioms of aboutness to get out of this, but such axioms won't take away the deep feeling that P should be about itself if and only if it is not. (With sets, by contrast, there is something right about supposing that no sets contain themselves.) So, we have a paradox on our hands that appears to be more serious than previous ones of its kind.

The paradox could perhaps be viewed as evidence against the reliability of our a priori faculties (though, of course, we'd have to rely on those same faculties to "see" this!) Or, more drastically, someone could view it as evidence that reality is at bottom absurd. I think it should be viewed as an invitation to gain a deeper understanding of the nature of propositions and aboutness.

Suggested ways of resolving the paradox are welcome. (I have a solution, but before I share it, I'd like to see how others might solve the problem.)

Monday, May 16, 2011

Brian Leiter Caves in to Pressure from the Continental Lobby: Metaphysicians Should Boycott Leiter Report :-)

For the interpretationally challenged, the title of this post is a joke (hence the smiley). For those who haven't followed the Synthese affair, the title paraphrases the one of this other post. In any case, readers of this blog may want to spoil the fun by voting en masse here for 'Should be mandatory' and and for 'Every department should have the subject as its central focus'. (Since this is not supposed to be a serious poll, I would even think you could vote multiple times from multiple locations if you are so inclined and have a lot of time in your hands)