Monday, June 7, 2010

Proxies for actualists and presentists

Suppose that, necessarily, propositions exist necessarily and that things that exist necessarily exist always. Also suppose that, necessarily, for any actual object x, there is a proposition that x=x. Then there are proxies for all non-actual objects. Say that a proposition p is a "self-identity proposition" if possibly there exists an x such that p is the proposition that x=x. Say that a self-identity proposition p is "about a" if there actually is an x such that x=a and p is the proposition that x=x. Say that the "proxies" are the self-identity propositions.

Then if w is a world (respectively, a time), P is a property, and p is a self-identity proposition, we can say that P*(p,w) iff it is true at w that: (a) there is an x such that p is about x and (b) x has P. So we have a proxy of world- (respectively, time-) relative predication for our proxies. We can similarly extend this to relations, as long as they are not inter-world (respectively, cross-time) relations.

What this seems to mean is that as long as all propositions exist necessarily, we don't specifically need haecceities to have proxies for actualists and presentists. But the gain is illusory. For if we want haecceities, we can define them using self-identity propositions: Necessarily, for all x, x's "haecceity" is the property of being such as to have the proposition that x=x be about one.

That all propositions exist necessarily follows from two plausible claims: (a) all necessary propositions exist necessarily; and (b) if a disjunctive proposition exists, so its disjunct propositions. For if p is any proposition, and q is any necessary proposition (say, that 1=1), then their disjunct is a necessary proposition, hence exists necessarily (by (a)) and hence its disjunct p exists necessarily.

I think it follows that the enemy of haecceities needs to deny, with Adams, that necessary propositions exist necessarily. And someone who wishes to deny the presentist the use of proxies needs to deny that necessary propositions exist always.


Jonathan D. Jacobs said...

Sounds right to me. Proxies have always struck me as something serious actualists and presentists should reject, since they seem ill suited as truthmakers.

Alexander R Pruss said...

Or, more generally, proxies are ill-suited for figuring in "in virtue of" claims, whether these involve truthmakers or not. It surely isn't the case that there have only been finitely many horses because some set of properties has finite cardinality.

Here's an argument against using proxies. Suppose I use proxies to count horses. So, I try to translate

(1) "There have only been finitely many horses"


(2) "The set of horse-proxies that have proxy-pastness is finite."

(If proxies are haecceities, then proxy-pastness is the property of being such that it was once the case that one's instance exists(ed?).)

But even though necessarily (2) holds iff (1) does, (2) is surely not the same proposition as (1). For there are many possible systems of proxies, and there does not seem to be a canonical one. For instance, proxies could be self-identity propositions, or singular existential propositions, or right-identity-with-y properties (being an x such that x=y), or left-identity-with-y properties (being an x such that y=x; this might be the same as the previous, or maybe not), or .... (Even if there are haecceities, the same problems are apt to come up for them.)

Actually, this also afflicts yesterday's suggestion for what presentists can do about counting. For while that suggestion didn't use proxies, the suggestion was sufficiently complicated as to make it implausible that it was the unique canonical one. That may be why I only claimed to give a necessary and sufficient condition, not a translation.