tag:blogger.com,1999:blog-3891434218564545511.post9081779969749565282..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: Quasi-quantifiersAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3891434218564545511.post-15042799287452392002013-12-03T11:02:14.971-06:002013-12-03T11:02:14.971-06:00Heath:
Yeah, there are serious difficulties here....Heath:<br /><br />Yeah, there are serious difficulties here.<br /><br />Here's one line of thought that both complicates what I said and points towards an answer to you.<br /><br />There clearly are no doppelgangers. (I could say that that's true by stipulation. Tell me what there is, and I can construct doppelgangers, or aleph17-gangers, on top of that!) So the doppelganged quasi-quantifiers aren't quantifiers. That's a clear case.<br /><br />But we can make the clear case muddy. We can state the semantic theory of the truth conditions for the doppelganged language in a doppelganged metalanguage. And this semantic theory will look just like one for a language with ordinary quantifiers.<br /><br />At this point, I see three ways forward:<br /><br />1. We've discovered that the distinction between doppelganged quasi-quantifiers and quantifiers is bogus. <br /><br />2. Say that the real quantifiers are those quasi-quantifiers that quasi-quantify over the domain of quantification in our natural language.<br /><br />3. Require that the relevant semantic theory is the most fundamental theory of how the world makes sentences true.<br /><br /><br />Now, (1) is the end of ontology and, what is worse, the rejection of the very intuitive claim that there really are no doppelgangers. <br /><br />Option (2) has the problem that the domain of quantification in our natural language is highly contingent. We can imagine our natural language evolving in such a way that we would using doppelganged quasi-quantifiers for some reason. So "the real quantifiers" ends up being relative to a particular metalanguage at a particular time, and that's no better than (1).<br /><br />That leaves (3). I don't think (3) by itself settles the question of whether quantifiers quantify only over the fundamental things. For it could be that the most fundamental semantic theory actually treats fundamental and non-fundamental things on par. I think it doesn't. But that's a further question. <br /><br />One might have a minimalist disquotational semantic theory which does, after all, and one might insist that that is the deepest and most fundamental semantic truth of the matter. Why would I reject that? Because that leads back to the same sort of conclusions we get in (1) and (2), namely a denial of the intuition of the mereness of the doppelganged quantifiers.<br /><br />p.s. Animals are fundamental.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-28750226668856050832013-12-03T10:05:52.789-06:002013-12-03T10:05:52.789-06:00I am sympathetic to this suggestion. It promises ...I am sympathetic to this suggestion. It promises an irenic solution to some tough problems. A few thoughts:<br /><br />What really seems to be going on is that quantifiers range over fundamental objects while quasi-quantifiers range over non-fundamental objects. The difference is the semantics of the two categories of (quasi-)quantifier, and to make any hay out of this difference we have to use the concept of “metaphysical fundamentality” in semantics. But as you note, it is hard to actually use this concept in real cases for natural language. So one question would be what is the motivation or philosophical payoff for making the distinction.<br /><br />(On a similar note: it seems to me that if we have existential quantifiers and existential quasi-quantifiers, the corresponding difference in the objects they pick out is not “[real] existence” and “quasi-existence” but “fundamental existence” and “non-fundamental existence.” )<br /><br />Another wrinkle is that there is not just one level of ontological dependence. There are particles, blowguns composed of particles, bundles composed of blowguns, etc. Do we need quasi-quasi-quantifiers? What happens if there are no fundamental objects, but an infinite regress of fundamentality? <br /><br />Another thought: one might treat fundamentality as a context-relative notion. E.g. for most practical purposes a herd is composed of animals. Now it may be that animals are composed of, say, atoms, and thus herds are composed of atoms. But for most purposes where we want the truth-conditions of statements about herds, we are willing to treat animals as the stopping-points of analysis and not interested in proceeding to analysis in terms of atoms. <br /><br />I think this gets to two possible views about what a semantic theory is. On one view, a semantic theory is in effect a comprehensive metaphysical picture of the world. On another view, a semantic theory is a tool for telling an interested party the meanings of words he doesn’t know in terms of meanings of words he does know. The first view needs a strong, context-independent notion of metaphysical dependence. The second view needs only a context-relative notion of epistemological dependence. (E.g. you could probably define cows as the constituents of herds.) <br /><br />Now, developing a semantics (and corresponding logic) that reflected a comprehensive metaphysical picture of the world is a project one could pursue. But there are many strands of philosophy today that would question the necessity, or interest, or maybe possibility of doing it. So again I would raise the question of what is the motivation or philosophical payoff for pursuing it.<br /><br />Heath Whitehttps://www.blogger.com/profile/13535886546816778688noreply@blogger.com