Wolfgang Schwarz

I don't feel like reading Russell to you, but why isn't "There is nothing such that it is round and square" an easy way out for the 2nd question and for the first sth. like "There are numerous non-vague objects such that being M.E. is true of them"?

M.

I'd like to stick up for objectual quantification over impossible objects. Let me suggest a non-Meinongian version of this view. A lot of us think we should quantify over merely possible objects, but don't think they are concrete objects which the applicable descriptions might suggest: e.g. possible talking donkeys are neither donkeys, nor do they talk. Rather, something modal or counterfactual is true of them - their being talking donkeys is strictly implied by their world being actualised, for example (assuming "world bound" objects of a certain sort). Abstractionists vary a lot about exactly what their possibilia have to do with the tempting characterisations of them.

Anyway, once we have abstract possibilia, abstract impossibilia are a short step away. An oject such that it would be a round square if it was actualised; or an object which is actualised according to its impossible world; or an object that otherwise, somehow, has the relation to impossible situations that possible objects have to possible situations, doesn't seem too bad, and might plausibly be associated with our ordinary quantification over impossibilia, just as the abstractionist possibilia candidates might plausibly be the subject of our usual apparent possibilist quantification, or some of it.

This might not strike you as tempting if you're convinced that we need concrete modal realism - if a statue I could have made this afternoon, but didn't, is a statue, in just the same way Michelangelo's David is. Since concrete impossibilia sound like trouble. (Though this is controversial). Is that why you don't like objectual quantification over impossibilia?

Hi Daniel, I should have been clearer about what I meant by "impossible objects". I had in mind objects that instantiate contradictory properties, like something that is both round and not round, or both married and a bachelor. Such objects cannot exist because there are no true contradictions.

I don't object to things that somehow *represent* impossibilia, in the way abstract properties or open sentences might represent possibilia. If quantification over merely possible donkeys is really quantification over donkey representations, then quantification over impossible donkeys could indeed be understood as quantification over impossible-donkey representations. I have no objection to that (except that I'm not sure this kind of quantification over impossibilia is particularly useful).

M., your suggestions concern the interpretation of sentences like "the round square does not exist". But I was interested in sentences like "there are impossible objects (e.g. the round square)". I'm not sure I see how your suggestions carry over to them.

These look like cases to me where the quantifier is supposed to have a certain inferential role, and where the standard interpretatation of the quantifier ranging over a domain of objects doesn't give it that inferential role. Substitutional interpretation would give it the inferential role, but there are also other options. I think cases like these should be taken at face value and not be explained away. The tricky part is to say how a quantifier can have the inferential role on some occasions, but not on others. It seems to me that quantifiers in general are semantically underspecified and that they can have inferential role and "domain conditions" readings. The former corresponds to the substitutional reading, though I think its better understood in other terms. (I argued for this in more detail in "Quantification and non-existent objects" and others, to put in a plug for a paper). So, I agree with your examples, but it seems to me that similar cases are everywhere, thought the difference only becomes prominent when we talk about non-existent objects, or even impossible ones.

It’s problem of the many week around here. First Peter Unger’s argument for dualism using the many as a vital step, now Robbie Williams on many mountains. Since Robbie’s paper is 9 pages while Peter’s is 158, and I already promised to talk about Robbie’s argument, I’ll talk about his today. I always thought that my various views about vagueness were in some amount of tension. What I say about truer requires that the supervaluationist’s precisifications be theoretically unimportant, at best things we can construct out of what is theoretically important, i.e. the truer relation. But what I say about the Problem of the Many seems to require that precisifications matter quite a lot. I’ve never really figured out how to resolve that tension, and that’s basically why I’ve never written a book on vagueness. Now Robbie argues (among other things) that I don’t have a tension in my views,...