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Bryan Pickel

Hi Dan,

I haven't read the paper, I think I agree with you that Sider's argument can be avoided if one "intensionalizes" the semantic value of the quantifiers. Nonetheless, I don't think that this sort of strategy should be tied to the success of a Frege-style 2nd-level property account of quantification.

2nd level property accounts of the existential quantifier have trouble delivering accounts of iterated quantification as occurs in 'ExEyRxy'. It looks like this sentence is processed by feeding the semantic value of 'Rxy' into 'Ey' and then feeding the result into 'Ex'. The trouble is that semantic value of 'Rxy' is either interpreted as being of sentence type, in which case the semantic value of the quantifier is going to be something which takes things of sentence type and yields another sentence, so not a second level property. Or, it is going to be a 2-place relation.

In the latter case, 'Ey' can't be interpreted as designating a property of a monadic property. But then we'd have to go in for type shifting of the existential quantifier, since the semantic value of 'Ex' is going to have to accept the semantic value of 'EyFxy' as its argument. So, the trouble is your quantifiers will have to type shift a whole lot. Type shifting can be avoided if one complicates the syntax so that there's a level of semantic processing between 'Fxy' which is of sentence type and 'Ey'. This is somewhat standard in the semantics of natural language. The trouble is that these kinds of accounts still tend to require a domain semantics, which is, I take it, what you're trying to get away from.

Anyhow, even if one takes the quantifiers as sentential operators there's nothing in itself wrong with making them intensional, even if one interprets them a sentential operators rather than properties of properties.

Dan Korman

Thanks Bryan, this is helpful. Is this trouble with iterated quantification a well-known problem for Fregean accounts?

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