[FOM] re Plural Logic/Foundations

[Richard Heck]

On 04/23/2016 02:30 AM, Colin McLarty wrote:
> On Fri, Apr 22, 2016 at 12:54 PM, Richard Heck <richard_heck at brown.edu
> <mailto:richard_heck at brown.edu>> wrote:
>  
>
>     Plural quantification is very common. Consider e.g.:
>
>     (1) Some critics hate Shakespeare.
>
>     It's true of course that we can formalize this using first-order
>     logic, i.e.,
>     without doing anything special about the plural "Some critics".
>     But from
>     the point of view of linguistic theory, this isn't terribly relevant.
>     Moreover, note that (1) can reasonably be followed by:
>
>     (2) Yeah, and they only listen to one another.
>
>     Clearly, (2) has the force of a Geach-Kaplan sentence, which means
>     that the
>     plural pronoun "they" must really be understood as plural.
>     Moreover, it
>     needs
>
>
> It seems to me that (2) says critics who hate Shakespeare only listen
> to critics who hate Shakespeare.  This is plain first order
> quantification.

I didn't say that (2) involves plural quantification. I said that it
involves plural *reference*, via the plural pronoun "they", which nearly
all linguists would take to be completely obvious. To be sure, (2) is in
some sense equivalent to "Critics who hate Shakespeare only listen to
critics who hate Shakespeare", but, from a linguistic point of view,
this is not relevant. And if that is right, then, as I went on to say,
"they" needs an antecedent in (1), and this suggests that (1) itself
involves plural quantification. The fact that (1) *can* be formalized
using first-order (individual) quantification is not relevant, from a
linguistic point of view.

> The sentence "Some critics only listen to one another" might make a
> better case for plural quantification, where we have not specified
> which critics it is who only listen to one another.  But I only see
> sentences like that in papers on plural quantification.  I would like
> to see more naturally occurring examples.

First, let me just note that I made a mistake in rendering the relevant
sentence, which should be:

(3) Some critics listen only to one another.

With "only" before "listen", the sentence has a first-order equivalent.
It's only if "only" follows "listen" that it does not. The point is that
(3) implies that the critics in question do listen to one another,
whereas the other version may not.

In any event, the point of sentences like (3) is to show that there are
sentences of English that have no first-order equivalent that does not
use predicates absent from the original sentence. I am happy to agree
that such sentences are not terribly common in ordinary usage, though
sentences like Quine's:

(4) Some of Fiorecchio's men entered the building unaccompanied by
anyone else.

strike me as very natural, and (4), on its most natural reading, is not
first-order-izable.

But my point was simply that it does not follow from the fact that
non-first-order-izable sentences are rare that plural quantification is
rare. (1) above arguably involves plural quantification, and sentences
of that form are completely common.

Richard


-- 
-----------------------
Richard G Heck Jr
Professor of Philosophy
Brown University

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