[FOM] a series of grammatical confusions
slaterbh@cyllene.uwa.edu.au
slaterbh at cyllene.uwa.edu.au
Sun Feb 19 07:42:11 EST 2006
Michael Kramer asks about my use of 'collection' in the previous posting.
But I gave quantified expressions for 'there is a number of Ps' and 'there
is a set of apples', there, and 'collection' surely works in the same way.
This is perhaps the point to intersperse a seemingly needed counter to a
point that Neil Tennant, amonst others, has made about numerical
quantification. The point originates in Frege, I believe, and it would
disallow quantification into the numerical place in what is sometimes
written '(nx)Px', i.e. 'there are n Ps'. But that place is open to
anaphoric referential phrases, as in, for example, 'There is a number of
apples on the table, and there is the same number of pears there'.
And another thing, once that is remembered. Being fussy to get things
right, I would symbolise this '(En)(nx)Ax.([en(nx)Ax]y)Py' (where 'e' is
epsilon). I use such epsilon terms for expressions like 'the number of
As' in parts of the rest of my AJP paper. But I would be reasonably
happy, for now, if others were satisfied with '(En)[(nx)Ax.(ny)Py]' - at
least it would show they have not accepted Tennant's line on such
matters.
Hartley
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