[FOM] natural language and the F of M

[Hartley Slater]

Peter Apostoli has claimed (FOM Digest Vol 4, Issue 12)

>Frege was deeply aware
>of the the lacunas you mention above in his concept script. He gave
>expression
>to it in his problem about JC, which stems from the formal incompleteness of
>his identity theory.

I pointed out privately that the mass/count issue has no connection 
with the Julius Caesar problem, and Apostoli has replied

>  >As Michael Dummett forcefully pointed out in 'Frege: Philosophy of
>Mathematics' Duckworth, London, 1991, p94 (c.f. Mary Tiles, 'The
>Philosophy of Set Theory'  Blackwell, Oxford 1989, p151, Crispin
>Wright 'Frege's Conception of Numbers as Objects', Aberdeen U.P.
>Aberdeen, 1983, p3, Bob Hale and Crispin Wright 'The Reason's Proper
>Study' Clarendon, Oxford, 2001, pp315, 385, 415), Frege presumed that
>the concept of number was applicable to all concepts whatever, and
>so, in particular, provided no formalisation of the difference between
>count nouns and mass terms.
>
>I missed this the first time around. Are the above authors claiming that
>Frege counted German mass nouns among names of genuine concepts (begriffs)?
>[Thanks for the page references but I don't have the texts handy now].
>This is a bit of a shocker for me.

Harvey Friedman has parallel problems (FOM Digest Vol4 Issue 13):

>*Rather than have FOM readers go find Bunt's book to see if they are
>interested, it would be much better if you could briefly sketch the
>basics of the theory.*


>Again, rather than have FOM readers go find Lavine's book to see if
>they are interested, it would be much better if you could briefly
>sketch it and indicate what is more natural.

I'm not normally one to save people a rewarding walk to the library, 
and it would be absurd, in any case, to try to summarise what the 
above six, important writers have had to say in their  books and 
papers.  Nevertheless, I will just mention a few more things.

On Frege, the mass/count issue, and its relation to the theory of 
number, Bob Hale, for instance, says 'numbers may only properly be 
assigned to genuine sortal concepts', reiteratiing Wright's early 
thoughts in 1983.  Dummett abuses Frege on the matter; Tiles is more 
academic, and merely questions him; Wright (at one place, in 2001) is 
more constructive, suggesting a way in which non-sortals might be 
accommodated.  One of the points that Bunt makes, which ties in with 
these others, is that mass nouns do not pluralise in the appropriate 
way: we say 'the number of Ps is n' (where 'n' may still be zero), 
but with mass terms it is just 'there is some/no P'.  Bunt also makes 
a great many other linguistic points of this kind.

On Bunt's formal work, his 'Ensemble Theory', as I said, *includes* 
Set Theory as just a special case, so his treatment of mass terms is 
*additional to* his treatment of count terms, which means that, from 
his point of view, there is *more to* mathematics than what can be 
included in Set Theory.  Friedman admits:

>The unanswered question is whether anything is to be gained by this
>mereological approach to water, for the foundations of mathematics. I
>believe that it is philosohically interesting.

So Friedman might find Bunt's book of considerable interest (I am 
surprised he has not already read Lavine's).  My own contribution has 
been to point out that, by replacing 'being a member of a proper 
class' with 'being part of a mereological totality' one can do 
justice to mass terms while producing a combined theory with some 
resemblance to the von Neumann-style axiomatisation of traditional 
Set Theory.  It also gives an immediate and natural way out of 
Russell's Paradox, and the like.


-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 9380 1246 (W), 9386 4812 (H)
Fax: (08) 9380 1057
Url: http://www.arts.uwa.edu.au/PhilosWWW/Staff/slater.html