[FOM] Unschooled grammatical intuition v. theoretical identities

[Hartley Slater]

At 10:33 PM -0400 16/10/03, Neil Tennant wrote, about exclusive variables:
>This deviant interpretation
>had its brief day in a paper by Hintikka long ago in the JSL.

Yes: that paper was on identity in the Tractatus, one of the most 
discussed books in 20th century, and so something I could expect 
people to be aware of.  And if the referees at Theoria hadn't taken 
(to date) 12 months to read 13 pages they might have heard more about 
this matter already.  In the meantime, electronic copies of 'The 
Central Error in the Tractatus' can be obtained from me on request, 
to demonstrate that Tennant's supposition about me being 'evasive' is 
mistaken:

>your "hint" that I should "suppose" that numbering variables "has 
>implications"
>is little more than hand-waving evasion at being corrected on an obvious
>and elementary point concerning standard logical notation.


At 10:33 PM -0400 16/10/03, Neil Tennant wrote:
>Your claim that "the 'n' is clearly a variable" is a comment on a schema
>of definition provided in the metalanguage.

We had the object-meta issue out in FOM on this before.  In the FOM 
posting referred to before Tennant said (about his schema N, i.e. 
'#xFx=n iff (nx)Fx'):

>where the right-hand side has to be spelled out without use of sharp, and
>without any apparent reference to numbers, or quantification over numbers,

As before, using numbered variables makes the otherwise implicit 
reference to numbers apparent.  Whether 'deviant' or not, it does the 
trick!

At 10:33 PM -0400 16/10/03, Neil Tennant wrote:
>Thank you for quoting Schema N to me; but I'm afraid I don't agree that it
>shows that I share your grammatical intuitions at all. That would be
>immediately apparent if you read the careful explanation in the book of
>how to identify the sentences that are to go on the right-hand side of
>Schema N.

My prime interest in Tennant's schema was the following question 
about whether there was anything similar in von Neumann, not what 
there was elsewhere in Tennant.  But Tennant is clearly struggling if 
he wants to say that #xFx=n iff (nx)Fx, and yet not that '#x' is 
'iota-m(mx)', when the one of these reads 'the number of x's such 
that' and the other 'the m such that there are m x's such that'.  I 
showed before that iota-m(mx)Fx = n iff (nx)Fx, so this variant of 
schema N can be proved once the reference to numbers on the right is 
made apparent, allowing quantification over the numeral place there 
to become unproblematic.
-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
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Url: http://www.arts.uwa.edu.au/PhilosWWW/Staff/slater.html