[FOM] Frege's error

Hartley Slater slaterbh at cyllene.uwa.edu.au
Thu Jul 14 21:40:13 EDT 2005

Neil Tennant writes:

>Hartley Slater's allegation of an error on Frege's part involves an
>anachronistic us of closed lambda terms to explicate what he thought Frege
>was saying. But Frege would have resisted the use of closed lambda terms
>in any explanation of what he might have meant by transforming the
>function x>y into the function x>x. For Frege, functions were inherently

If one cannot talk about Frege in a language he would not use, then 
we cannot criticise him on a scientific basis.  We cannot tell him, 
for instance, that sentences are not referring terms (as I did in my 
previous message), since 'for Frege' they are, so our remarks, it 
might be said, are not about what he was talking about, namely 'Frege 
sentences' which are referring terms, by definition.  Popper had a 
lot to say about this sort of thing in connection with closed 
societies, and pseudo-science.  One might as well say one cannot 
refute Priest by using a 'not' which obeys Reductio, since that is 
not (sic) a 'not' he chooses to use - or even recognise.

Not only are sentences not referring phrases, also predicates are not 
referring phrases, even though 'for Frege' they were - and Frege's 
thought at that point was what got him into his paradox about the 
concept *horse*.  Are we just to stick with the thought processes 
which landed him in this quandary?  No.  Following Cocchiarella, for 
instance, we can distinguish the concept LxHx from the predicate 
'LxHx[ ]', and so see that it is the latter, and not the former, 
which is unsaturated.  We thereby advance, and move over to a clearer 
formal language without Frege's paradox - in fact it is a formal 
language which more directly mirrors the everyday language we 
ordinarily use.

Tennant does not take me up on my main point, although certainly 
these are not irrelevant issues.  I wrote about Frege's error with 
reflexives in my previous message, and specifically about what led 
him to overlook the impossiblity of it being generally the case that 
LyLzRyz[x][x] = LyRyy[x].  So that was the historical point I was 
mainly concerned about - how it was likely his move from Mathematics 
to Logic which led him astray.  For more on reflexives, as well as 
the above and related matters, see my 'Choice and Logic' just out in 
the Journal of Philosophical Logic 34 (April 2005) pp. 207-216, and 
the two electronic papers referenced at the foot of the first page.
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater

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