[FOM] The Irrelevance of definite descriptions in the Slingshot Argument?

[Hartley Slater]

Arhat Virdi asks about the comparative validity of certain slingshot 
arguments, one involving sets and the other iota terms.  More 
important, in the history of logic, is their clear invalidity in 
certain other cases.  A major argument Frege had, for instance, for 
his view  that truth-values are the referents of sentences was what 
is commonly called his 'slingshot' (see Neale, S. 1995, 'The 
Philosophical Significance of Gödel's Slingshot', Mind 104.413, 
761-825, p765, see also pp791-5).  But the irony with this argument 
is that it is plainly invalid if complete individual terms are used 
for referential phrases (Neale 1995, p795f), and Frege's extensional 
logic (unlike Russell's, for instance, where iots terms were used) 
did employ such complete individual terms to symbolise definite 
descriptions.  As it stands that point provides merely an ad hominem 
argument against Frege, but I have argued in many piblications (see, 
for the latest, 'Epsilon Calculi' just published last week by 
advanced access in the Logic Journal of the IGPL) that a better 
representation of definite descriptions is obtained using certain 
other complete terms, namely Hilbert's epsilon terms, and so the 
inadequacy of Frege's 'slingshot' argument can be argued for much 
more generally.
-- 
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