[FOM] Slater and numbers

[Hartley Slater]

Randall Holmes (FOM Digest Vol 10 Issue 8) replies to my previous 
message 'Tangential to Holmes/Slater debate' by saying (a) that I 
should read Hazen more carefully, (b) that I confuse theory and 
meta-theory, and (c) that I am not clear about what is standard.  But 
(a) Hazen himself proposed a logic in which the numerical place in 
'(nx)Fx' can be quantified over, and likewise, paradoxically, Holmes 
has also done so himself, with omega-logic, (b) with numbered 
variables there is a reference to numbers in the standard 
re-expression of numerical quantifiers, so Holmes has to explain what 
is crucially different between that mode of representtaion and 
others, and (c) I am very clearly aware that it has been standard to 
represent the natural numbers as finite von Neumann ordinals (the 
case in question Holmes was writing about): that is what, amongst 
other things, I have been arguing against, and my point about appeals 
to what is 'standard' was that the fact that something is such does 
not make it right.

What Holmes has to understand is that the foundations of mathematics 
have been completely misrepresented for the last 100 years.
-- 
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) 9380 1246 (W), 9386 4812 (H)
Fax: (08) 9380 1057
Url: http://www.arts.uwa.edu.au/PhilosWWW/Staff/slater.html