[FOM] Tangential to Slater and Numbers

Hartley Slater slaterbh at cyllene.uwa.edu.au
Wed Oct 8 21:02:54 EDT 2003

Some of the offerings under this head have indeed been tangential.  I 
gave an argument for my position, which people might like to address, 
concerning a diagonal function....

Neil Tennant wrote:
>Where is the explicit `counting of the
>variables' in the logically equivalent formal sentence
>	(Ex)(Ey)(-x=y & (z)(Fz <-> (z=x v z=y))) ?

I claimed the counting of variables was explicit in another, 
logically equivalent formula.   And (to other respondents) the other 
formula was introduced with 'If one represents 'there are exactly two 
Fs' as '(E1x)(E2x)(y)(Fy <-> y=x1 v y=x2) then...' so you were 
invited to construe that formula appropriately.

Arnon Avron  wrote:
>   On the other hand I find as extremely odd Slater's argument
>that identifying the natural numbers with the finite von Neumann ordinals is
>a grammatical mistake. ...

>I bet that most people, if pressed about this point,
>    will say at the end that a number n is always the cardinality of the
>    set of numbers less than n (including 0):
>    n=Card({k| k<n})

So {{}, {{}}} = Card ({k| k<2})?

Randall Holmes wrote:

>The foundations of mathematics are in good hands.  Leave them there.

(Should I make the implication of the last three lines explicit?) 
Holmes also wrote:

>I'll grant that 2 is distinct from {{}, {{}}} in my interpretations

Thank you.
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

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