[FOM] Parallel to Slater on Numbers

Hartley Slater slaterbh at cyllene.uwa.edu.au
Fri Oct 10 01:24:20 EDT 2003

```Arnon Avron writes
>Do you reject the propositions:
>"The pair <0,1> isin the exponential function" and "the exponential function
>is a subset of the upper half-plane" as ungrammatical?

I think that is enough of 'tangential' issues.  What Avron should
concentrate on is not confusing the value of a function with either
an argument of that function, or the set of arguments for which the
function has that value.  It boils down to accuracy: what Avron is
taking to be 'identity' is merely 'close association'.  Certainly N
is associated with p in 'd(p)=N', and  and with {e|e || p} in
'{e|d(e)=N}={e|e || p}', but that does not make for identities in
either case.

Harvey Friedman expands in a private email following his recent FOM
>  Why don't you make at least a simple short posting to the
>FOM to the effect that this is NOT to be taken as a suggestion that f.o.m.
>is fraudulent, or misguided, or anything like this. It is easy to read what
>you wrote that way.

I think you need special interests to bring in that reading, since my
remark about making explicit the implications of my rhetorical
question to Avron, 'So {{}, {{}}}=Card{k|k<2}?', in the context of
Holmes' sanguinity about the safety of current FOM, merely reflected
on my (surely) known disbelief in the (presumed) positive answer from
Avron (subsequently given), and Tennant's previous question about
explicitness.  Avron believes that cardinalities themselves have
cardinalities, indeed he must say that Card{{}, {{}}} = {{}, {{}}},
and likewise for all the finite von Neumann ordinals. I find that
very shaky. There was also the discrepancy between Avron's and
Holmes' views on '2={{}, {{}}}', which I documented, which does not
inspire confidence in people (like me) who do not  think one can
treat or define numbers in several ways making this equation
sometimes true and sometimes false.  If that is the case then FOM is
really wobbly.  Hello paraconsistency!  (And you might know my views
--
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

```