FOM: Friedman on Realism/Philosophy (reply)

[wtait@ix.netcom.com]

Franzen writes (2/3/98)
> Russell remarked of an
>earlier manuscript of his (I think the Philosophical Remarks) that
>they contained "a lot of stuff about infinity, which is always in
>danger of becoming what Brouwer has said, and has to be pulled up
>short whenever this danger becomes apparent".
It is not clear what is being ascribed to W and what to R.
>In these earlier
>writings, Wittgenstein did not make the clear demarcation between
>philosophical reflection and mathematical practice that he later
>urged, and even suggested (perhaps influenced by Brouwer) that a
>philosophically sound mathematics would differ from that currently
>practiced.
In the earlier and later writings, I believe that he thought that a lot 
of what we count as mathematics (mathematical practice) was 
philosophy---i.e. language on holiday. His exposure to set theory was 
from the works of Frege and Russell.

The influence of Brouwer, often refered to, puzzles me. The analysis of 
`following a rule' in _Phil Investigations_ would seem, whether 
accidently or not, to be aimed precisely at Brouwer's doctrine of 
mathematics as a lnanguage-less activity. For Brouwer, we may have an 
intension to compute a numerical function, say, and this intension 
carries within it the criterion of validity for all the indefinitely many 
computations of values. It is this which W attacks, and asserts that it 
is the established practice of mathematics that is the source of norms 
for computing. (Note that this isn't Jon's `black death of 
postmodernism', which says that to say that the computation is correct is 
to make a statement about what people do, did do or will do. W's 
doctrine, rather, is that it is only in the context of the practice that 
questions of correctness have any meaning and that we may separate the 
question of what is correct or not in the practice from the fact that it 
is our practice.)