[FOM] Wittgenstein Inspired Skepticism
jacques.gentzen at gmail.com
Sun Feb 26 18:01:52 EST 2017
> In my view, the question of whether mathematics successfully avoids
> vagueness boils down to the question of whether Kripkenstein is silly or not.
> The tacit consensus among mathematicians is that Kripkenstein is silly,
> and so we have access to a bedrock non-vague system of syntactic rules
> on which everything else can be solidly built.
I have the impression that the tacit consensus is rather that Turing
machines successfully nail down what is meant by rule following.
However, this doesn't mean that there would be a consensus that this
solves all problems related to language and meaning. And I cannot see
why mathematics should be free of vagueness iff Kripkenstein is silly.
The ontological commitments of mathematics (and set theory) seem to go
further than the mere existence of Turing machines (or the existence
of a bedrock non-vague system of syntactic rules).
> Harvey Friedman wrote:
>> In this way, I do not view WIS as any kind of serious contribution to
>> f.o.m. Only as a cute tease to get us to think about minimizing
> If one is fundamentally committed to f.o.m. and is interested in other
> topics only insofar as they advance the f.o.m. agenda, then I agree that WIS
> doesn't accomplish much other than to turn the spotlight onto the problem of
> minimizing commitments.
> However, even though this is basically a "negative" achievement rather than
> a "positive" achievement, I consider it to be a pretty significant
> achievement, ...
> ... It's no minor achievement to be able to show that there
> is no canonical place to draw a line, even way down at the low end.
If it would really show that, than it would indeed be a major
achievement. But then it should be clarified how it is different from
the skeptic denying any possibility to communicate meaning at all.
Or to put it differently, the initial mail nicely illustrated
Wittgenstein's paradox, but here you suddenly draw significant
conclusions from that paradox and it remains unclear whether those
conclusions just arise as a consequence of some implicit
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