[FOM] Wittgenstein Inspired Skepticism
silver_1 at mindspring.com
Mon Feb 27 14:27:49 EST 2017
I wish to repeat that addition of whole numbers (including decimals) is *totally* pinned down; every sum is right or wrong. This is achieved, as indicated before, by having a table for *single* digit adding, and simple rules for “carrying”. You just line up additions in columns. E.g., start on the right, 9+2 equals 1, carry the 1 to the column to its left. To wit:
1, carry the 1 to the column to the left, etc.
On the other hand, “continuing in the same way” is undetermined, since there are infinitely many different ways to continue a finite series. I have no doubt that Kripke realized “quus” did not work, which explains Kripke’s continued distancing himself from Witt.
> On Feb 26, 2017, at 3:01 PM, Thomas Klimpel <jacques.gentzen at gmail.com> wrote:
> tchow wrote:
>> 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).
> tchow wrote:
>> 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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