[FOM] Wittgenstein Inspired Skepticism

Josef Urban josef.urban at gmail.com
Sun Feb 26 01:47:06 EST 2017

On Sat, Feb 25, 2017 at 12:11 AM, tchow <tchow at alum.mit.edu> wrote:

> Harvey Friedman wrote:
> As I indicated before on FOM,
>> http://www.cs.nyu.edu/pipermail/fom/2017-February/020312.html
>> I view WIS = Witt inspired Skepticism, is a clever shock meant to
>> challenge us to make f.o.m. rely on "less commitments". Also to
>> explore the idea of their being a minimal level of commitments needed
>> to f.o.m. Or, alternatively, that there is a kind of nonending series
>> of ever smaller levels of commitments sufficient for f.o.m..
>> 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
>> commitments.
> 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, because I think that mathematicians, generally speaking, are
> not only unaware of their commitments, but have a strong tendency to deny
> that their own commitments involve drawing a somewhat arbitrary line in a
> continuum of possible commitments.  Most rabid skeptics of infinite set
> theory, and rabid skeptics of the consistency of PA, and rabid skeptics of
> arbitrarily large integers, strike me as being rather similar at an
> emotional level: They feel that they have figured out where all the
> monsters live, and have found the canonical boundaries of an absolutely
> safe, monster-free haven.  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.

I totally agree. Petr Vopenka had a seminar developing new foundations.
Once he was explaining that small natural numbers (1,2,3) are "safe"
because our intuition about them is clear. I argued that in the two-slit
experiment, our intuition about the "number of photons" is utterly
destroyed (and quantum physics claims this applies to everything). He sort
of agreed, but said that he needs to start somewhere.

I can imagine that even very "basic" notions like "number" are just
(simplified and useful) artifacts of the way our brains interact with the
rest of the physical world. So perhaps Kripkenstein is "silly", but only
until we meet the aliens whose "brains" work very differently (and/or until
we evolve ourselves - "mentally" or "physically"). There are probably
already many examples in the history of mankind of "obvious intuition"
turning non-obvious.

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