[FOM] Wittgenstein Inspired Skepticism

[tchow]

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.

Tim