Tim Chow on Bivalence and Unknowability

[Dennis E. Hamilton]

Alan Weir wrote,

 "Most mathematicians will surely care very little about whether or not an
even number of elephants died on this day 1000 years ago. But they may well
not reject (or even be agnostic on) bivalence with respect to the question
just because they don't care or just because the answer is unknowable ...
with respect to this proposition EE (for Even number of Elephants) ... "

I submit that the proposition EE is not a mathematical question at all.  It
is at best a proposition about an empirical matter that is not verifiable by
any means in our contingent reality, however rigorously it is seemingly
elaborated.  That's rather different that considering how far we can go in
reasoning about abstract theoretical entities (divorced from interpretations
in nature that might be posed) by strictly mathematical means including how
mathematicians arrive at agreement on "proof."

CH is a different matter, hinging on a particular notion of cardinality at
the heart of set theory.  It seems to me that much applied mathematical work
(including in computer science) is indifferent to whether or not CH is the
case and having the validity of CH be unknowable or independent is not
troublesome.  Wrestling with CH (and AC) as foundational matters seems
inescapable though.

 - Dennis