FOM: The argument from personal incredulity

[Lee J. Stanley]

The subject line of this post is an expression I ran
across just today, in connection with something quite different.

Yet, it summarizes quite nicely, to my eyes, the nature of
some of the posts I have seen recently and not so recently
suggesting that full ZF is somehow unreasonably strong and
about inherently murky notions.

Things like:

"I have difficulty in arriving at a sufficiently deep
understanding of X to satisfy my high standards of what
counts as mathematics, or understanding, or both, therefore, ...

Version (1)  " ... X is necessarily and inextricably a murky notion
             and will remain so forever, and attempts to shed some
             light on it are not serious, or not mathematics, or ... ."

Version (2)  " ... the intuitions which first led us to X
             were REALLY about some scaled down version of X."

RE Version 2:  we do sometimes HAVE TO scale back.  Russell's Paradox.
More recently, a nontrivial elementary embedding of V to V
always seemed to me to be perhaps the most intuitively appealing large
cardinal axiom.  Alas ...  But one doesn't scale back without compelling
reason to do so.  Further, the scalebacks are rarely as robust, and
always more technical looking than the full X, which casts doubt
on the assertion that that is what the INTUITIONS were about in the
first place:  one imagines with extreme difficulty arriving at the
scalebacks without the "detour" via full X.  The scalebacks reflect
concessions to consistency which the intutions may HAVE TO make.  Once
again, emphasis on HAVE TO.

I don't want to enter into further disputing either Version (1) nor Version (2)
AT THE MOMENT, as there is really no reason to do so:
the only justifications for either, that I have seen offered so far, are,
essentially, nothing more substantial than avowals of personal incredulity.

Best Wishes,

Lee Stanley

PS.  The context in which I saw the phrase had to do with arguments
for the existence of God, or a "purposeful design" at any rate, along
the lines of "gee whiz, it just strikes me as hard to believe that
something as wonderful and precarious and complex as life could arise
any other way."