[FOM] 461: Reflections on Vienna Meeting

[Nick Nielsen]

On 5/14/11, Timothy Y. Chow <tchow at alum.mit.edu> wrote:

> F.o.m. experts sometimes try to characterize "ordinary mathematical
> reasoning" as being "reasoning formalizable in some specific system X."
> "Ordinary mathematicians" may unwittingly aid and abet this
> characterization by giving lip service to it.  However, I think that if we
> more carefully examine how mathematicians think, we find that the question
> of what assumptions are acceptable is *context-dependent*.  That is, an
> assumption that would be perfectly admissible in one context might not be
> admissible in another context.

Isn't this sort of like saying that, for foundational thought,
reasoning is formally context-dependent (i.e., dependent upon choice
of formalism), while for mathematical thought simpliciter reasoning is
intuitively context-dependent (i.e., dependent upon choice of
assumptions)?

Very Respectfully Yours,

Nick Nielsen