[FOM] informal poll special terms in logic
tchow
tchow at alum.mit.edu
Mon May 8 16:18:05 EDT 2017
Harvey Friedman wrote:
> In the legitimate and important movement to replace the term "pure
> mathematics" with "theoretical mathematics", perhaps the use of
> "theoretical physics" should be cited? Note that the physicists were
> not so stupid as to fall into the trap of adopting the term "pure
> physics".
There was a famous article in 1993 by Jaffe and Quinn with the term
"theoretical mathematics" in the title.
http://www.ams.org/journals/bull/1993-29-01/S0273-0979-1993-00413-0/S0273-0979-1993-00413-0.pdf
Roughly speaking, they were suggesting the use of the term to refer to
non-rigorous mathematics in the style of theoretical physics. They
claimed that some well-known people were making mathematical assertions
that were not exactly conjectures (because they were backed up with
arguments) but were not exactly theorems either (because the level of
rigor of the arguments was similar to the level of rigor used in
theoretical physics, not the level of rigor used in traditional
mathematics). They felt that this practice was harming the field by
discouraging others from pursuing rigorous proofs because all the
"credit" for the result had already been pre-empted. They felt that
introducing the term "theoretical mathematics" might help address this
(alleged) problem by clarifying the status of such results.
This is not to say that the term "theoretical mathematics" can't be
co-opted for other purposes; it's just a warning that the term has
already been used to mean something different from what Friedman is
suggesting.
Tim
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