EricS, You write:
*I bring up this debate in mathematics because it seems significant to mehow long and how intensely it has been going on, with both sides wanting anotion of “truth”, and neither being able to claim to have achieved it in termssatisfied by the other. If the intuitionists had never been able to build areal system around their position, the formalists could just declare victoryand go home. But the debate seems still live, even within math and not only inphilosophy, with clear trade-offs that there are proofs that each side willaccept that the other rejects.* It would surprise me to meet a mathematician who feels intensely one way or an other about a particular choice of topos. For mathematical-logicians, what seems more interesting are the geometric morphisms between toposes. I would argue that the formalists to some extent *did* *just declare victory* many times over and that their are still pockets of scientific/mathematical culture that believe everything can be *reduced to bits*. Still, and not just as with the intuitionists, richer toposes are there to be found and explored. My two favorite examples come from algebraic geometry and from quantum cosmology. In the former case, Grothendieck arrives at the idea of a non-boolean topos while writing the foundations of algebraic geometry. In the latter, Fontini Markopoulou-Kalamara <https://en.wikipedia.org/wiki/Fotini_Markopoulou-Kalamara> develops her non-boolean topos in the context of quantum gravity†. Jon †) Tangentially related to other parts of the overall discussion, Fotini is also a design engineer working on embodied cognition technologies.
-- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
