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(0 1)-category-theory 2-category 2-category-theory 2-monad abelian-categories accessible adjoint algebra algebraic algebraic-geometry analysis arithmetic beauty book bug bundle categories category category-theory chern-simons-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry conference connection constructive constructive-mathematics cosmology database deformation-theory descent differential differential-cohomology differential-geometry duality enriched enriched-category-theory enrichment examples factorization-system fiber fibration forms foundation foundations functional-analysis functor galois-theory gauge-theory gebra general topology geometric geometric-quantization geometry gravity group-theory higher higher-algebra higher-category-theory higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory homtopy-type-theory infinity-groupoid infinity-topos integration-theory internal-categories kan lie-algebras lie-theory limit limits linear linear-algebra locale localization localization-theory logic manifolds mathematics measure measure-theory mechanics meta modal-logic model model-category-theory monoidal monoidal-category monoidal-category-theory morphism n-groups newpage noncommutative noncommutative-geometry object operator operator-algebra order-theory philosophy physics predicative pretopology pro-object probability-theory quantum quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry set set-theory sheaf simplicial site space stable-homotopy-theory stack string string-theory subobject supergeometry symplectic-geometry tannaka tensor terminology theory topologica-quantum-field-theory topology topos topos-theory torsor tqft type type-theory universal weighted-limit

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 14th 2009
   • PermaLink
   Author: Urs
   Format: Markdowncreated [[effects of foundations on "real" mathematics]] and linked to it from [[foundations]]. This is to archive an exchange between Toby and James on the blog [here](http://golem.ph.utexas.edu/category/2009/10/a_dual_for_set.html#c027844). The hope would be that eventually the list of examples is expanded here.

   created effects of foundations on "real" mathematics and linked to it from foundations.

   This is to archive an exchange between Toby and James on the blog here. The hope would be that eventually the list of examples is expanded here.

2. • CommentRowNumber2.
   • CommentAuthorJonAwbrey
   • CommentTimeOct 15th 2009
   • (edited Oct 15th 2009)
   • PermaLink
   Author: JonAwbrey
   Format: Markdown_I come to bury foundations, not to raze them …_ I passed through my first foundational crisis many years ago, and have gradually since come to distrust the very word "foundations" — all despite our best intentions, it has a funny way of turning mathematicians into Bourbaki-thumping fundamentalists, though even their word "magma" would have paved a better road. I cannot say if there's a better word ahead — for the Time Being, in the Mean Time, I have settled happily enough on the word "medium".

   I come to bury foundations, not to raze them …

   I passed through my first foundational crisis many years ago, and have gradually since come to distrust the very word "foundations" — all despite our best intentions, it has a funny way of turning mathematicians into Bourbaki-thumping fundamentalists, though even their word "magma" would have paved a better road.

   I cannot say if there's a better word ahead — for the Time Being, in the Mean Time, I have settled happily enough on the word "medium".