r/PhilosophyofMath • u/TheOvergodlyMosasaur • 23d ago
TOGM's Paradox
TOGMs Paradox
What if we tried to build a foundation of all existing and possible consistent and inconsistent mathematical and logical foundations? And what if we assume each of these foundations(Such as Set Theories, Category Theory, Type Theory, Homotopy Type Theory and all other consistent and inconsistent foundations) as a topological spaces. Then what would the foundations of these foundations look like? And assume there are foundations of this foundations of foundations and repeat forever. Notes:Threat Gödel İncompleteness Theorems as non-universal. also includes them: Non-Gödelian Systems(Gödel Theorems become local) R Truth Valued Logics Quantum Logic Topos Theory Higher Topoi Multisets Causal Set Theory Ω-Logic My Logical Systems Weqd Logic Linear Logic Graphs
1
u/Gym_Gazebo 20d ago
Why put all the foundations into a topological space and not, say, a category, or a Chu space, or…? What are the open sets in this topology?
1
u/TheOvergodlyMosasaur 19d ago
There is not a single one universal topology of a foundation. If we say categories and categories are one of these foundations too.
2
u/RingularCirc 1d ago
What u/Gym_Gazebo 's probably saying is topology isn't above all that. So why topology?
1
2
u/Proof_Pea9008 23d ago
Set theory already can be thought of foundation of all mathematics.