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Past, Present, and Future Directions in Foundations of Mathematics
Published on May 23, 20117820 Views
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Chapter list
Past, present, and future directions in the foundations of mathematics00:00
Agenda01:16
The foundational life 02:13
Foundational life04:40
Philosophical life06:35
Mathematical life, scientific life09:10
An ambition10:20
Foundations of mathematics foundations of physical science11:50
Foundations of applied mathematics12:45
Profound uneasiness - 114:33
Profound uneasiness - 216:13
First main step epsilon delta17:01
Number systems17:33
Real number system multiple definitions18:38
Infinite upper shift Kernel theorem20:17
Rationals and integers21:05
Grand unification22:30
Pure set theory immutable objects23:59
Exploding universe25:41
Assertions and proofs27:21
Logical structure28:07
Proof assistants29:27
Understanding trivialities30:40
Strict reverse mathematics32:03
Fundamental foundation moves: consistency, completeness, incompleteness33:45
Incosistent systems useful?34:32
Gödel's second incompleteness Theorem36:10
Four completeness theorems37:04
Gödel's first incompleteness theorem38:09
First mathematically natural incompleteness39:16
Consistency, and the incorporation of new notions40:03
Concept calculus42:25
Completeness, and delicate choice of fragments44:33
0 - Minimality - 145:21
0 - Minimality - 245:21
Incompleteness, and concreteness, simplicity, naturalness47:47
Maximal clique embedding48:59