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Foundational Concerns and Mathematical Concerns
Published on May 20, 20116283 Views
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Chapter list
Foundational concerns and mathematical concerns00:00
Introduction03:46
What do I understand by a foundational concern?09:22
Geometry10:06
Examples11:02
Numbers12:33
Mathematics without Foundations14:51
The various e ects of foundational e orts19:13
Set theory and the rest of mathematics24:11
Concerns around Axioms and Incompleteness35:36
Concerns around Axioms and Incompleteness,continued37:49
What did Formalization bring?38:31
What did Incompleteness bring?39:00
Predictions42:22
Abstraction, Category Theory, Cohomology57:36
The present place of set theory01:01:36
Guessing at future crises or dramas01:02:59
Categoricity01:04:13
Categoricity Continued01:04:21