Set Theory
Different Types of Set Theory:
How mathematics forgot the lessons of the past when trying to develop a theory of sets
Russell’s paradox:
How Russell’s paradox showed that Cantor’s set theoretical ideas were fatally flawed
Natural Set Theory:
What a Natural Set Theory is and why it is very different to “naive” set theory
Non-Natural Set Theory:
Why non-natural set theoretical ideas are the root of all problems in set theories
The ‘Empty Set’:
Why the notion of an ‘Empty Set’ generates more problems than it solves
Foundations of Mathematics:
Is Set Theory really the Theory of Everything for Mathematics for all time?
Containers:
The concept of Containers as analogous to physical containers
Other Menus
Incompleteness
Philosophical notes
The Infinite
Logic & Language
Mathematical Curios
Platonism
Paradoxes
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Rationale: Every logical argument must be defined in some language, and every language has limitations. Attempting to construct a logical argument while ignoring how the limitations of language might affect that argument is a bizarre approach. The correct acknowledgment of the interactions of logic and language explains almost all of the paradoxes, and resolves almost all of the contradictions, conundrums, and contentious issues in modern philosophy and mathematics.
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