Combining Texts

Ideas for 'Defending the Axioms', 'Introduction to Mathematical Logic' and 'Meaning and Necessity'

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7 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic

17749

Post proved the consistency of propositional logic in 1921 [Walicki]

17765

Propositional language can only relate statements as the same or as different [Walicki]

4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables

17764

Boolean connectives are interpreted as functions on the set {1,0} [Walicki]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set

17752

The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]

17753

The empty set avoids having to take special precautions in case members vanish [Walicki]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

17610

The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]

4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets

17759

Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]