Combining Texts
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'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'A Tour through Mathematical Logic'
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12 ideas
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
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8077
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Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
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13520
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A 'tautology' must include connectives [Wolf,RS]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
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13524
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Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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20791
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Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius]
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4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
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13522
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Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS]
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13521
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Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS]
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4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
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13523
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Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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17833
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The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
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17834
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Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / e. Axiom of the Empty Set IV
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13529
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Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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13526
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Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
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17837
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Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
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