Combining Texts
Ideas for
'fragments/reports', 'A Tour through Mathematical Logic' and 'Set Theory and Its Philosophy'
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13 ideas
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 / 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 / 1. Set Theory
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10702
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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10713
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Usually the only reason given for accepting the empty set is convenience [Potter]
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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 / f. Axiom of Infinity V
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13044
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Infinity: There is at least one limit level [Potter]
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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 / 5. Conceptions of Set / e. Iterative sets
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10708
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Nowadays we derive our conception of collections from the dependence between them [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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13546
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
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4. Formal Logic / G. Formal Mereology / 1. Mereology
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10707
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Mereology elides the distinction between the cards in a pack and the suits [Potter]
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