Combining Philosophers
Ideas for Tertullian, Oliver,A/Smiley,T and Robert S. Wolf
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12 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 / 3. Types of Set / b. Empty (Null) Set
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14239
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The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
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14240
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The empty set is something, not nothing! [Oliver/Smiley]
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14241
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We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
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14242
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Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
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14243
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The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
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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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