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Single Idea 18803
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
]
Full Idea
The classical semantics of natural language propositions says 1) valid arguments preserve truth, 2) no statement is both true and false, 3) each statement is either true or false, 4) the familiar truth tables.
Gist of Idea
Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.10
The
12 ideas
with the same theme
[overview of the logical relationships between propositions]:
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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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8083
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Boole applied normal algebra to logic, aiming at an algebra of thought
[Boole, by Devlin]
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7727
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Boole's notation can represent syllogisms and propositional arguments, but not both at once
[Boole, by Weiner]
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9535
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'Contradictory' propositions always differ in truth-value
[Lemmon]
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8085
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Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens
[Devlin]
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7726
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Aristotelian logic dealt with inferences about concepts, and there were also proposition inferences
[Weiner]
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8472
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Sentential logic is consistent (no contradictions) and complete (entirely provable)
[Orenstein]
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7786
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Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations
[Girle]
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7798
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There are three axiom schemas for propositional logic
[Girle]
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17749
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Post proved the consistency of propositional logic in 1921
[Walicki]
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17765
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Propositional language can only relate statements as the same or as different
[Walicki]
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18803
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Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables
[Rumfitt]
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