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Single Idea 17749
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
]
Full Idea
A proof of the consistency of propositional logic was given by Emil Post in 1921.
Gist of Idea
Post proved the consistency of propositional logic in 1921
Source
Michal Walicki (Introduction to Mathematical Logic [2012], History E.2.1)
Book Ref
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.35
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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