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Single Idea 9535
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
]
Full Idea
Two propositions are 'contradictory' if they are never both true and never both false either, which means that ¬(A↔B) is a tautology.
Gist of Idea
'Contradictory' propositions always differ in truth-value
Source
E.J. Lemmon (Beginning Logic [1965], 2.3)
Book Ref
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.70
The
12 ideas
with the same theme
[overview of the logical relationships between propositions]:
8077
|
Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms
[Chrysippus, by Devlin]
|
8083
|
Boole applied normal algebra to logic, aiming at an algebra of thought
[Boole, by Devlin]
|
7727
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Boole's notation can represent syllogisms and propositional arguments, but not both at once
[Boole, by Weiner]
|
9535
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'Contradictory' propositions always differ in truth-value
[Lemmon]
|
8085
|
Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens
[Devlin]
|
7726
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Aristotelian logic dealt with inferences about concepts, and there were also proposition inferences
[Weiner]
|
8472
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Sentential logic is consistent (no contradictions) and complete (entirely provable)
[Orenstein]
|
7786
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Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations
[Girle]
|
7798
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There are three axiom schemas for propositional logic
[Girle]
|
17749
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Post proved the consistency of propositional logic in 1921
[Walicki]
|
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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