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Full Idea
Sentential logic has been proved consistent and complete; its consistency means that no contradictions can be derived, and its completeness assures us that every one of the logical truths can be proved.
Gist of Idea
Sentential logic is consistent (no contradictions) and complete (entirely provable)
Source
Alex Orenstein (W.V. Quine [2002], Ch.5)
Book Ref
Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.98
A Reaction
The situation for quantificational logic is not quite so clear (Orenstein p.98). I do not presume that being consistent and complete makes it necessarily better as a tool in the real world.
| 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 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
| 9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
| 8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
| 7726 | Aristotelian logic dealt with inferences about concepts, and there were also proposition inferences [Weiner] |
| 8472 | Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein] |
| 7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle] |
| 7798 | There are three axiom schemas for propositional logic [Girle] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |