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Full Idea
Where Aristotle had 19 different inference rules (his valid syllogisms), modern propositional logic carries out deductions using just one rule of inference: modus ponens.
Clarification
'Modus ponens' says if p implies q, and p is true, then q must be true
Gist of Idea
Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens
Source
Keith Devlin (Goodbye Descartes [1997], Ch. 4)
Book Ref
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.80
A Reaction
At first glance it sounds as if Aristotle's guidelines might be more useful than the modern one, since he tells you something definite and what implies what, where modus ponens just seems to define the word 'implies'.
| 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] |