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Lecture

Jan 19 Lecture Note

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Department
Philosophy
Course
PHIL 1050
Professor
Mark Mc Cullagh
Semester
Winter

Description
thJan 19 Lecture Pg 4957THEORY OF SYLLOGISM Aristotle described 14 valid forms of syllogistic argumentThere are 4 possible quantifiers any of which can attach to any sentence in a syllogism of any figure Each syllogism has 3 sentences 4 options of quantifier for the first second and third sentence therefore there are 4x4x464 distinct syllogistic forms in each figure and since there are 4 figures there are 256 distinct forms of syllogistic arguments altogetherAristotle held that the valid syllogisms of the first figure are perfect by which he meant that their validity is obvious and selfevidentrequires no proofTo show the first Aristotle assumed certain rules of conversation which are really logical rules for inferring one sentence from another Aristotle rules of conversation includeRule 1 From No X are Y infer No Y are XRule 2 From All X are Y infer Some Y are XRule 3 From Some X are Y infer Some Y are Xnd Wish there rules some of the valid syllogisms of the 2third figures can be derived from the valid stsyllogisms of the 1 figureStart w the premises of a second or third figure syllogism If the perfect syllogism shares its conclusion w the original second or third figure syllogism it follows that the original syllogism is valid assuming the first figure perfect syllogisms are validthat the rules of conversation preserve truth An argument is valid if and only if it is not possible for its premises to be trueits conclusion false LIMITATIONS OF ARISTOTLES SYLLOGISTIC THEORY OF DEDUCTIVE ARGUMENT The theory of syllogism cannot account for even the simplest demonstrations in Euclids elements 1 The propositions of geometry are
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