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Do Syllogisms Commit the Petitio Principii? The Role of Inference-Rules in Mill's Logic of Truth

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It is a common complaint that the syllogism commits a petitio principii. This is discussed extensively by John Stuart Mill in ‘A System of Logic’ [1882. Eighth Edition, New York: Harper and Brothers] but is much older, being reported in Sextus Empiricus in chapter 17 of the ‘Outlines of Pyrrhonism’ [1933. in R. G. Bury, Works, London and New York: Loeb Classical Library]. Current wisdom has it that Mill gives an account of the syllogism that avoids being a petitio by virtue of construing the universal premise as an inference-rule. I will show that both the problem and the role of inference-rules in its solution have been misunderstood. Inference-rules have very little to do with this problem, and I will argue further that nothing is gained with regard to this problem by the introduction of inference-rules in preference to premises.
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Document Type: Research Article

Affiliations: IFILNOVA, FCSH, Universidade Nova de Lisboa, 26-C Av. de Berna, Lisbon, Portugal, 1069-061

Publication date: July 3, 2014

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