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Homepage > Logic > Syllabus > Commentary and Analyses |
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A Commentary on "Achilles and the Tortoise"
Lewis Carroll’s purpose in this short paper is to demonstrate, by means Carroll establishes this point by means of the following argument: (A) Things that are equal to the same are equal to each other. (B) The two sides of this triangle are things that are equal to the same. (Z) The two sides of this triangle are equal to each other (Carroll, 118). In order for Z to follow validly from A and B, the reasoning process must be permitted by a rule of inference: (C) If A and B are true, Z must be true (Carroll, 118). Moreover, in order for the argument that Z follows from A, B, and C to be valid, another rule of inference is necessary: (D) If A and B and C are true, Z must be true (Carroll, 119). Consequently, according to Carroll the argument can never be completed. If he is correct in this claim, then there is no compelling reason to accept any inference as legitimate. Carrolls paper is therefore a strong argument for skepticism. I. M. Copi distinguishes between a logical relation and an arguments premisses and conclusion. One might interpret this distinction to imply that the criterion of the correctness or incorrectness of arguments is not part of the specific argument. Since logic is a normative discipline, correct arguments must conform to rules, but this consideration is not a sufficient reason to presuppose that the rules are themselves premisses in specific arguments. While I cannot be certain that I. M. Copi would respond to Carrolls argument in
this way, this distinction (if correct) falsifies Carrolls Notes
2. I. M. Copi, Introduction to Logic (New York: Macmillan, 1994).
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