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Abstract: This page shows an example commentary on a logic paper written by Lewis Carroll. This example illustrates the nature of a commentary logic paper, its three main parts, and its evaluation. Example Logic Commentary PaperA 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. Carroll’s paper is therefore a strong argument for skepticism. I. M. Copi distinguishes between a logical relation and an argument’s 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 Carroll’s argument in this way,
this distinction (if correct) falsifies Carroll’s
Notes
2. I. M. Copi, Introduction to Logic (New York: Macmillan, 1994).
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Arguments | Language | Fallacies | Propositions | Syllogisms | Translation | Symbolic |
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of a reductio ad absurdum argument, that a rule of inference
cannot be considered as a premiss of an argument. If a rule of inference is
given as one of the premisses, then some other rule of inference must be accepted
in order for the argument to be valid. Nevertheless, if this second rule is added
to the premisses, then a third rule is needed and so on ad infinitum.
assumption that a rule of logic must be a premiss. In addition, I. M. Copi defines
"rules of inference" as " rules that permit valid inferences from
statements assumed as premisses" (Copi, 704). However, he does not explicitly
write that elementary rules of inference are not part of the premisses. Indeed, if
the rules were to be considered part of the premisses, I. M. Copi’s definition
would fall prey to Carroll’s argument for logical skepticism.
1. Lewis Carroll, "Achilles and the Tortoise," in
Readings on Logic, ed. I. M. Copi and J. A. Gould (New York: Macmillan,
1972), pp. 117-118.
