6 Categorical Syllogisms
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Categorical Syllogisms 6.1 Standard-Form Categorical Syllogisms 6.2 The Formal Nature of Syllogistic Argument 6.3 Venn Diagram Technique for Testing Syllogisms 6.4 Syllogistic Rules and Syllogistic Fallacies 6.5 Exposition of the Fifteen Valid Forms of the Categorical Syllogism Appendix: Deduction of the Fifteen Valid Forms of the Categorical Syllogism 6 6.1 Standard-Form Categorical Syllogisms We are now in a position to use categorical propositions in more extended rea- soning. Arguments that rely on A, E, I, and O propositions commonly have two categorical propositions as premises and one categorical proposition as a conclusion. Such arguments are called syllogisms; a syllogism is, in general, a deductive argument in which a conclusion is inferred from two premises. The syllogisms with which we are concerned here are called categorical because they are arguments based on the relations of classes, or categories—rela- tions that are expressed by the categorical propositions with which we are famil- iar. More formally, we define a categorical syllogism as a deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions. Syllogisms are very common, very clear, and readily testable. The system of categorical syllogisms that we will explore is powerful and deep. The seventeenth-century philosopher and mathematician Gottfried Leibniz said, of the invention of the form of syllogisms, that it was “one of the most beauti- ful and also one of the most important made by the human mind.” Syllogisms are the workhorse arguments with which deductive logic, as traditionally practiced, has been made effective in writing and in controversy. It will be convenient to have an example to use as we discuss the parts and features of the syllogism. Here is a valid standard-form categorical syllogism that we shall use as illustrative: No heroes are cowards. Some soldiers are cowards. Therefore some soldiers are not heroes. 224 M06_COPI1396_13_SE_C06.QXD 10/16/07 9:17 PM Page 224
Transcript of 6 Categorical Syllogisms
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