Aristotle

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Poetics by Aristotle
Organon (Aristotle’s Logical Treatises): The Syllogism
Summary
Aristotle’s most famous contribution to logic is the syllogism, which he discusses primarily in the Prior Analytics. A syllogism is a three-step argument containing three different terms. A simple example is “All men are mortal; Socrates is a man; therefore, Socrates is mortal.” This three-step argument contains three assertions consisting of the three terms Socrates,man, and mortal. The first two assertions are called premises and the last assertion is called the conclusion; in a logically valid syllogism, such as the one just presented, the conclusion follows necessarily from the premises. That is, if you know that both of the premises are true, you know that the conclusion must also be true. Aristotle uses the following terminology to label the different parts of the syllogism: the premise whose subject features in the conclusion is called theminor premise and the premise whose predicate features in the conclusion is called the major premise. In the example, “All men are mortal” is the major premise, and since mortal is also the predicate of the conclusion, it is called the major term. Socrates” is called the minor term because it is the subject of both the minor premise and the conclusion, and man, which features in both premises but not in the conclusion, is called the middle term. In analyzing the syllogism, Aristotle registers the important distinction between particulars and universals. Socrates is a particular term, meaning that the word Socrates names a particular person. By contrast, man andmortal are universal terms, meaning that they name general categories or qualities that might be true of many particulars. Socrates is one of billions of particular terms that falls under the universal man. Universals can be either the subject or the predicate of a sentence, whereas particulars can only be subjects. Aristotle identifies four kinds of “categorical sentences” that can be constructed from sentences that have universals for their subjects. When universals are subjects, they must be preceded by every, some, or no. To return to the example of a syllogism, the first of the three terms was not just “men are mortal,” but rather “all men are mortal.” The contrary of “all men are mortal” is “some men are not mortal,” because one and only one of these claims is true: they cannot both be true or both be false. Similarly, the contrary of “no men are mortal” is “some men are mortal.” Aristotle identifies sentences of these four forms—“All X is Y,” “Some X is not Y,” “No X is Y,” and “Some X is Y”—as the four categorical sentences and claims that all assertions can be analyzed into categorical sentences. That means that all assertions we make can be reinterpreted as categorical sentences and so can be fit into syllogisms. If all our assertions can be read as premises or conclusions to various syllogisms, it follows that the syllogism is the framework of all reasoning. Any valid argument must take the form of a syllogism, so Aristotle’s work in analyzing syllogisms provides a basis for analyzing all arguments. Aristotle analyzes all forty-eight possible kinds of syllogisms that can be constructed from categorical sentences and shows that fourteen of them are valid. In On Interpretation,Aristotle extends his analysis of the syllogism to examine modal logic, that is, sentences containing the words possibly ornecessarily. He is not as successful in his analysis, but the analysis does bring to light at least one important problem. It would seem that all past events necessarily either happened or did not happen, meaning that there are no events in the past that possibly happened and possibly did not happen. By contrast, we tend to think of many future events as possible and not necessary. But if someone had made a prediction yesterday about what would happen tomorrow, that prediction, because it is in the past, must already be necessarily true or...
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