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The Syllogism Revised

Published online by Cambridge University Press:  14 March 2022

Hans Reichenbach
Hans Reichenbach*
Affiliation:
University of California at Los Angeles
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Extract

The syllogism has often been criticized. Yet the theory of the syllogism cannot be omitted from logic. Even if it were not for its historical significance, its nature as a chapter of class logic assigns to it a place in any presentation of logic.

The usual exposition of the theory of the syllogism, however, whether given by the use of the familiar rules of the syllogism, or by the help of diagrams, appears clumsy and lacks the lucidity of modern chapters of logic. The reason seems to be given in the inefficient notation, taken over from ancient and medieval logic. In the following I should like to present an improved notation, which combines some of the traditional features with modern ones, and which is based on the criticism of the syllogistic theory which I have given elsewhere. It will be seen that in the revised form the theory of the syllogism is apt to meet the standards of modern logic.

Type
Research Article
Information
Philosophy of Science , Volume 19 , Issue 1 , January 1952 , pp. 1 - 16
Copyright
Copyright © Philosophy of Science Association 1952

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References

1 In my book Elements of Symbolic Logic, New York 1947, §36. The book will be quoted as ESL.

2 De Interpretatione (tranl. Ross), chap. 10, 20a—if this book is not, as some believe, an addition by later commentators.

3 See her article “Some proposed reforms in common logic,” Mind, vol. 15, 1890; and her article “Propositions” in J. M. Baldwin, Dictionary of Philosophy and Psychology, New York 1920.

4 Logic, Cambridge 1921, vol. 1, p. 140.

5 Smith's A Primer of Logic, Pulaski, Va., 1917, and Churchman's Elements of Logic and Formal Science, Phila., 1940, p. 109.

6 Sometimes the prefix indicates, not the complement class, but an opposite extreme. There exists a class of specific properties ordered on a linear scale (see ESL, p. 302, p. 314); P is the joint class of specific properties at one end of the scale, and un-P is a corresponding joint class at the other end. Aristotle knew this difference without, of course, giving this modern explanation for it. But he argued that “Kallias is unjust” is not the same as “Rallias is not just” (De Interpretatione, chap. 14, 23a). If the prefix “un” or “in” has the meaning of an extreme, modern language uses the prefix “non” for the mere negation. For instance, we distinguish between “unessential” and “non-essential”, or between “immoral” and “non-moral”. In such cases, the term “un-P”, or “in-P”, would be symbolized as a positive term “Q”. The transition from conversational language to the symbolic expression is often ambiguous; but this fact does not make the logical forms ambiguous. On the contrary, the symbolism often compels us to make terms clear that were used previously in an ambiguous meaning.

7 For the division by groups and the proof of the schemata, see ESL, §36, p. 205 and formulas (3), (10), (14), (15). A similar classification of syllogisms is found in D. Hilbert and W. Ackermann, Grundzüge der theoretischen Logik, Berlin 1928, p. 37.

8 Contraposition was already used by Aristotle for his reduction of figures; see Analytica Priora, 29a, 35. It was applied by Christine Ladd Franklin for the construction of an inferential relationship which she called antilogism; see her article on “syllogism” in J. M. Baldwin's Dictionary of Philosophy and Psychology, New York 1920.