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Charles S. Peirce suggested that a formal distinction between his three types of argumentation, deduction, induction, and retroduction, could be drawn using syllogistic figures. However, he never developed the concept of formal validity for non-deductive arguments beyond that point. His failure to do so may have been due in part to inadequacies in the theory of syllogisms as it was known at the time. Using an expanded syllogistic, with quantifiers between 'all' and 'some', this paper shows that it is possible to derive distinct groups of deductive, inductive, and retroductive syllogisms.
Keywords: Charles Peirce, induction, retroduction, abduction, syllogisms, intermediate quantifiers, validity.
The idea that there are three types of argumentation, deduction, induction, and a third type variously called hypothesis, abduction, or retroduction, first appeared in an 1867 paper by Charles S. Peirce, "On the Natural Classification of Arguments" (CP 2.461-516 , W 2:23-48). According to Peirce's tripartite division of argumentation, induction is not merely any form of argument that fails to be deductive, but argumentation that generalizes from a sample. In later writings Peirce broadened his notion to mean any testing of hypotheses through observation-as Peirce said, "trying how things will act" (PPM 276, 1903). If we understand an observation to be a sample of experience, as Peirce did in 1901 (R L 409:3, letter to S. P. Langley2), the early conception and the later conception are not necessarily at odds with each other. Retroduction, in contrast to both induction and deduction, is argumentation aimed at suggesting a hypothesis, but it does not involve the subsequent process of testing it. That is the province of induction.
The concept of the three types of argumentation was suggested to Peirce by variations in the structure of the syllogism. There are, Peirce knew, only three basic syllogistic figures. Deductive syllogisms in the first three figures are related to each other by a transformation known as ecthesis, which involves replacing one premiss with the denial of the conclusion, and then replacing the conclusion with the denial of the replaced premiss. From the 1st figure, ecthesis on the minor premiss produces a 2nd figure syllogism; ecthesis on the major premiss produces a 3rd figure syllogism. For example,
Barbara Baroco Bocardo
All M are P. All M are P....