Analogical Deduction via a Calculus of Predicables

Logik, Naturphilosophie, Dialektik, Zur Modernen Deutung der Aristotelischen Logik, 10 (2014)
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Abstract

The deductive validity of arguments from analogy is formally demonstrable. After a brief survey of the historical development of doctrines relevant to this claim the present article analyzes the “analogy of proper proportionality”, which meets two requirements of valid deduction. First, the referents of analogues by proportionality must belong to a common genus. Here it must be cautioned, however, that the common genus does not constitute the basis of the deductive inference. Rather, it is a prerequisite for the second and decisive requirement, that the different logical content to which an analogous middle term corresponds must exhibit the same proportional relation to this common genus. In Section II I translate a natural language argument with such an analogous middle term into the language of classical first-order predicate calculus, and show that its conclusion follows from its premises with the force of deductive necessity. The rule of inference justifying the analogical entailment of the conclusion from the premises functions much like the familiar modus ponens rule, and could be called “modus ponens analogice”. The validity of this rule ought to be judged on the same basis as that of the traditional modus ponens rule – immediate logical intuition. The present article endeavors to facilitate this logical intuition by making the logical structure of inference by analogy formally explicit.

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Joseph P. Li Vecchi
University of Akron

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