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Confirming Inexact Generalizations

Published online by Cambridge University Press:  31 January 2023

Ernest W. Adams
Ernest W. Adams*
Affiliation:
University of California-Berkeley
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Extract

An inexact generalization like ‘ravens are black’ will be symbolized as a prepositional function with free variables thus: ‘Rx ⇒ Bx.’ The antecedent ‘Rx’ and consequent ‘Bx’ will themselves be called absolute formulas, while the result of writing the non-boolean connective ‘⇒’ between them is conditional. Absolute formulas are arbitrary first-order formulas and include the exact generalization ‘(x)(Rx → Bx)’ and sentences with individual constants like ‘Rc & Bc.’ On the other hand the non-boolean conditional ‘⇒’ can only occur as the main connective in a formula. We shall also need to consider formulas with more than one free variable such as ‘xHy ⇒ xTy,’ which might express ‘if x is the husband of y then x is taller than y.’ Though it is inessential, it will simplify things to work in ‘n-languages’ with a finite number of individual constants c1,…, cn, which are interpreted as denoting the elements of the domains of the ‘n-models’ to be described below.

Type
Part I. Confirmation and Scientific Laws
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1988 , Issue 1: Volume One: Contributed Papers 1988 , 1988 , pp. 10 - 16
Copyright
Copyright © Philosophy of Science Association 1988

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