Approximate truth

Journal of Philosophical Logic 16 (2):203 - 227 (1987)
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Abstract

The technical results presented here on continuity and approximate implication are obviously incomplete. In particular, a syntactic characterization of approximate implication is highly desirable. Nevertheless, I believe the results above do show that the theory has considerable promise for application to the areas mentioned at the top of the paper.Formulation and defense of realist interpretations of science, for example, require approximate truth because we hardly ever have evidence that a particular scientific theory corresponds perfectly with a portion of the real world. Realists need to assert, then, that evidence for a theory is evidence for its approximate truth, not its truth (see [3] and [18]). Approximate truth is, however, a vague notion, and specification of quantity terms and of a sense of approximation are needed to make precise applications of it. Suitability of both vocabulary and sense of approximation depend on the subject matter, and their selection is a partly empirical matter that raises complex issues. In light of the number of common inferences which are not continuous, realists also need to be concerned about indiscriminate use of deductive logic to derive consequences from approximately true theories. These issues will be considered further in a future paper.Approximate truth also has potential application in areas of artificial intelligence that require inference from inaccurate data. In the ‘qualitative’ physical theories of de Kleer and Brown [6], for example, ‘qualitative’ values are derived by partitioning the real numbers into regions. Inferences leading from inside to outside a region must be identified and avoided, and approximate implication and continuity may prove useful in doing this. More generally, growing use of predicate logic as a programming language invites application of the theory of approximate truth as a symbolic substitute for numerical evaluation of computation errors. This too will be the subject of a future paper

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References found in this work

Truth, belief, and vagueness.Kenton F. Machina - 1976 - Journal of Philosophical Logic 5 (1):47-78.
A qualitative physics based on confluences.Johan De Kleer & John Seely Brown - 1984 - Artificial Intelligence 24 (1-3):7-83.
Fuzzy Sets.Lofti A. Zadeh - 1965 - Information and Control 8 (1):338--53.
Verisimilitude reviewed.Graham Oddie - 1981 - British Journal for the Philosophy of Science 32 (3):237-265.

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