On the notion of effectiveness

History and Philosophy of Logic 1 (1-2):209-230 (1980)
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Abstract

This paper focuses on two notions of effectiveness which are not treated in detail elsewhere. Unlike the standard computability notion, which is a property of functions themselves, both notions of effectiveness are properties of interpreted linguistic presentations of functions. It is shown that effectiveness is epistemically at least as basic as computability in the sense that decisions about computability normally involve judgments concerning effectiveness. There are many occurrences of the present notions in the writings of logicians; moreover, consideration of these notions can contribute to the clarification and, perhaps, solution of various philosophical problems, confusions and disputes

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Stewart Shapiro
Ohio State University

Citations of this work

In defense of epistemic arithmetic.Leon Horsten - 1998 - Synthese 116 (1):1-25.
Remarks on the development of computability.Stewart Shapiro - 1983 - History and Philosophy of Logic 4 (1-2):203-220.
Essay Review.M. Detlefsen - 1988 - History and Philosophy of Logic 9 (1):93-105.
Arithmetic Sinn and Effectiveness.Stewart Shapiro - 1984 - Dialectica 38 (1):3-16.

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.
Introduction to mathematical logic.Elliott Mendelson - 1964 - Princeton, N.J.,: Van Nostrand.

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