Was the early calculus an inconsistent theory?

Abstract

The ubiquitous assertion that the early calculus of Newton and Leibniz was an inconsistent theory is examined. Two different objects of a possible inconsistency claim are distinguished: (i) the calculus as an algorithm; (ii) proposed explanations of the moves made within the algorithm. In the first case the calculus can be interpreted as a theory in something like the logician’s sense, whereas in the second case it acts more like a scientific theory. I find no inconsistency in the first case, and an inconsistency in the second case which can only be imputed to a small minority of the relevant community.

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2009-01-28

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Peter Vickers
Durham University

References found in this work

Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
Understanding the infinite.Shaughan Lavine - 1994 - Cambridge, Mass.: Harvard University Press.
The analyst: A discourse addressed to an infidel mathematician.George Berkeley - 1734 - Wilkins, David R.. Edited by David R. Wilkins.
Reason and the Search for Knowledge.Dudley Shapere - 1985 - Philosophy of Science 52 (2):310-312.

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