Was the early calculus an inconsistent theory?


Authors
Peter Vickers
Durham University
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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References found in this work BETA

Is Classical Electrodynamics an Inconsistent Theory?Gordon Belot - 2006 - Canadian Journal of Philosophy 37 (2):263-282.
Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
Reason and the Search for Knowledge.Dudley Shapere - 1985 - Philosophy of Science 52 (2):310-312.
Old Quantum Theory: A Paraconsistent Approach.Bryson Brown - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:397 - 411.

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Mathematical Pluralism.G. Priest - 2013 - Logic Journal of the IGPL 21 (1):4-13.

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