AbstractThe 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.
Similar books and articles
A systems theoretical formal logic for category theory.Carlos Pedro dos Santos Gonçalves & Maria Odete Madeira - unknown
The modal object calculus and its interpretation.Edward N. Zalta - 1997 - In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer Academic Publishers. pp. 249--279.
A new formulation of discussive logic.Jerzy Kotas & N. C. A. Costa - 1979 - Studia Logica 38 (4):429 - 445.
Miraculous Success? Inconsistency and Untruth in Kirchhoff’s Diffraction Theory.Juha Saatsi & Peter Vickers - 2011 - British Journal for the Philosophy of Science 62 (1):29-46.
Inconsistencies in constituent theories of world views: Quantum mechanical examples. [REVIEW]Diederik Aerts, Jan Broekaert & Sonja Smets - 1998 - Foundations of Science 3 (2):313-340.
The Situation Calculus: A Case for Modal Logic. [REVIEW]Gerhard Lakemeyer - 2010 - Journal of Logic, Language and Information 19 (4):431-450.
The origin of relation algebras in the development and axiomatization of the calculus of relations.Roger D. Maddux - 1991 - Studia Logica 50 (3-4):421 - 455.
Added to PP
Historical graph of downloads
Citations of this work
Mathematical Representation and Explanation: structuralism, the similarity account, and the hotchpotch picture.Ziren Yang - 2020 - Dissertation, University of Leeds
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, MA and London: Harvard University Press.
The analyst: A discourse addressed to an infidel mathematician.George Berkeley - 1734 - Wilkins, David R..