Vickers, Peter (2007) Was the Early Calculus an Inconsistent Theory? [Preprint]
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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