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Reply to H. Granger, Aristotle and the finitude of natural kinds, Philosophy 62 (1987), 52326, which discussed J. Franklin, Aristotle on species variation, Philosophy 61 (1986), 24552. 



Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...) 

Tylman has recently pointed out some striking conceptual and methodological analogies between philosophy and computer science. In this paper, I focus on one of Tylman’s most convincing cases, viz. the similarity between Plato’s theory of Ideas and the objectoriented programming paradigm, and analyze it in some more detail. In particular, I argue that the platonic doctrine of the Porphyrian tree corresponds to the fact that most objectoriented programming languages do not support multiple inheritance. This analysis further reinforces Tylman’s point regarding (...) 

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a selfevident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity. 

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...) 