Aberrations and variations within kinds of creatures required explanation to Western medievals, who took the Genesis creation narratives together with Aristotelian species to imply that change was limited to within species; consequently, species were presumed static. Medieval philosophers often explained variation—including “new” kinds like mules—as due to problems in procreation/gestation (following Aristotle) or by sin. I argue that Aquinas's explanation of variation in women, people with disabilities, and mules suggests that Aquinas cannot be taken to entirely reject the possibility of (...) new kinds, and parallels in his explanation of the existence of women and the possible existence of new kinds provides warrant for a re‐evaluation of his understanding of the notion of the natures or essences shared by kinds. Sin—individual or original—is an inadequate explanation for variation, and the argumentative parallels between Aquinas's treatment of women and mules challenge presumptions about what medievals mean by “static kinds” at all, revealing space for evolutionary thought. (shrink)

Reply to H. Granger, Aristotle and the finitude of natural kinds, Philosophy 62 (1987), 523-26, which discussed J. Franklin, Aristotle on species variation, Philosophy 61 (1986), 245-52.

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 (...) that ignorance of their nature is profound. (shrink)

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 object-oriented 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 object-oriented programming languages do not support multiple inheritance. This analysis further reinforces Tylman’s point regarding (...) the conceptual continuity between classical metaphysical theorizing and contemporary computer science. (shrink)

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 (...) explains the distinction and why it has proved to be one of the great organizing themes of mathematics. (shrink)