Crathorn on Extension
Abstract
In this paper, I analyze William Crathorn’s view on extension and compare it to William Ockham’s reductionist view, according to which extension is not really distinct from substance or quality. In my view, Crathorn elaborates a metaphysical machinery based on mereological and topological relationships in order to solve what he considers to be problems in Ockham’s account of quantity. In order to make my point, I reconstruct Crathorn’s main arguments in favor of his finitist atomism. Crathorn claims that certain fundamental spatial structures are of a mereological nature and that the mereological properties of located entities perfectly match those of their locations. This idea lies at the core of his solution to the paradox of touching and the metrical paradox. It allows him to redefine contiguity in such a way that extensionless magnitudes can touch and succeed each other. Crathorn goes one step further and claims that indivisibles are extended in the sense that they occupy an extended incorporeal space, which is their dimension. In this sense, they can come together to form a continuous magnitude. Thus, Crathorn succeeds in defining a concept of continuity that is compatible with his finitist atomism and that addresses what he takes to be a major weakness in Ockham’s view on extension, namely a murky concept of impenetrability.