Online research in philosophy

This article examines one aspect of Thomas Aquinas' understanding of abstraction. It shows in which way, according to Aquinas, universal material objects and individual material objects are the starting point for mathematical objects. It comes to the conclusion that for Aquinas there are not only universal mathematical objects (circle, line), but also individual mathematical objects (this circle, that line). Universal mathematical objects are properties of universal material objects and individual mathematical objects are properties of individual material objects. One type of (...) abstractio formae leads from individual material objects to universal mathematical objects, a second type from universal material objects to universal mathematical objects, and a third type from individual material objects to individual mathematical objects. Therefore, the concept of abstractio formae is ambiguous. (shrink)

This article analyzes one aspect of Bolzano’s metaphysics. It discusses the question of whether, according to Bolzano, substances are simple or not. In theopinion of some commentators, he accepts composed substances, that is, substances having substances as proper parts. However, it is easily possible to misinterpret his position. This paper first tries to reconstruct Bolzano’s definitions of the concept of substance and suggests that he should be able to agree with the following final definition: x is a substance if and (...) only if x is real and not a property. After this, it is shown that, according to Bolzano, every substance is simple in a fourfold sense: No substance has (1) adherences as parts, (2) substances as proper parts, (3) spatially extended parts, and (4) temporal parts. (shrink)