This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites Paradox and challenges classical logic and semantics.
The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, or neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates.
Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case.
In this paper I propose a notion of propria inspired by Aristotle, on which propria are non-essential, necessary properties explained by the essence of a thing. My proposal differs from the characterization of propria by Kit Fine and Kathrin Koslicki: unlike Fine, the relation of explanation on my account can’t be assimilated to a notion of logical entailment. In disagreement with Koslicki, I suggest that the explanatory relation at issue needs not be necessary. My account of essence is conceptually parsimonious: it illuminates the contribution of essence to explanation without relying on obscure notions such as Aristotelian form or identity.
Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between (i) substances and non-substantial attributes of substances, (ii) different kinds of substance, and (iii) different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at all. Instead, Euclid systematically uses different types of definition to distinguish between metaphysically different kinds of mathematical object.
On the one hand, Aristotle claims that the matter of a material thing is not part of its form. On the other hand, he suggests that the proper account of a natural thing must include a specification of the kind of matter in which it is realized. There are three possible strategies for dealing with this apparent tension. First, there may be two kinds of definition, so that the definition of the form of a thing does not include any specification of its matter, whereas the definition of a compound does. Second, the definition of a substance may not include a specification of its matter at all, but still reveal in what kinds of matter its form can be realized. Third, there may be a special kind of matter, functional matter, which belongs to the form of certain things. I will show that the functional matter of a thing does not belong to its form (in a strict sense of “form”), but that an adequate account of natural substances and their functions must nonetheless involve a reference to their functional matter. This means that the function of a natural thing is not the same as its form and that its adequate account as a natural thing is not a definition (in a strict sense of “form” and “definition”).
This paper offers an overview of the history of the axiom forma dat esse, which was commonly quoted during the Middle Ages to describe formal causality. The first part of the paper studies the origin of this principle, and recalls how the ambiguity of Boethius’s first formulation of it in the De Trinitate was variously interpreted by the members of the School of Chartres. Then, the paper examines the various declensions of the axiom that existed in the late Middle Ages, and shows how its evolution significantly follows the progressive decline of the Aristotelian model of formal causality.
This paper develops a valid reconstruction in first-order predicate logic of Leibniz’s argument for his complete concept definition of substance in §8 of the Discours de Métaphysique. Following G. Rodriguez-Pereyra, it construes the argument as resting on two substantial premises, the “merely verbal” Aristotelian definition and Leibniz’s concept containment theory of truth, and it understands the resulting “real” definition as saying not that an entity is a substance iff its complete concept contains every predicate of that entity, but iff its complete concept contains every predicate of any subject to which that concept is truly attributable. An account is suggested of why Leibniz criticises the Aristotelian definition as merely nominal and how he takes his own definition to overcome this shortcoming: while on the Aristotelian basis the predication relation could generate endless chains, so that substances as endpoints of predication would be impossible, Leibniz’s definition reveals lowest species as such endpoints, which he therefore identifies with individual substances. Since duplicate lowest species make no sense, the Identity of Indiscernibles for substances follows. The reading suggests a Platonist interpretation according to which substances do not so much have but are individual essences, natures or forms.