The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions ma...

One of the issues that deeply interested the philosophers of late antiquity, the Ancient Greek Commentators, concerns the priority of substances. While questions concerning ontological priority have recently attracted attention in Aristotelian scholarship and contemporary metaphysics, the Commentators’ discussions have not yet received the attention they deserve. My aim is to start to fill in this gap, by focusing on John Philoponus’s account of the priority of substances in his commentary on Aristotle’s "Categories". In particular, I aim to show how (...) Philoponus develops and defends the view that, while particular substances enjoy priority over accidents and concepts (“universals after the many”), they do not enjoy priority over all other things. Rather, a certain type of universal substance (“universals prior to the many”) enjoys priority over particulars. (shrink)

Aristotle's discussion of relatives in the Categories presented its eleventh- and twelfth-century readers with many puzzles. Their attempt to solve these puzzles and to develop a coherent account of the category led around the beginning of the twelfth century to the invention of relations as items which stand to relatives as qualities stand to qualified substances. In this paper, I first discuss the details of Aristotle's accounts of relatives and the related category of ‘situation’ and Boethius' commentary on them. I (...) then examine some of the earliest mediaeval commentaries on the Categories showing how the notion of relation, and in particular of individual relations, was developed. I conclude by showing how Peter Abaelard's treatment of relations in his Dialectica was part of an ongoing and sophisticated debate over the nature of relations. (shrink)

In his commentary on Aristotle’s Peri hermeneias,1 Abelard distinguishes the form of an expression2 (oratio) from what it says, that is, its content. The content of an expression is its understanding (intellectus). This distinction is surely the most well-known and central idea in Abelard’s commentary. It provides him with the opportunity to distinguish statements (enuntiationes) from other kinds of expressions without implying a diference in their content, since the ability of a statement to signify something true or false (verum vel (...) falsum)3 cannot be found in its content. More precisely, Abelard distinguishes statements both from complete expressions (orationes perfectae) that are not statements but rather questions, requests, commands, etc. and from incomplete expressions, that is, mere word strings (orationes imperfectae), such as homo albus. These kinds of expressions, according to Abelard, do not differ in the understanding they present but in the way they present it. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

According to the aspect theory of instantiation, a particular A instantiates a universal B if and only if an aspect of A is cross-count identical with an aspect of B. This involves the assumption that both particulars and universals have aspects, and that aspects can mediate between different ways of counting things. I will ask what is new about this account of instantiation and, more importantly, whether it is an improvement on its older relatives. It will turn out that the (...) part of it that is new is the notion of cross-count identity among aspects. As I will show, this notion is both dubious and unnecessary. I will end by presenting a simplified aspect theory of instantiation that does not involve cross-count identity. (shrink)