Aristotelian Logic and Metaphysics

A Ruth Norman Halls Colloquium

October 20th-21st, 2012

Abstracts

Jacob Rosen: "Proof by Assumption of the Possible in Prior Analytics 1.15"

In Prior Analytics 1.15, Aristotle undertakes to establish certain modal syllogisms of the form XQM (that is, their major premise is assertoric, their minor premise is a statement of two-sided possibility, and their conclusion is a statement of one-sided possibility). Although these syllogisms are central to his modal system, the proofs he offers for them are troublesome. The precise structure of the proofs is disputed, and it is often thought that they are invalid. We propose an interpretation which resolves the main difficulties with the proofs, showing that they are valid given a small number of intrinsically plausible assumptions. (On the other hand, certain aspects of the proofs are in tension with claims found elsewhere in Aristotle's modal syllogistic.) The proofs make use of a rule of propositional modal logic which we call the possibility rule. We consider how this rule interacts and coheres with the core elements of the modal syllogistic.

Marko Malink: "Essence and Modality in Aristotle"

Aristotle's modal syllogistic, found in Prior Analytics 1. 8-22, is the most complicated part of his logic. It has been disputed since antiquity, and is widely regarded as incoherent. This paper aims to arrive at a better understanding of the modal syllogistic by looking at the theory of predication which Aristotle develops in the Topics. Specifically, we will look at the Topics' theory of the ten categories (substance, quantity, quality, . . . ) and of the predicables (definition, genus, differentia, proprium, accident). I will show how this theory can help us to understand Aristotle's modal syllogistic, and to verify some of his central claims concerning the validity and invalidity of modal inferences (such as Barbara NXN, Celarent NXN, and the conversion rules for necessity propositions).

Laura Castelli: "Aristotle on 'Signifying the Same' and 'Signifying One': On the Limits and Nature of Linguistic and Ontological Competence in Dialectical Analysis"

In his influential study Aristotle on Meaning and Essence (Oxford 2000) David Charles provides an account of how the knowledge conveyed by an appropriate nominal definition can be detached from acquaintance with the existence of an object corresponding to the definition or from full knowledge of the essence of that object - if it exists. Charles focuses on names for natural kinds and regards the informed linguistic competence of craftsmen as the standard level of competence required for providing adequate nominal definitions. Within this picture, nominal definitions have the function of directing scientific enquiry towards the discovery of essences and causes.

Various aspects of this reconstruction have been discussed in the literature. I will focus on nominal definitions and semantic analysis in Aristotle in order to put the debate about the linguistic and ontological competence of the dialectician within a broader context. I consider three points: i) the dialectician need not have knowledge of essences in order to carry out an enquiry into dialectical definitions; ii) the dialectician, like the orator, does not have the knowledge characteristic of craftsmen; and iii) the dialectician seems to have the ability to deal with language appropriately enough to open the way for philosophical investigation - by, for instance, distinguishing the different ways in which the pollachos legomena are said.

I will explore the competence that the dialectician may display with reference to non-empty names which do not refer to natural kinds (e.g. 'one', 'being', 'chance', 'luck', etc.). Aristotle's analysis and use of arguments about sameness and difference based on dialectical topoi can be used to distinguish between (i) the ability to recognise pairs of linguistic expressions that 'signify the same' and (ii) the full knowledge of the 'one' that each of them signifies. Put in non-Aristotelian language, I suggest that Aristotle's broad use of sameness in signification is the basis for the dialectician's ability to identify equivalence classes for expressions that signify the same or that convey numerical sameness (cf. Top. I 7, VII 1). I suggest further that the dialectician's work on sameness, while not requiring a full grasp of essences and not using language that differs significantly from common use, presupposes a relatively developed (Aristotelian) conceptual framework that is presumably not expected from the average competent speaker.

Alan Code: "Subject and Predicate in Aristotle's Account of Sleep"

When stating the causes of natural phenomena Aristotle, among other things, identifies (i) a subject for predication, and (ii) a modification of that subject. I propose to look at his treatment of the cause of sleep as a case study to see how for this type of phenomenon he goes about specifying and making clear these two factors, and how they are related to the efficient cause that is responsible for that subject being modified in the relevant way. In particular, I consider the way which the modification is specified as a modification of that subject, and how the identification of an appropriate efficient cause makes clear what that modification is.

Benjamin Morison: "What is a Perfect Syllogism?"

Perfect syllogisms are often defined by commentators as those which are evident or obvious. I argue that this misunderstands and even mistranslates Aristotle's definition of perfection in Prior Analytics I 1. Perfect syllogisms are ones where the explanation of why the argument counts as a syllogism meets a certain condition, namely that the explanation makes reference to no other propositions involving the terms of the argument other than the premisses. I show how this is reflected in Aristotle's actual procedure in both the assertoric and modal syllogistic, and show how this solves a couple of puzzles arising in Prior Analytics I 7. I finish by reflecting on why Aristotle needs a notion of perfect syllogism.

Neil Lewis: "The Thirteenth Century Reception of Aristotle on Rational Powers"

Aristotle's doctrine of rational capacities in book 9 of the Metaphysics holds that rational agents have, in virtue of their possession of certain kinds of knowledge, capacities that extend to contraries in the sense that the self-same capacity can be exercised in contrary and thus incompatible ways. I examine a strand of the medieval commentary tradition on this doctrine, starting with Richard Rufus of Cornwall and ending with John Duns Scotus. I aim to show that this commentary tradition starts with the idea that if we are to have rational capacities we must also have what is now termed 'libertarian' free will, and reaches its culmination in Scotus' view that rational capacities are to be equated with the free will.

Carrie Swanson: "Aristotle on the Resolution of Disagreement in the Diagnosis of Fallacy"

In De Sophisticis Elenchis Aristotle argues that two arguments fall into the same class of sophistical refutation just in case they violate the same condition on genuine refutation. It follows that according to Aristotle, solving a sophism involves specifying the argument's violation of some particular condition on genuine refutation. However, some sophisms are more difficult to solve than others and Aristotle testifies in a number of passages that their solution was a matter of considerable controversy among his contemporaries. Aristotle's arguments for his own preferred solutions have struck many of his commentators as ad hoc or question-begging. I defend Aristotle's general theory of sophistical refutation from these charges by explaining how its methodology equips the dialectician with techniques for activating his dialectical knowledge in the face of difficult cases.

Rega Wood and Calvin Normore: "Aristotle was not Lying: Universals are not Substances"

Richard Rufus was the first Western university professor to lecture on Aristotle's Metaphysics. Commenting in the 1230's, he came to Aristotle's metaphysics from a background in logic and Neoplatonic natural philosophy, but his education in Aristotle had included only the Categories and On Interpretation. He had available to him only two incomplete and badly translated versions of the Metaphysics. The material was so new and the translation was so bad that he, like his contemporaries, depended heavily on the extensive commentaries Ibn Rushd wrote in the late 12th century, translations which were not available until shortly before Rufus lectured. Rufus' first set of questions on the Metaphysics suggest that Rufus began by barely understanding what was going on. Such was his reliance on Ibn Rushd that Renee Gauthier rightly referred to Rufus and his contemporaries as the first Western Averroists.

However, unlike Albert the Great and Thomas Aquinas, who defended as much of Aristotle and Averroes (Ibn Rushd) as they could, Richard Rufus responded ever more critically to Aristotle and his commentator. Still, our presentation begins by explaining why Richard Rufus endorses Aristotle's claim that universals are not substances and why Rufus thinks Aristotle could have been accused of lying when he said that a universal was predicated of many. Rufus defends Aristotle on the grounds that he was not talking about the universal forms we know but about the universal forms that actualize extramental composites. But though mental universals are ontologically different from extramental universals, they are not essentially different from the substances we know when our thoughts are actualized by the corresponding mental universals. More relevant to Aristotelian universals, Rufus held that though an incompletely actualized species and the individuals which instantiate it are not numerically the same, they are essentially the same, which is why a species can be predicated of individuals.

Such considerations make Rufus' claims about weak identity basic to his theory of universals. Rufus' commitment to the concept of weak identity also helps to explain why he thought that an adequate theory of universals must include a theory of appellation & supposition that somewhat resembles modern theories of reference. This will be our first topic. It will be followed by a discussion of the problems that arise in Rufus' treatment of the claim that the beings of things exist. Finally we will try to shed some light on the relation between propositions and being-a-proposition that Rufus also considered fundamental to his theory of universals. And we may conclude that Rufus thought that, despite being truthful, Aristotle had good reason to worry about the liar paradox.

Herakles wrestling a triton
"Herakles Wrestling Triton"
From an Attic Greek Black-Figure Hydria
Attributed to the Roycroft Painter ca. 520-510 BCE
Indiana University Museum
Gift of Thomas T. Solley, 77.33

 

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