Research Statement Phil Corkum, University of Alberta October 2011
My current research is on Aristotle’s metaontology and metaphysics of properties. I ascribe to Aristotle the view that universals are mereological sums of individuals. The relationship holding between a universal and its particular instances is then the distinctive ontological dependence relationship holding between a whole and its parts: namely, constitution. The research has significance for our understanding of Aristotle’s semantics and philosophy of logic as well as the history of metaphysics.
The work emerges from my “Aristotle on Ontological Dependence” Phronesis
2008, where I argue that ontological independence in Aristotle is not a capacity for separate existence.1 In the Phronesis article, I hint that there is not a single notion of ontological dependency in Aristotle but a variety of notions, and much of my subsequent work might be seen as cashing out this teaser. For example, “Attention, Perception and
Thought in Aristotle,” Dialogue 2010, concerns in part the independence ascribed to the soul. Aristotle holds that there are individuals and universals in both substantial and such non-substance categories as quality and quantity. “Aristotle on Non- substantial Individuals,” Ancient Philosophy 2009 and “Aristotle on Mathematical
Truth,” British Journal for the History of Philosophy forthcoming, concern the cross- categorical dependency tie obtaining between a substance and an item in a non-substance category. My most recent work concerns the infra-categorical tie obtaining between a universal and an individual.
In my “Aristotle on Predication,” under review,2 I hold off identifying universals with mereological sums of individuals and argue for the weaker claim that a mereological Research Statement Phil Corkum, University of Alberta October 2011
sum is the contribution a universal term makes to the conditions under which any sentence containing that term expresses a true thought. The relevant mereological relation is what became known as the quantitative part-whole relation, and there's textual evidence to characterize the quantitative mereology as a proper part mereology
(irreflexive, transitive, weakly supplementary). The ascription sheds light on such aspects of Aristotle's philosophy of language as the existential import of universal affirmations, quantification and negation, and other issues. I discuss the first of these consequences in
“Existential Import in Aristotle,” currently in draft form.
I also discuss Aristotle’s philosophy of logic and related issues in the philosophy of logic. In “Aristotle on Logical Consequence,” under review,3 I argue in that Aristotle provides an account of logical consequence in terms of mereological principles such as the transitivity of containment, and compare this project to the contemporary model theoretic definition of logical consequence as truth preservation in all models. In recent scholarship, the syllogistic tends to be assimilated to one or other of two paradigms, a paradigmatic theory such as an axiomatic system, or a paradigmatic logic such as a natural deduction system. In “Is the Syllogistic a Logic?” under review,4 I argue that the syllogistic exhibits some of the features of a pardigmatic theory and some of the features of a paradigmatic logic.
The research will be developed along two lines. I will develop an interpretation of
Aristotle’s metaontology. Aristotle’s view that there are several distinct and irreducible kinds of ties of dependency among entities within distinct categories resembles Research Statement Phil Corkum, University of Alberta October 2011
contemporary ontological pluralism. Unlike pluralists such as McDaniels and Turner,
Aristotle’s pluralism is not the claim that ‘there exists’ refers ambigously to various existential quantifiers with distinct domains. So Aristotle provides a framework for discussing ontology that rivals the currently dominant Quinean framework, under which questions of ontology concern quantifier domains. Schaffer (2009) draws on my (2008) to defend the characterization of this rival approach to ontology as ‘Aristotelian’.5 I will assess the historical accuracy of this characterization.
Secondly, I will test the hypothesis that universals are identical with mereological sums of individuals. I will discuss the metaphysics of universals as mereological sums, argue for the ascription of the position to Aristotle, and compare the position to
Aristotelian realism, class nominalism and other positions in the metaphysics of properties. If I am correct that the tie between individuals and universals is a proper part relation, then as an irreflexive and transitive relation, the tie is a strict partial order. And so the ties among individuals and universals impose considerable structure on the world. I will test the conjecture that this the work Aristotle intends for universals. Aristotle has little interest in the so-called problem of universals (to explain attribute agreement) or
Lewis’ new work (joint-carving). Rather, he aims to reveal ontological structure. Such structure is the content of scientific understanding and is perspicuously represented by demonstrations in the Posterior Analytics.
1 I expand on Aristotle’s views on substance and ontological independence in an invited contribution to Ontological Dependence, Supervenience, and Response-Dependence, edd. Research Statement Phil Corkum, University of Alberta October 2011
Schnieder, Steinberg and Hoeltje, Basic Philosophical Concepts Series, Philosophia Verlag (Munich), forthcoming. I discuss a recent rival proposal in the commissioned “Critical Notice of Michail Peramatzis, Priority in Aristotle’s Metaphysics” Canadian Journal of Philosophy. 2 Abstract. It is a commonplace today to distinguish predications and identity claims and existence claims. Under a standard interpretation, Aristotle conflates these three. I argue that predications for Aristotle are distinct from, but related to, both identity and existence claims. In “Aristotle on Predication,” I discuss predication and identity claims. Some ascribe to Aristotle the view that, if both subjects and predicates refer, then a sentence is true if the subject and predicate name one and the same thing. Since there is evidence that predicates refer, this view suggests that predications are for Aristotle identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle’s core semantic notion is not identity but the weaker relation of constitution: for example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle’s view, just in case the mereological sum of humans is a part of the mereological sum of mortals. In “Existential Import in Aristotle,” I discuss predication and existence claims. True universal affirmations entail existence claims for Aristotle: the truth of ‘All men are mortal’ entails that there is at least one man. This surprising entailment and other unusual features of Aristotle’s semantics have led many to ascribe to Aristotle a unitary semantic notion underwriting both predications and existence claims. I will argue that the mereological interpretation of Aristotle’s semantics offered in this paper provides a pleasing explanation of these features without charging Aristotle with the conflation of predications and existence claims. 3 Abstract. Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception of logical consequence to the topic- neutral conception. Such a project would dispel the alleged obscurity of the notion of necessity employed in the modal conception in favour of the clarity of an account of logical consequence given in terms of tractable notions of logical form, universal generalization and truth simpliciter. In a series of publications, John Etchemendy has characterized the model-theoretic definition of logical consequence as truth preservation in all models as intended to provide just such an analysis. In this paper, I will argue that Aristotle intends to provide an account of a modal conception of logical consequence in topic-neutral terms and so is engaged in a project comparable to the one described above. That Aristotle would be engaged in this sort of project is controversial. Under the Research Statement Phil Corkum, University of Alberta October 2011
standard reading of the Prior Analytics, Aristotle does not and cannot provide an account of logical consequence. Rather, he must take the validity of the first figure syllogisms (such as the syllogism known by its medieval mnemonic ‘Barbara’: A belongs to all B; B belongs to all C; so A belongs to all C) as obvious and not needing justification; he then establishes the validity of the other syllogisms by showing that they stand in a suitable relation to the first figure syllogisms. I will argue that Aristotle does attempt to provide an account of logical consequence—namely, by appeal to certain mereological theorems. For example, he defends the status of Barbara as a syllogism by appeal to the transitivity of mereological containment. There are, as I will discuss, reasons to doubt the success of this account. But the attempt is not implausible given certain theses Aristotle holds in semantics, mereology, the theory of relations and metaphysics. 4 Abstract. Much of the last fifty years of scholarship on Aristotle’s syllogistic suggests a conceptual framework under which the syllogistic is a logic, a system of inferential reasoning, only if it is not a theory, a system concerned with general features of the world. In this paper, I will argue that this a misleading interpretative framework. The syllogistic is something sui generis: by our lights, it is neither clearly a logic, nor clearly a theory, but rather exhibits certain characteristic marks of logics and certain characteristic marks of theories. The debate between a theoretical and a logical interpretation of the syllogistic centers on the interpretation of syllogisms as either implications or inferences. But the significance of this question has been taken to concern the nature and subject-matter of the syllogistic, and how it ought to be represented by modern techniques. For one might think that, if syllogisms are implications, then the syllogistic is a theory concerned with general features of the world and so ought to be represented by an axiomatic system. On the other hand, if syllogisms are inferences, then the syllogistic is a logic, a system of inferential reasoning, and ought to be represented as a natural deduction system. I will argue that one can disentangle these questions and that we must if we are to have a historically accurate understanding of Aristotle. 5 J. Schaffer, “On What Grounds What,” Metametaphysics. edd. Chalmers, Manley and Wasserman. Oxford: OUP. 2009.