Achille C. Varzi

Teaching

1. Seminars
2. Graduate Courses
3. Undergraduate Courses

1. Seminars

• Topics in Metaphysics (G9515): On What Is Not (co-taught with Graham Priest)
  General Description. It seems clear that in some sense the world contains things that are: people and planets, societies and works of art, and maybe numbers and other abstract objects. Many philosophers have held that it contains, equally, things that are not. But if they are not, how can such things be in the world? Indeed, does the notion of something that is not even make sense? This seminar will investigate. Some of the topics and philosophers we may meet include: Plato on non-being; non-existent objects (Meinong); negative facts (Russell); omissions, absences, and our perception thereof (Sartre, Nyāyā philosophers); nothingness (Heidegger, Nishida); holes, silences, pauses; negative epistemic states; the empty world, the null mereological individual—and what-not.
  Requirements. The first class will be an introduction; the last class will be a wind-up. For the other classes, students are expected to do the required reading in advance and come along prepared to discuss it. The final grade for the course will be determined by a term paper on a topic to be approved in advance.
  Readings. All readings will be distributed in electronic form. See sample Syllabus for details.

• Topics in Metaphysics (G9515): Boundaries
  General Description. There is a basic distinction, in geography, between "natural" boundaries (borders, frontiers) and "artificial" ones. The former are just the physical boundaries of old, such as mountain ranges, coastlines, river banks, etc. The latter are exemplified especially by boundaries induced through human decisions and conventions and lie skew to any physical differentiations in the underlying territory, as with the frontier between Mexico and the United States, the borders of Wyoming, or the imaginary lines separating the US portion of Lake Erie from the Canadian portion. As we shall see, there is a lot to be said about the important role of this distinction in the history and dynamics of our political culture. But we can say more. For boundaries are not a prerogative of geography. They are at work in articulating every aspect of the world around us. Boundaries stand out in every map we draw, from the contents of perception to the scientific modeling of reality in terms of objects, kinds, and properties, and this ubiquity of boundaries goes hand in hand with the natural/artificial opposition. Indeed, once the opposition has been recognized, it can be drawn across the board: not merely in relation to boundaries but also in relation to those entities that have boundaries. If something enjoys a natural boundary, its existence and identity conditions appear to be independent of us; it is a bona fide, mind-independent entity of its own. By contrast, if its boundary is of the artificial sort, then the entity itself is to some degree a fiat entity, a construct, a product of our worldmaking. In short, the natural/artificial distinction betokens the general opposition between what is found or discovered and what is made or created, and this takes us straight to the metaphysical debate between realism and antirealism. Here we shall be especially interested in the antirealist stance corresponding to the limit case: What if there were no natural boundaries? What if all boundaries—hence all entities—were on closer look and to some extent the result of a fiat articulation reflecting our cognitive biases and our social practices and conventions?
  Requirements. E-credit (letter grade): Active participation + a short seminar presentation + a final paper; R-credit: Active participation + a short seminar presentation.
  Readings. All readings, primary and supplemental, will be made available in electronic form through CourseWorks. See sample Syllabus for details.

• Topics in Metaphysics (G9515): Nominalism
  General Description. Nominalism comes in at least two varieties. In one of them, it is the rejection of universals: at bottom, there are just particulars. In the other, it is the rejection of abstract entities: at bottom, everything is concrete. This seminar will examine the motivations behind these two varieties of nominalism and the main strategies available to their supporters to resist the challenges and indispensability arguments raised by their opponents.
  Requirements. E-credit (letter grade): Active participation + a short seminar presentation + a final paper; R-credit: Active participation + a short seminar presentation.
  Readings. All readings, primary and supplemental, will be made available in electronic form through CourseWorks. See sample Syllabus for details.

• Topics in Metaphysics (G9515): Mereology
  General Description. Is a whole something more than the sum of its parts? Are there things composed of the same parts? If you divide an object into parts, and divide those parts into smaller parts, will this process ever come to an end? Can something lose parts or gain new ones without ceasing to be the thing it is? Does any multitude of things (including disparate things such as you, this book, and the tail of a cat) compose a whole of some sort? Questions such as these have occupied us for at least as long as philosophy has existed. They define the field that has come to be known as mereology—the study of all relations of part to whole and of part to part within a whole—and have deep and far-reaching ramifications in metaphysics as well as in logic, the foundations of mathematics, the philosophy of language, the philosophy of science, and beyond. This seminar will aim to provide a comcomprehensive, up-to-date, and formally rigorous picture of this important and ever-evolving field of inquiry. The first part will cover the more classical aspects of mereology; the rest of the seminar will deal with variants and extensions.
  Requirements. E-credit (letter grade): Active participation + a short seminar presentation + a final paper; R-credit: Active participation + a short seminar presentation.
  Readings. The seminar will be structured around a book in progress: Mereology, by A. J. Cotnoir and A. C. Varzi. Additional readings, primary and supplemental, will be made available as the semester progresses. See sample Syllabus for details.

• Ontology of the Arts (G9509) (co-taught with Lydia Goehr)
  General Description. What is Art? What sort of thing is a Work of Art—a physical object, an event, ideal kind, imaginary entity, platonic form? Is there just one kind of WoA or are there subtantive ontological differences between, say, paintings, sculptures, and musical works? How is art bounded by time and space? What would a geography of art look like? Do aesthetic or artistic differences make an ontological difference? How are WoAs related to the mental states and/or intentions of artists, critics, audiences? What role does interpretation and description play in determining the meaning or essence of art? What criteria of identity and individuation are relevant to WoAs? Under what conditions do WoAs come into existence, survive, or cease to exist? How do history and convention affect their ontology? What are hybrid arts or mixed-media artworks?
  Requirements. Reading is essential; discussion is expected and will determine a significant part of the grade. For E-credit (letter grade) students, one final essay is due in the last week of classes. Topics should be approved in advance and ideally by mid-term. R-credit students are required to attend all classes and participate in a lively manner.
  Readings. The readings, primary and supplemental, are drawn from classic and contemporary literature of the analytic tradition and with a special emphasis on music. All readings will be made available in electronic form through CourseWorks. See sample Syllabus for details.

• Topics in Medieval Metaphysics (G9172) (co-taught with Wolfgang Mann)
  General Description. This seminar will focus on selected topics central to the metaphysical thought of Western medieval philosophers, with special emphasis on those issues that bear relevance to the work of contemporary metaphysicians. We will spend roughly the first five weeks on the ‘logical’ (i.e., the logico-semantic) framework in which the issues are framed and debated, via a reading of Paul V. Spade’s Thoughts, Words and Things, supplemented with Fridugisus of Tours’s Letter on the Being of Nothing and Shadows, as well as extensive selections from Parts I and II of William of Ockham’s Summa Logicae, from the "Longer Treatise" of Walter Burley’s De Puritate Artis Logicae, and from Jean Buridan’s Summulae de Dialectica. Topics to be covered include: the kinds of terms, the kinds of suppositio of terms, the so-called predicables (genus, species, differentia, proprium, and accident), the referents of syncategorematic expressions (like ‘something’ and ‘nothing’), the kinds of propositions, the truth conditions for propositions, modal and tensed propositions, and propositions with non-referring expressions. The rest of the term will then be devoted to considering a number of specific metaphysical quaestiones, with a view both to becoming clear about the underlying principles relied on in the argumentation (pro and contra) and to assessing the cogency of those arguments. Among the topics addressed by such quaestiones are: existence vs. essence, simple vs. composite and material vs. immaterial substances, Divine simplicity, causation, motion, the problem of universals, the theory of location, the structure of space. For primary texts, we will rely on selected portions of Henry of Harclay’s Ordinary Questions and Ockham’s Quodlibetal Questions. We might also consider some questions from Buridan’s In Metaphysicen [sic] Aristotelis, which we will translate ourselves.
  Requirements. The seminar presupposes some familiarity with metaphysics and some acquaintance with elementary logical notions and techniques. For R-credit, the requirements are: (i) regular attendance and participation in class, and (ii) keeping up with the readings. For E-credit (letter grade), the requirements are: (i) regular attendance and participation in class, (ii) keeping up with the readings, and (iii) either one long paper (c. 20 pp.) or two shorter papers (c. 8 pp. and 12 pp.).
  Readings. All readings, primary and supplemental, will be made available in electronic form through CourseWorks. See sample Syllabus for details.

• Events (G9610)
  General Description. Reference to events—things that happen or occur, such as Brutus’s stabbing of Caesar or Alf’s falling in love with Beth—is a pervasive feature of human thought and language. Moreover, the event concept plays a dominant role in the formulation and analysis of a wide variety of philosophical issues, such as causation, the mind-body problem, or the nature of time. The aim of this seminar is to set up the main coordinates for an understanding of this concept and for a critical assessment of its philosophical implications and applications. Topics to be discussed include: arguments pro or against the inclusion of events in one’s ontology; the role of events in the logical and semantic analysis of natural language; their metaphysical status; their identity and individuation criteria; the distinction and classification of various types of events and event-like entities (such as processes and states, and perhaps facts); their role in the philosophy of action and causation; their role in the philosophy of space and time.
  Requirements. This is an advanced graduate seminar. It presupposes some familiarity with the use of formal methods in analytic philosophy. No specific background is required, except for some acquaintance with elementary logical notions (and a willingness to work at a certain level of abstraction and rigor). There is no specific requirement for R-credit, except for regular and active participation. For E-credit (letter grade), the requirements are regular and active participation, a short seminar presentation, and a final paper.
  Readings. Readings from Davidson, Chisholm, Kim, Quine, M. Brand, Anscombe, A. Goldman, Hacker, Vendler, J. Bennett, T. Parsons, J. J. Thomson, and others. Most of these works are reprinted in the anthology by R. Casati and A. C. Varzi, entitled Events (Aldershot: Dartmouth Publishing, 1996). See sample Syllabus for details.

• Formal Ontology (G9509)
  General Description. There are two main ways, philosophically, of characterizing the business of ontology, and it is good practice to try and keep them separate. On one account, made popular by Quine, ontology is concerned with the question of what there is. The other way of characterizing ontology stems from a different concern, and made its way into our times through Brentano and his pupils. On this second account, the task of ontology is not to specify what there is but, rather, to lay bare the formal structure of all there is, whatever it is. Regardless of whether our domain of quantification includes universals along with particulars, abstract entities along with concrete ones, and so on, it must exhibit some general features and obey some general laws, and the task of ontology would be to figure out such features and laws. For instance, it would pertain to the task of ontology to assert that every entity, no matter what it is, is self-identical, or that no entity can consist of a single proper part, or that some entity can depend on another only if the latter does not depend on the former. More generally, it would pertain to the task of ontology to work out a general theory of such formal relations as identity, parthood, dependence—what Husserl called a pure theory of objects as such, if not a theory of being qua being in Aristotle’s sense. And the truths of the theory would possess the same sort of generality and topic-neutrality that characterizes the truths of logic. They would hold as a matter of necessity and should be discovered a priori. Following common usage, we may speak of material ontology and formal ontology, respectively, to fix the distinction. The focus of this seminar is mainly with the latter. And within the broad domain of formal ontology, we shall focus especially on two main chapters: (1) the general theory of identity; (2) the formal theory of parthood (or “mereology”), i.e., the theory of the relations of part to whole and the relations of part to part within a whole.
  Requirements. This is an advanced graduate seminar. It presupposes some familiarity with the use of formal methods in analytic metaphysics. No specific background is required, except for some acquaintance with elementary logical notions and techniques. There is no specific requirement for R-credit, except for regular and active participation. For E-credit (letter grade), the requirements are regular and active participation, a short seminar presentation, and a final paper.
  Readings. All readings, primary and supplemental, will be made available in electronic form through CourseWorks. See sample Syllabus for details.

• Truth (G9531) (co-taught with Haim Gaifman)
  General Description. This seminar will survey the main philosophical theories of truth and the connections of truth and meaning, and truth and realism. Among the topics to be covered are: the correspondence theory, minimalist theories, Tarski’s "semantic conception of truth", the prosentential theory, truth and meaning in Davidson and Dummett, the semantical paradoxes, the linguistic hierarchy, various solutions to the paradoxes.
  Requirements. Familiarity with formal logic and a background in the philosophy of language will be presupposed. The course will be run as a seminar and students are encouraged to participate actively, including class presentations.
  Readings. Readings will cover works by Austin, Davidson, Dummett, Field, Grover, Haack, Hornsby, Horwich, Kripke, McDowell, Misak, Putnam, Russell, Strawson, Tarski, Wright, and others. See sample Syllabus for details.

• Vagueness (G9525) (occasionally co-taught with Haim Gaifman)
  General Description. A comprehensive examination of the main issues raised by the phenomenon of vagueness in logic, metaphysics, and the philosophy of language. Topics include: semantic vagueness, vagueness in the world, vagueness and perception, the logic of vagueness, higher-order vagueness. Critical appraisal of various competing theories, including: semanticism, epistemicism, intuitionism, fuzzy-logicism, supervaluationism, pragmatism, nihilism.
  Requirements. Familiarity with formal logic and a background in the philosophy of language will be presupposed. The course will be run as a seminar and students are encouraged to participate actively, including class presentations.
  Readings. Works by Black, Dummett, Edgington, Evans, Fine, Graff Fara, Kamp, Keefe, Lewis, Raffman, Russell, Sainsbury, Sorensen, Tye, Williamson, Wright, and others. Some of these works are reprinted in Vagueness: A Reader, edited by R. Keefe and P. Smith (Cambridge, MA, and London: MIT Press, 1997). See sample Syllabus for details.

• Mind, Brain, and Space (G4485) (co-taught with Michele Miozzo)
  General Description. There are brain-damaged patients who systematically exchange the left and right parts of the objects with which they interact. Other patients can see only one half of the objects, or can only eat from one half of the plate. Neuroscientists believe that cases such as these can help us understand how the brain represents the space around us—the space in which we live and move and in which we locate ordinary objects and events. Philosophers, on the other hand, view the representation of space as a privileged entry point into the study of the external world. Different objects occupy different places and different parts of an object are spatially related to the whole, but where do these spatial properties come from? If nothing existed except a single hand, would it have to be either a left hand or a right hand? If not, what would explain the difference between that world and its mirror image? And why do mirrors reverse left/right but not up/down? The aim of this seminar is to bring together these neuroscientific and philosophical perspectives in a joint effort to better understand the two sides of space—its inner representation in the brain and its outer realization in the objects around us.
  Requirements. The final grade will be determined on the basis of (a) class participation (10%), (b) a short paper (3-5 pages) to be presented during one of the three discussion sessions (30%); (c) a final paper (60%).
  Readings. All required readings are collected in a packet available in the Psychology Department Library, 409 Schermerhorn Hall. See sample Syllabus for details.

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2. Graduate Courses

• History of Logic: From De Morgan to Frege (G4451) (co-taught with Souleymane Bachir Diagne)
  General Description. The roots of logic may be traced to Aristotle, who systematized and codified the subject in a way that was not significantly surpassed for over two millennia. Logic was revived in the mid-nineteenth century, at the beginning of a revolutionary period when the subject developed into a rigorous discipline whose exemplar was the exact method of proof used in mathematics. The development of so-called “symbolic” or “mathematical” logic during this period is the most significant in the two-thousand-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history. The aim of this course is to provide a critical reconstruction of such a development along with an assessment of its philosophical significance. After some general background devoted to the history of the subject from Aristotle to Leibniz and beyond, the course will focus on the work of such logicians as Augustus De Morgan, George Boole, William Jevons, John Venn, and Ernst Schröder, which may be seen collectively as setting the stage for the definitive step in the revolution that resulted in logic as we know it today—Gottlob Frege’s Begriffsschrift.
  Prerequisites. One term of formal logic (V3411/G4415, Symbolic Logic, or G4801, Mathematical Logic).
  Readings. All readings, primary and supplemental, will be made available in electronic form through CourseWorks. See sample Syllabus for details.

• Philosophy of Language (W4481)
  General Description. This course aims to provide an introduction to some major topics and issues in contemporary philosophy of language. Most of these center around the notion of meaning: What are the ingredients of meaning? How does the meaning of an expression contribute to the meaning of a sentence containing it? What is involved in understanding the meaning of what is said? What form should be taken by a theory of meaning for a specific language? The first part (weeks 2-5) will focus especially on the interplay between meaning and reference. This will take us through the work of the early authors (Mill, Frege, Russell, Carnap) up to the recent debate on the causal theory of reference (Donnellan, Kripke, Putnam). The second part (weeks 7-10) will focus on the interplay between meaning and truth and will cover such topics as the indeterminacy of translation (Quine), the nature of interpretation, holism, realism and antirealism (Dummett). These are topics that lie at the core of the programmes of such authors as Tarski, Quine, Davidson, and Dummett. Finally, in the third part (weeks 11-13), we shall consider some aspects of the interplay between meaning and use, focusing on the theory of speech acts (Austin, Grice, Searle) and the nature of linguistic rules and conventions (Wittgenstein, Chomsky, Lewis).
  Prerequisites. This is an introductory course and presupposes no previous acquaintance with the field. It is not, however, an elementary course, since some of the topics are difficult and the issues reach far and deep into other areas of philosophy, such as logic, the philosophy of mind, epistemology, metaphysics. Familiarity with some of these areas will be of help.
  Readings. Most of the required readings are available in A. P. Martinich’s anthology, The Philosophy of Language (Third Edition, Oxford University Press, 1996). The other required readings are collected in a packet that can be bought at the Philosophy Department. See sample Syllabus for details.

• Symbolic Logic (G4415)
  See below, Symbolic Logic (V3411/G4415)
  

• Set Theory (W4431)
  General Description. Set theory is the foundation of mathematics: all mathematical concepts can be characterized in terms of the primitive notions of set and membership. (Some would go as far as saying that all rigorous concepts—whether belonging to mathematics or to other disciplines—should be so characterizable.) But set theory is also a branch of mathematics, with its own subject matter, basic results, open problems. The aim of this course is to give a general introduction to both aspects, with an eye for the unifying philosophical issues that lie behind them. The first part focuses on the question of providing an axiomatic formulation of set theory. The specific axiom system to be examined is a version of ZAC, Zermelo set theory with the Axiom of Choice, eventually supplemented with Fraenkel’s Axiom of Replacement (ZFAC). In the second part, the strength of theory is tested and applied: topics covered include the natural numbers, well-ordered sets, transfinite induction and recursion, fixed point theorems, infinite cardinal and ordinal arithmetic. The final part of the course is devoted to questions of consistency and relative independence. Natural models of various set-theoretic principles are studied and, if time permits, compared some non-standard set universes, including Aczel’s "antifounded universe".
  Prerequisites. Symbolic Logic (V3411/G4415) or Mathematical Logic (G4801).
  Readings. The text for this course is Y. N. Moschovakis’s Notes on Set Theory (Springer-Verlag, 1994). See sample Syllabus for details.

• Modal Logic (G4424)
  General Description. This course has two main aims. One is to explain what modal logic is, and how it is done. The other is to give a detailed survey of the large variety of modal logic systems found in the literature, with an eye to both their formal properties (consistency, completeness, decidability) and their philosophical significance. The focus is on modal sentential logic, i.e., the modal logic of a language whose atomic constituents are either unanalyzed sentences or logical connectives. If time permits, some aspects of modal predicate logic (whether, how far, and in what ways various properties of sentential modal logics carry over to their predicate logic counterparts) are addressed in the final part of the course.
  Prerequisites. Symbolic Logic (V3411/G4415) or Mathematical Logic (G4801).
  Readings. The main text for this course is B. Chellas’ Modal Logic. An Introduction (Cambridge University Press, 1980). This is a rather technical, dense book, and some might want to integrate it with G. E. Hughes and M. J. Cresswell’s classic, A New Introduction to Modal Logic (Routledge, 1996). Further suggested readings are indicated as the course develops. The last part of the course is based mostly on lecture notes. See sample Syllabus for details.

• Non-classical Logics (W4137)
  General Description. An introductory survey of the main alternatives to classical logic, i.e., theories that deviate from the classical account of logical validity. The focus is on theories that depart from classical logic with regard to the principle of bivalence (every statement is either true or false) or to the principle of non-contradiction (no statement is both true and false), or both—including sentential and predicate versions of many-valued logics, fuzzy logics, partial logics, free logics, inclusive logics, and paraconsistent logics. Details of the semantics and proof-theories of these logics are considered along with the relevant philosophical motivations.
  Prerequisites. Symbolic Logic (V3411/G4415) or Mathematical Logic (G4801).
  Readings. There is no textbook for this class. Instead, required readings are assigned for each session and lecture notes made available through the course website. See sample Syllabus for details.

• Mathematical Logic (G4801)
  General Description. This course will study, from a metalogical perspective, the concepts and principles that form the basis of classical elementary logic. The focus will be on the interplay between semantic (model-theoretic) and syntactic (proof-theoretic) properties of classical sentential and quantificational logic, up to Gödel’s and Henkin’s completeness theorems and related results.
  Prerequisites. Symbolic Logic (V3411/G4415) or equivalent.
  Readings. The text for the course is H. B. Enderton’s A Mathematical Introduction to Logic (Academic Press, 1972). See sample Syllabus for details.