Achille C. Varzi

Teaching

1. Seminars
2. Graduate Courses
3. Undergraduate Courses

1. Seminars

• Seminar on Events (G9610)
  General Description. In the last three decades, the view that events are part of our basic conceptual scheme has been the focus of an extensive debate in philosophy, with implications reaching far into the concern of other disciplines as well (above all linguistics and cognitive science). It is a view that many authors have accepted, mostly on account of the prominent role played by the concept of event in the formulation and the analysis of a wide variety of philosophical issues. However, there has not been much agreement as to the precise nature of such entities, and a wide range of alternative theories have been put forward. The aim of this course is to set up the main coordinates for a critical examination of these theories, paving the way to an understanding of the role played by events in our representation of the world.
  The focus will be on the following main issues: (i) the role of events in the logical and semantic analysis of natural language; (ii) the metaphysical status of events; (iii) their identity and individuation criteria; (iv) the distinction and classification of various types of events and event-like entities (such as processes and states, and perhaps facts); (v) their role in the analysis of action, causality, 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).
  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 Syllabus for details.

• Seminar on Formal Ontology (G9509)
  General Description. This seminar examines the hypothesis that mereology (the study of the relations between parts and wholes) and topology (understood as the study of the qualitative relations of connection and compactness) jointly provide a fundamental framework for the formal-ontological analysis of the objects of ordinary experience.
  The seminar begins by reviewing classical extensional part-whole theories (Lesniewskian Mereologies, the Calculus of Individuals, recent formulations): this serves the twofold purpose of introducing the main concepts and principles and of displaying the main limits of pure extensional mereology. The rest of the seminar looks at two major lines of development. The first goes in the direction of intensional mereology: this includes a study of modal and temporal part-whole relations as well as of related notions such as, for instance, the relation of ontological dependence. (Questions to be addressed include: Is an object the mere sum of its parts? Is there an object corresponding to any arbitrary sum of parts? Are any parts essential to the whole? Could the parts exist without the whole? Could an object have different parts from the ones it actually has?). The second line of development exploits the view that, independently of how exactly those questions are answered, a mereological theory must be supplemented with concepts and principles of a topological nature if it is to provide a sufficient framework for formal-ontology: mereology is a theory of parthood, and one need step into the territory of topology to account for the property of wholeness. How exactly these territories are related, and how the underlying principles should interact with one another, is still a rather unexplored issue.
  Eventually, the seminar’s aim is to give a good picture of the prospects (or limits) of a unified theory of parts and wholes broadly describable as "intensional mereotopology".
  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 a willingness to work at a certain level of abstraction and rigor).
  Readings. The two main readings are Material Constitution: A Reader, by M. Rea (Rowman & Littlefield, 1997), and Parts and Places: The Structures of Spatial Representation, by R. Casati and A. C. Varzi (MIT Press, 1999). Additional readings include chapters from Parts. A Study in Ontology, by P. Simons (Oxford, Clarendon, 1987), and Holes and Other Superficialities, by R. Casati and A. C. Varzi (MIT Press, 1994). See Syllabus for details.

• Seminar on 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. Symbolic logic is a prerequisite, as well as a graduate course in the philosophy of language or the philosophy of logic. 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, Horwich, Kripke, McDowell, Putnam, Russell, Strawson, Tarski, Wright, and others. See Syllabus for details.

• Seminar on Vagueness (G9525) (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. This is an advanced graduate seminar. Familiarity with formal logic and a background in the philosophy of language will be presupposed.
  Readings. Works by Black, Dummett, Evans, Fine, Kamp, Lewis, 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 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 Syllabus for details.

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2. Graduate Courses

• 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.
  Text. 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 Syllabus for details.

• 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. One term of formal logic (V3411/G4415, Introduction to Symbolic Logic, or G4801, Mathematical Logic) and a willingness to master technicalities and to work at a certain level of abstraction.
  Text. The text for this course is Y. N. Moschovakis’s Notes on Set Theory (Springer-Verlag, 1994). See 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. One term of formal logic (V3411/G4415, Introduction to Symbolic Logic, or G4801, Mathematical Logic) and a willingness to master technicalities and to work at a certain level of abstraction.
  Texts. 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 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 (as studied e.g. in the prerequisite course V3411/G4415, Introduction to Symbolic Logic). 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. One term of formal logic (V3411/G4415, Introduction to Symbolic Logic, or G4801, Mathematical Logic) and a willingness to master technicalities and to work at a certain level of abstraction.
  Texts. 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 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 (as studied e.g. in the prerequisite course V3411/G4415, Introduction to Symbolic 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. The course is technically self-contained and a background in mathematics is not required (except for some familiarity with normal everyday set-theoretic apparatus). However, a willingness to master technicalities and to work at a certain level of abstraction and rigor is essential.
  Text. The text for the course is H. B. Enderton’s A Mathematical Introduction to Logic (Academic Press, 1972). See Syllabus for details.

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3. Undergraduate Courses

• Introduction to Symbolic Logic (V3411/G4415)
  General Description. This course is designed as an advanced introduction to classical sentential and predicate logic.
  Prerequisites. The course is self-contained and carries no prerequisites. Nonetheless, a willingness to master technicalities and to work at a certain level of abstraction is desirable.
  Text. The text for this course is H. Gaifman’s A Course in Symbolic Logic. This book is not yet in print; bound copies of a draft version may be purchased at the Village Copier shop on 2872 Broadway (between 111th and 112th St.), phone: 212-666-0600. See Syllabus for details.

• Metaphysics (V3601)
  General Description. An advanced introduction to some major topics in metaphysics: existence, identity, the nature of attributes, the nature of concrete particulars, persistence through time, indeterminacy, modality, causation, determinism. Readings from contemporary authors.
  Prerequisites. The course is self-contained. There are no prerequisites except for some familiarity with the methods of analytic philosophy.
  Texts. The main text for the course is M. L. Loux, Metaphysics: A Contemporary Introduction (Third Edition), London, Routledge, 2006. Additional readings from M. L. Loux (ed.), Metaphysics: Contemporary Readings, London, Routledge, 2001. See Syllabus for details.

• Elementary Logic (F1401)
  General Description. This course aims to provide an introductory grounding in the concepts and methods of modern logic, with emphasis on its significance for the analysis of meaning and the appraisal of complex patterns of reasoning.
  Prerequisites. The level is elementary. There are no prerequisites.
  Text. J. Nolt, D. Rohatyn, and A. C. Varzi, Logic, Second Edition, New York, McGraw-Hill (Schaum’s Outline Series), 1998. See Syllabus for details.