**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 (15-20 pp.). 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 are available in electronic form through*CourseWorks*, section*Class Files*, folder*Shared Files*. See 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*, section*Class Files*, folder*Shared Files*. See Syllabus for details.**Events (G9610)**

*General Description.*In the last four 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.**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 letter grade, the requirements are regular and active participation, a short seminar presentation, and a final paper (approximately 15 pages).

*Readings.*All readings, primary and supplemental, will be made available in electronic form through*CourseWorks*. See 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.*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.**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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**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*).

*Text.*All readings, primary and supplemental, will be made available in electronic form through*CourseWorks*. See 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.

*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.**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.*One term of formal logic (V3411/G4415,*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,*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,*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,*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,*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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**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.

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