- Non-classical Logics (G4137)
Professor : Achille Varzi
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.
- Modal Logic (G4424)
Professor : Haim Gaifman or Achille Varzi
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. - Set Theory (G4431)
Professor : Haim Gaifman or Achille Varzi
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”. - Philosophy of Logic (G4450)
Professor : Haim Gaifman
Description : Topics in philosophical semantics, such as the relation of formal logic and natural language, sense and reference, semantical paradoxes, the nature of logical truth, and modal and intensional notions. - Philosophy of Mathematics (G4451)
Professor : Haim Gaifman - Probability and Decision Theory (G4561)
Professor : John Collins or Haim Gaifman or Jeffery Helzner
Description : Our focus in this course will be on a group of topics – e.g., probability and utility — that emerge naturally from the study of rational choice. It is perhaps not too much of a stretch to view a majority of the most interesting human activities as instances of rational choice. In light of this it should come as no surprise that many of the topics that we will consider are also discussed at length in other subjects such as economics, psychology, and statistics. Despite this apparent overlap, our concern with these topics will be a bit different from what is typical in the context of these other disciplines. For example, it is often maintained that scientists are concerned primarily with explaining or predicting facts. On this view the study of rational choice is of interest to economists and psychologists to the extent that it allows such scientists to explain or predict psychologically or economically relevant facts. In contrast, our interest in rational choice will be mostly foundational in the sense that our ultimate goal is to understand the structure of (and relations between) the concepts that are presupposed in such applications. - Rational Choice (G4565)
Professor : John Collins or Haim Gaifman or Jeffery Helzner
Description : Examines the criteria for rational choice, primarily focused on individual decision making, with some attention to collective decision making. Discusses concepts of probability, belief, and value employed in formulating principles of choice. Considers such principles as maximization of expected utility, minimal loss and regret, and maximum and optimism-pessimism and their relevance to moral and political decision is also considered. - Mathematical Logic I (G4801)
Professor : Haim Gaifman or Jeffery Helzner or Achille Varzi
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. - Mathematical Logic II (G4802)
Professor : Haim Gaifman
Description : The course will focus on Gödel’s incomplete results and related topics.
*The above is an incomplete list of courses, the course descriptions are taken from the professors who offered the course.