Josh Dever

This course examines the interaction between formal logic and the foundations of mathematics. We will take as our centerpiece a careful examination of some of the important results of set theory, including the paradoxes of naive set the- ory and the reformulation of set theory using the Zermelo-Frankel axioms, the development of the theory of infinite cardinals and ordinals in set theory, the formal details of the iterative conception of sets, and the basic methods of prov- ing independence results in set theory. We will couple this investigation with an examination of various results in the metatheory of first order logic that bear on the foundations of math, such as the completeness and compactness theorems, the Lo ?wenheim-Skolem theorems, and the Go ?del incompleteness theorems. 

The course focuses on various philosophical issues concerning language. Topics to be discussed include, but are not limited to, the following: speaker-meaning, conversational implicature, sentence/expression-meaning, reference, modality, and propositional attitude ascriptions. 

The course focuses on various philosophical issues concerning language. Topics to be discussed include, but are not limited to, the following: speaker-meaning, conversational implicature, sentence/expression-meaning, reference, modality, and propositional attitude ascriptions. 

This is a first course in deductive symbolic logic. We'll study formal languages for representing sentences
in logically precise ways, we'll study algorithms for evaluating arguments as logically valid or invalid, and
we'll get an introduction to some of the surprising discoveries logicians have made about what tasks no
algorithm can possibly do.

The course focuses on various philosophical issues concerning language. Topics to be discussed include, but are not limited to, the following: speaker-meaning, conversational implicature, sentence/expression-meaning, reference, modality, and propositional attitude ascriptions. 

Description: This class develops modal logic both as a device for better understanding the nature and boundaries of logic and as a tool with a wide variety of applications throughout philosophy. We examine Kripke frame semantics for modal logic, and the use of Kripke frames to characterize a family of modal logics. Applications of modal logic to deontic and epistemic reasoning are then explored, with a special focus on extensions to systems of dynamic epistemic logic for modelling group and interactive epistemology. We examine the role of modal logic in metaphysics, and in the logic of vagueness. We then consider the application of Kripke frame semantics to the characterization of non-classical logics such as intuitionistic and relevance logics.

Texts: Modal Logic (Blackburn, Venema, and de Riijke), and Logical Dynamics of Information and Interaction (van Benthem).

Grading Policy: Grades are based on a combination of four problem sets (50%), a midterm exam (20%), and a final exam (30%).

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This course is the required graduate logic seminar. The course will introduce students to a variety of issues in logic that are of importance for work across philosophy. Possible topics include: modal logic and systems of propositional modal logi;  quantified modal logic, de re and de dicto readings, possiblist and actualist quantifiers, and necessitism and contingentism; counterfactual conditionals; multi-valued logic; formal theories of truth including Kripke’s fixed-point construction and revision theories; supervaluationism and the semantics of vagueness; proof theory and Gentzen systems; intuitionistic logic; relevance logic and contradiction-friendly paraconsistent logics; systems of non-monotonic inference; generalized quantifier theory; Bayesianism, probabilistic decision theory, and game theory; social choice theory; and core results of classical first-order metatheory including completeness, compactness, and the Godel incompleteness results.

Grading

Grading will be based on periodic problem sets.

Texts

Readings will be made available as required.

This course is an introduction to the use of formal logical techniques in the analysis of arguments and texts, with an eye to the applicability of such formal techniques in the humanities, social sciences, and natural sciences. We will study formal propositional logic as a tool for extracting information from definite-information premises; modal logic as a tool for modeling reasoning situations involving multiple agents or information sources; probability and probabilistic decision theory as tools for reasoning under uncertainty; and game theory as a tool for making theoretical and practical decisions in multi-agent situations.

NEW TITLE: A Dozen Philosophical No-Go Theorems

Prerequisites

Graduate Standing and Consent of Graduate Advisor or instructor required.

Course Description

A Dozen Philosophical No-Go Theorems

Philosophical progress is often driven (and sometimes frustrated), by no-go or impossibility theorems showing that some pre-theoretically desirable situation cannot be obtained. The grandparent of all no-go theorems is perhaps the Liar paradox, or its formal realization in Tarski’s Undefinability Theorem, showing that a truth predicate with certain features can’t be obtained. In this seminar we will consider twelve philosophically important no-go theorems. One of the goals is simply to become familiar with the various theorems (some of which have been greatly underappreciated in the philosophical literature) and to think about both what escape routes might be available and what alternative paths might be explored if the no-go barrier survives testing. Another goal is to consider some common structural elements, themes, and philosophical sources that may underlie many of the no-go theorems collectively. (The genetic stamp of the Liar ancestor can be seen in several cases.) Finally, we’ll engage in some metaphilosophical reflection on the question of whether the very idea of a no-go theorem is philosophically applicable and philosophically profitable.

The planned list of no-go theorems is (with a very brief statement of each):

(1) Tarski’s undefinability theorem (a language cannot contain its own truth predicate)

(2) Godel’s first and second incompleteness theorem (a sufficiently rich theory must be incomplete and cannot prove its own completeness)

(3) Arrow’s theorem (a fair voting system inevitably creates a dictatorship)

(4) Lewis triviality theorem (a language assigning probabilities to conditionals must assign only probabilities of 0 and 1)

(5) Kaplan-Prior theorem (propositions cannot be modelled using possible worlds)

(6) Bell’s theorem (quantum behavior cannot be explained using hidden variables)

(7) Gardenfors’ triviality theorem (conditionals make belief change impossible)

(8) Arrhenius’ theorem (any population-level axiology is sadistic)

(9) Probabilistic gap theorem (no probability function assigning probabilities to all propositions)

(10) Gibbard-Satterthwaite theorem (dictatorship is the only non-manipulable social choice procedure)

(11) Third-order reflection theorem (certain natural reflection principles make set theory inconsistent when extended to a natural point)

(12) Williamson’s luminosity theorem (there can’t be a logical guarantee of introspective knowledge)

Grading Policy

Grade based on final seminar paper and class participation.

Texts

Various readings made available in the class.

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This course is the required graduate logic seminar. The course will introduce students to a variety of issues in logic that are of importance for work across philosophy. Possible topics include: modal logic and systems of propositional modal logi;  quantified modal logic, de re and de dicto readings, possiblist and actualist quantifiers, and necessitism and contingentism; counterfactual conditionals; multi-valued logic; formal theories of truth including Kripke’s fixed-point construction and revision theories; supervaluationism and the semantics of vagueness; proof theory and Gentzen systems; intuitionistic logic; relevance logic and contradiction-friendly paraconsistent logics; systems of non-monotonic inference; generalized quantifier theory; Bayesianism, probabilistic decision theory, and game theory; social choice theory; and core results of classical first-order metatheory including completeness, compactness, and the Godel incompleteness results.

Grading

Grading will be based on periodic problem sets.

Texts

Readings will be made available as required.

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This course is the required graduate logic seminar. The course will introduce students to a variety of issues in logic that are of importance for work across philosophy. Possible topics include: modal logic and systems of propositional modal logi;  quantified modal logic, de re and de dicto readings, possiblist and actualist quantifiers, and necessitism and contingentism; counterfactual conditionals; multi-valued logic; formal theories of truth including Kripke’s fixed-point construction and revision theories; supervaluationism and the semantics of vagueness; proof theory and Gentzen systems; intuitionistic logic; relevance logic and contradiction-friendly paraconsistent logics; systems of non-monotonic inference; generalized quantifier theory; Bayesianism, probabilistic decision theory, and game theory; social choice theory; and core results of classical first-order metatheory including completeness, compactness, and the Godel incompleteness results.

Grading

Grading will be based on periodic problem sets.

Texts

Readings will be made available as required.

TITLE: Philosophy of Game Theory

Prerequisites

Graduate standing and consent of Graduate Advisor or instructor required.

Course Description

Game theory is a rich area of formal tools developed over the last 70 years or so for the modelling of certain kinds of rational interaction. It can be thought of (not uncontroversially, but reasonably standardly) as an extension of probabilistic decision theory to cases involving negotiating with co-scheming agents. In this seminar, we will look at a number of major formal results in game theory. We will also consider several areas in which game theory has thought to play an important philosophical role. We will examine the question of whether game theory provides genuinely distinctive norms of practical reasoning beyond the expected-value-maximization norm of probabilistic decision theory. We will look at the possible role of game theory in grounding social conventions, and in particular consider some recent work suggesting that game theory can play an important explanatory role in linguistic phenomena. We will consider the role that game theory can have in the foundations of morality, and we will also consider whether game theory might play a distinctive epistemological role as “formalized mind reading”. We will also consider the role of game theory in “game theoretic semantic” accounts of logical consequence.

Grading

Grade determined by final research paper, together with class participation.

Texts

Various articles, to be distributed to seminar participants.

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This is the required logic seminar for graduate students in the philosophy program. The goal of the seminar is to gain familiarity with core formal tools from a variety of areas of logic, and consider the applications of these formal tools across a wide range of philosophical areas. We will focus especially on modal logic and non-classical logics, considering the application of modal logic to the analysis of conditionals and propositional attitudes and issues that emerge in the interaction between modal logic and quantification, and exploring non-classical logics such as intuitionism, relevance logic, and many-valued logics. We will also consider non-monotonic logics, dynamic logics, and logics based on probability theory and accounts of partial belief.

Grading

Grades will be based on periodic problem sets and a final exam.

Texts

Introduction to Non-Classical Logic, Graham Priest

This course is an introduction to the use of formal logical techniques in the analysis of arguments and texts, with an eye to the applicability of such formal techniques in the humanities, social sciences, and natural sciences. We will study formal propositional logic as a tool for extracting information from definite-information premises; modal logic as a tool for modeling reasoning situations involving multiple agents or information sources; probability and probabilistic decision theory as tools for reasoning under uncertainty; and game theory as a tool for making theoretical and practical decisions in multi-agent situations.

Graduate Standing and consent of graduate advisor or instructor required.

Course Description

"Much Ado About Nothing"

One might have thought that negation was a simple matter: it's an operation that inverts truth values, changing the true to the false and the false to the true. But concerns about negation are surprisingly widespread across philosophy. We will start with some concerns localized in the philosophy of logic, thinking about issues that come up in the treatment of negation in some non-classical logics such as intuitionistic logic and multi-valued logic. These concerns will lead us to think about a mysterious totalizing aspect of negation: negations encompass all of the ways of making a sentence false, even if we are incapable of sketching the boundaries of these ways. We'll consider the ramifications for this totalization for the role of negation in the semantic paradoxes and for thinking about the (note: negated) notion of infinity. This will lead us to think a bit about positive and negative speech acts, metalinguistic negation, and some related questions about the role of negation in natural language semantics. From here, we'll wander into metaphysical territory, by thinking a bit about negative facts and problems of non-existence. Time permitting, we may also think some about negation-dual pairs of permission and obligation in normativity, apophatic theology, and maybe even whether the Nothing noths.

Grading Policy:

Final grade will be based on a combination of seminar participation and a final research paper.

Prerequisite: Admission to the Plan II Honors Program

Description:

This course is an introduction to the use of formal logical techniques in the analysis of arguments and texts, with an eye to the applicability of such formal techniques in the humanities, social sciences, and natural sciences. We will study formal propositional logic as a tool for extracting information from definite information premises; modal logic as a tool for modelling reasoning situations involving multiple agents or information sources; probability and probabilistic decision theory as tools for reasoning under uncertainty; and game theory as a tool for making theoretical and practical decisions in multi-agent situations.

Texts/Readings:

An Introduction to Non-Classical Logic, Graham Priest

An Introduction to Decision Theory, Martin Peterson

Assignments:

Your grade in the course will be based on the following:

1. Short Problem Sets: There will be eight short problem sets assigned over the course of the semester. Each will consist of two or three problems designed to test your understanding of the current material. 5% each (for a total of 40%)

2. Long Problem Sets: There will be two longer problem sets over the course of the semester. These longer problem sets consist of substantially more difficult problems that ask you to take the concepts and techniques developed in class and apply and extend them in novel ways to a variety of logical puzzles. You should expect the long problem sets to require a significant commitment of time and mental energy.  12% each (for a total of 24%)

3. Exams: There will be two in-class exams. These exams will cover the same sort of material as is covered in the short problem sets. The exams are open-book and open-note. 16% (for a total of 32%)

4. Class Participation: Primarily, attendance of and participation in the weekly discussion section. 4%

There is no final exam for this course. Late work will not be accepted. All work should be done individually.

About the Professor:

Josh Dever received his Ph.D. in philosophy from the University of California at Berkeley in 1998. He works primarily in the philosophy of language and the philosophy of logic, and is the author of Complex Demonstratives, Compositionality as Methodology, Binding Into Character, and other works. His recent interests include the semantics, logic, and philosophical applications of conditionals, and foundational issues in the nature of semantic values. When he's not doing philosophy, he's usually reading English Renaissance drama or watching movies without plots.

Prerequisites

Graduate standing and consent of Graduate Advisor or instructor required.

Course Description

This seminar explores the consequences of the following thought: if the best formal model for natural language semantics is as a tool for altering conversational contexts, and if conversational contexts are best modeled as bodies of mutually shared information, then formal models of language will become entangled with formal models of belief and knowledge revision. We will thus investigate various tools from formal epistemology -- we will consider primarily qualitative tools such as AGM belief revision models, but will also look at quantitative methods such as Bayesianism and Dempster-Shafer theory -- and then consider a range of natural language phenomena whose semantics might require the tools from formal epistemology, such as modals and conditionals. Along the way we will consider some puzzles from formal epistemology, such as the Sleeping Beauty paradox, and think about whether these puzzles have implications for natural language semantics, and we will consider whether puzzles in natural language semantics, such as relativism-like behaviour of epistemic modals, can teach us anything about the best ways to model rational belief updating.

Grading

Class grading will be based primarily on a final substantial research paper, and secondarily on seminar participation (including possible presentations). 

This course satisfies the M&E requirement

This course examines the interaction between formal logic and the foundations of mathematics. We will take as our centerpiece a careful examination of some of the important results of set theory, including the paradoxes of naive set the- ory and the reformulation of set theory using the Zermelo-Frankel axioms, the development of the theory of infinite cardinals and ordinals in set theory, the formal details of the iterative conception of sets, and the basic methods of prov- ing independence results in set theory. We will couple this investigation with an examination of various results in the metatheory of first order logic that bear on the foundations of math, such as the completeness and compactness theorems, the Lo ?wenheim-Skolem theorems, and the Go ?del incompleteness theorems. 

Prerequisites

Graduate Standing and Consent of Graduate Advisor or instructor required.

Course Description

This seminar is an overview of major philosophical and mathematical issues in set theory. We will cover the core mathematical results in set theory, including the standard ZFC axiomatization, the development of the theory of ordinals and cardinals, the metamathematics of simple relative consistency results, and the use of inner models in proving the consistency of the axiom of choice and the generalized continuum hypothesis with ZFC. At the same time, we will trace important philosophical issues in set theory. These may include, but are not limited to, reactions to the paradoxes of naive set theory (including the use of non-clasdical logics to avoid those paradoxes), the development of alternative conceptions of the set-theoretic universe such as the "limitation of size" model and the "iterative hierarchy" model, the dispute between predicative and non-predicative mathematics, the nature of non-foundational sets, the metaphysics of sets and the Lewisian mereology-plus-megethology conception, and the role and status of large cardinal hypotheses. We will inter alia pay some attention to the historical development of views on set theory and its place in math, logic, and philosophy.

Grading

Grading will be based on class participation and a substantial final paper

Texts

Our two central texts will be Michael Potter's Set Theory and Its Philosophy and

Ken Kunen's Set Theory: An Introduction to Independence Proofs

Graduate Standing and Consent of Graduate Advisor or Instructor required.

Description:

 Bert and Ernie are both in the forest. A bear rears threateningly before Bert, while Ernie stands at a distance with a gun. Bert and Ernie have all the same objective information about the world. They both know about the bear, about the tree to Bert's left, about Ernie's gun. Bert and Ernie also have all the same objective desires. Both, in particular, desire that Bert not be eaten by a bear. Yet they do, and ought to do, different things. Bert climbs, and ought to climb, the tree; Ernie shoots, and ought to shoot, the bear. If actions are caused and rationalized by beliefs and desires, this is a puzzle.One solution to the puzzle is to hold that Bert and Ernie, while having all of the same objective information, differ in their perspectival information. Bert and Ernie both know that there is a bear before Bert. But only Bert knows the first-personal fact that there is a bear before *him*. Pursuing this solution entails a commitment to producing a theory of perspectival information. In this seminar, we will examine various models for perspectival content (Fregeanism, centered worlds contents, relativist contents) and various philosophical desiderata for an adequate theory of perspectivality. Issues in language, mind, action, epistemology, perception, and metaphysics will interact in these desiderata.

Grading Policy: 

A final research-level paper

Texts: 

Selected Papers

This course examines the interaction between formal logic and the foundations of mathematics. We will take as our centerpiece a careful examination of some of the important results of set theory, including the paradoxes of naive set the- ory and the reformulation of set theory using the Zermelo-Frankel axioms, the development of the theory of infinite cardinals and ordinals in set theory, the formal details of the iterative conception of sets, and the basic methods of prov- ing independence results in set theory. We will couple this investigation with an examination of various results in the metatheory of first order logic that bear on the foundations of math, such as the completeness and compactness theorems, the Lo ?wenheim-Skolem theorems, and the Go ?del incompleteness theorems. 

Prerequisites

Graduate Standing and Consent of Graduate Advisor required.

Course Description

I am a child of the direct reference wars. I saw the best minds of my generation destroyed by propositional attitude contexts, starved for epistemic transparency, dragging themselves through hyperintensionality looking for a Fregean Sinn.

In the wake of Kripke's Naming and Necessity, philosophy of language in the 1980s and 1990s was dominated by the dispute between direct reference theorists and Fregeans on the reference of proper names. An apparently narrow question in the semantics of natural languages expanded into an issue that had ramifications in epistemology, philosophy of mind and action, and metaphysics. In the last decade or so, the direct reference wars have died down in philosophy of language, although offshoots of the conflict have sprung up in related subdisciplines. In this seminar, we will consider the question: what did we learn from the direct reference wars? A variety of putative lessons will be considered -- some will be accepted, some rejected, and some accepted only after substantial modification. Issues will include the connection between propositional attitudes and the explanation of action, the role of the principle of compositionality in formal semantics, the question of whether there is a level of mental experience that is epistemically transparent, the relation between thought and language, the nature of fictional and non-existent objects, and the interaction between semantics and meta-semantics.

Grading

Grading will be based on seminar discussion participation and on a final research paper.

Texts

Salmon, Frege's Puzzle
Soames, Beyond Rigidity
+ various articles

Prerequisites:

Graduate Standing and Consent of Graduate Advisor required.

Course Description: A survey of major formal results in modal logic.

Topics include: the modal system K and its extensions; frame definitions of modal systems; frame completeness proofs; bisimulations and ultrafilter extensions; sahlqvist formulas; frame incompleteness; algebraic semantics; and quantified modal logic.

Text:

Blackburn, de Rijke, and Venema: Modal Logic

Prerequisites

This course is restricted to first year graduate students in philosophy

This course examines the interaction between formal logic and the foundations of mathematics. We will take as our centerpiece a careful examination of some of the important results of set theory, including the paradoxes of naive set the- ory and the reformulation of set theory using the Zermelo-Frankel axioms, the development of the theory of infinite cardinals and ordinals in set theory, the formal details of the iterative conception of sets, and the basic methods of prov- ing independence results in set theory. We will couple this investigation with an examination of various results in the metatheory of first order logic that bear on the foundations of math, such as the completeness and compactness theorems, the Lo ?wenheim-Skolem theorems, and the Go ?del incompleteness theorems. 

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This course is the required graduate logic seminar. The course will introduce students to a variety of issues in logic that are of importance for work across philosophy. Possible topics include: modal logic and systems of propositional modal logi;  quantified modal logic, de re and de dicto readings, possiblist and actualist quantifiers, and necessitism and contingentism; counterfactual conditionals; multi-valued logic; formal theories of truth including Kripke’s fixed-point construction and revision theories; supervaluationism and the semantics of vagueness; proof theory and Gentzen systems; intuitionistic logic; relevance logic and contradiction-friendly paraconsistent logics; systems of non-monotonic inference; generalized quantifier theory; Bayesianism, probabilistic decision theory, and game theory; social choice theory; and core results of classical first-order metatheory including completeness, compactness, and the Godel incompleteness results.

Grading

Grading will be based on periodic problem sets.

Texts

Readings will be made available as required.

Past topics include identity and substitutivity; philosophy of logic; discourse representation. 

This course examines the interaction between formal logic and the foundations of mathematics. We will take as our centerpiece a careful examination of some of the important results of set theory, including the paradoxes of naive set the- ory and the reformulation of set theory using the Zermelo-Frankel axioms, the development of the theory of infinite cardinals and ordinals in set theory, the formal details of the iterative conception of sets, and the basic methods of prov- ing independence results in set theory. We will couple this investigation with an examination of various results in the metatheory of first order logic that bear on the foundations of math, such as the completeness and compactness theorems, the Lo ?wenheim-Skolem theorems, and the Go ?del incompleteness theorems. 

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This course is the required graduate logic seminar. The course will introduce students to a variety of issues in logic that are of importance for work across philosophy. Possible topics include: modal logic and systems of propositional modal logi;  quantified modal logic, de re and de dicto readings, possiblist and actualist quantifiers, and necessitism and contingentism; counterfactual conditionals; multi-valued logic; formal theories of truth including Kripke’s fixed-point construction and revision theories; supervaluationism and the semantics of vagueness; proof theory and Gentzen systems; intuitionistic logic; relevance logic and contradiction-friendly paraconsistent logics; systems of non-monotonic inference; generalized quantifier theory; Bayesianism, probabilistic decision theory, and game theory; social choice theory; and core results of classical first-order metatheory including completeness, compactness, and the Godel incompleteness results.

Grading

Grading will be based on periodic problem sets.

Texts

Readings will be made available as required.

The course focuses on various philosophical issues concerning language. Topics to be discussed include, but are not limited to, the following: speaker-meaning, conversational implicature, sentence/expression-meaning, reference, modality, and propositional attitude ascriptions. 

Past topics include identity and substitutivity; philosophy of logic; discourse representation. 

Prerequisites

Graduate Standing and Consent of Graduate Advisor or instructor required.

Course Description

This course will be an advanced survey of contemporary issues in the philosophy of language. We will focus on various philosophical issues concerning language, including, but not limited to, the following: speech act theory, sentence/expression meaning, reference, quantification, propositional attitude ascriptions, and context sensitivity.  An overarching aim of the course is to get clear (or at least clearer) on the relationship between mental content, the content of our speech acts, and the literal context-invariant meanings of the sentences we use in performing such acts. 

Grading

Grades will be determined solely on the basis of a term paper (90%) and one in-class presentation (10%).  

Texts

Readings will include many classics in 20th century analytic philosophy of language, as well as numerous articles from the last decade.  All readings will be posted on our course Canvas site

Past topics include identity and substitutivity; philosophy of logic; discourse representation. 

This course examines the interaction between formal logic and the foundations of mathematics. We will take as our centerpiece a careful examination of some of the important results of set theory, including the paradoxes of naive set the- ory and the reformulation of set theory using the Zermelo-Frankel axioms, the development of the theory of infinite cardinals and ordinals in set theory, the formal details of the iterative conception of sets, and the basic methods of prov- ing independence results in set theory. We will couple this investigation with an examination of various results in the metatheory of first order logic that bear on the foundations of math, such as the completeness and compactness theorems, the Lo ?wenheim-Skolem theorems, and the Go ?del incompleteness theorems. 

Topic 1: Philosophy and Feminism

Past topics include identity and substitutivity; philosophy of logic; discourse representation. 

Past topics include identity and substitutivity; philosophy of logic; discourse representation. 

Topic 1: Philosophy and Feminism

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This course is the required graduate logic seminar. The course will introduce students to a variety of issues in logic that are of importance for work across philosophy. Possible topics include: modal logic and systems of propositional modal logi;  quantified modal logic, de re and de dicto readings, possiblist and actualist quantifiers, and necessitism and contingentism; counterfactual conditionals; multi-valued logic; formal theories of truth including Kripke’s fixed-point construction and revision theories; supervaluationism and the semantics of vagueness; proof theory and Gentzen systems; intuitionistic logic; relevance logic and contradiction-friendly paraconsistent logics; systems of non-monotonic inference; generalized quantifier theory; Bayesianism, probabilistic decision theory, and game theory; social choice theory; and core results of classical first-order metatheory including completeness, compactness, and the Godel incompleteness results.

Grading

Grading will be based on periodic problem sets.

Texts

Readings will be made available as required.

Past topics include identity and substitutivity; philosophy of logic; discourse representation. 

This course examines the interaction between formal logic and the foundations of mathematics. We will take as our centerpiece a careful examination of some of the important results of set theory, including the paradoxes of naive set the- ory and the reformulation of set theory using the Zermelo-Frankel axioms, the development of the theory of infinite cardinals and ordinals in set theory, the formal details of the iterative conception of sets, and the basic methods of prov- ing independence results in set theory. We will couple this investigation with an examination of various results in the metatheory of first order logic that bear on the foundations of math, such as the completeness and compactness theorems, the Lo ?wenheim-Skolem theorems, and the Go ?del incompleteness theorems. 

Prerequisites

This course is restricted to first year graduate students in philosophy

Topic 1: Philosophy and Feminism

Prerequisites

This course is restricted to First Year Philosophy Graduate Students.

Course Description

This course is the required graduate logic seminar. The course will introduce students to a variety of issues in logic that are of importance for work across philosophy. Possible topics include: modal logic and systems of propositional modal logi;  quantified modal logic, de re and de dicto readings, possiblist and actualist quantifiers, and necessitism and contingentism; counterfactual conditionals; multi-valued logic; formal theories of truth including Kripke’s fixed-point construction and revision theories; supervaluationism and the semantics of vagueness; proof theory and Gentzen systems; intuitionistic logic; relevance logic and contradiction-friendly paraconsistent logics; systems of non-monotonic inference; generalized quantifier theory; Bayesianism, probabilistic decision theory, and game theory; social choice theory; and core results of classical first-order metatheory including completeness, compactness, and the Godel incompleteness results.

Grading

Grading will be based on periodic problem sets.

Texts

Readings will be made available as required.

The course focuses on various philosophical issues concerning language. Topics to be discussed include, but are not limited to, the following: speaker-meaning, conversational implicature, sentence/expression-meaning, reference, modality, and propositional attitude ascriptions. 

Topic 1: Philosophy and Feminism

Past topics include basic issues in metaphysics; particulars and universals; identity and individuation; realism and antirealism; mind-body issues. 

This course has two primary goals. One goal is to introduce students to philosophy. The other is to help students acquire and improve critical thinking and communication skills. To achieve these goals, we’ll first discuss some basics of critical thinking.  Then we’ll move on to the bulk of the course, which consists of extended discussions of four perennial philosophical issues: the existence of god, the nature of persons, the problem of free will, and the nature of morality. There are many other philosophical issues and topics we could discuss. But I have chosen these particular issues since they clearly and immediately bear on how we understand ourselves, our actions, and our place in nature. And most people already have views on each of these topics.