Students have two opportunities to study with Professor Keith Simmons in Spring 2025! Check out the descriptions below for PHIL 3214: Symbolic Logic II and PHIL 3298: Paradoxes. Interested? Sign up today in Student Admin or contact Dr. Simmons to request the syllabus.
PHIL 3214: Symbolic Logic II
This is a course in modal logic, the logic of possibility and necessity. We will study propositional and quantified modal logic. We will study a variety of modal systems from both the semantic and the proof-theoretic points of view. We will also study the metalogic of these systems.
As time allows, we’ll go on to explore modal logic in three directions: (i) further topics in quantified modal logic, (ii) applications, and (iii) philosophical issues.
Our main text for the course is A New Introduction to Modal Logic, by G.E. Hughes and M.J. Cresswell (henceforth H&C).
The core of the course
- Review of propositional logic.
- The basic modal notions: L, M, validity, the modal game (H&C, Chapter 1).
- The systems K, T and D (H&C, Chapter 2).
- The systems S4, B, S5, Triv and Ver (H&C, Chapter 3).
- Review of the predicate calculus (H&C, Chapter 13, pp.235-243).
- The modal predicate calculus (H&C, Chapter 13, pp.243-255).
Further topics in quantified modal logic
- Expanding domains (H&C, Chapter 15).
- Modality and existence (H&C, Chapter 16).
- Identity and descriptions (H&C, Chapter 17).
- Intensional objects (H&C, Chapter 18).
- Further issues: multiple indexing, counterpart theory (H&C, Chapter 19)
Applications
- Possible world semantics in the philosophy of language.
- Counterfactuals
Philosophical issues
- The problem of interpreting quantified modal logic (‘quantifying in’).
- The metaphysics of modality: the ontological status of possible worlds.
- The interpretation of two-dimensional semantics.
- The epistemology of modality: imagination, conceivability, and possibility.
PHIL 3298: Paradoxes
This is a Philosophy course about paradoxes. Paradoxes have been a driving force in Philosophy since the 5th Century B.C.E. They force us to rethink old ideas and conceptions. Plato and Aristotle famously said that Philosophy begins in wonder - and they had in mind the kind of deep puzzlement that paradoxes generate.
In this seminar, we will study a wide range of paradoxes: Zeno's paradoxes about space, time and motion, moral paradoxes, Sorites paradoxes about vagueness (such as the paradox of the heap), paradoxes of rationality (Newcomb's paradox and the Prisoner's dilemma), paradoxes of belief (including paradoxes of confirmation, and the surprise examination paradox), paradoxes about time travel, and logical paradoxes (Russell's paradox about classes and the Liar paradox about truth).
As we explore these paradoxes, we will wrestle with some central philosophical questions: What is the nature of space, time, and motion? Are there genuine moral dilemmas? Is the world a fully determinate place? What is it to act rationally? When is a belief justified? Are the foundations of mathematics secure? What is the nature of truth?
The paradoxes are not just important - they are fun too. They encourage us to think creatively, in new and surprising ways. In this seminar, you will be given the opportunity to tackle the paradoxes yourselves, through group discussions and frequent written assignments. Philosophy is best viewed as a practice, as something that one does. By actively engaging with the paradoxes, both orally and in your written work, you will develop the intellectual skills that make philosophical progress possible.