square of opposition


Philosophy 142: Philosophical Logic Professor John MacFarlane
UC Berkeley, Spring 2016 TuTh 12:30-2, 130 Wheeler


“Philosophical logic” includes both (a) the philosophical investigation of the fundamental concepts of logic and (b) the deployment of logical methods in the service of philosophical ends. We’ll tackle five interconnecting topics in philosophical logic:


You may think you learned everything there is to know about quantifiers in Philosophy 12A. But in fact, there are quite a few quantificational idioms that we can’t understand in terms of the quantification theory you learned. We’ll look at the logic of identity, numerical quantifiers, generalized quantifiers, definite descriptions, substitutional quantifiers, and plural quantifiers.

In addition to talking about what is the case, we talk about what might have been the case and what could not have been otherwise. Modal logic gives us tools to analyze reasoning involving these notions. We’ll get a basic grasp on some of the fundamentals of propositional modal logic, and then delve into some hairy conceptual problems surrounding quantified modal logic, explored by Quine, Kripke, and others. We’ll also look at the famous “slingshot argument,” which was used by Quine and Davidson to reject modal logic and correspondence theories of truth. At this point our work on definite descriptions will come in handy!

Logical consequence

If you ask what logic is about, a reasonable (though not completely satisfactory) answer is that it’s the study of what follows from what, that is, of logical consequence. But how should we think of this relation? We’ll start by looking at Tarski’s account of logical consequence, which has become the orthodox account. On this account, logical consequence is a matter of truth preservation: Q follows from P if there is no model on which P is true and Q false. We’ll talk about how this account relates to the older idea that Q follows from P if it is impossible for P to be true and Q false. Then we’ll consider some alternatives. One alternative is to define consequence in terms of proof. We’ll look at a version of this idea by Dag Prawitz, which yields a nonclassical logic called “intuitionistic logic.” We’ll then look at the suggestion that relevance in addition to truth preservation is required for logical consequence. We’ll see how one might develop a nonclassical “relevance logic,” and we’ll consider some technical and philosophical issues that speak for and against a requirement of relevance. Finally, we’ll consider how, exactly, logic relates to reasoning.


In Philosophy 12A you were taught to translate English conditionals using the “material conditional,” a truth-functional connective. This leads to some odd results: for example, “If I am currently on Mars, then I am a hippopotamus” comes out true (since the antecedent is false). We’ll start by considering some attempts to defend the material-conditional analysis of indicative conditionals in English. Then we’ll consider some alternatives, inculding Edgington’s view that indicative conditionals have no truth-conditions and Stalnaker’s elegant modal account. Finally, we’ll look at McGee’s “counterexample to modus ponens,” and consider whether this sacrosanct inference rule is actually invalid!


Finally we’ll turn to the “sorites paradox,” or paradox of the heap, which argues: five thousand grains of sand make a heap; taking one grain away from a heap still leaves you with a heap; so…one grain of sand makes a heap. Philosophical logicians have suggested that it is a mistake to use classical logic and semantics in analyzing this argument, and they have proposed a number of alternatives. We’ll consider three of them: (a) a three-valued logic, (b) a continuum-valued (or fuzzy) logic, and (c) a supervaluational approach that preserves classical logic (mostly) but not classical semantics. If there’s time, we’ll also look at a short argument by Gareth Evans that purports to show that vagueness must be a semantic phenomenon: that is, that there is no vagueness “in the world.”


Since this is an upper-level course in philosophy, students must have taken at least two prior courses in philosophy. At least one must be an introductory course in symbolic logic, at the level of Philosophy 12A (translations, natural deduction proofs, and semantics for propositional logic and predicate logic.) Students who do not have a solid grasp of the material presented in 12A will not be able to do well in this course. I will not presuppose knowledge of logic beyond what is covered in 12A. If you find me using logical machinery you do not understand, please stop me and ask me to explain it. I will be happy to do so!


The only book is a course reader, which should soon be available at Copy Central on Bancroft (just across from the Pacific Film Archive on campus). We will make extensive use of handouts that will be distributed in class and on the website.


Students are expected to do the assigned readings and be prepared to discuss them in class.

The course grade will be based chiefly on the following assignments, although in borderline cases, consideration will be given to class participation.

  • Three graded problem sets (one on quantifiers, one on modal logic, one on logical consequence), plus one ungraded problem set (12A review).
  • One 7-8 page paper, due at the end of the term, on one of the topics we are covering in the course. Please check with your GSI to make sure your topic is appropriate before getting too far into the paper.
  • Final exam (in class, Thursday, May 12, 2016, 3-6 PM, location TBA)

The final grade will be based one third on the problem sets (taken together), one third on the paper, and one third on the final exam.


Please do not use laptops or other computing devices during class. Even if you have superhuman powers of distraction-avoidance, you may distract others behind you.


All students taking the course for credit must attend a discussion section. Sections will be led by Justin Vlasits (), a PhD student in Philosophy. We will be scheduling sections through bCourses, and sections will begin meeting the second week of class.

Academic Integrity

Plagiarism and cheating will not be tolerated in this course: students caught cheating or plagiarizing will receive an F in the course. Please read the handout entitled “Plagiarism and Academic Integrity” (on the website). You may work with others on the problem sets, but if you do, make sure that you write up your answers on your own, in your own words, and acknowledge on your problem sets that you worked with so and so.


My office is 231 Moses Hall. I am best reached by email at . Regular office hours will be Tu and Th 3–4 (but check at http://johnmacfarlane.net for updates).

Justin Vlasits’ office is 301 Moses Hall. He can be reached at .