Logic and Language
Time: Tuesday/Thursday 11:00 am to 12:15 pm
Location: MHP 102
Kenny Easwaran - easwaran AT usc DOT edu
Office: STO 227
Office Hours: Wed 2:30 to 4:00 and by appointment
Gabriel Uzquiano - uzquiano AT usc DOT edu
Office: STO 230
Office Hours: Tue 2:00 to 3:30 and by appointment
TA - Julia Staffel - philosophy352 AT gmail DOT com
Logic is one of the central tools in philosophy, both for the general purpose of drawing the distinction between valid and invalid arguments in all areas of philosophy and for the speciﬁc purpose of helping us clarify central notions in language and mathematics. This course will cover both aspects of logic, but with rather more focus on the speciﬁc applications in language and mathematics than is common in a ﬁrst course in logic.
The ﬁrst nine weeks of the semester will be an overview of the basic syntax and semantics of propositional and predicate (or ﬁrst-order) logic. This will familiarize students with the workings of one of the standard formal systems for representing logical reasoning. The last six weeks of the semester will focus on more special topics, to help students understand the importance of the formal system they have been studying. For half of this time, we will be looking at classic works in the philosophy of language, by Frege, Russell, Kripke, and Grice, which make use of the toolbox of formal logic to help clarify the meaning of certain natural language expressions and explore the connection between logic and meaning more generally. This leads naturally to other classes in philosophy of language, and linguistics. The rest of this time will consist of an introduction to some of the exciting topics in more advanced logic, where we demonstrate some of the specific strengths and limitations of formal logic. In particular, we will provide outlines of some of the classic results of Gödel and Tarski, showing that formal logic is capable of representing its own meta-theoretic notion of provability, but is still essentially incomplete since it cannot represent its own notion of truth. This leads naturally to more advanced topics covered in PHL 450, and classes in computer science or mathematics.
There is only one required textbook for this course:
Gamut, L. F. (1990) Logic, Language and Meaning, Vol. 1. University of Chicago Press.
Additional readings will be made available online. Students who prefer published versions of
these readings will ﬁnd most or all of them in the following collections:
Ludlow, P. (ed.) (1997) Readings in the Philosophy of Language. Cambridge: MIT Press.
Martinich, A. P. (ed.) (2000) The Philosophy of Language. Oxford: Oxford University Press. 4th edition.
The following books cover additional material on the philosophy of language.
Gamut, L. F. (1990) Logic, Language and Meaning, Vol. 2. University of Chicago Press
Soames, S. (2010) Philosophy of Language. Princeton University Press.
The following text provides an informal exposition of Gödel’s incompleteness theorems covered in the third part of the course.
Franzen, T. (2005) Gödel’s Theorem. An Incomplete Guide to its Use and Abuse. A K Peters Ltd.
The semester will be divided in three parts, each addressing a different set of topics. There will be different methods of assessment in each block:
There are nine assignments for the ﬁrst part of the course. Late assignments will not be accepted under any circumstances. However, the lowest two scores will be dropped in computing the average from this section of the class. This will account for 40 % of the ﬁnal grade for the course.
Students will be asked to write a paper (1000–1500 words) for the second part of the course, which will be due on Tuesday, April 10. Please note that extensions will only be granted for good reasons, and (unless it is a medical emergency), the extension has to be requested before the deadline. Late papers are marked down 1/3 grade (like A to A-) for each day the paper is late. This will account for 20 % of the ﬁnal grade for the course.
• Advanced Topics
Students will be asked to complete a take-home essay quiz for the third part of the course. This will account for an additional 20 % of the ﬁnal grade for the course.
The ﬁnal exam will account for another 20 % of the ﬁnal grade for the course.
All students are expected to understand and abide by these principles. SCampus, the Student Guidebook, contains the Student Conduct Code in Section 11.00, while the recommended sanctions are located in Appendix A:
Students will be referred to the Ofﬁce of Student Judicial Affairs and Community Standards for further review, should there be any suspicion of academic dishonesty. The Review process can be found at:
Statements for students with disabilities
Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter of veriﬁcation for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to us as early in the semester as possible. DSP is located in STU 301 and is open 8:30 a.m. to 5:00 p.m., Monday through Friday. The phone number for DSP is (213) 740-0776.
Jan 10, 12. Arguments and validity
Logic, Language and Meaning, Chapter §§1.1 – 1.2.
Jan 17, 19. Propositional logic
Logic, Language and Meaning, Chapter 2, §§2.1, 2.2, 2.3, 2.5.
Jan 24, 26. Formalization in propositional logic
Logic, Language and Meaning, Chapter 2, §§2.1, 2.2, 2.3, 2.5.
Jan 31, Feb 2. Predicate logic: syntax
Logic, Language and Meaning, Chapter 3, §§3.1 – 3.4.
Feb 7, 9. Predicate logic: semantics
Logic, Language and Meaning, Chapter 3, §§3.5 – 3.6.
Feb 14, 16. Formalization in predicate logic
Logic, Language and Meaning, Chapter 3, §3.4.
Feb 21, 23. Natural deduction: propositional logic
Logic, Language and Meaning, Chapter 4, §§4.1 – 4.3.
Feb 28, Mar 2. Natural deduction: predicate logic
Logic, Language and Meaning, Chapter 4, §4.3.
Mar 7, 9. Identity
Logic, Language and Meaning, Chapter 3, §3.7.
Mar 14, 16 - Spring Break
Mar 21, 23. Deﬁnite descriptions
Logic, Language and Meaning, Chapter 5, §5.2.
Soames, S. (2010) Philosophy of Language. Chapter 1. §§1.23 – 1.24.
Russell, B. (1919). Introduction to Mathematical Philosophy, Chapter 16. Reprinted as ‘Descriptions’ in Ludlow, P. (ed.) and Martinich, A. P. (ed.).
Strawson, P. (1950) ‘On Referring,’ Mind, 59: 320-344. Reprinted in Ludlow, P. (ed.) and Martinich, A. P. (ed.).
Mar 28, 30. Proper names
Soames, S. (2010) Philosophy of Language. Chapters 1, §1.1, and 4, §§4.1 – 4.2.
Frege, G. (1892) ‘On Sense and Reference.’ Reprinted in Ludlow, P. (ed.) and Martinich, A. P. (ed.).
Kripke, S. (1980) Naming and Necessity, Lectures I and II. Lecture II is reprinted in Ludlow, P. (ed.). Extracts from both lectures are available in Martinich, A. P. (ed.).
Apr 4, 6. Pragmatics
Logic, Language and Meaning, Chapter 6.
Soames, S. (2010) Philosophy of Language. Chapter 7.
Grice, P. ‘Logic and Conversation’ in Grice, P. (1989) in Studies in the Ways of Words. Reprinted in Martinich, A. P. (ed.).
III. Advanced Topics
Apr 11, 13. Tarski’s theory of truth
Soames, S. (2010) Philosophy of Language. Chapter 2. §§2.1 – 2.2.
Tarski, A. (1944) ‘The Semantic Conception of Truth and the Foundations of Semantics’. Reprinted in Martinich, A. P. (ed.).
Apr 18, 20. Tarski’s undeﬁnability theorem
Soames, S. (1999) Understanding Truth. Chapter 3. (‘Truth and proof’)
Tarski, A. (1969) ‘Truth and Proof’ Scientiﬁc American 220, 63 – 77.
Apr 25, 27. Gödel’s incompleteness theorem
Franzen, T. (2005) Gödel’s Theorem. An Incomplete Guide to its Use and Abuse, Chapter 2.