- Course: PHIL 414 / PHIL 652. Concordia University. Credits: 3.
- Time & Place: Wed. 6 PM–8:15 PM, Room S 201, Campus SGW
- Instructor:
Ulf Hlobil, Assistant Professor, Department of Philosophy, Faculty of Arts and Sciences, Concordia University.

Office phone: (514) 848-2424 ext. 2536

E-mail: please use email only for administrative issues and solicited items; other substantive philosophical discussion should happen in person because email doesn't suit it: ulf.hlobil@concordia.ca

Office hours: Monday 10:00–11:30, or by appointment, in S-M 309 (2145 Mackay). - Notice: In the event of extraordinary circumstances beyond the university's control (e.g. a strike), the course contents, evaluation scheme and other parts of this syllabus may be subject to change.

The goal of this course is to enable you to understand and think critically about recent developments in non-classical logic and the philosophy of logic. We will focus one a couple of narrow topics within these broad fields. After taking this course, you will know some philosophical views about what (logical) consequence is. You will also be familiar with some particular logical systems, such as the nontransitive logic STT. Along the way, you will learn how to prove important metalogical theorems. After taking this course, you should be able to do the following:

- Explain what it means for a calculus to be sound and complete with respect to a semantics.
- Prove that classical propositional logic (e.g. in a natural deduction formulation) is sound and complete with respect to its standard model theory.
- Prove that classical predicate logic is sound and complete with respect to its standard model theory.
- Explain what the usual structural properties of classical consequence are.
- Compare the virtues of noncontractive and nontransitive approaches to the Liar Paradox and the Curry Paradox.
- Explain what logical inferentialism, bilateralism, and logical expressivism are.
- Explain the motivations behind relevance logic and what variable sharing is.
- Explain the basics of different approaches to nonmonotonic logic.
- Discuss ideas connected to logical pluralism and the normativity of logic.

All required readings are available on Moodle (you will need a password that you can get from me during class). The Barwise and Etchemendy textbook can be found online at:

http://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf.

http://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf.

What is a logic? A first rough idea: consequence, proofs, models. Some reasons to be unhappy with classical logic. We refresh our knowledge of classical propositional logic.

- Readings:
Excerpts from Chaps. 4, 6, 7, and 8 of Barwise, Jon & Etchemendy, John (1999).
*Language, Proof and Logic*. London: Seven Bridges Press.

*Background reading*: Shapiro, S. (2002). “Necessity, meaning, and rationality: The notion of logical consequence,” in Dale Jacquette (ed.).*A Companion to Philosophical Logic*(pp. 227–240).Oxford: Blackwell.

We prove that the natural deduction formulation of classical propositional logic is sound and complete with respect to truth tables. To do that, we must look at some basic mathematical tools: a bit of set theory, inductive definitions and proofs by induction.

- Readings:
Excerpts from Chaps. 8 and 17 of Barwise, Jon & Etchemendy, John (1999).
*Language, Proof and Logic*. London: Seven Bridges Press.

*Background reading*: Excerpts from van Frasen's*Formal Semantics and Logic*. Available online at:

https://www.princeton.edu/~fraassen/Formal%20Semantics%20and%20Logic.pdf - Homework: Problem Set 1 due

We look at the standard model theory for classical first-order logic. We prove the soundness of first-order logic with respect to its standard model theory.

- Readings:
Excerpts from Chaps. 18 of Barwise, Jon & Etchemendy, John (1999).
*Language, Proof and Logic*. London: Seven Bridges Press. - Homework: Problem Set 2 due

- Readings:
Excerpts from Chaps. 18 of Barwise, Jon & Etchemendy, John (1999).
*Language, Proof and Logic*. London: Seven Bridges Press. - Homework: Problem Set 3 due

- Readings:
1. Excerpts from Chaps. 18 of Barwise, Jon & Etchemendy, John (1999).
*Language, Proof and Logic*. London: Seven Bridges Press.

2. Boolos, G. (1994). Godel's Second Incompleteness Theorem Explained in Words of One Syllable.*Mind*103: 1–3. - Homework: Problem Set 4 due

- Readings:
1. Gentzen, G. (1964). Investigations into Logical Deduction 1.
*American Philosophical Quarterly*1(4): 288–306.

2. excerpts of Chap. 2 of Bimbó, K. (2014).*Proof theory: Sequent calculi and related formalisms*. Boca Raton: CRC Press. - Homework: Problem Set 5 due

- Readings:
1. Tarski, Alfred (2002). On the Concept of Following Logically.
*History and Philosophy of Logic*23(3): 155–196.

2. Excerpts from Chaps. 4, 6–9 of Etchemendy, John (1990).*The Concept of Logical Consequence*. Harvard University Press.

- Readings:
1. Steinberger, Florian & Murzi, Julien (2017). Inferentialism. In
*Blackwell Companion to Philosophy of Language*. Wiley Blackwell. pp. 197-224.

2. Prawitz, Dag (1974). On the idea of a general proof theory.*Synthese*27(1-2): 63–77.

3. Brandom, “Semantic Inferentialism and Logical Expressivism”, i.e. Chap. 1 of Brandom, Robert (2009).*Articulating reasons*. Harvard University Press.

*Optional*: Brandom, R. (ms). “From Logical Expressivism to Expressivist Logic: Sketch of a Program and Some Implementations”; Read, Stephen (1994). Formal and material consequence.*Journal of Philosophical Logic*23(3): 247–265.

- Readings:
1. Prior, A. N. (1960). The Runabout Inference-Ticket.
*Analysis*21(2): 38.

2. Belnap, Nuel (1962). Tonk, Plonk and Plink.*Analysis*22(6): 130–134.

3. Ripley, David (2015). Anything Goes.*Topoi*34 (1): 25–36.

*Background*: Ripley, D. (ms). “Bilateralism, Coherence and Warrant”

- Readings:
1. Ripley, David (2013). Paradoxes and Failures of Cut.
*Australasian Journal of Philosophy*91(1): 139–164.

2. Barrio, Eduardo; Rosenblatt, Lucas & Tajer, Diego (forthcoming). Capturing naive validity in the Cut-free approach.*Synthese*: 1–17.

*Background*: Cobreros, Pablo; Égré, Paul; Ripley, David & van Rooij, Robert (2013). Reaching Transparent Truth.*Mind*122: 841–866.

- Readings:
1. Beall, Jc & Murzi, Julien (2013). Two Flavors of Curry's Paradox.
*Journal of Philosophy*110(3):143–165.

2. Zardini, Elia (2013). Naive Logical Properties and Structural Properties.*Journal of Philosophy*110(11):633–644.

- Readings:
1. Mares, Edwin D. & Meyer, Robert K. (2001). “Relevant logics”. In Lou Goble (ed.),
*The Blackwell Guide to Philosophical Logic*. Blackwell. pp. 280–308.

2. Meyer, Robert K. (1971). Entailment.*The Journal of Philosophy*68(21): 808–818.

- Readings:
1. Horty, J. F. (2001). Nonmonotonic Logic. In L. Goble (ed.),
*The Blackwell Guide to Philosophical Logic*(pp. 336–361). Malden, MA: Blackwell.

2. Makinson, David (2003). Bridges between Classical and Nonmonotonic Logic.*Logic Journal of the IGPL*11(1): 69–96.

For other rights and responsibilities, see the Concordia Code of Rights and Responsibilities at: http://www.concordia.ca/students/rights.html

- homework that consists in problem sets for meetings 2–6, so there will be 5 problem sets, each worth 10%;
- a term paper of roughly 12 pages.

The most common offense under the Academic Code of Conduct is plagiarism which the code defines as ”the presentation of the work of another person [an author of a book, a journal, a fellow student, etc.] as one’s own or without proper acknowledgment.”

This could be material copied word by word from books, journals, internet sites, professor's course notes, etc. It could be material that is paraphrased but closely resembles the original source. It could be the work of a fellow student, for example, an answer on a quiz, data for a lab report, a paper or assignment completed by another student. It might be a paper purchased through one of the many available sources. Plagiarism does not refer to words alone—it can also refer to copying images, graphs, tables, and ideas. “Presentation” is not limited to written work. It also includes oral presentations, computer assignments and artistic works. Finally, if you translate the work of another person and do not cite the source, this is also plagiarism. In simple words: *Do not copy, paraphrase or translate anything for anywhere without saying from where you obtained it!*

Please make sure that you comply with it. Help regarding how to cite your sources correctly can be found here: http://library.concordia.ca/help/howto/citations.html.

The Access Center for Students with Disabilities coordinates academic accommodations and services for all eligible students with disabilities. If you have a disability for which you wish to request accommodations and have not contacted the Access Center for Students with Disabilities, please do so as soon as possible. Information about their services can be found at http://www.concordia.ca/offices/acsd.html/. Please contact me privately in regard to your needs in this course.

- Philosophy Tutoring: Through the Students of Philosophy Association (SoPhiA):

https://sophiaconcordia.wordpress.com/tutoring/ - Philosophy Academic Advisors:

Prof.*Emilia Angelova*(UGS) and Prof.*Andrea Falcon*(GS). - Concordia Counseling & Psychological Services:

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