Syllabus: Advanced Topics in Logic, Fall Term 2017

  1. Course: PHIL 414 / PHIL 652.  Concordia University.  Credits: 3.
  2. Time & Place: Wed.  6 PM–8:15 PM, Room S 201, Campus SGW
  3. 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:
    Office hours:   Monday 10:00–11:30, or by appointment, in S-M 309 (2145 Mackay).
  4. 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.

Table of Contents

Course Description and Overview

Calendar Course Description:    This course presents the fundamentals of an advanced topic in logic.
Prerequisite: PHIL 314, or permission of the Department.
Expanded Course Description:    A course on recent developments in non-classical logics and the philosophy of logic. The overarching question will be: What does it mean to say that something follows (perhaps logically) from something else? Topics include: logical inferentialism, bilateralism, proof-theoretic validity, different notions of logical consequence, atomic systems, nonmonotonic logics, nontransitive logics, and other substructural logics. We will focus on proof-theoretic approaches. We will look at natural deduction and sequent calculus formulations of a wide variety of non-classical logics.


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

Seminar Schedule and Texts

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:,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf.

3.1 Classical Logic: Meta-Theory

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.
  1. 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.
  1. 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:
  2. 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.
  1. Readings: Excerpts from Chaps. 18 of Barwise, Jon & Etchemendy, John (1999). Language, Proof and Logic. London: Seven Bridges Press.
  2. Homework: Problem Set 2 due
We prove completeness of first-order logic.
  1. Readings: Excerpts from Chaps. 18 of Barwise, Jon & Etchemendy, John (1999). Language, Proof and Logic. London: Seven Bridges Press.
  2. Homework: Problem Set 3 due
We look at Gödel's two incompleteness theorems. We will spend some time on the diagonal lemma.
  1. 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.
  2. Homework: Problem Set 4 due
Sequent Calculus, focusing on Gentzen's LK and LJ.
  1. 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.
  2. Homework: Problem Set 5 due

3.2 Conceptions of Logic and Logical Consequence

The semantic conception of logical consequence.
  1. 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.
Inferentialism and Logical Expressivism, with a view to atomic systems.
  1. 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.
Inferentialism: critique and responses, with a view to conservativeness and nontransitive logic.
  1. 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”

3.3 Structure vs. Expressive Power

Bilateralism: with a view to nontransitive solutions to paradoxes.
  1. 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.
The v-Curry Paradox and its Cousins, with a view to non-contractive solutions.
  1. 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.

3.4 Nonmonotonic Logics

Relevance Logics: Going Sub-classical.
  1. 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.
Supra-classical nonmonotonic logics.
  1. 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.

3.5 Do You Need a Logic? If Yes, How Many?

Logical Pluralism
  1. Readings: 1.   Chaps. 2 and 3 of Beall, Jc & Restall, Greg (2005). Logical Pluralism. Oxford University Press.
    2.   MacFarlane, “In What Sense (If Any) Is Logic Normative for Thought?” available at:
    : Chap. 2 of Harman, Gilbert (1986). Change in View. MIT Press; and Hjortland, Ole Thomassen (2013). Logical Pluralism, Meaning-Variance, and Verbal Disputes. Australasian Journal of Philosophy 91(2):355–373; Russell, Gillian (2008). One true logic? Journal of Philosophical Logic 37(6): 593–611.

Class Requirements, Policies, and Grading

4.1 General Rules & Advice

Office hours: If you have any questions or difficulties with the material, I encourage you to visit me in my office during office hours. During office hours I can discuss questions in more depth and I can give you detailed feedback on assignments.
Readings: In order to meet the class objectives it is essential that you read the assigned texts completely and carefully before each meeting and actively participate in classroom discussion are preconditions for this and, hence, required. I will introduce material that is not in the readings during class, so attendance at each and every class is essential if you want to do well in the course.
Special Circumstances: If a special condition or circumstance in your life may or will affect your performance, please let me know about it as soon as possible. It will be treated with the strictest confidence. Please do not wait until the condition or circumstance is impending or has already happened before telling me about its impact on you. If something unanticipated occurs, bring it to my attention and we will work out a way of dealing with it.
Assignments: Start your writing assignments early. Writing a philosophy paper takes time. An excellent set of tips on how to write good philosophy texts is also provided by Prof. Jim Pryor on this webpage: You must keep a copy of all your work—your original submissions as well as graded copies I return to you. According to the calendar (, “students are responsible for the preservation of any material, in its entire and original form, which has been returned to them.” It hence is a good idea to regularly back up your data.
Laptops, phones, tablets, etc.: New research shows that students who use laptops or phones or iPods and the like in class perform markedly more poorly than others and unfairly diminish the performance of others (see here and here). As Maryellen Weimer, an author for Faculty Focus, puts it here: “students are way too convinced that multitasking is a great way to work. They think they can do two or three tasks simultaneously and not compromise the quality of what they produce. Research says that about 5% of us multitask effectively. Proof of the negative effects of multitasking in learning environments is now coming from a variety of studies.”
Religious or Cultural Holidays: If you celebrate holidays that the university calendar does not accommodate and this creates any kind of conflicts with this course, please see me about this at least one month prior to the holiday; I will consider such matters on a case-by-case basis.
Gender Neutral Language & Human Diversity: In addition to all the other reasons for using gender neutral language and language that attends to human diversity, there are philosophical reasons for this too. Using gender neutral language in your writing and speaking reminds us that human beings are diverse in gender, that not all of them are “he.” There are different ways of approaching the task of keeping gender and other differences in mind, e.g., substituting “she” where “he” might have traditionally been expected, alternating systematically between the two, using “she/he,” and so on. No formal procedure is entirely adequate to the task, for the task is improving your thinking and that of our culture and future generations, and the form of thinking adequate to this cannot be set in advance. The American Philosophical Association has provided helpful “Guidelines for the Nonsexist Use of Language.” (online at
For other rights and responsibilities, see the Concordia Code of Rights and Responsibilities at:

4.2 Grading and Requirements

Your grade in this course has two components, which are weighted equally, i.e., 50% each:
  1. homework that consists in problem sets for meetings 2–6, so there will be 5 problem sets, each worth 10%;
  2. a term paper of roughly 12 pages.
Homework, problem sets: Homework has to be submitted in person and as hard copy at the start of the class at the date on which it is due. You cannot submit homework late (unless you have extraordinary good reasons). Your answers must be easy to read, and you must indicate clearly which question you are answering. In order to get an A on a problem set, you must solve all problems correctly and completely.
Paper: The paper is due at the last class meeting. I will give you three topic options, with one being wide open (to leave room for creativity). In the paper, you should discuss and defend a thesis about a problem in the philosophy of logic. The paper must be roughly 12 pages long and formatted in the usual way (e.g.  11 pt font size, 1.4 spacing, 1 inch margins, footer with page number, etc.). Citations must follow some widely used citation style, such as APA or Chicago.
Expectations: You should come to every class, do all the readings very carefully, do your homework and hand it in at the beginning of class, participate actively and respectfully in class discussions, and write an insightful and interesting paper. If you do all that, you will do very well in this course.
Grading Scale: Depending what is suitable for the assignment I will use points out of one hundred, letter grades, or grade point scores to grade the assignments. These scales can be converted into one another according to the table below. The table also includes the interpretation of the qualitative descriptions of grades by the department of philosophy:
My feedback policies: I strive to grade problem sets within 1 week and papers within 2 weeks of submission. If you have not received your grade or feedback after 2 weeks and I haven't addressed this issue, please contact me.
Moodle: Routinely check the Moodle page for posted material and updates. You may also receive grades and feedback via Moodle.
Submission Rules: Assignments must be submitted via Moodle as files in pdf, doc, or dox formate. You can submit papers in English or French. However, it might take longer to grade papers in French, and I will comment on your paper in English. Concordia's Writing Assistance Program can help you improve your general writing as well as your English language skills.
Policies on late work and policies on early work: For paper assignments or other writing submissions: You lose two thirds of a letter grade per day that the paper is late. I am happy to look at drafts, and typically will provide feedback on them verbally during a meeting in my office.
General remark: I strive to be very clear in my expectations, because I think fairness requires this. Fairness to all people in class also requires that in ordinary circumstances (extraordinary cases are another matter) no one person can have a special extended deadline or write a test at an unusual time. If you foresee difficulty meeting a deadline or scheduled evaluation, please discuss this with me well in advance of the deadline or evaluation. I’m happy to make exceptions to grading policies, but only for what I judge to be exceptionally good reasons.

4.3 Academic Integrity and Plagiarism

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!
The Academic Code of Conduct can be found here: policies /Academic-Code-Conduct-2015.pdf
Please make sure that you comply with it. Help regarding how to cite your sources correctly can be found here:
Plagiarism and academic dishonesty are highly disruptive of the learning that we should be doing here. Should I detect any form of academic dishonesty, including plagiarizing from the internet, from books, journals, other students, etc., I will report it directly to the Vice-Dean of Academic Affairs. The penalties for plagiarism tend to be rather severe, and in any case undermine your learning process. So avoid it. In case of doubt as to what counts at plagiarism, ask me. Cite your sources and inspirations; this enriches your ideas by showing their roots in the thoughts of other people, and does not detract from your exposition, articulation, and development of ideas.

4.4 Special Needs

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 Please contact me privately in regard to your needs in this course.

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