McGill.CA / History & Philosophy of Mathematics

Course offerings

Students interested in HPM@McGill are encouraged to take a look at the courses listed below, which are offered regularly in the Department of Philosophy.

PHIL 311 offers a general introduction to philosophy of mathematics. Specialized topics are offered in PHIL 411 and in the seminar PHIL 511. Most recently, PHIL 411 has covered the developments from Newton and Leibniz to Dedekind (including MacClaurin, Gauss, Bolzano, Frege), as well as Frege's Foundations of Arithmetic and its modern analyses by Wright, Boolos, etc.; PHIL 511 has covered Philosophy of Geometry (Winter 2013).

PHIL 311. Philosophy of Mathematics.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Faculty of Arts)
This course is not offered this catalogue year.

Description

This course provides an historically informed introduction to philosophy of mathematics. It gives the student an overview of prominent issues and arguments, to enable her to follow and discuss contemporary research in philosophy of mathematics.
  • Prerequisite: PHIL 210

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PHIL 411. Topics in Philosophy of Logic and Mathematics.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Faculty of Arts)
This course is not offered this catalogue year.

Description

A course focusing on some philosophical issue (e.g., the nature of numbers or the relation of truth to provability) as it arises in the study of mathematics and logic.
  • Prerequisites: PHIL 210 or the equivalent, and one intermediate course in philosophy

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PHIL 611. Seminar: Philosophy of Logic and Mathematics.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Graduate Studies)
This course is not offered this catalogue year.

Description

Seminar on a particular topic in philosophy of logic and mathematics.
  • Restriction(s): Not open to students who have taken PHIL 511.

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In addition, History and Philosophy of Ancient Science also frequently covers mathematical topics:

PHIL 350. History and Philosophy of Ancient Science.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Faculty of Arts)
This course is not offered this catalogue year.

Description

Topics in ancient pure mathematics (geometry and number theory), "mixed mathematics" (astronomy, music theory, optics, mechanics), and/or natural science (including medicine), studied with a view to philosophical issues raised by the content of ancient science and/or by the logic of scientific argument.

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Depending on the instructor, PHIL 481 may also be of interest. As 'Mathematics in early modern philosophy' it covers the role of mathematics in the philosophical work of Descartes, Locke, Leibniz and Kant.

PHIL 481. Topics in Philosophy.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Faculty of Arts)
This course is not offered this catalogue year.

Description

Topics in philosophy. Topic varies by year.

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Related courses in other departments at McGill:

MATH 338. History and Philosophy of Mathematics.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.

Description

Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed, culminating in the discovery of the infinitesimal and integral calculus by Newton and Leibnitz. Demonstration of how mathematics was done in past centuries, and involves the practice of mathematics, including detailed calculations, arguments based on geometric reasoning, and proofs.
  • Fall
  • Prerequisites: MATH 133, MATH 141.

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See also ourses offered within the inter-faculty programs of

Logic

Logic is offered at various levels at McGill, e. g.,

PHIL 210. Introduction to Deductive Logic 1.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Faculty of Arts)
Terms Offered: Summer 2025
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Description

An introduction to propositional and predicate logic; formalization of arguments, truth tables, systems of deduction, elementary metaresults, and related topics.
  • Restriction: Not open to students who are taking or have taken MATH 318
  • Restriction: Not open to students who are taking or have taken MATH 318

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PHIL 310. Intermediate Logic.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Faculty of Arts)
This course is not offered this catalogue year.

Description

A second course in Logic. NB. The course will be technical in nature, and some mathematical aptitude is essential. The emphasis is on the expressive properties of standard logical systems, including implications for the philosophy of mathematics. We will study the Completeness of First-Order Logic, then the 'limitative' theorems of Tarski and Gödel.
  • Prerequisite: PHIL 210 or equivalent

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Course information not available.

PHIL 610. Seminar on Advanced Logic 2.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Philosophy (Graduate Studies)
This course is not offered this catalogue year.

Description

Seminar on a particular topic in advanced logic. Topic varies by year.
  • Prerequisite(s): Permission of the instructor .
  • Restriction(s): Not open to students who have taken PHIL 510.

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COMP 230. Logic and Computability.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Computer Science (Faculty of Science)
This course is not offered this catalogue year.

Description

Propositional Logic, predicate calculus, proof systems, computability Turing machines, Church-Turing thesis, unsolvable problems, completeness, incompleteness, Tarski semantics, uses and misuses of Gödel's theorem.
  • 3 hours
  • Prerequisite: CEGEP level mathematics.

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MATH 318. Mathematical Logic.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.

Description

Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.
  • Fall
  • Prerequisite(s): MATH 235 or MATH 240 or MATH 242.

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For more specialized topics, see also the Computation and Logic Group in the School of Computer Science.

Related courses in other departments in Montreal:

Students can also take courses at Concordia, Université de Montréal, and UQÀM.

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