The purpose of this course in the Liberal Arts program is to demonstrate the nature of formal reasoning in general and mathematical reasoning in particular. The course aims to demonstrate the elegance, beauty, and power of logic and mathematics. With respect to the objectives of the Liberal Arts program, this course aims to develop "Critical Thought and Reflection", with its two specific objectives: "Recognition of how knowledge is organized, how it is divided into disciplines in the fields of social science, science, logic, mathematics, arts, and letters; and its limits" and "Recognition, assessment, criticism, and formulation of valid arguments in these disciplines".

OBJECTIVES    Students should be able to:

• Understand and use the vocabulary of formal reasoning and mathematics, and be able to distinguish: rationality vs. logic; inductive vs. deductive arguments; logical argument vs. metaphor vs. description vs. example.
• Understand the strategies and frameworks of formal argument.
• Construct and evaluate formal deductive arguments, both verbal and symbolic / mathematical.
• Recognize the forms of argument and kinds of evidence appropriate in mathematical and logical reasoning.
• Understand the relationship between pure logical / mathematical reasoning and its application in other fields of knowledge.
• Understand the limits of deductive reasoning in mathematics and in non-mathematical domains.
• Respond aesthetically to elegant proofs.
• Understand certain "non-classical" logics and their philosophical significance.
• Apply the techniques of a formal logic to a suitable non-logical context.

COURSE CONTENT

• The vocabulary of formal reasoning, mathematics, and metamathematics: (e.g., reasoning and rational, logic and logical, valid, sound, infer and inference, imply and implication, axiom, postulate, assumption, premise, proof, tautology and contradiction, conclusion, formal system, completeness, consistency, derivation, paradox, etc.).
• Postulational formal systems. Interpretation of a formal system. Pure vs. applied mathematics. Mathematics as language ("the language of science").
• Numeracy. The nature of number.
• Time permitting, Gödel's incompleteness theorems; application of the proof theory of formal systems to linguistics, and possibly to other domains.

REQUIRED TEXT

• The principle course text is R.A.G. Seely, Principles of Mathematics and Logic.
• You will also be asked to read Harry Frankfurt, On Bullshit.

METHODS   At least two (usually three) lectures each week will be devoted to articulating and discussing the concepts and demonstrating the methods of logic and mathematics. Some two-hour "labs" will be spent constructing arguments and proofs and solving problems.

ATTENDANCE    Attendance at all classes is mandatory. Students who miss more than 10 hours of classes ( i.e. roughly two weeks of the semester) for any reason should not expect to pass the course. Doctors' notes or other evidence of serious reasons for absence are not a substitute for attendance.

EVALUATION    Grades will be based on:

• Five class tests (given roughly every third Friday). The test getting the lowest mark will count toward 10% of the final grade, and the others will each count toward 20% of the final grade.
• Informed participation in class discussion (10%). Participation will be judged on the amount of involvement in class discussion, demonstrated familiarity with assigned readings and lecture material, and on the soundness and originality of the ideas expressed.

COURSE COSTS:    About $25 for the text.

AVAILABILITY    To get help, students may call me at 457-6610 (Ext. 5865) (my office, where you can leave a "voice-mail" message) or email me at rags@math.mcgill.ca. My office is in Herzberg (main Maths Study Area).

NOTE: Cheating and Plagiarism are unacceptable to John Abbott College. For more information on Student Academic Rights and Responsibilities consult the IPESA.

Grade review: It is the responsibility of students to keep all assessed material for at least one month past the grade review deadline in the event that they would want to request a grade review. Students can learn more about their rights and responsibilities by reading the IPESA.