The History of Logic and Paradoxes

Paradoxes are various cases of unacceptable propositions demonstrated in ways that seem appropriate. Logic is the process of elucidating and
systematizing the laws of proper argumentation. As such, knowledge of logic supports an accurate understanding of paradoxes. Further, paradoxes are
also notably sometimes deeply connected to historical achievements in logic and mathematics.. This course will introduce students to meaningful
paradoxes and practical argumentation techniques against a background of the history of logic and mathematics.

Science literacy, logical thinking

1) Introduction... What is logic? What is a paradox?
2) Arguments in the conduct of science
3) Validity of deduction and the challenges of logic
4) Inference rules of natural deduction [1]
5) Inference rules of natural deduction [2]
6) Zeno's Paradox / Practicing natural deduction [1]
7) Set cardinality and power sets / Practicing natural deduction [2]
8) Binary and diagonal reasoning / Practicing natural deduction [3]
9) Power sets and Cantor's paradox / Practicing natural deduction [4]
10) Russell's paradox / Practicing natural deduction [5]
11) The Hilbert Program and intuitive logic / Practicing natural deduction [6]
12) Diagonal reasoning and self-references / Practicing natural deduction [7]
13) First incompleteness theorem / Practicing natural deduction [8]
14) Second incompleteness theorem / Practicing natural deduction [9]
15) Summary / Practicing natural deduction [10] / Course survey

Syllabus (Japanese site only)