Syllabus
* Mandatory: 1. RUSSELL R.: Introduction to Mathematical Philosophy. 9th ed. London: Allen and Unwin. 1956. 2. DESCARTES R.: Regulae ad directionem ingenii / Rules for the Direction of the Natural Intelligence. 1st ed. Amsterdam: Rodopi. 1998. 3. DESCARTES R.: Discourse on the Method. In: The Philosophical Writings of Descartes, vol. I. 1st ed. Cambridge: The Pitman Press. 1985.
* Recommended: 4. ARISTOTLE. Prior Analytics. Book I. (translated with an Introduction and Commentary by Gisela Striker) 1st ed. Oxford: Oxford University Press. 2009. 5. RUSSELL R, WHITEHEAD, A. N.: Principia Mathematica I. 2dn ed. Cambridge: Cambridge University Press. 1927.
Annotation
The course focuses on the idea of analysis (as “disentanglement” or “resolving complex expressions into simpler or more basic ones”): an analysis of arguments, thoughts, ideas, proofs, Etc. What does it mean to analyze? How do we do it? Do we learn art of analysis by theory or by a practice? The idea of analysis comes from Aristotle. The modern mathematical analysis has its roots founded in the early modern thinking of René Descartes and in his method. Besides, this course introduces the main ideas and skills of modern symbolic logic and foundations of mathematics (the ideas of proposition, variable, propositional function, first-order language, and the skills of proving propositions) as they are inscribed in Principia Mathematica by Bertrand Russell and Alfred N. Whitehead. All the necessary texts, notes, and exam materials will be provided to students.
1. Analysis (Aristotle)
2. Laws of Thought
3. Principia Mathematica: Primitive ideas
4. Axioms, definitions
5. Proofs I
6. Proofs II
7. Proofs III
8. Paradoxes
9. Paradoxes solved
10. Type theory
11. Method (Descartes)
12. Analysis reconsidered
13. Limits of imagination
14. Limits of Algebra