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History and Philosophy of Mathematics

History and Philosophy of Mathematics

Code	14772
Year	2
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	N.A.
Learning outcomes	The main aim of this subject is to introduce contents of history and philosophy of mathematics. It is made a continuum between philosophy and mathematics, where relevant episodes of the history of mathematics underpin philosophical problems. The following questions are addressed. What is the nature of mathematical knowledge? What are the mathematical foundations? Is it mathematics indispensable to other sciences? How can mathematics explain natural phenomena? Does a Turing machine think? Main outcomes to be developed by the students: 1) Critical, autonomous and independent thought. 2) To contextualize relevant mathematical theories and applications in its history and philosophy. 3) To relate cognitive contents of mathematics and other sciences. 4) To express clear and rigorous thoughts about the program themes.
Syllabus	1. Introduction to History and Philosophy of Mathematics. 2. Geometrical knowledge. Euclidian geometry: platonism, empirism and the synthetic a priori (Kant). The rising of non-euclidian geometries: conventionalism (Poincaré). 3. Mathematical foundations: logicism (Frege), intuitionism (Brouwer) and formalism (Hilbert). 4. Pot-pourri of contemporary topics: platonism vs. nominalism; the problem of mathematical knowledge (Benacerraf); scientific naturalism (Quine) vs. mathematical naturalism (Maddy); mathematical indispensability; mathematical explanation; Chinese room (Turing vs. Searl).
Main Bibliography	- Frege, G. (1992), Os Fundamentos da Aritmética, (Lisboa: INCM). - Friend, M. (2007), Introducing Philosophy of Mathematics, (Stocksfield: Acumen). - George, A. & Velleman, D. (2002), Philosophies of Mathematics, (GB: Blackwell). - Kant, I. (1994), Crítica da Razão Pura, (Lisboa: FCG). - Kline, M. (1982), The Loss of Certainty, (NI: OUP). - Kline, M. (1990), Mathematical Thought from Ancient to Modern Times, (NI: OUP). - Poincaré, H. (2010), Filosofia da Matemática – Breve Antologia de Textos, (Lisboa: Centro de Filosofia das Ciências da Universidade de Lisboa). - Quine, W. (1995), Filosofia e Linguagem, (Porto: Asa). - Shapiro, S. (2000), Thinking About Mathematics, (Nova Iorque: OUP). - Shapiro, S. (2005), The Oxford Handbook of Philosophy of Mathematics and Logic, (Nova Iorque: OUP). - Sklar, L. (1977), Space, Time and Spacetime, (LA: UCP). - Weiner, J. (2004), Frege Explained, (EUA: Open Court).
Teaching Methodologies and Assessment Criteria	Presentation by the teacher. Argumentatively disciplined discussion between the teacher and students. Writing of written assignments. Oral presentation by students. Continuous assessment 1 written assessment test + written assignments Date of the written assessment test: June 3, 2025. Grading of the teaching-learning process: Arithmetic average of the written test and written assignments.
Language	Portuguese. Tutorial support is available in English.