Study-Unit Description

Study-Unit Description


TITLE Philosophy of Mathematics

LEVEL 03 - Years 2, 3, 4 in Modular Undergraduate Course



DESCRIPTION This study-unit will deal with the special questions that arise from our acquisition of mathematical knowledge. Therefore it touches upon metaphysics, epistemology, the philosophy of science and the philosophy of perception. Hence two important questions to be explored are (1) What, if anything, are mathematical objects like whole numbers? (2) How (if at all) do we gain mathematical knowledge?

Study-unit Aims:

This study-unit aims to introduce students to basic concepts in the philosophy of mathematics through a close engagement with different streams of thought in the histories of philosophy and of mathematics (including the contemporary debate) and specific texts so as to encourage students to think critically and to discuss the subject.

The study-unit will also offer students from two different areas of study the opportunity to engage meaningfully and critically with themes in philosophy and in mathematics.

Learning Outcomes:

1. Knowledge & Understanding
By the end of the study-unit the student will be able to:

- engage critically with notions in the philosophy of mathematics and reflect about the area of study one is undertaking;
- analyse, through close reading, primary texts in the philosophy of mathematics;
- identify and review relevant secondary literature concerning specific authors and/or themes in the philosophy of mathematics.

2. Skills
By the end of the study-unit the student will be able to:

- read analytically and critically a broad selection of texts in the philosophy of mathematics;
- identify and reflect upon key concepts and discussions in the philosophy of mathematics;
- engage in meaningful discussions on specific topics covered in the Unit;
- present coherent arguments related to the topics in the philosophy of mathematics;
- write an assignment on a specific author/theme in the philosophy of mathematics.

Main Text/s and any supplementary readings:

Main Texts:

Colyvan, M (2012) An Introduction to the Philosophy of Mathematics, Cambridge University Press.
Linnebo, Ø (2017) Philosophy of Mathematics, Princeton University Press.
Marcus R (2016) An Historical Introduction to the Philosophy of Mathematics: A Reader, Bloomsbury Academic.
Moore, A (2001) The Infinite, second edition, New York: Routledge.
Putnam, H (1983) Philosophy of Mathematics: Selected Readings 2nd edition, Cambridge University Press.

Supplementary Texts:

Benacerraf, P (1965) ‘What numbers could not be’, Philosophical Review 74, pp47-73; (1973) ‘Mathematical Truth’, Journal of Philosophy 70, pp661-80 – Putnam, H (1983) Philosophy of Mathematics: Selected Readings 2nd edition, Cambridge University Press.
Blackburn, S (1984) Spreading the word. Oxford: Clarendon Press.
Brouwer, J (1949) ‘Consciousness, Philosophy and Mathematics’, in Benacerraf & Putnam (1983), pp90-6.
Brown, J R (2008) Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures, Routledge.
Dummett, M (1973) ‘The philosophical basis of Intuitionistic Logic’, in Benacerraf & Putnam (1983), pp97-130
Field, H (1980) Science without numbers. Oxford: Blackwell.
Fine, K (2002) The Limits of Abstraction, Oxford: Oxford University Press.
Frege, G (1879) Die Grundlagen der Arithmetik; trans. Austin (1950) as Foundations of Arithmetic. Oxford:Blackwell; (1893) Die Grundgesetze der Arithmetik. Vol I, Olms: Hildesheim.
Gödel, K (1947) ‘What is Cantor’s Continuum Problem?’, American Mathematical Monthly 54, pp515-25, reprinted in Benacerraf & Putnam (1983), pp470-86.
Hale, B. & Wright, C (2001) The Reason’s Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics, Oxford: Oxford University Press.
Hellman, G (1989) Mathematics without number. Oxford; Clarendon Press.
Hilbert, D (1925) ‘On the Infinite’, in Benacerraf & Putnam 1983, 183–201.
Putnam, H (1971) Philosophy of Logic. New York: Harper.
Quine, W. V. O. (1970), The Philosophy of Logic, second edition. Englewood Cliffs, NJ : Prentice-Hall.
Resnik, M (1981) ‘Mathematics as a science of patterns: Ontology and Reference’, Noûs 15, pp529-49; (1982),‘Mathematics as a science of patterns- Epistemology’, Noûs 16, pp95-105.
Russell, B (1902) ‘Letter to Frege’, in van Heijenoort 1967, 124–125.
Shapiro, S (1991) Foundations without foundationalism. Oxford Logic Guides 17, Oxford University Press; Philosophy of Mathematics: Structure and Ontology. Oxford University Press.
Shapiro, Stewart, editor (2005), The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford: Oxford University Press.
Wittgenstein, Ludwig (1983), Remarks on the Foundations of Mathematics, revised edition. Cambridge, MA: MIT Press.
Wright, C (1983) Frege’s conception of numbers as objects. Scots Philosophical Monographs, Aberdeen University Press.
Zermelo, E (1930) ‘On Boundard Numbers and Domains of Sets’, translated by M. Hallett, in W. Ewald (ed.), From Kant to Hilbert: A Source Book in Mathematics (Volume 2), Oxford: Oxford University Press, 1996, pp. 1208–1233.


Assessment Component/s Assessment Due Resit Availability Weighting
Assignment SEM2 Yes 100%

LECTURER/S Mark Sultana

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It should be noted that all the information in the description above applies to study-units available during the academic year 2020/1. It may be subject to change in subsequent years.