History and Philosophy of Mathematics
Mathematics
(08/09)
Description
At UBI,
History of Philosophy of Mathematics (HPM) is a subject according to the
traditional principles of analytic philosophy. That is, HPM aims to express clear,
rigours and argumentative thoughts. In particular, in this subject there is a
naturalist continuum between philosophy and mathematics/science where
historical episodes of mathematics/science are used as
a source of philosophical problems.
Here are some of the questions
that are discussed in HPM: What is the nature of
mathematical knowledge? Could mathematics be reduced
to logical principles? Are all mathematical proofs valid? Is mathematics
nothing more than symbol manipulation like a game? Are there
mathematical objects or, indeed, are mathematical objects fictions created by
the mathematician? Is mathematics indispensable to scientific theories?
Syllabus
1. Introduction to History and Philosophy of
Mathematics.
2.
Geometrical knowledge: Platonism, Empiricism, synthetic a priori (Kant) and Conventionalism (Poincaré).
3.
Foundations of mathematics: Logicism (Frege’s Grundlagen) and Intuitionism.
4.
Contemporary topics of philosophy of mathematics: Platonism vs. Nominalism; Holism, Naturalism and Ontological Commitment (Quine); Mathematical Naturalism (Maddy); Benacerraf’s
problem; Indispensability.
To
develop critical and individual thought about problems, conceptions, theories,
theses, ideas and arguments concerning HPM.
a) Colyvan, M. (2001), “Indispensability Arguments in the
Philosophy of Mathematics”, (Stanford Encyclopedia of
Philosophy).
b) Balaguer, M. (2008), “Mathematical Platonism”, in Gold &
Simons, Proof and other Dilemas, Mathematical Association of
c)
Frege,
G. (1992), Os Fundamentos da Aritmética,
(Lisboa: INCM).*
d) Friend, M. (2007), Introducing
Philosophy of Mathematics, (Stocksfield: Acumen),
Caps. 1 e 2.
e) George, A. & Velleman, D. (2002), Philosophies of Mathematics, (GB: Backwell), caps. 1, 2, 4.*
f)
Heck,
R. (1999), “Teorema de Frege: uma Introdução”, in Zilhão (org.), Do Círculo de Viena à Filosofia Analítica
Contemporânea, (Lisboa: Livros de Areia, 2007)
g)
Kant,
I. (1994), Crítica da Razão Pura,
(Lisboa: FCG), p. 36-49 e 61-70.
h) Maddy, P. (2005), “Three Forms of Naturalism”, in Shapiro (org.), The
i)
Poincaré,
H. (1968), A Ciência e a Hipótese,
(Alfragide: Galeria Panorama), caps. 3, 4.
j)
Quine,
W. (1975), “Cinco Marcos do Empirismo” in Quine, Filosofia e Linguagem, (Porto: Asa,
1995), p. 11-17.
k)
Quine,
W. (1975), “Postulações e Realidade” in Quine, Filosofia e Linguagem, (Porto: Asa,
1995), p. 177-187.
l)
Resnik, M. (2005), “Quine and the Web of Belief”, in
Shapiro (org.), The
m) Shapiro, S. (2000), Thinking About
Mathematics, (Nova Iorque: OUP).*
n) Sklar, L. (1977), Space, Time and Spacetime, (LA: UCP),
cap. 2 (sec.: A, B (1, 2), E, F, G e H).*
o) Weiner, J. (2004), Frege Explained,
(EUA:
Blackburn, S. (1997), Dicionário de Filosofia, (Lisboa: Gradiva).*
Branquinho, J. & Murcho, D.
(2001), Enciclopédia de Termos Lógico-Filosóficos, (Lx: Gradiva).
Lecourt, D. (1999), Dictionnaire d’Histoire et Philosophie des
Sciences, (Paris: PUF).*
* Available in UBI’s library
The
teacher gives the other material.
Correspondence between points of syllabus and reading
list
1. m) (chap.1).
2. g), i),
n).
3. Logicism: c),
e) (chap. 2) o); Intuitionism: d), e) (chap. 4).
4. a), b) h),
j), k) l).
Assessment Requirements
1 or 2 papers (1-2 pages) + essay (and oral
presentation) + test.
Grosso modo, the essay is a way to learn technical skills of writing scientific
philosophical papers.
Wed, 11h (Office 4.06)
Stanford Encyclopedia
of Philosophy