20-23 September 2013
Cambridge, England
Foundations of the Formal Sciences VIII
FotFS VIII: History and Philosophy of Infinity
http://www.math.uni-bonn.de/people/fotfs/VIII/
20-23 September 2013
Corpus Christi College
Cambridge, England
KEYNOTE SPEAKERS:
Haim Gaifman (Columbia University, U.S.A.)
Marcus Giaquinto (University College London, England)
Catherine Goldstein (Institut de Mathematiques de Jussieu, France)
Christian Greiffenhagen (University of Nottingham, England)
Luca Incurvati (University of Cambridge, England)
Matthew Inglis (Loughborough University, England)
Charles Parsons (Harvard University, U.S.A.)
Michael Potter (University of Cambridge, England)
Christian Tapp (Ruhr-Universität Bochum, Germany)
Pessia Tsamir (Tel Aviv University, Israel)
Dina Tirosh (Tel Aviv University, Israel)
Jean Paul Van Bendeghem (Vrije Universiteit Brussel, Belgium)
The concept of infinity has fascinated philosophers and mathematicians for many
centuries: e.g., the distinction between the potential and actual infinite
appears in Aristotle's Physics (in his treatment of the paradoxes of Zeno) and
the notion was implied in the attempts to sharpen the method of approximation
(starting as early as Archimedes and running through the middle ages and into
the nineteenth century). Modern mathematics opened the doors to the wealth of
the realm of the infinities by means of the set-theoretic foundations of
mathematics.
Any philosophical interaction with concepts of infinite must have at least two
aspects: first, an inclusive examination of the various branches and
applications, across the various periods; but second, it must proceed in the
critical light of mathematical results, including results from
meta-mathematics.
The conference History & Philosophy of Infinity will emphasize philosophical,
empirical and historical approaches. In the following, we give brief
descriptions of these approaches with a number of questions that we consider
relevant for the conference:
1. In the philosophical approach, we shall link questions about the
concept of infinity to other parts of the philosophical discourse, such
as ontology and epistemology and other important aspects of philosophy
of mathematics. Which types of infinity exist? What does it mean to
make such a statement? How do we reason about infinite entities? How do
the mathematical developments shed light on the philosophical issues
and how do the philosophical issues influence the mathematical
developments?
2. Various empirical sciences deal with the way we as finite human beings
access mathematical objects or concepts. Research from mathematics
education, sociology of mathematics and cognitive science is highly
relevant here. How do we represent infinite objects by finite means?
How are infinite objects represented in the human mind? How much is our
interaction with infinite concepts formed by the research community?
How do we teach the manipulation of infinite objects or processes?
3. Infinity was an important concept in philosophy and theology from the
ancient Greeks through the middle ages into the modern period. How did
the concepts of infinity evolve? How did questions get sharpened and
certain aspects got distinguished in the philosophical debate? Did
important aspects get lost along the way?
Scientific Committee. Brendan Larvor (Hatfield, U.K.), Benedikt Loewe (chair;
Amsterdam, The Netherlands & Hamburg, Germany), Peter Koellner (Cambridge MA,
U.S.A.), Dirk Schlimm (Montreal, Canada).
FotFS VIII is sponsored by the ESF network INFTY: New frontiers of infinity.