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.