Foundations of the Formal Sciences VIII:
History & Philosophy of Infinity
the network INFTY
in the series FotFS
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
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:
Brendan Larvor (Hatfield, U.K.),
Benedikt Löwe (chair; Amsterdam, The Netherlands & Hamburg, Germany),
Peter Koellner (Cambridge MA, U.S.A.),
Dirk Schlimm (Montréal, Canada).
- 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?
- 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?
- 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?
Contact: bloewe (at) science.uva.nl
The conference FotFS VIII: History & Philosophy of Infinity is
generously sponsored by the ESF research network INFTY and the Division for Logic, Methodology and Philosophy of
Science of the International Union for History and Philosophy of