FotFS VIII: History and Philosophy of Infinity

Title: FotFS VIII: History and Philosophy of Infinity
Location: Cambridge, England
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Start Date: 2013-09-20
End Date: 2013-09-23

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 Löwe (chair; Amsterdam, The Netherlands & Hamburg, Germany), Peter Koellner (Cambridge MA, U.S.A.), Dirk Schlimm (Montréal, Canada).