Projective Theory of Technology

PHD Kolloquium Summer 2012: Computation, and the question of the applicability of arithmetics

PhD Kolloquium in Projective Theory on Technology, Summer semester 2012, LAV CAAD Swiss Federal Institute of Technology ETH Zürich, Switzerland

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Computation is treated today as an art, just as Mechanics had been in the Renaissance and the Baroque periods. This basically means that its actual performance is widely recognized and welcome, striking in effect, unexpected, fascinating and also convincing-by-fact, while at the same time the actual methods and procedures are applied rather like recipes. Over time, this gives rise to: 1) a lot of the same, boredom. And 2) to vast disputes around ancient questions on the rôle of technics in the nature of reasoning, intelligence, science.

We want to gain a better insight about the modern theoretical context of these involved topoi, and will start with reading Michael Potter‘s introductory book to the main stances Reason‘s Nearest Kin –Philosophies of Arithmetics from Kant to Carnap, Oxford University Press 2002.

Meetings are held on Wednesdays, 11 am (Swiss Time) via skype, between the CAAD Chair in Zürich and the NUS / ETHZ Future Cities Laboratory in Singapore.

Compulsory reading

Michael Potter, Reason‘s Nearest Kin – Philosophies of Arithmetics from Kant to Carnap, Oxford University Press 2002.


Wednesday February 22 2012
Chapter O – Introduction

Wednesday February 29 2012
Chapter 1 – Kant

Wednesday March 7 2012
Chapter 2 – Grundlagen

Wednesday March 14 2012
Chapter 3 – Dedekind

Wednesday April 4 2012
Chapter 4 – Frege‘s Account of Classes

Wednesday April 11 2012
Chapter 5 – Russell‘s Account of Classes

Wednesday April 18 2012
Chapter 6 – The Tractatus

Wednesday May 2 2012
Chapter 7 – The Second Edition of Principia

Wednesday May 9 2012
RECAP chapters 1-7

Wednesday May 16 2012
Chapter 8 – Ramsey

Tuesday May 22 2012
Chapter 9 – Hilbert‘s Programme

Tuesday May 29 2012
Chapter 10 – Gödel

Tuesday June 5 2012
Chapter 11 – Carnap

Tuesday June 12 2012
Chapter 12 – Conclusion

Elective reading suggestions
on Dedekind‘s notion of numerical ideality and the rôle of abstraction therein

Richard Dedekind, Essays on the Theory of Numbers, transl. by Wooster Woodruff Beman, Project Gutenberg, released 2007.

Erich H. Reck, “Dedekind’s Contributions to the Foundations of Mathematics”, The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), edited by Edward N. Zalta.

Erich H. Reck, “Dedekind, Structural Reasoning, and Mathematical Understanding” in: New Perspectives on Mathematical Practices, B. van Kerkhove, ed., Singapore: WSPC Press, 2009, pp. 150-173.

W.W. Tait, “Frege versus Cantor and Dedekind: On the Concept of Number” in Frege: Importance and Legacy, M. Schirn, ed., de Gruyter: Berlin, pp. 70– 113.

Sephorah Mangin, “Dedekind Abstraction and the ‘Free Creation’ of the Natural Numbers”, online: Dedekind_Abstraction.pdf

Vera Bühlmann, “Continuing the Dedekind Legacy today: Some ideas concerning architectonic computation” paper delivered at Turing 2012: International Conference on Philosophy, Artificial Intelligence and Cognitive Science at the De la Salle University in Manila, Philippines, March 27-28 2012.

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