00388 - Philosophy of Science

Course contents

 Characters of Scientific Knowledge

The concept of measure is crucial for philosophy of science. What is meant by measuring? Is it possible to measure the infinite? How to give a numeric value for a physical quantity through measurement? In the Greek mathematics, the issue of incommensurable quantities determined the divergence between arithmetic and geometry. In some sense, a similar question arises in quantum physics from the difficulty of reconciling the continuous description of an isolated system with the uncertainty relations between observable quantities.

How does the observer affect the measurement process? How does geometry take hold of the mind of nature? Seeing perspective drawing as an art of measure, the Renaissance painters were first to gain a clear awareness of the ideal character of geometry.

This course aims to clarify the dialectic contrast “real-ideal” by exploring the link between artistic and scientific representation, and to show the opposition discrete-continuous not as a problem to be solved, but rather as an inescapable presupposition for defining both the notion of “real number” and the notion of “observable quantity”.

 

Mathematical Ideas

• Incommensurability
• Infinity: Potential and Actual
• The Euclidean Space
• Perspective
• Ideal Elements
• Effective Calculability
• Real Numbers

Physical Forms

• Observable Quantities
• Measuring and "Seeing"
• The Sensible World
• Virtual Reality
• The Representation Space
• The Uncertainty Principle
• The Continuity Principle

 

Readings/Bibliography

Feynman R. P., Leighton R. B., Sands M. (1965), "Quantum Behaviour", The Feynman Lectures on Physics, Addison-Wesley, Reading MA (chap 1)

Stillwell J. (2016), Elements of Mathematics. From Euclid to Gödel, Princeton University Press

 

Cassirer E. (1927), The Individual and the Cosmos in Renaissance Philosophy, Univ. of Pennsylvania Press, Philadelphia 1963

• Platon, Republic , VI-VII
• Cusanus N. [1440], On Learned Ignorance, (Book I: Chaps 1-17, Book III)

 

Dedekind R. [1872], “Continuity and Irrational Numbers,” in Ewald W. (ed.), From Kant to Hilbert (Vol. 2), Oxford Univ. Press, Oxford 1996 (765–779)

Hilbert D. [1930], "Logic and the Knowledge of Nature”, (Ewald 1996: 1157–1165)

 

Deutsch D. (1997), The Fabric of Reality, Penguin, London

Weyl H. (1932), "The Open World", in Mind and Nature, edited by P. Pesic, Princeton Univ. Press, Princeton 2009

Further Reading

Alberti L. B. [1436], On Painting, Penguin Books, London 2004

Gillies D. (1993), Philosophy of Science in the Twentieth Century, Blackwell, Oxford

Kline M. (1953), Mathematics in Western Culture, Penguin Books, London 1987

Popper K. R. (1956), The Open Universe. An Argument for Indeterminism from the Postscript to the Logic of Scientific Discovery, Routledge, London & New York

Lupacchini R., Angelini A. (eds), The Art of Science. From Perspective Drawing to Quantum Randomness, Springer 2014

Weyl H. (1949), Philosophy of Mathematics and Natural Science, Princeton Univ. Press, Princeton

Teaching methods

Lectures

Students are advised to attend classes regularly.

Assessment methods

Written and oral examination.

Office hours

See the website of Rossella Lupacchini