27387 - Methods of Scientific Knowledge

Learning outcomes

Students are guided to focus on and analyze topics and issues emerging from a methodological reflection on logic-mathematical knowledge and scientific investigation.

Course contents

Beauty as a Method

«The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics» (Hardy, A Mathematician's Apology, 1940).

While Leonardo prompts the painter to transmute itself into the very mind of nature and be the interpreter between it and art, the physician – according to Paul Dirac – must embrace the nature's criteria of beauty:

«In constructing his theory of gravitation, Einstein did not attempt to explain some observational result. On the contrary, his whole way of working aimed at seeking a beautiful theory, such as the theory which Nature would choose» (Dirac, The Test of Time, 1979).

But would nature choose quantum theory?

Why is there general agreement about the beauty of relativity theory, whereas the opinions regarding quantum theory continue to be controversial?

How does the beauty of scientific image mirror the beauty of nature?

Is there a relationship between beauty and truth?

What is beauty?

More than to find answers, this course aims to explore the meaning of the questions above through a critical analysis of key notions – such as harmony, simplicity, symmetry – involved in the idea of beauty.

 

 

Module 2

 

The second module of the course will introduce the most important philosophical reflections on the nature of space and time as forged by the methods and developments of physics, first of all by the Einsteinian revolution of Special and General Relativity Theories that swept away the old, but still intuitive and close to common sense, Newtonian conception.
Space and time are extraordinarily deep but also exceptionally elusive concepts that physics and philosophy together have often tried to capture thanks to the acumen of some of their greatest thinkers, from Descartes to Newton to Leibniz, from Kant to Reichenbach, from Mach to Poincaré, from Einstein to Gödel. Some of the traditional questions these authors have tried to answer, along with the more recent debates arisen within the philosophy of physics, and which will be addressed in the course, are:
What kind of entities are space and time (and spacetime)?
Are they genuine substances, existing in the same way as material objects, or are they relations?
Are physical fields and matter more real than space and time?
Does time really "flow"?
Is only the present real, or is the past real as well? And what of the future?
What is the "shape" of space?
Does the geometry of physical space capture objective facts concerning real space, or is it merely, in some way, conventional?
Are time travels possible, conceptually and physically, or paradoxical?
What is cosmic time at the base of modern relativistic cosmology?
In what sense is the space of the universe expanding?
What role do space and time play in the multiverse scenario envisaged by some modern cosmological theories?
Special technical knowledge (of mathematics and physics) is not required: the useful notions will be introduced during the course as cleanly and accessibly as possible.

Readings/Bibliography

Module 1

Cassirer E. (1924), «Eidos und Eidolon. Das Problem des Schönen und der Kunst in Platons Dialogen», in Saxl F. (eds) Lectures of the library Warburg, Teubner, Wiesbaden [https://link.springer.com/chapter/10.1007/978-3-663-15764-9_1]

Cassirer E. (1945), «Goethe and the Kantian Philosophy», in Rousseau, Kant, Goethe, Princeton Univ. Press, Princeton (pp. 61-98)

Deutsch D. (2004), «It from Qubit», in J.D. Barrow, P.C.W. Davies, C.L.Harper Jr. (eds.), Science and Ultimate Reality, Cambridge Univ. Press, Cambridge 

Dirac E. (2019), La bellezza come metodo, Cortina, Milano

Kemp M. (1990), The Science of Art, Yale UP, New Haven 

Panofsky, E. (1927). “Die Perspektive als ‘symbolische Form”’, Vorträge der Bibliothek Warburg, B. G. Teubner, Leipzig-Berlin

Plato, Timeo

Wheeler J. A. (1986), «How Come the Quantum», Annals of the New York Academy of Science, 480

 

Further Reading

• Deutsch D. (2011), The Beginning of Infinity, Allen Lane
• Feynman R (1965), The Character of Physical Law, Penguin Books, London-New York
• Stewart J. (2007), Why Beauty is Truth, Basic Books, New York 
• van Fraassen B. C. (2008), Scientific Representation: Paradoxes of Perspective, Oxford UP, Oxford
• Weyl H. (1952), Symmetry, Princeton UP, Princeton

 

Module 2

Main References

Dainton, B. (2010), Time and Space, 2a ed., Durham, Acumen Publishing Limited.

Jammer, M. (1966), Concepts of space. The history of theories of space in physics. Third enlarged edition, Dover Publications, 1993)

Norton, J. D. (2015), Einstein for Everyone, https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/

Secondary References

Boniolo, G. e Dorato, M. (1997), “Dalla Relatività Galileiana alla Relatività Generale”, in G. Boniolo (a cura di), Filosofia della Fisica, Milano, Bruno Mondadori, pp. 5-167.

Dorato, M. (2005), “La filosofia dello spazio e del tempo”, in V. Allori, M. Dorato, F. Laudisa e N. Zanghì (a cura di), La natura delle cose. Introduzione ai fondamenti e alla filosofia della fisica, Roma, Carocci, pp. 15-137.

Dorato, M. (2013), Che cos’è il tempo? Einstein, Gödel e l’esperienza comune, Roma, Carocci

Earman, J. (1989), World Enough and Space-Time. Absolute Versus Relational Theories of Space and Time. Cambridge, Massachusetts, MIT Press.

Earman, J. e Norton, J. (1987), 'What Price Space-Time Substantivalism? The Hole Story',The British Journal for the Philosophy oj Science 38, pp. 515-25.

Einstein, A. (1952), “La relatività e il problema dello spazio”, in A. Einstein, Relatività: Esposizione divulgativa, Torino, Bollati Boringhieri, 1967, pp. 294-313.

Esfeld, M. (2018), Filosofia della natura. Fisica e ontologia, Torino, Rosenberg & Sellier (fino a p. 73).

Huggett, N. (2010), Everywhere and Everywhen. Adventures in Physics and Philosophy, Oxford, Oxford University Press (da cap. 4 a cap. 15).

Mathieu, V. (1963), Epistolario Leibniz-Clarke, in V. Mathieu (a cura di), G. W. Leibniz. Saggi filosofici e lettere, Editori Laterza, Bari, pp. 385-467.

Macchia, G. (2006), “L’Argomento del buco di Einstein nel recente dibattito sull’ontologia dello spaziotempo”, Isonomia,http://www.uniurb.it/Filosofia/isonomia/2006macchia.pdf .

Macchia, G. (2015), “Relatività generale e cosmologia: basi teoriche e questioni filosofiche”, in P. Pecere (a cura di), Il libro della natura. II. Scienze e filosofia da Einstein alle neuroscienze contemporanee, Carocci, Roma, pp. 115-139.

Morganti, M. (2016), Filosofia della fisica. Un’introduzione, Roma, Carocci, (pp. 69-96 e 183-196).

Norton, J. D. (1992), “Philosophy of Space and Time”, in M. H. Salmon et al. (eds.), Introduction to the Philosophy of Science, Englewood Cliffs, New Jersey, Prentice-Hall, pp. 179-232; reprint Hackett Publishing Company, UK, 1999.

Norton, J. D. (2019), The Hole Argument, in N. Zalta (ed.), Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/spacetime-holearg/

Rugh, S. E. e Zinkernagel, H. (2009), “On the Physical Basis of Cosmic Time”, Studies in History and Philosophy of Modern Physics 40, pp. 1-19.

Torrengo, G. (2011), I viaggi nel tempo. Una guida filosofica, Roma-Bari, Laterza.

 

Further Reading

DiSalle, R. (2009), Capire lo spazio-tempo. Lo sviluppo filosofico della fisica da Newton a Einstein, Torino, Bollati Boringhieri (Vers. Orig. Understanding Space-Time. The Philosophical Development of Physics from Newton to Einstein, 2006, Cambridge University Press).

Kostro, L. (2001), Einstein e l'Etere: Relatività e Teoria del Campo Unificato. Bari: Ediz. Dedalo.

Maudlin, T. (2012), Philosophy of Physics: Space and Time, Princeton and Oxford, Princeton University Press.

Nerlich, G. (2004), What spacetime explains. Metaphysical essays on space and time, Cambridge University Press.

Teaching methods

Lectures

Assessment methods

Oral examination

Marks:

30 cum laude - excellent as to knowledge, philosophical lexicon and critical expression.

30 – Excellent: knowledge is complete, well argued and correctly expressed, with some slight faults.

27-29 – Good: thorough and satisfactory knowledge; essentially correct expression.

24-26 - Fairly good: knowledge broadly acquired, and not always correctly expressed.

21-23 – Sufficient: superficial and partial knowledge; exposure and articulation are incomplete and often not sufficiently appropriate

18-21 - Almost sufficient: superficial and decontextualized knowledge. The exposure of the contents shows important gaps.

Exam failed - Basic skills and knowledge are not sufficiently acquired. Students are requested to show up at a subsequent exam session.

Office hours

See the website of Rossella Lupacchini

See the website of Giovanni Macchia