85020 - Methods of Scientific Knowledge (1)

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

Spacetime Morphology

 MODULE 1: The Nature of Space and the Art of Nature

Defining a representational space as an intersection of the visual pyramid, the perspectiva pingendi plays a dual methodological role for the construction of the physical world. On the one hand, it encourages mathematicians to test the validity of Euclid's axiomatics, on the other, it urges physicists to refine the logical analysis of our spacial intuition. It also shows that a geometry capable of describing the dynamics of forms is missing.

The aesthetic sense of the continuity of nature, which emanates from Leonardo's drawings, becomes a basic principle of Leibniz's mathematical philosophy. The «law of continuity» leads the construction of geometry as well as of the theory of nature. Although the classical physics has followed the road indicated by Newton, the Leibnizian road seems to reemerge in the spacetime relativistic physics.

• How does the beauty of an artistic or scientific representation  mirror the beauty of nature?
•  Is there a relationship between beauty and truth?
•  What is the relation between Leibniz's geometric view and the visual geometry born of painting?
•  How far is the Leibnizian space-time from the Kantian space-time?

Addressing these questions, the main goal of the course will be to highlight an active dimension in the spacetime intuition, which, from various areas of the philosophical and scientific reflection, called for a deepening of the conceptual analysis and an improvement of the mathematical instruments.

 

MODULE 2: Spacetime Physics

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

Main References 

Kemp M. (1990), The Science of Art, Yale UP, New Haven (chaps. 1-2)

Stillwell J. (2006), Yearning for the Impossible, A. K. Peters Ltd., Wellesley MA (chaps 3, 5-6)

Weyl H. (1949), Philosophy of Mathematics and Natural Science, Princeton UP 1949 (chap. 4) 

Essays

Cassirer, E. (1902), Leibniz’ System in seinen wissenschaftlichen Grundlagen, Elwert, Marburg

• Descartes R. [1644], «Estension and Motion», in Principia philosophiae...
• Leibniz G. W. [1679], La caractétistique géométrique, ed. J. Echeverría and M. Parmentier, Librairie philosophique J. Vrin, Paris 1995
• Newton I. [1686], «Space, Matter, and Force», in Philosophiae Naturalis Principia Mathematica...
• The Leibniz-Clarke correspondence, ed. H. G. Alexander, Manchester UP, Manchester 1965 
• Kant: Selected Pre-Critical Writings and Correspondence with Beck, eds. G. Kerferd and D. Walford, Manchester 1968
• Goethe J. W. [1824-28], Scientific Studies, ed. D. Miller, Suhrkamp Publishers, New York 1988
  
  

Hilbert D. (1930), «Logic and the Knowledge of Nature», in From Kant to Hilbert, ed. W. Ewald, Oxford UP 1996 (pp. 1157–1165)

Einstein A. (1952), «Relativity  and  the Problem of Space»

 

Further Reading

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 UP, Princeton (pp. 61-98)

Friedman M. (2012), «Kant on Geometry and Spatial Intuition», Synthese 186 (pp. 231-255)

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

 

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

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