Abstract
I would like to start with a historical question or, more precisely, a question pertaining to the history of science itself. It is a widely accepted idea that Aristotelism has been an obstacle to the emergence of modern physical science, and this was for at least two reasons. The first one is the cognitive role Aristotle is supposed to have attributed to perception. Instead of considering perception as an origin of error (even if this may be the case in exceptional situations, if the perceiving subject is sick for instance), Aristotle thinks that our senses provide us with a reliable image of the external world. The perceptive knowledge is a kind of knowledge in its own right, and the theoretical knowledge is, in fact, the continuation of the perceptive knowledge in some way. The second reason is the presumed inability of the Aristotelian philosophers to apply mathematics to the physical world. This was a formidable obstacle because modern physics came to be but as a mathematical physics. Aristotelianism had therefore to be, so to speak, superseded by the Platonic movement that originated in Florence around Ficino in order to give modern physics the conditions of its appearance. Galileo had to say that “Nature is written with mathematical letters” and Descartes that “our senses do not teach us what things are, but to what extent they are useful or harmful to us”. Alexandre Koyré is right to consider Galilean physics to be basically Platonic. The theoretical justification Aristotle offers for the impossibility of a convergence between mathematics and physics seems to be based on some fundamental features of his philosophy, i.e. he rejects the Platonic conception of a unique science, encompassing all things, and replaces it with the doctrine of the incommunicability of genera, whose corollary is that there is but one science for each genus.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
εἰ δέ τί ἐστιν ἀΐδιον καὶ ἀκίνητον καὶ χωριστόν, φανερὸν ὅτι θεωρητικῆς τὸ γνῶναι, οὐ μέντοι φυσικῆς γε (περὶ κινητῶν γάρ τινων ἡ φυσική) οὐδὲ μαθηματικῆς, ἀλλὰ προτέρας ἀμφοῖν. ἡ μὲν γὰρ φυσικὴ περὶ ἀχώριστα μὲν ἀλλ’ οὐκ ἀκίνητα, τῆς δὲ μαθηματικῆς ἔνια περὶ ἀκίνητα μὲν οὐ χωριστὰ δὲ ἴσως ἀλλ’ ὡς ἐν ὕλῃ· ἡ δὲ πρώτη καὶ περὶ χωριστὰ καὶ ἀκίνητα.
- 2.
ἐπεὶ ὅτι καὶ αὐτὸς ὁμολογεῖ μηδὲν εἰρηκέναι πρὸς τὰς ἐκείνων ὑποθέσεις μηδ’ ὅλως παρακολουθεῖν τοῖς εἰδητικοῖς ἀριθμοῖς, εἴπερ ἕτεροι τῶν μαθηματικῶν εἶεν, μαρτυρεῖ τὰ ἐν τῷ δευτέρῳ τῶν Περὶ τῆς φιλοσοφίας ἔχοντα τοῦτον τὸν τρόπον· “ὥστε εἰ ἄλλος ἀριθμὸς αἱ ἰδέαι, μὴ μαθηματικὸς δέ, οὐδεμίαν περὶ αὐτοῦ σύνεσιν ἔχοιμεν ἄν· τίς γὰρ τῶν γε πλείστων ἡμῶν συνίησιν ἄλλον ἀριθμόν;” ὥστε καὶ νῦν ὡς πρὸς τοὺς πολλοὺς τοὺς οὐκ εἰδότας ἄλλον ἢ τὸν μοναδικὸν ἀριθμὸν πεποίηται τοὺς ἐλέγχους, τῆς δὲ τῶν θείων ἀνδρῶν διανοίας οὐδὲ τὴν ἀρχὴν ἐφήψατο.
- 3.
Ian Mueller, “Aristotle on Geometrical Objects”, Archiv für Geschichte der Philosophie 1970, pp.156–171. Jonathan Lear, “Aristotle ’s Philosophy of Mathematics”, The Philosophical Review, Avril 1982, pp. 161–192. Edward Hussey, “Aristotle on Mathematical Objects”, in I. Mueller (ed). Peri Tôn Mathêmatôn, Apeiron Décembre 1991, pp. 105–133. Michel Crubellier, “La Beauté du monde. Les sciences mathématiques et la philosophie première”, Revue internationale de Philosophie 1997–3, pp. 307–331.
- 4.
περὶ τούτων μὲν οὖν πραγματεύεται καὶ ὁ μαθηματικός, ἀλλ’ οὐχ ᾗ φυσικοῦ σώματος πέρας ἕκαστον οὐδὲ τὰ συμβεβηκότα θεωρεῖ ᾗ τοιούτοις οὖσι συμβέβηκεν· διὸ καὶ χωρίζει· χωριστὰ γὰρ τῇ νοήσει κινήσεώς ἐστι.
- 5.
ὁ δὲ γεωμέτρης οὔθ’ ᾗ ἄνθρωπος οὔθ’ ᾗ ἀδιαίρετος ἀλλ’ ᾗ στερεόν. ἃ γὰρ κἂν εἰ μή που ἦν ἀδιαίρετος ὐπῆρχεν αὐτῷ, δῆλον ὅτι καὶ ἄνευ τούτων ἐνδέχεται αὐτῷ ὑπάρχειν [τὸ δυνατόν], ὥστε διὰ τοῦτο ὀρθῶς οἱ γεωμέτραι λέγουσι, καὶ περὶ ὄντων διαλέγονται, καὶ ὄντα ἐστίν· διττὸν γὰρ τὸ ὄν, τὸ μὲν ἐντελεχείᾳ τὸ δ’ ὑλικῶς
- 6.
Cf. Physics II, 7, 198a35: “The principles that cause natural motion are two, of which one is not natural, since it has no internal principle of motion. Of this kind is whatever causes motion without being moved, such as what is completely unchangeable, the primary being [i.e. the Prime mover], and the essence of a thing, i.e. the form”.
- 7.
Op. cit. p. 316.
- 8.
Reading γεωμετρητά at 79a9 like the ms. usually corrected as γεωμετρικά, “geometrical”.
- 9.
τὰ γὰρ μαθήματα περὶ εἴδη ἐστίν οὐ γὰρ καθ’ ὑποκειμένου τινός· εἰ γὰρ καὶ καθ’ ὑποκειμένου τινὸς τὰ γεωμετρητά ἐστιν, ἀλλ’ οὐχ ᾗ γε καθ’ ὑποκειμένου. ἔχει δὲ καὶ πρὸς τὴν ὀπτικήν, ὡς αὕτη πρὸς τὴν γεωμετρίαν, ἄλλη πρὸς ταύτην, οἷον τὸ περὶ τῆς ἴριδος· τὸ μὲν γὰρ ὅτι φυσικοῦ εἰδέναι, τὸ δὲ διότι ὀπτικοῦ, ἢ ἁπλῶς ἢ τοῦ κατὰ τὸ μάθημα. ἡ μὲν γὰρ γεωμετρία περὶ γραμμῆς φυσικῆς σκοπεῖ, ἀλλ’ οὐχ ᾗ φυσική, ἡ δ’ ὀπτικὴ μαθηματικὴν μὲν γραμμήν, ἀλλ’ οὐχ ᾗμαθηματικὴ ἀλλ’ ᾗ φυσική. πολλαὶ δὲ καὶ τῶν μὴ ὑπ’ ἀλλήλας ἐπιστημῶν ἔχουσιν οὕτως, οἷον ἰατρικὴ πρὸς γεωμετρίαν ὅτι μὲν γὰρ τὰ ἕλκη τὰ περιφερῆ βραδύτερον ὑγιάζεται, τοῦ ἰατροῦ εἰδέναι, διότι δὲ τοῦ γεωμέτρου.
- 10.
ἐπεὶ δὲ τὸ ἀγαθὸν καὶ τὸ καλὸν ἕτερον (…), οἱ φάσκοντες οὐδὲν λέγειν τὰς μαθηματικὰς ἐπιστήμας περὶ καλοῦ ἢ ἀγαθοῦ ψεύδονται. (…) μάλιστα· οὐ γὰρ εἰ μὴ ὀνομάζουσι τὰ δ’ ἔργα καὶ τοὺς λόγους δεικνύουσιν, οὐ λέγουσι περὶ αὐτῶν. τοῦ δὲ καλοῦ μέγιστα εἴδη τάξις καὶ συμμετρία καὶ τὸ ὡρισμένον, ἃ μάλιστα δεικνύουσιν αἱ μαθηματικαὶ ἐπιστῆμαι. καὶ ἐπεί γε πολλῶν αἴτια φαίνεται ταῦτα (λέγω δ’ οἷον ἡ τάξις καὶ τὸ ὡρισμένον), δῆλον ὅτι λέγοιεν ἂν καὶ τὴν τοιαύτην αἰτίαν τὴν ὡς τὸ καλὸν αἴτιον τρόπον τινά. μᾶλλον δὲ γνωρίμως ἐν ἄλλοις περὶ αὐτῶν ἐροῦμεν.
References
Aristotle. (1984). The complete works of Aristotle. In J. Barnes (Ed.), The revised Oxford translation, Vol. 2. Princeton University Press.
Crubellier, Michel. (1997). La Beauté du monde. Les sciences mathématiques et la philosophie première. Revue Internationale de Philosophie, 3, 307–331.
Hussey, E. (1991). Aristotle on mathematical objects. In I. Mueller (Ed.), Peri Tôn Mathêmatôn, Apeiron, pp. 105–133.
Lear, J. (1982). Aristotle’s philosophy of mathematics. The Philosophical Review, pp. 161–192.
Mueller, I. (1970). Aristotle on geometrical objects. Archiv für Geschichte der Philosophie, pp. 156–171.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Pellegrin, P. (2018). Mathematics and the Physical World in Aristotle. In: Tahiri, H. (eds) The Philosophers and Mathematics. Logic, Epistemology, and the Unity of Science, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-93733-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-93733-5_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93732-8
Online ISBN: 978-3-319-93733-5
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)