Skip to main content
SpringerLink
Log in

Plato on chemistry

  • Published:
Foundations of Chemistry Aims and scope Submit manuscript

Abstract

It is a notion commonly acknowledged that in his work Timaeus the Athenian philosopher Plato (c. 429–347 BC) laid down an early chemical theory of the creation, structure and phenomena of the universe. There is much truth in this acknowledgement because Plato’s “chemistry” gives a description of the material world in mathematical terms, an approach that marks an outstanding advancement over cosmologic doctrines put forward by his predecessors, and which was very influential on western culture for many centuries. In the present article, I discuss inter-transformations among Plato’s four types (fire, air, water, and earth) as well as the interpretation they received in the literature. I find that scientists and scholars generally emphasized (and often misunderstood) mathematical aspects of these “reactions” over the philosophical ones. I argue that Plato’s “chemistry” in fact bears on crucial topics of his philosophical system, such as Forms, Becoming, causation and teleology. I propose that consideration of these doctrines help to understand not only the sense of his “chemical” reactions, but also the reason why their stoichiometry is by surface balance and is restricted only to types that come to be and pass away but not to those that provoke the inter-transformations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. In the literature Plato’s γένη is also translated ‘kinds’,’roots’ and cognate terms, including ‘elements’. Here I will always use the last to denote Plato’s elementary triangles, which as we will see are the irreducible elements (στοῖχεια) from the combination of which Plato’s types form.

  2. I will refer to passages from Plato’s dialogs and other ancient texts the using the denotations listed in the List Abbreviations given below.

  3. Aristotle objected to this disparity among Plato’s types, and argued that only earth qualifies as an “element” (στοιχεῖον) because earth alone is never dissolved (ἀδιάλυτος) into anything else (εἰς ἄλλο σῶμα) as a (true) element never is, Arist. Cael. 306 a19–21.

  4. Unless noted otherwise, all translations of Greek passages are my own.

  5. In his commentary on Aristotle’s Categories, Simplicius (sixth century AD) reports the statement made by the Neopatonist Iamblichus (c. AD 245-c. 325) that for Plato the surfaces of sensible objects are material, Simpl. in Cat. 271, 5–20. See also Arist. Metaph. 1077 b17-1078 a31; Annas (1976, pp. 148–152).

  6. “The Demiurge here chooses a spatial likeness for the sort of non-spatial completeness that characterizes the formal paradigm.” (Johansen 2014, p. 317). For the sphere see also Arist. Cael. 286 b34 – 287 a6.

  7. See Johansen (2020, p. 22) “Or he makes the world complete in the image of the model by making it spherical, where the model has no geometrical shape at all (33b).”.

  8. By inference τὸ κάλλιστον applies also to the companion isosceles elementary triangle, (Artmann and Schäfer 1993). Specifically, the hypotenuse of the selected scalene, and the catetus of the isosceles identify the center and the radius of the circle circumscribing the face under construction (Eucl. El. I, post. 3) at the very first stage of generation, see Paparazzo (2015a, p. 141).

  9. The notion of circularity, or more generally, the “round (τὸ στρογγύλον), is a common reference of Plato’s philosophy, which applies to both circle and sphere, see. Prm. 137E and Seventh Letter 342B, as well as to the revolution of reason (τῇ τοῦ νοῦ περιόδῳ), Leg. 898A. In a recent article, (Myers 2018) argues that circularity is a characteristic rhetorical feature of Plato’s narrative in the Timaeus.

  10. Cfr. Phlb. 26E.

  11. I borrow the translation of εἰκώς = reasonable from Burnyeat, 2005, p. 148. This scholar held that Plato “exploits the full range of his key word” (sc. εἰκώς), i.e., ‘appropriate’, ‘fitting’, ‘natural’, ‘reasonable’… ‘likely’ or ‘probable’), Burnyeat 2005, p. 147, but that translating εἰκώς as "reasonable" clearly distinguishes this section of the Timaeus from poetic accounts of creation such as Hesiod's Theogony. For a different view, see Johansen (2014, pp. 303-304n.12, and p. 317).

  12. See especially Johansen (2014, pp. 303–304).

  13. Burnyeat (2005, p. 156).

  14. According to Johansen (2019, p. 291), the “temporal reading” of the section Tim. 28–30 is a metaphorical, didactic exposition of the generation process which aims to describe the relation between Being and Becoming and not the succession of actual events.

  15. Aristotle, at least in passages that I quote here on “cause”, always calls it αἰτία, which according a classification derived from forensic language is usually applied to Greek philosopy to mean the explanation of how a cause, called “αἴτιος “or “τὸ αἴτιον” produced its effect, Frede (1987, pp. 222–227); Sedley (1998), Johansen (2014, p. 312). According to the same classification αἴτιος is a thing, not an event, whereas αἰτία is an account of it, that is, a description that possesses a propositional character, Frede (1987, p. 222). Sedley (1998, pp. 115–116), says that in the Phaedo Plato is most of the time consistent with following the distinction between αἴτιος and αἰτία.

  16. For a detailed analysis, see Annas (1982, pp. 311–315).

  17. As I understand it, Fine makes a distinction between a) the acquisition on the part of a sensible object (X) of the property.

    of a given Form (Y), that is X becomes F, owing to a cause which is a thing (such as the demiurge), see Sedley (1998), p. 116; and, b) the possession of that property, i.e. a non-causal event, namely a state of affairs expressed by the proposition X is Y, which is something not necessarity related to a type transformation.

  18. Cornford (1997, p. 51) says that a (geometrical) proportion “cannot be connected with the construction of the four regular solids which are later assigned to the primary bodies; the proportion does not fit any of the sets of numbers there involved.”.

  19. According to symmetry principles, (Cotton 1971, pp. 39–45), the tetrahedron, octahedron, and icosahedron—the solids of F, A, and W, which in Plato’s theory do inter-transform into each other, belong to the three different point groups Td, Oh, and Ih, respectively. Conversely, the cube and the octahedron—the solids of E and A, which according to Plato do not inter-transform into each other, belong to the same point group Oh, see Paparazzo (2015c, p. 144).

  20. In Diog. Laert. III, 24 we read that Plato introduced the notion of “plane surface” (τὴν ἐπίπεδον ἐπιφάνειαν) into philosophical discourse.

  21. Aristotle himself would probably have objected to Plato’s stoichiometry, as part of his polemic, against the latter’s doctrine of resolving solids into plane surfaces, in which he laments that Plato illegitimately assimilates geometrical figures to physical quantities, a consequence of which is, e.g., the confusion of the notion of lightness/heaviness with that of density, Arist. Cael. 299 a3-31 and 308 b29- 309 b18.

  22. Plato expounds an analogous doctrine at Tim. 46C-E, for which see Sedley (1989, p. 376), Johansen (2014, pp. 313–314), Johansen (2020, p. 27). Cfr. Plt. 281D.

Abbreviations

Arist. Cael. :

Aristotle [On the Heavens (De Caelo)]

Arist. GC :

Aristotle [On Coming to Be and Passing Away (De Geneneratione et Corruptione)]

Arist. Metaph. :

Aristotle (Metaphysics)

Arist. Phys.:

Aristotle (Physics)

Diog. Laert.:

Diogenes Laertius (Lives and Opinions of Renown Philosophers)

Euc. El. I, post. 3:

Euclid [Elements, Book I, Postulate 3]

Leg. :

Plato [Laws (Leges)]

Phd. :

Plato (Phaedo)

Phlb. :

Plato (Philebus)

Plt.:

Plato [Statesman (Politicus)]

Prm. :

Plato (Parmenides)

Seventh Letter :

Plato (Seventh Letter)

Simpl. in Cat. :

Simplicius (Commentary on Aristotle’s Categories)

Tim. :

Plato (Timaeus)

References

  • Annas, J.: Aristotle’s Metaphysics. Books M and N. Clarendon Press, Oxford (1976)

    Google Scholar 

  • Annas, J.: An Introduction to Platoʼs Republic. Oxford University Press, Oxford (1981)

    Google Scholar 

  • Annas, J.: Aristotle on inefficient causes. Philos. Quart. 32, 311–326 (1982)

    Article  Google Scholar 

  • Artmann, B., Schäfer, L.: On Platoʼs ‘fairest triangles.’ Hist. Math. 20, 255–264 (1993)

    Article  Google Scholar 

  • Bruins, E.M.: La chimie du Timée. Revue De Métaphysique Et De Morale 56, 269–282 (1951)

    Google Scholar 

  • Burnyeat, M.F.: Plato on why mathematics is good for the soul. In: Smiley, T. (ed.) Mathematics and Necessity: Essays in the History of Philosophy, pp. 1–81. Oxford University Press, Oxford (2000)

    Google Scholar 

  • Burnyeat, M.F.: ΕΙΚΩΣ ΜΥΘΟΣ. Rhizai: Journal for Ancient Philosophy and Science 2, 143–165 (2005)

    Google Scholar 

  • Byrd, M.: Mathematics, mental imagery, and ontology: a new interpretation of the divided line. Int. J. Platonic Tradit. 12, 111–131 (2018)

    Article  Google Scholar 

  • Cornford, F.M.: Platoʼs Cosmology. Hackett Publishing Company, Indianapolis (1997)

    Google Scholar 

  • Cotton, F.A.: Chemical Applications of Group Theory. Wiley Interscience, New York (1971)

    Google Scholar 

  • Di Giacomo, F.: Early theoretical chemistry: Plato’s chemistry in Timaeus. Found. Chem. (2020). https://doi.org/10.1007/s10698-020-09364-6

    Article  Google Scholar 

  • Dillon, J.: The Timaeus in the Old Academy. In: Reydams-Schils, G.J. (ed.) Plato’s Timaeus as Cultural Icon, pp. 80–94. University of Notre Dame Press, Notre Dame (IN) (2003)

    Google Scholar 

  • Fermi, E.: Thermodynamics. Dover Publications Inc, New York (1956)

    Google Scholar 

  • Fine, G.: Forms as causes: Plato and Aristotle. In: Fine, G. (ed.) Plato on Knowledge and Forms Selected Essays, pp. 350–396. Oxford University Press, Oxford (2003a)

    Google Scholar 

  • Fine, G.: Separation. In: Fine, G. (ed.) Plato on Knowledge and Forms Selected Essays, pp. 252–300. Oxford University Press, Oxford (2003b)

    Google Scholar 

  • Frede, M.: The original notion of cause. In: Barnes, J., Burnyeat, M.F., Schofield, M. (eds.) Doubt and Dogmatism: Studies in Hellenistic Epistemology, pp. 217–249. Oxford University Press, Oxford (1987)

    Google Scholar 

  • Friedländer, P.: Plato 1. An introduction. Routledge & Kegan Paul, London (1958)

    Google Scholar 

  • Furley, D.: The Greek cosmologists. Volume 1. The Formation of the Atomic Theory and its Earliest Critics. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  • Gaiser, K.: Plato’s enigmatic lecture ‘On the Good.’ Phronesis 25, 5–37 (1980)

    Article  Google Scholar 

  • Hardie, R.P., Gaye, R.K.: Physics. In: Barnes, J. (ed.) The Complete Works of Aristotle, pp. 315–456. Princeton University Press, Princeton (1995)

    Google Scholar 

  • Harte, V.: Plato on Parts and Wholes. The Metaphysics of Structure. Oxford University Press, Oxford (2002)

    Book  Google Scholar 

  • Heisenberg, W.: Physics and Philosophy. The Revolution in Modern Science. Harper & Brothers Publishers, New York (1958)

    Google Scholar 

  • Irwin, T.H.: The theory of Forms. In: Fine, G. (ed.) Plato 1. Metaphysics and Epistemology, pp. 143–170. Oxford University Press, Oxford (1999)

    Google Scholar 

  • Johansen, T.K.: Why the cosmos needs a craftsman: Plato, Timaeus 27d5-29b1. Phronesis 59, 297–320 (2014)

    Article  Google Scholar 

  • Johansen, T.K.: The Timaeus on the principles of cosmology. In: Fine, G. (ed.) The Oxford Handbook on Plato, 2nd edn., pp. 287–308. Oxford University Press, Oxford (2019)

    Google Scholar 

  • Johansen, T.K.: Plato’s teleology. In: McDonough, J.K. (ed.) Teleology. A History, pp. 14–38. Oxford University Press, Oxford (2020)

    Google Scholar 

  • Kotrč, R.F.: The dodecahedron in Plato’s Timaeus. Rheinisches Museum Für Philologie 124, 212–222 (1981)

    Google Scholar 

  • Lewowicz, L., Lombardi, O.: Stuff versus individuals. Found. Chem. 15, 65–77 (2013)

    Article  Google Scholar 

  • Molnár, G.L.: Elements and isotopes. In: Vértes, A., Nagy, S., Klencsár, Z., Lovas, R.G., Rösch, F. (eds.) Handbook of Nuclear Chemistry, pp. 487–504. Springer, Dordrecht (2011)

    Google Scholar 

  • Mueller, I.: Mathematical method and philosophical truth. In: Kraut, R. (ed.) The Cambridge Companion to Plato, pp. 170–199. Cambridge University Press, Cambridge (1992)

    Chapter  Google Scholar 

  • Myers, B.R.H.: One, two, three: narrative circles in Plato’s Timaeus. Arethusa 51, 55–72 (2018)

    Article  Google Scholar 

  • Nehamas, A.: Plato on the imperfection of the sensible world. Am. Philos. Quart. 12, 105–117 (1975)

    Google Scholar 

  • Nehamas, A.: Plato on imitation and poetry. In: Moravcsik, J.M.E., Temko, P. (eds.) Plato on Beauty, Wisdom, and the Arts, pp. 47–78. Rowman & Littlefield, Totowa (1982)

    Google Scholar 

  • Paparazzo, E.: Surfaces-lost and found. Nat. Mater. 2, 351–353 (2003)

    Article  Google Scholar 

  • Paparazzo, E.: How old is surface science? J. Electron. Spectrosc. Relat. Phenom. 134, 9–24 (2004)

    Article  Google Scholar 

  • Paparazzo, E.: Why five worlds? Plato’s Timaeus 55C–D. Apeiron 44, 147–162 (2011)

    Article  Google Scholar 

  • Paparazzo, E.: It’s a world made of triangles: Plato’s Timaeus 53B–55C. Archiv Für Geschichte Der Philosophie 97, 135–159 (2015a)

    Article  Google Scholar 

  • Paparazzo, E.: A note on the construction of the equilateral triangle with scalene elementary triangles in Plato’s Timaeus: Pl. Ti. 54A-B. Classical Quart. 65, 552–558 (2015b)

    Article  Google Scholar 

  • Paparazzo, E.: Does present-day symmetry underlie the cosmology of Plato’s Timaeus? A response to D.R. Lloyd. Apeiron 48, 123–148 (2015c)

    Article  Google Scholar 

  • Paparazzo, E.: Plato’s attitude toward painting and mathematics. In: Hedreen, G., Kwakkelstein, M. (eds.) Material World: The Intersection of Art, Nature, and Science, in Ancient Literature and its Renaissance Reception. Brill, Leiden (2022)

    Google Scholar 

  • Penrose, R.: The Road to Reality: A Complete Guide to the Laws of the Universe. Jonathan Cape, London (2004)

    Google Scholar 

  • Pohle, W.: The Mathematical foundations of Plato’s atomic physics. Isis 62, 36–47 (1971)

    Article  Google Scholar 

  • Popper, K.R.: The nature of philosophical problems and their roots in science. Br. J. Philos. Sci. 3, 124–156 (1952)

    Article  Google Scholar 

  • Pritchard, P.: Plato Philosophy of Mathematics. Academia Verlag, Sankt Augustin (1995)

    Google Scholar 

  • Russell, B.: A History of Western Philosophy. Simon and Schuster Inc, New York (1945)

    Google Scholar 

  • Schofield, M.: Plato in his time and place. In: Fine, G. (ed.) The Oxford Handbook on Plato, 2nd edn., pp. 41–68. Oxford University Press, Oxford (2019)

    Google Scholar 

  • Sedley, D.: Two conceptions of vacuum. Phronesis 27, 175–193 (1982)

    Article  Google Scholar 

  • Sedley, D.: Teleology and myth in the Phaedo. Proc. Boston Area Colloquium Ancient Philos. 5, 359–383 (1989)

    Article  Google Scholar 

  • Sedley, D.: Platonic causes. Phronesis 43, 114–132 (1998)

    Article  Google Scholar 

  • Sedley, D.: Form-particular resemblance in Plato’s “Phaedo.” Proc. Aristot. Soc. 106, 311–327 (2006)

    Article  Google Scholar 

  • Sedley, D., Long, A.: Meno an Phaedo. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  • Shorey, P.: Plato. The Republic Books VI–X. Harvard University Press, Cambridge (MA) (2006)

    Google Scholar 

  • Taylor, A.E.: A Commentary on Platoʼs Timaeus. Clarendon Press, Oxford (1928)

    Google Scholar 

  • Visintainer, J.: A potential infinity of triangle types. On the chemistry of Plato’s Timaeus. Hyle 4, 117–128 (1998)

    Google Scholar 

  • Vlastos, G.: Plato’s Universe. Clarendon Press, Oxford (1975)

    Google Scholar 

  • Vlastos, G.: Elenchus and mathematics: a turning-point in Plato’s philosophical development. Am. J. Philol. 109, 362–396 (1988)

    Article  Google Scholar 

  • White, N.P.: Plato’s metaphysical epistemology. In: Kraut, R. (ed.) The Cambridge Companion to Plato, pp. 277–310. Cambridge University Press, Cambridge (1992)

    Chapter  Google Scholar 

  • Wicksteed, P.H., Cornford, F.M.: Aristotle. The Physics Books I-IV. Harvard University Press, Harvard (2005)

    Google Scholar 

  • Williams, R.J.P., FraústodaSilva, J.J.R.: Bringing Chemistry to Life: From Matter to Man. Oxford University Press, Oxford (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche (ISM-CNR), Via del Fosso del Cavaliere 100, 00133, Rome, Italy

    Ernesto Paparazzo

Authors
  1. Ernesto Paparazzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ernesto Paparazzo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Paparazzo, E. Plato on chemistry. Found Chem 24, 221–238 (2022). https://doi.org/10.1007/s10698-022-09426-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10698-022-09426-x

Keywords

Search

Navigation