Skip to main content

Poincaré’s aesthetics of science


This paper offers a systematic analysis of Poincaré’s understanding of beauty in science. In particular, the paper examines the epistemic significance Poincaré attributes to aesthetic judgement by reconstructing and analysing his arguments on simplicity and unity in science. I offer a consistent reconstruction of Poincaré’s account and show that for Poincaré simplicity and unity are regulative principles, linked to the aim of science—that of achieving understanding of how phenomena relate. I show how Poincaré’s account of beauty in science can be incorporated within his wider philosophy of science.

This is a preview of subscription content, access via your institution.


  1. It is interesting to consider whether these particular properties are sought after in all scientific disciplines or whether they are particularly valued in physics and the mathematical sciences.

  2. There is also a debate concerning whether aesthetic judgements are indeed aesthetic. Todd (2008) argues that aesthetic judgements are epistemic because they are associated with normative claims.

  3. Poincaré’s argument here is an instance of non-eliminative instrumentalism. Mach (1984), on the other hand, endorses an eliminative instrumentalism, arguing that “all metaphysical elements are to be eliminated as superfluous and as destructive of the economy of science” (Mach 1984, p. xxxviii).

  4. Note here that Poincaré uses ‘harmony’ and ‘unity’ both as properties of theories and of the phenomena, and that he takes harmony to reduce to unity.

  5. While there is no explicit reference to Kant’s aesthetic theory in Poincaré’s writing, a middle position between objectivism and subjectivism would imply a Kantian influence here. According to Kant, aesthetic judgements depend on the subject’s reflection on the object rather than in some property in the object itself. However, Kant claims that rather than being completely subjective emotional responses, aesthetic judgements demand the agreement of others and thus have intersubjective validity (Kant 2000).

  6. Note the parallels and differences here with Poincaré’s contemporary Pierre Duhem. While Duhem argues that aesthetic values such as ‘simplicity’ and ‘elegance’ “are essentially subjective, contingent, and variable with time, with schools, and with persons” (Duhem 1954, p. 288), there is still a need to explain how scientists come to an agreement about the aesthetic properties of theories. Just like David Hume, Duhem appeals to the concept of ‘good sense’, which an impartial scientist possesses. Duhem argues that scientists who have good sense can appreciate the aesthetic properties of theories because they are unbiased and objective. It is good sense that ensures that despite the subjective nature of aesthetic judgment, scientists with good sense can come to an objective agreement about the aesthetic properties of theories [see Stump (2007) and Ivanova (2010)].

  7. ‘Nature’ is to be understood here as the objects of our experience.

  8. Morrison (2008) investigates the relationship between the unification project in contemporary physics and Kant’s account of unification in the sciences.

  9. For a detailed discussion of Poincaré’s account of creativity, see Livingston (2009).

  10. While opposing the atomic hypothesis for the majority of his life, Poincaré accepted the atom in 1912 claiming that there is sufficient experimental evidence for its existence. He draws (1963[1913]) an important distinction between the ‘metaphysical’ atom, which is supposed to be indivisible and unifying, and ‘the atom of the chemist’, for which there is sufficient evidence but which has proven to lead to more complexity. For more details on Poincaré’s argument, see Stump (1989) and Ivanova (2013).

  11. According to structural realism, we can know the relations between unobservable entities, but not their properties (their nature). We can differentiate three mutually exclusive views regarding unobservable entities, which structural realists can endorse. A structural realist can be (1) agnostic as to whether there are unobservable entities. Or, (2) she can hold that there are unobservable entities, but our epistemic restriction does not allow us to know their ’nature’ (that is, their first order properties). Or (3) a structural realist can employ the argument for coherence between epistemology and metaphysics and suggest that since all we can know is relations and not the entities themselves, then we should eliminate the unobservable entities from our ontology. This version is compatible with Ladyman’s (1998) ontic structural realism.

  12. Ivanova (2015) has recently defined several different meanings of the term conventionalism associated with Poincaré’s position and related it to his structuralism and neo-Kantianism.

  13. While Poincaré continued endorsing the synthetic a priori, he ‘corrected’ the Kantian framework in light of the existence of non-Euclidean geometries by claiming that they have conventional and not synthetic a priori status. Ben-Menahem (2006) gives a detailed account of Poincaré’s conventionalism, while Friedman (1999) explains the neo-Kantian elements in Poincaré’s epistemology. What concerns me here are the similarities between Poincaré’s and Kant’s theories of aesthetic judgement, that have not yet been noted in the literature.

  14. An exception is Massimi (2011) who develops an internalist neo-Kantian form of structural realism. Massimi claims that unobservable entities, and mathematical structures evolve together in relation to empirical evidence. Our best scientific theories do not represent a mind-independent reality (unobservable entities that exist independently of us). On the contrary, the unobservable entities, the mathematical structures evolve with the development of scientific knowledge. Massimi’s position can be seen as a much more helpful way of thinking about Poincaré’s own position in the scientific realism debate.


  • Ben-Menahem, Y. (2006). Conventionalism: From Poincaré to Quine. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Dirac, P. A. M. (1980). The excellence of Einstein’s theory of gravitation. In M. Goldsmith, A. Mackay, & J. Woudhuysen (Eds.), Einstein: The first hundred years (pp. 41–46). Oxford: Pergamon Press.

    Chapter  Google Scholar 

  • Duhem, P. (1954[1906]). The aim and structure of physical theory. Princeton: Princeton University Press.

  • Feynman, R. (1967). The character of physical law: The 1964 messenger lectures. Cambridge: MIT Press.

    Google Scholar 

  • Friedman, M. (1999). Reconsidering logical positivism. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Gower, B. S. (2000). Cassirer, Schlick and Structural Realism: The philosophy of the exact sciences in the background to early logical empiricism. British Journal for the History of Philosophy, 8, 71–106.

  • Heisenberg, W. (1971). Physics and beyond: Encounters and conversations. (A. J. Pomerans, Trans.). London: George Allen and Unwin.

  • Ivanova, M. (2015). Conventionalism, structuralism and neo-Kantianism in Poincaré’s philosophy of science. Studies in the History and Philosophy of Modern Physics, 52, 114–122.

    Article  Google Scholar 

  • Ivanova, M. (2013). Did Perrin’s experiments Convert Poincaré to scientific realism? HOPOS: The Journal of the International Society for the History of Philosophy of Science, 3(1), 1–19.

  • Ivanova, M. (2010). Pierre Duhem’s good sense as a guide to theory choice. Studies in the History and Philosophy of Science, 41, 58–64.

    Article  Google Scholar 

  • Kant, I. (2000). Critique of the power of judgement (E. Matthews, Ed., P. Guyer & E. Matthews, Trans.). Cambridge: Cambridge University Press.

  • Ladyman, J. (1998). What is structural realism? Studies in History and Philosophy of Science, 29, 409–424.

    Article  Google Scholar 

  • Livingston, P. (2009). Poincaré’s delicate sieve: On creativity and constraints in the arts. In Michael Krausz, Denis Dutton, & Karen Bardsley (Eds.), The idea of creativity (pp. 129–146). Leiden: Brill.

    Google Scholar 

  • Mach, E. (1984). The analysis of sensations and the relation of the physical to the psychical (C. M. Williams, Trans.). La Salle: Open Court.

  • Massimi, M. (2011). Structural realism: A neo-Kantian perspective. In P. Bokulich & A. Bokulich (Eds.), Scientific structuralism (Vol. 281, pp. 1–25). Berlin: Springer.

    Google Scholar 

  • McAllister, J. (1996). Beauty and revolution in science. Ithaca, NY: Cornell University Press.

    Google Scholar 

  • Morrison, M. (2008). Reduction, unity and the nature of science: Kant’s Legacy? In M. Massimi (Ed.), Kant and philosophy of science today (Vol. 63, pp. 37–62). Cambridge: Royal Institute of Philosophy Supplements.

    Google Scholar 

  • Poincaré, H. (1963[1913]). Mathematics and science: Last essays. New York: Dover.

  • Poincaré, H. (2001 [1902, 1905, 1908]). Science and hypothesis. In Gould, S. (Ed.), The value of science: essential writings of Henri Poincaré. New York: Modern Library.

  • Stump, D. (2007). Pierre Duhem’s virtue epistemology. Studies in History and Philosophy of Science, 38, 149–159.

    Article  Google Scholar 

  • Stump, D. (1989). Henri Poincaré’s philosophy of science. Studies in the History and Philosophy of Science, 20, 335–363.

    Article  Google Scholar 

  • Todd, S. C. (2008). Unmasking the truth beneath the beauty: Why the supposed aesthetic judgements made in science may not be aesthetic at all. International Studies in the Philosophy of Science, 22, 61–79.

    Article  Google Scholar 

  • Watson, J. D. (1968). The double helix: A personal account of the discovery of the structure of DNA. London: Weidenfeld and Nicolson.

    Google Scholar 

  • Worrall, J. (1996[1989]). Structural realism: The best of both worlds? In Papineau, D. (Ed.), The Philosophy of science (pp. 139–166). Oxford: Oxford University Press.

  • Zahar, E. (2001). Poincaré’s philosophy: From conventionalism to phenomenology. New York: Open Court Publishing Company.

    Google Scholar 

Download references


I would like to thank the two anonymous referees for this journal for their helpful comments, as well as the audiences at the Munich Center for Mathematical Philosophy, Universities of Helsinki, Rome and Konstanz. Matt Farr deserves special thanks for his support and encouragement during the time in which this paper was written. I dedicate this work to Dr. Domenika Turkiewicz and the team at the Mater Breast Cancer Center in Brisbane for their great care.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Milena Ivanova.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ivanova, M. Poincaré’s aesthetics of science. Synthese 194, 2581–2594 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Aesthetic Values
  • Simplicity
  • Unity
  • Henri Poincaré
  • Scientific realism