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.
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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.
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.
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.
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).
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)].
‘Nature’ is to be understood here as the objects of our experience.
Morrison (2008) investigates the relationship between the unification project in contemporary physics and Kant’s account of unification in the sciences.
For a detailed discussion of Poincaré’s account of creativity, see Livingston (2009).
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) 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).
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.
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.
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.
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.
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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.
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Ivanova, M. Poincaré’s aesthetics of science. Synthese 194, 2581–2594 (2017). https://doi.org/10.1007/s11229-016-1069-1
- Aesthetic Values
- Henri Poincaré
- Scientific realism