Abstract
Jules Henri Poincaré is famous for his “conventionalist” philosophy of science. But what exactly does this mean? Poincaré invented the category of convention because he thought that there are some central principles in science that are neither based on intuition , empirical data, nor that are arbitrary stipulations. His views here resemble those of Wittgenstein , in particular, as presented in On Certainty. The invention of convention is lauded (for example, by Robert DiSalle ) as a genuine philosophical discovery. But it is also critiqued (for example by Michael Friedman ) as yielding a vision of science that is too rigid – one that is refuted by general relativity . This paper aims to defend Poincaré’s views about conventions by focusing on his central idea that conventional choices, though “free”, are “guided” by experience . I will argue that conventionalism is not a commitment to fixed a priori stipulations, as DiSalle and Friedman propose. Rather, it mandates empirically motivated shifts in (even geometric) conventions – a view surprisingly in accord with Friedman’s “relativized a priori”, and thus more consistent with general relativity than is generally thought.
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Notes
- 1.
The idea of the relative, or relativized, a priori has recently taken hold, owing largely to the influence of Friedman 1999 and 2001. There is a growing body of literature on the topic, including several new essays by Friedman extending and modifying his views (for example, Friedman 2011, and 2012). See Stump 2011 for an account of Arthur Pap’s similar “functional a priori”, and Poincaré ’s influence on Pap. Like Stump, I support an interpretation of Poincaré’s conventionalism as rather close to the relativized a priori.
- 2.
For just one example, he comes to accept the existence of atoms after first denying them, thus giving up a principle of the continuity of nature.
- 3.
In writing this paper I realize I have entered a thick territory. The literature on, and related to, Poincaré ’s conventionalism is enormous and I cannot pretend to have mastered it. I have approached the topic by first re-reading Poincaré’s central texts and then by addressing just a few secondary works that have particularly influenced me. I hope to make a small contribution to this literature by supporting a slightly more empirical interpretation of conventions. I thank Maria de Paz and Robert DiSalle for inviting me to contribute to this volume; Michael Friedman , Robert Disalle and David Stump for their excellent work on this topic; and David Stump for comments on an earlier, written draft. Several audiences should also be thanked for putting up with early, half-baked talks on some of this material, including those at our Poincaré session at HOPOS, June 2012, and especially those attending the Foundations of Physics and Mathematics Workshop at the University of Western Ontario, May 2012.
- 4.
Thanks to David Stump for making me clarify this point.
- 5.
- 6.
Though note: Stump 1989 cautions that any holism Poincaré endorses is specific; that is, Poincaré does not advance a general holism or appeal to general under-determination considerations to advance the flexibility of conventions.
- 7.
It might be objected here that since mathematical geometry is about ideal objects, Poincaré ’s emphasis on the empirical preconditions for geometry – for its “genesis” – may simply result from confusing the context of discovery with the context of justification. That is, just because certain empirical conditions need to be met in order to account for the existence of geometry does not mean that, once established, the empirical preconditions are relevant to its subject matter. After all, we also need blood in our brains to do arithmetic; but arithmetic is still a bona fide a priori area of mathematics despite this precondition. The difference is that there being blood in the brain is a mere precondition; and has no bearing on what arithmetic is about. In contrast, the empirical preconditions in part define the subject matter of geometry: systems of rigid body motions. This context of discovery, in other words, is relevant to the subject matter of geometry in a way unlike the arithmetic case.
- 8.
Of course, a physical theory that is not empirically adequate would be very inconvenient!
- 9.
As mentioned above, along these lines, Stump argues that in contrast with Quine , Poincaré ’s holism is not general, but limited to special cases. Poincaré rejects Newtonian absolute space, and any substantival understanding of space. So adjustments in geometry are legitimate because geometry is not describing a thing with its own properties (space); rather it is just a tool for describing the relationships of bodies. (And Poincaré comes into conflict with GR precisely here since GR is essentially a substantival theory of space.) Whereas I am connecting the degree of protection a principle gets to its position in the hierarchy, Stump is furthering an account of a deeper reason why something is a convention , and thus why it occupies a protected position in the hierarchy. See Stump 1989, section V.
- 10.
Of course Poincaré famously did not think we would ever make such a choice ; continuing: “It is needless to add that every one would look upon this solution as the more advantageous. Euclidean geometry , therefore, has nothing to fear from fresh experiments” (1902a/1952, 73). This confidence was probably based on the assumption that the alternative would require too deep of a shift to be worth the scientific and conceptual upheaval. Indeed, relativity was a revolutionary shift, involving changes at many levels, including conceptual levels, and resulting in new relationships between mathematics and physics . Nevertheless Poincaré recognized the possibility of revising a geometric choice when faced with new data; it was not the policy of conventionalism to prohibit such changes. He asserted that we would not adopt a different geometry, not that we could not or should not.
- 11.
Friedman points out, interestingly, that Poincaré ’s conventionalism is the only option to GR that Einstein himself recognized (Friedman 2001, 111).
- 12.
Similarly, Friedman argues that the special theory of relativity proceeds “in perfect conformity with Poincaré ’s underlying philosophy in Science and Hypothesis, by ‘elevating’ an already established empirical fact into the radically new status of what Poincaré calls a ‘definition in disguise’” (Friedman 2001, 111).
- 13.
Interestingly, Einstein also saw GR as a kind of ether theory. Einstein 1920, referenced in Stump 1989, 362, note 104.
- 14.
Indeed, as Wittgenstein argues, in any domain of objective, empirical judgment (See Wittgenstein 1969).
- 15.
Recall, the group concept is part of an explanation of why we are geometrical beings, and why we are naturally limited to a small class of geometries.
- 16.
Apriority for Poincaré does not thereby guarantee applicability; this is just one way his vision seems quite different from Kant ’s.
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Folina, J. (2014). Poincaré and the Invention of Convention. In: de Paz, M., DiSalle, R. (eds) Poincaré, Philosopher of Science. The Western Ontario Series in Philosophy of Science, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8780-2_2
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