David Corfield Friedman's Dynamics of Reason

Idea

This is my attempt to modify Michael Friedman’s Dynamics of Reason by redefining aspects of the role played by mathematics in his schema. My 2005 draft makes a start, but I now see that the case study there can be developed to describe a full-blown revolution in mathematical physics. Modal HoTT allows for the expression of the geometry needed for modern physics, and even a non-perturbative M-theory (see Hypothesis H). (Notes of the newer ideas are here and here.)

Friedman draws attention to the retrospective rationality acting through a revolution, casting the old theory as an approximate case of the new theory (e.g., Cartan’s rendition of Newtonian space and time as a Riemannian manifold). He points also to a prospective rationality where meta-scientific work is done on fundamental principles. His paradigm case is Einstein’s work after the metascientific enquiries of Helmholtz, Hertz, Poincaré, following revolutionary changes to geometry by Riemann, Lie, Klein, Hilbert, etc. In the case of quantum mechanics, this metascientific work is taken to have been lacking. Instead we have untimely interventions (DR, 120-121), as in the ad hoc philosophical speculations of Wigner and Schroedinger.

After a revolution, important philosophical work is done, integrating the new science into a novel philosophical framework. E.g., Kant integrating Newtonian science and Leibnizian metaphysics, and the Logical Positivists understanding general relativity.

Friedman draws a distinction between mathematics and physics, which I question in change in status of principles. This is illustrated by cohomology, which plays an important role in modern physics and which is part of higher category theory as revolution. I bring together various themes in diagnosis. Some objections and observations to this line of thinking.

Friedman himself has since developed his views, see ‘Extending the Dynamics of Reason’, his chapter in the Domski and Dixon volume 2010, and in responses to papers in Studies in History and Philosophy of Science 43(1), 2012. Note in his essay in Domski and Dixon, Friedman moves in what I agree is a good direction:

The difficulty arises when one accepts the sharp distinction, emphasized by Schlick, between an uninterpreted axiomatic system and intuitive perceptible experience, and one then views the constitutive principles in question (which, following Reichenbach, I called “coordinating principles” or “axioms of coordination”) as characterizing an abstract function or mapping associating the former with the latter. This picture is deeply problematic, I now believe, in at least two important respects: it assumes an overly simplified “formalistic” account of modern abstract mathematics, and, even worse, it portrays such abstract mathematics as being directly attached to intuitive perceptible experience at one fell swoop. (pp. 697-8)

Our problem, therefore, is not to characterize a purely abstract mapping between an uninterpreted formalism and sensory perceptions, but to understand the concrete historical process by which mathematical structures, physical theories of space, time, and motion, and mechanical constitutive principles organically evolve together so as to issue, successively, in increasingly sophisticated mathematical representations of experience. (p. 698)

In my reconceived version of transcendental philosophy, therefore, integrated intellectual history of both the exact sciences and scientific philosophy (a kind of “synthetic history”) takes over the role of Kant’s original synthetic method; and, in particular, constructive historical investigation of precisely this kind replaces Kant’s original transcendental faculty psychology. (p. 702)

The larger picture allows an intricate interwoven story to be told, including of philosophical currents leading to the inferentialism of modal HoTT, see DoR-inferentialism.

The new exemplar I’m presenting makes sense of Witten’s comments:

String theory at its finest is, or should be, a new branch of geometry. (p. 95)

I would consider trying to elucidate this proper generalization of geometry as the central problem of physics, certainly the central problem of string theory. (p. 96)

What should have happened, by rights, is that the correct mathematical structures should have been developed in the twenty-first or twenty-second century, and then finally physicists should have invented string theory as a physical theory that is made possible by these structures. (p. 102)

we are paying the price for the fact that we didn’t come by this thing in the usual way. (p. 103)

P C W Davis & J Brown (eds.), Superstrings: A theory of everything?, Cambridge University Press 1988, 1991, Canto 1992

There is a much clearer idea of the new geometry now, involving homotopification and supergeometry.

Bibliography

• Mary Domski and Michael Dickson (eds.) (2010), Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science, Open Court Publishing.

• Friedman, M. (2011) Extending the Dynamics of Reason Erkenntnis 75 (3):431-444.

• Friedman, M. (2010a). Synthetic history reconsidered. In Domski and Dickson (Eds.), pp. 571–813.

• Friedman, M. (2010b). A post-Kuhnian approach to the history and philosophy of science. The Monist, 93, 495–515. (Extended version of 2011.)

• Friedman, M. (2010c). Kant, Einstein and the a priori. In M. Suárez, M. Dorato, & M. Rédei (Eds.). EPSA philosophical issues in the sciences: Launch of the European Philosophy of Science Association (Vol. 2, pp. 65–73). Dordrecht and New York: Springer.

• Friedman, M. (2009). Newton and Kant on absolute space: from theology to transcendental philosophy. In M. Bitbol, P. Kerszberg, & J. Petitot (Eds.), Constituting objectivity: transcendental perspectives on modern physics (pp. 35–50). Berlin

• Friedman, M. (2008). Ernst Cassirer and Thomas Kuhn: The Neo-Kantian Tradition in History and Philosophy of Science. Philosophical Forum 39 (2):239-252.

• Friedman, M. (1993). “Remarks on the History of Science and the History of Philosophy.” In Horwich (ed.), World Changes, MIT Press, 37–54.

• Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science (1986)

• Kant and the Exact Sciences (1992)

• Reconsidering Logical Positivism (1999)

• A Parting of the Ways: Carnap, Cassirer, and Heidegger (2000)

• Dynamics of Reason (2001)

• Kant’s Construction of Nature (2013)