From positivism to conventionalism: Comte,Renouvier, and Poincaré

Considered in its historical context, conventionalism is quite different from the way in which it has been caricatured in more recent philosophy of science, that is, as a conservative philosophy that allows the preservation of theories through arbitrary ad hoc stratagems. It is instead a liberal outgrowth of Comtean positivism, which broke with the Reidian interpretation of the Newtonian tradition in France and defended a role for hypotheses in the sciences. It also has roots in the social contract political philosophy of Renouvier, who explicitly drew the analogy between conventions in political life and the conventional acceptance of hypotheses in the sciences, and conceived a philosophy that permits scientists to set aside foundational worries and explore new ideas. Although Poincaré and Renouvier may have hesitated to accept certain then recent developments in mathematics and the sciences such as non-Euclidean geometries, this conservatism cannot necessarily be attributed to their conventionalism. It may instead reflect the engineering background they shared with Comte, which emphasizes practical applications. Although Renouvier and Poincaré may have seen no practical use for these new ideas, unlike Comte they did not prohibit others from pursuing them, reflecting conventionalism's more liberal attitude toward recent developments in the sciences.     

Theory (In-)Equivalence and conventionalism in f(R) gravity

f(R) Gravity is the most natural extension of General Relativity within Riemannian Geometry. Due to (inter alia) its potential capacity for a unified treatment of early and late-time cosmic expansion, it has enjoyed recent attention in astrophysics and cosmology. I critically examine three inter-related claims found in the pertinent physics literature, of general interest to the philosopher of science. 1. f(R) Gravity is equivalent to a particular Brans-Dicke Theory. 2. The spacetime geometry underpinning f(R) Gravity has substantial conventional elements. 3. f(R) Gravity is an instance of a theory in which the distinction between matter and spacetime is conventional. Whilst the first claim can be vindicated in precise terms, the remaining two claims, I submit, are unwarranted – at least for the reasons usually adduced. On different grounds, though, the case for conventionalism about spacetime geometry in f(R) Gravity (as well as General Relativity) turns out to be considerably stronger.     

Conventionalism about what? Where Duhem and Poincaré part ways

This paper examines whether, and in what contexts, Duhem's and Poincaré's views can be regarded as conventionalist or structural realist. After analysing the three different contexts in which conventionalism is attributed to them—in the context of the aim of science, the underdetermination problem and the epistemological status of certain principles—I show that neither Duhem's nor Poincaré's arguments can be regarded as conventionalist. I argue that Duhem and Poincaré offer different solutions to the problem of theory choice, differ in their stances towards scientific knowledge and the status of scientific principles, making their epistemological claims substantially different.     

On the sources and implications of Carnap’s Der Raum

Der Raum, Carnap’s earliest published work, finds him largely a follower of Husserl. In particular, he holds a distinctively Husserlian conception of the synthetic a priori—a view, I will suggest, paradigmatic of what he would later reject as ‘metaphysics’. His main purpose is to reconcile that Husserlian view with the theory of general relativity. On the other hand, he has already broken with Husserl, and in ways which foreshadow later developments in his thought. Especially important in this respect is his use of Hans Driesch’s Ordnungslehre.     

String dualities and empirical equivalence

String dualities establish empirical equivalence between theories that often look entirely different with respect to their basic ontology and physical structure. Therefore, they represent a particularly interesting example of empirical equivalence in physics. However, the status of duality relations in string physics differs substantially from the traditional understanding of the role played by empirical equivalence. The paper specifies three important differences and argues that they are related to a substantially altered view on the underdetermination of theory building.     

Realism,functions, and the a priori: Ernst Cassirer's philosophy of science

This paper presents the main ideas of Cassirer's general philosophy of science, focusing on the two aspects of his thought that—in addition to being the most central ideas in his philosophy of science—have received the most attention from contemporary philosophers of science: his theory of the a priori aspects of physical theory, and his relation to scientific realism.     

Space–time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry,conventionality, and underdetermination

What if gravity satisfied the Klein–Gordon equation? Both particle physics from the 1920–30s and the 1890s Neumann–Seeliger modification of Newtonian gravity with exponential decay suggest considering a “graviton mass term” for gravity, which is algebraic in the potential. Unlike Nordström׳s “massless” theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman–Cunningham conformal group. It therefore exhibits the whole of Minkowski space–time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein׳s principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the ‘true’ geometry, one might wonder, in line with Poincaré׳s modal conventionality argument? Infinitely many theories exhibit this bimetric ‘geometry,’ all with the total stress–energy׳s trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers–Pirani–Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities—indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein׳s equations along the lines of Einstein׳s newly re-appreciated “physical strategy” and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz found in 1939). The Putnam–Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th–21st century space–time philosophy in the light of particle physics. An appendix reconsiders the Malament–Weatherall–Manchak conformal restriction of conventionality and constructs the ‘universal force’ influencing the causal structure.Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space–time theory that would have blocked Moritz Schlick׳s supposed refutation of synthetic a priori knowledge, and how Einstein׳s false analogy between the Neumann–Seeliger–Einstein modification of Newtonian gravity and the cosmological constant Λ generated lasting confusion that obscured massive gravity as a conceptual possibility.     

From Helmholtz to Schlick: The evolution of the sign-theory of perception

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zur?ck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his ‘method of coincidences’, similar to the ‘point-coincidences’ featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism.     

Conventionalism,structuralism and neo-Kantianism in Poincaré׳s philosophy of science

Poincaré is well known for his conventionalism and structuralism. However, the relationship between these two theses and their place in Poincaré׳s epistemology of science remain puzzling. In this paper I show the scope of Poincaré׳s conventionalism and its position in Poincaré׳s hierarchical approach to scientific theories. I argue that for Poincaré scientific knowledge is relational and made possible by synthetic a priori, empirical and conventional elements, which, however, are not chosen arbitrarily. By examining his geometric conventionalism, his hierarchical account of science and defence of continuity in theory change, I argue that Poincaré defends a complex structuralist position based on synthetic a priori and conventional elements, the mind-dependence of which precludes epistemic access to mind-independent structures.