Reichenbach on causality in 1923: Scientific inference,coordination, and confirmation

In The Theory of Relativity and A Priori Knowledge (1920b), Reichenbach developed an original account of cognition as coordination of formal structures to empirical ones. One of the most salient features of this account is that it is explicitly not a top-down type of coordination, and in fact it is crucially “directed” by the empirical side. Reichenbach called this feature “the mutuality of coordination” but, in that work, did not elaborate sufficiently on how this is supposed to work. In a paper that he wrote less than two years afterwards (but that he published only in 1932), “The Principle of Causality and the Possibility of its Empirical Confirmation” (1923/1932), he described what seems to be a model for this idea, now within an analysis of causality that results in an account of scientific inference. Recent reassessments of his early proposal do not seem to capture the extent of Reichenbach's original worries. The present paper analyses Reichenbach's early account and suggests a new way to look at his early work. According to it, we perform measurements, individuate parameters, collect and analyse data, by using a “constructive” approach, such as the one with which we formulate and test hypotheses, which paradigmatically requires some simplicity assumptions. Reichenbach's attempt to account for all these aspects in 1923 was obviously limited and naive in many ways, but it shows that, in his view, there were multiple ways in which the idea of “constitution” is embodied in scientific practice.     

Brokering Instruments in Napoleon's Europe: The Italian Journeys of Franz Xaver von Zach (1807–1814)

This paper explores the interactions between scientific travel, politics, instrument making and the epistemology of scientific instruments in Napoleon's Europe. In the early 1800s, the German astronomer Franz Xaver von Zach toured Italy and Southern France with instruments made by G. Reichenbach in his newly-established Bavarian workshop. I argue that von Zach acted as a broker for German technology and science and that travel, personal contacts and direct demonstrations were crucial in establishing Reichenbach's reputation and in conquering new markets. The rise of German instrument making highlights the complexity of the scientific relationship between the centre and the peripheries in Napoleon's empire, and reveals the existence of diverging views on the role of instruments and of their makers. In von Zach's view, Reichenbach's instruments could not penetrate the French market because Parisian astronomers focused on mathematical astronomy and, for both political and epistemological reasons, dismissed instruments and material innovations from the peripheries. The German astronomer and his Italian colleagues, on the contrary, regarded Reichenbach's technical achievements as outstanding contributions to astronomy, and considered the political and cultural hegemony of the capital as a hindrance to the advancement of science.     

Hans Reichenbach's and C.I. Lewis's Kantian philosophies of science

Recent work in the history of philosophy of science details the Kantianism of philosophers often thought opposed to one another, e.g., Hans Reichenbach, C.I. Lewis, Rudolf Carnap, and Thomas Kuhn. Historians of philosophy of science in the last two decades have been particularly interested in the Kantianism of Reichenbach, Carnap, and Kuhn, and more recently, of Lewis. While recent historical work focuses on recovering the threatened-to-be-forgotten Kantian themes of early twentieth-century philosophy of science, we should not elide the differences between the Kantian strands running throughout this work. In this paper, I disentangle a few of these strands in the work of Reichenbach and Lewis focusing especially on their theories of relativized, constitutive a priori principles in empirical knowledge. In particular, I highlight three related differences between Reichenbach and Lewis concerning their motivations in analyzing scientific knowledge and scientific practice, their differing conceptions of constitutivity, and their relativization of constitutive a priori principles. In light of these differences, I argue Lewis's Kantianism is more similar to Kuhn's Kantianism than Reichenbach's, and so might be of more contemporary relevance to social and practice-based approaches to the philosophy of science.     

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.     

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.     

Energy Conservation in GTR

The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g_ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Mach's principle.     

Does Kant have a pre-Newtonian picture of force in the balance argument? An account of how the balance argument works

In this paper, I discuss whether the Metaphysical Foundations of Natural Science version of Kant’s argument that space-filling matter requires both attractive and repulsive forces betrays a pre-Newtonian picture of forces as Warren (2010) argues. More generally, I discuss Kant’s overall strategy for securing the possibility of space-filling matter and I describe what motivates Kant to think of the argument in the way, I believe, he does. Ultimately, I argue that Kant’s argument does not suggest a pre-Newtonian picture of forces. Along the way, I discuss the status of quantity of matter and the nature of forces in the Dynamics chapter of that work so as to better clarify what is at work in the balance argument.     

Conventionalism in Reid’s ‘geometry of visibles’

The subject of this investigation is the role of conventions in the formulation of Thomas Reid’s theory of the geometry of vision, which he calls the ‘geometry of visibles’. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid’s ‘geometry of visibles’ and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the construction and assignment of its various properties, especially metric properties, and this fact undermines the claim for a unique non-Euclidean status for the geometry of vision. Finally, a suggestion is offered for trying to reconcile Reid’s direct realist theory of perception with his geometry of visibles.While Thomas Reid is well-known as the leading exponent of the Scottish ‘common-sense’ school of philosophy, his role in the history of geometry has only recently been drawing the attention of the scholarly community. In particular, several influential works, by N. Daniels and R. B. Angell, have claimed Reid as the discoverer of non-Euclidean geometry; an achievement, moreover, that pre-dates the geometries of Lobachevsky, Bolyai, and Gauss by over a half century. Reid’s alleged discovery appears within the context of his analysis of the geometry of the visual field, which he dubs the ‘geometry of visibles’. In summarizing the importance of Reid’s philosophy in this area, Daniels is led to conclude that ‘there can remain little doubt that Reid intends the geometry of visibles to be an alternative to Euclidean geometry’;¹ while Angell, similarly inspired by Reid, draws a much stronger inference: ‘The geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764 ...’² The significance of these findings has not gone unnoticed in mathematical and scientific circles, moreover, for Reid’s name is beginning to appear more frequently in historical surveys of the development of geometry and the theories of space.³Implicit in the recent work on Reid’s ‘geometry of visibles’, or GOV, one can discern two closely related but distinct arguments: first, that Reid did in fact formulate a non-Euclidean geometry, and second, that the GOV is non-Euclidean. This essay will investigate mainly the latter claim, although a lengthy discussion will be accorded to the first. Overall, in contrast to the optimistic reports of a non-Euclidean GOV, it will be argued that there is a great deal of conceptual freedom in the construction of any geometry pertaining to the visual field. Rather than single out a non-Euclidean structure as the only geometry consistent with visual phenomena, an examination of Reid, Daniels, and Angell will reveal the crucial role of geometric ‘conventions’, especially of the metric sort, in the formulation of the GOV (where a ‘metric’ can be simply defined as a system for determining distances, the measures of angles, etc.). Consequently, while a non-Euclidean geometry is consistent with Reid’s GOV, it is only one of many different geometrical structures that a GOV can possess. Angell’s theory that the GOV can only be construed as non-Euclidean, is thus incorrect. After an exploration of Reid’s theory and the alleged non-Euclidean nature of the GOV, in 1 and 2 respectively, the focus will turn to the tacit role of conventionalism in Daniels’ reconstruction of Reid’s GOV argument, and in the contemporary treatment of a non-Euclidean visual geometry offered by Angell ( 3 and 4). Finally, in the conclusion, a suggestion will be offered for a possible reconstruction of Reid’s GOV that does not violate his avowed ‘direct realist’ theory of perception, since this epistemological thesis largely prompted his formulation of the GOV.     

The constitutive a priori and the distinction between mathematical and physical possibility

This paper is concerned with Friedman׳s recent revival of the notion of the relativized a priori. It is particularly concerned with addressing the question as to how Friedman׳s understanding of the constitutive function of the a priori has changed since his defence of the idea in his Dynamics of Reason. Friedman׳s understanding of the a priori remains influenced by Reichenbach׳s initial defence of the idea; I argue that this notion of the a priori does not naturally lend itself to describing the historical development of space-time physics. Friedman׳s analysis of the role of the rotating frame thought experiment in the development of general relativity – which he suggests made the mathematical possibility of four-dimensional space-time a genuine physical possibility – has a central role in his argument. I analyse this thought experiment and argue that it is better understood by following Cassirer and placing emphasis on regulative principles. Furthermore, I argue that Cassirer׳s Kantian framework enables us to capture Friedman׳s key insights into the nature of the constitutive a priori.     

Hobbes on natural philosophy as “True Physics” and mixed mathematics

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the ‘why’ in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience.     

Is there a stability problem for Bayesian noncommutative probabilities?

A stability condition for Bayesian statistical inference, which Redei [(1992). When can non-commutative statistical inference be Bayesian? International Studies in the Philosophy of Science, 6, 129–132; (1998). Quantum logic in algebraic approach. Dordrecht: Kluwer Academic Publishers] formulated as a rationality constraint holding in classical probability theory, is shown to fail in quantum mechanics. That allegedly challenges a Bayesian interpretation of quantum probabilities. In this paper we demonstrate that Redei's argument does not apply to quantum mechanics. Moreover, we provide a solution to the problem of Bayesian noncommutative statistical inference arising from the violation of stability condition in general probability spaces.     

Duncan F. Gregory,William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.     

Subjective probability and quantum certainty

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent's degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent's prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent's prior beliefs. Quantum certainty is therefore always some agent's certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system.     

Kant and the scope of the analytic method

The paper investigates Kant's pre-critical views on the use of analytic and synthetic methods in Newtonian science and in philosophical reasoning. In his 1755/56 writings, Kant made use of two variants of the analytic method, i.e., conceptual analysis in a Cartesian (or Leibnizean) sense, and analysis of the phenomena in a Newtonian sense. His Prize Essay (1764) defends Newton's analytic method of physics as appropriate for philosophy, in contradistinction to the synthetic method of mathematics. A closer look, however, shows that Kant does not identify Newton's method with conceptual analysis, but just suggests a methodological analogy between both methods. Kant’s 1768 paper on incongruent counterparts also fits in with his pre-critical use of conceptual analysis. Here, Kant criticizes Leibniz’ relational concept of space, arguing that it is incompatible with the phenomenon of chiral objects. Since this result was in conflict with his pre-critical views about space, Kant abandoned the analytic method of philosophy in favour of his critical method. The paper closes by comparing Kant's pre-critical analytic method and the way in which he once again took up the methodological analogy between Newtonian science and metaphysics, in the preface B to the Critique of Pure Reason, in the context of his thought experiment of pure reason.     

How to (properly) strengthen Bell's theorem using counterfactuals

Bell's theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell's theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein's criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein's criterion rather than the locality assumption.     

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.     

On Cartwright's models for EPR

We assess Cartwright's models for probabilistic causality and, in particular, her models for EPR-like experiments of quantum mechanics. Our first objection is that, contrary to econometric linear models, her quasi-linear models do not allow for the unique estimation of parameters. We next argue that although, as Cartwright proves, Reichenbach's screening-off condition has only limited validity, her generalized condition is not empirically applicable. Finally, we show that her models for the EPR are mathematically incorrect and physically implausible.     

Measurement,coordination, and the relativized a priori

The problem of measurement is a central issue in the epistemology and methodology of the physical sciences. In recent literature on scientific representation, large emphasis has been put on the “constitutive role” played by measurement procedures as forms of representation. Despite its importance, this issue hardly finds any mention in writings on constitutive principles, viz. in Michael Friedman׳s account of relativized a priori principles. This issue, instead, was at the heart of Reichenbach׳s analysis of coordinating principles that has inspired Friedman׳s interpretation. This paper suggests that these procedures should have a part in an account of constitutive principles of science, and that they could be interpreted following the intuition originally present (but ultimately not fully developed) in Reichenbach׳s early work.     

The roots of the silver tree: Boyle,alchemy, and teleology

Though Robert Boyle called final causes one of the most important subjects for a natural philosopher to study, his own treatise on the subject, the Disquisition about Final Causes, has received comparatively little scholarly attention. In this paper, I explicate Boyle's complex argument against the use of teleological explanations for inanimate bodies, such as metals. The central object of this argument is a mysterious allusion to a silver plant. I claim that the silver plant is best understood as a reference to alchemical product: the Arbor Dianae, an offshoot of George Starkey's recipe for the Philosophers' Stone. Then, I show how the context of alchemy not only clarifies Boyle's argument but also places it within a wider dialectic about matter and teleology. I then contrast the parallel arguments of Boyle and John Ray on the question of whether metals have divine purposes and show that the difference is explained by Boyle's belief in the transmutation of metals.     

The material theory of induction and the epistemology of thought experiments

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn't been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton's fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position.