This article introduces Harvey Brown and Oliver Pooley’s ‘dynamical approach’ to special relativity, and argues that it may be construed as a relationalist form of Einstein’s ‘practical geometry’. This construal of the dynamical approach is shown to be compatible with related chapters of Brown’s text and also with recent descriptions of the dynamical approach by Pooley and others.

There is now a significant body of literature on consequentialist ethics that propose satisficing instead of maximizing accounts. Even though epistemology recently witnessed a widespread discussion of teleological and consequentialist theories, a satisficing account is surprisingly not developed yet. The aim of this paper is to do just that. The rough idea is that epistemic rules are justified if and only if they satisfice the epistemic good, i.e., reach some threshold of epistemic value (which varies with practical context), and believing (...) is justified if and only if it follows said rules.I argue that this alternative to the implicitly established way of thinking in maximizing terms has significant advantages. First, maximizing epistemic value can be unreasonably demanding; second, a satisficing theory can make finding reasonable rules for belief formation and sustenance much more accessible; and third, a satisficing approach is a better alternative to both general subjectivist and maximizing objectivist attempts to spell out epistemic blame. (shrink)

A central issue in the philosophical debates over general relativity concerns the status of the metric field: should it be regarded as part of the background arena in which physical fields evolve, or as a physical field itself? In this paper, we approach this debate through its relationship to the so-called "Problem of Space": the problem of determining which abstract, mathematical geometries are candidate descriptions of physical space. In particular, we explore the way that Hermann Weyl tackled the Problem of (...) Space in the wake of general relativity, and argue that Weyl’s proposed solution reveals a “middle way” between bare-manifold and manifold-plus-metric accounts of spacetime. (shrink)

Celem artykułu jest częściowe uzasadnienie negacji tezy, którą nazywam tezą o genezie realizmu strukturalnego. Dotyczy ona postulowanych w obrębie pewnej metafilozoficznej narracji związków między współczesnymi stanowiskami zwanymi epistemicznym realizmem strukturalnym i ontycznym realizmem strukturalnym a poglądami filozofów z początku XX wieku. W artykule rekonstruuję wymienione dwa stanowiska, postulowane związki, jakie mają one mieć z dwoma filozofami, Henri Poincarém oraz Ernstem Cassirerem, a następnie przedstawiam, dlaczego te postulowane związki są nietrafnie rozpoznane. Niesie to za sobą wnioski dotyczące swoistości wymienionych stanowisk oraz (...) pojęć obiektywności i rzeczywistości w ich kontekście. (shrink)

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...) of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them. (shrink)

Hermann von Helmholtz’s geometrical papers have been typically deemed to provide an implicitly group-theoretical analysis of space, as articulated later by Felix Klein, Sophus Lie, and Henri Poincaré. However, there is less agreement as to what properties exactly in such a view would pertain to space, as opposed to abstract mathematical structures, on the one hand, and empirical contents, on the other. According to Moritz Schlick, the puzzle can be resolved only by clearly distinguishing the empirical qualities of spatial perception (...) from those describable in terms of axiomatic geometry. This paper offers a partial defense of the group-theoretical reading of Helmholtz along the lines of Ernst Cassirer in the fourth volume of The Problem of Knowledge of 1940. In order to avoid the problem raised by Schlick, Cassirer relied on a Kantian view of space not so much as an object of geometry, but as a precondition for the possibility of measurement. Although the concept of group does not provide a description of space, the modern way to articulate the concept of space in terms of transformation groups reveals something about the structure and the transformation of spatial concepts in mathematical and natural sciences. (shrink)

The main goal of part 1 is to challenge the widely held view that Poincaré orders the sciences in a hierarchy of dependence, such that all others presuppose arithmetic. Commentators have suggested that the intuition that grounds the use of induction in arithmetic also underlies the conception of a continuum, that the consistency of geometrical axioms must be proved through arithmetical induction, and that arithmetical induction licenses the supposition that certain operations form a group. I criticize each of these readings. (...) More fully, I argue that the justification Poincaré offers for the use of the group notion in geometry appears to extend to set-theoretic notions that would suffice to put arithmetic on a logical foundation, thus undermining his own case for the necessity of intuition in arithmetic. In part 2, I offer an interpretation of intuition’s role on which it justifies the use of group-theoretic, but not set-theoretic, notions. (shrink)

One of the most influential arguments against the possibility of drawing a principled fact-convention distinction consists in the insight that because our beliefs are necessarily evaluated together, any statement can be retained or given up in the face of experience. The purpose of this paper is to establish that this argument does not undermine Poincaré s conventionalism in virtue of the fact that this doctrine does not simply amount to the claim that there are principles that are immune to revision. (...) It will be argued that Poincaré’s most important insight into the structure of theoretical knowledge is that there exist principles that cannot be empirically tested because they make possible the application of theoretical terms to experience. (shrink)

Given how thoroughly the history of quantum physics has been excavated, it might be wondered what these two hefty volumes by a physicist (Duncan) and a historian (Janssen) bring to the table. Aside from their inclusion of a wide range of recent work in this area, including some notable publications by themselves, the answer is twofold: first, as they state explicitly in the preface to the first volume, derivations of the key results are presented ‘at a level that a reader (...) with a command of physics and mathematics comparable to that of an undergraduate in physics should be able to follow without having to take out pencil and paper’ (vol. 1, p. vi). In response to those who might raise Whiggish eyebrows, I shall simply play the ‘you-try-reading-Pascual-Jordan's-groundbreaking-work-in-the-original’ card. As the authors suggest, by using modern notation and streamlining derivations whilst also, they maintain, remaining conceptually faithful to the original sources (ibid.), the book is rendered suitable for classroom use, albeit at the higher undergraduate or graduate levels. (shrink)

Philosophy of science in the twentieth century tends to emphasize either the logic of science (e.g., Popper and Hempel on explanation, confirmation, etc.) or its history/sociology (e.g., Kuhn on revolutions, holism, etc.). This dichotomy, however, is neither exhaustive nor exclusive. Questions regarding scientific understanding and mathematical explanation do not fit neatly inside either category, and addressing them has drawn from both logic and history. Additionally, interest in scientific and mathematical practice has led to work that falls between the two sides (...) of the dichotomy. We might call these less narrow approaches ‘holistic’. Prior to 1918, work in the philosophy of science was also somewhat more holistic and interdisciplinary in nature. An exemplar of this type of approach is found in the work of Henri Poincaré. In this paper I will consider one particularly flexible tool Poincaré uses throughout his philosophical writings about science and mathematics: the tool of the unifying concept. More specifically, I will focus on one unifying concept: that of structure. I aim to show first, that structure is a unifying scientific concept for Poincaré; second, a focus on structure helps explain his scientific and mathematical success; lastly, this case study may provide a model for how unifying concepts can facilitate progress in mathematics and science. (shrink)

Poincaré’s conventionalism has been interpreted in many writings as a philosophical position emerged by reflection on certain scientific problems, such as the applicability of geometry to physical space or the status of certain scientific principles. In this paper I would like to consider conventionalism as a philosophical position that emerged from Poincaré’s scientific practice. But not so much from dealing with scientific problems, as from the use of two specific methodologies proper to modern mathematics and the modern natural sciences: methodological (...) structuralism and the hypothetical-deductive method—thus, as a philosophical position which emerged from a way (or rather, two ways) ofdoingscience. With this approach, I try to deepen the analysis of connections between Poincaré’s scientific practice and his philosophy. (shrink)

This book proposes to identify three long-term structures in causal reasoning - in particular, in terms of the relationship between cause and identity - that appear to be of value in categorizing and organizing various trends in philosophical thought.<br>Such conceptual schemes involve a host of philosophical dilemmas (such as the problem of relativism), which are examined in the first chapter. A number of naturalistic and transcendental approaches to this problem are also analysed.<br>In particular, the book attempts to construct a theoretical (...) basis for Foucault's tripartite classification of epistemological structures in European thought.<br>The final chapter attempts to buttress the above schema by extending the analysis from cause and identity to growth, change, and stability, critiquing certain ideas of Foucault and Heidegger, as well as examining the contemporary thought of process philosophy and complexity theory.<br><br>Contents<br><br>Contents: Plurality and Causality - What is a Paradigm? - Paradigms and Causal Structure - Universality and Mathesis Universalis - Temporality and Visibility - Classical and Modern Probability Theory - The Environment and Non-Monotonicity - The Marburg School and the Limit Concept; Foucault's concept of 'Man' - Nineteenth Century Philosophy of Science - A Dynamic Model - Foucault and the Birth of the Clinic - Process, Growth and Complexity - Time and History. (shrink)

Poincare’s arguments for his thesis of the conventionality of metric depend on a relationalist program for dynamics, not on any general philosophical interpretation of science. I will sketch Poincare’s development of the relationalist program and show that his arguments for the conventionality of metric do not depend on any global strategies such as a general empiricism or Duhemian underdetermination arguments. Poincare’s theory of space, while empirically false, is more philosophically sophisticated than his critics have claimed.

This paper provides a comprehensive critique of Poincaré’s usage of the term intuition in his defence of the foundations of pure mathematics and science. Kant’s notions of sensibility and a priori form and Parsons’s theory of quasi-concrete objects are used to impute rigour into Poincaré’s interpretation of intuition. In turn, Poincaré’s portrayal of sensible intuition as a special kind of intuition that tolerates the senses and imagination is rejected. In its place, a more harmonized account of how we perceive concrete (...) objects is offered whereby intuitive knowledge is consistently a priori whatever the domain of application.Keywords: Immanuel Kant; Charles Parsons; Henri Poincaré; Quasi-concrete object; Sensible intuition; Sensibility. (shrink)

According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincaré in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincaré’s Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In a quixotic effort to save the Euclidean geometry that relied on this axiom, Poincaré extended (...) the purview of his doctrine of space to cover both space and time. The centerpiece of this new doctrine is what he called the ‘‘principle of physical relativity,’’ which holds the laws of mechanics to be covariant with respect to a certain group of transformations. For Poincaré, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime). Either way, physical space and time are the result of a convention. (shrink)

Resumen: Janet Folina ha propuesto una interpretación del convencionalismo de Poincaré contraria a la que ofrecen Michael Friedman y Robert DiSalle. Ambos afirman que la propuesta de Poincaré queda refutada por la relati-vidad general pues supone una noción restrictiva de los principios a priori. Folina sostiene que el convencionalismo de Poincaré no es contradictorio con la relatividad general porque permite una noción relativizada de los princi-pios a priori. Intento mostrar que la estrategia de Folina es ineficaz porque Poincaré no puede (...) explicar el papel de la variedad de Riemann en la rela-tividad general. Concluyo que la tentativa de reconstruir el desarrollo de la relatividad general a partir de la filosofía de Poincaré puede constituir un obs-táculo para comprender la radicalidad del cambio que la relatividad generó en las relaciones entre física y geometría.: Janet Folina has proposed an interpretation of Poincaré’s conven-tionalism against Michael Friedman and Robert DiSalle. They both state that Poincaré’s proposal is refuted by general relativity, since it implies a restrictive notion of a priori principles. Folina claims that Poincaré’s conventionalism is not in conflict with general relativity because from Poincaré’s proposal it is possible to extract a relativized notion of a priori principles. I intend to show that Folina’s strategy is ineffective due to Poincaré’s inability to explain the role of Riemann manifold in general relativity. I conclude that the attempt to reconstruct the development of general relativity from Poincaré’s philosophy may be an obstacle to understanding the radical nature of the change that relativity brought to the relationship between physics and geometry. (shrink)

This paper aims at understanding the concept of convention in mechanics as a notion transferred from the field of jurisprudence. This enables us to clarify it as a new epistemic category having a pertinent role in the transformation of mechanics in the nineteenth century. Such understanding permits a separation from linguistic and arbitrary conventions, thus highlighting its epistemic features and not transforming fundamental principles into mere arbitrary agreements. After addressing the main references in the literature discussing the role of convention (...) in mechanics, we analyze its classical use as a concept originating from law. Then we explain its use by Carl G. Jacobi, Ferdinand F. Reech, and J. Henri Poincaré. Here we also show how their uses conform to the features analyzed regarding conventions in jurisprudence. Finally, we try to explain how the use of this concept, among other factors, contributed to the transformation of mechanics. (shrink)

From Kant’s first published work to recent articles in the physics literature, philosophers and physicists have long sought an answer to the question, why does space have three dimensions. In this paper, I will flesh out Kant’s claim with a brief detour through Gauss’ law. I then describe Büchel’s version of the common argument that stable orbits are possible only if space is three-dimensional. After examining objections by Russell and van Fraassen, I develop three original criticisms of my own. These (...) criticisms are relevant to both historical and contemporary proofs of the dimensionality of space (in particular, a recent one by Burgbacher, F. Lämmerzahl, C., and Macias). In general I argue that modern “proofs” of the dimensionality of space have gone off track. (shrink)

Jean-Pierre Dupuy argues that our failure to prevent the looming climate catastrophe results from a faulty metaphysics of time: because we believe the present can proceed down one of the many branches that extend into the future, some of which bypass the catastrophe, we do not think it is absolutely urgent to take drastic action now. His solution to this problem of demotivation is “enlightened doomsaying” in “projected time”, which means that we affirm the coming catastrophe as something real in (...) the future rather than being a mere possibility; thus, we regard it seriously enough that we are motivated to take the needed actions to prevent it. One potential obstacle to this proposal is that it requires the forming of consensus and coordination with the powerful players who benefit from our current path and whose apparently near-total grip on this catastrophic future may itself discourage action. We then consider an alternative model based on Gilles Deleuze’s philosophy of the present–future relation. Although it has the branching structure that Dupuy is wary of, it may not suffer from the same problem of demotivation on account of the way it conceives the complex structure of the present event. For this reason, the Deleuzian model may be more suited to motivating action in a world where the future must be fought for rather than unanimously agreed upon. (shrink)

Although Eddington's philosophy of physics has been subjected to critical re-evaluation in recent years, neither the exact nature of his structuralist views nor his response to criticism by the likes of Braithwaite have been made clear. In this paper I trace, in particular, the incorporation into Eddington's structuralism of the non-classical indistinguishability of quantum objects. His metaphysical view of such objects as the product of group-theoretical analysis is crucial for understanding his response to Braithwaite's criticisms of the whole structuralist endeavor. (...) These criticisms closely resemble more recent attacks on structural realism in the philosophy of science. I conclude with a brief comparison between these more modern forms of structuralism and Eddington's. (shrink)

The goal of this paper is to answer the following question: Does it make sense to speak of thought experiments not only in physics, but also in mathematics, to refer to an authentic type of activity? One may hesitate because mathematics as such is the exercise of reasoning par excellence, an activity where experience does not seem to play an important role. After reviewing some results of the research on thought experiments in the natural sciences, we turn our attention to (...) experiments and thought experiments in mathematics, especially in fundamental mathematics, and investigate what thought experiments can teach us there. If we accept the principle that mathematical practice can sometimes be best described by a pragmatist approach where the concept of experience in mathematics is considered from a new perspective, thought experiments can in some cases be a useful instrument different from both ‘mathematical experiments’ and ‘formal’ proofs: they are mathematical experiments using deviant methods. (shrink)

According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

Abstract Schlick quite clearly maintains that the shift from classical physics to the theories of relativity is not necessitated by experience, but motivated by the pragmatic payoff of simplifying space-time ontology. However, there is in his work another, heretofore unrecognized argument for the revolutionary shift from classical to relativistic physics. According to this conceptual line of argument, the principles that define simultaneity and motion in classical physics fail to establish a univocal correspondence to physical quantities, and therefore must be revised, (...) along with the notions of absolute space and time that they underpin. Though these insights appear only intermittently in Schlick’s work, I will seek to elaborate on them in an effort to clarify his views on conventions within physics and the nature of revolutionary science, and to suggest that these views are invulnerable to the criticisms of pragmatic empiricists such as Quine. Content Type Journal Article Pages 1-17 DOI 10.1007/s12136-011-0131-3 Authors Steven Bland, Department of Philosophy, Huron University College, 1349 Western Rd, London, Ontario, Canada N6G 1H3 Journal Acta Analytica Online ISSN 1874-6349 Print ISSN 0353-5150. (shrink)

How was Poincaré’s conventionalism connected to his relationism? How, in other words, is it the case that the basic principles of geometry and mechanics are, ultimately, freely chosen conventions and that, at the same time, science reveals to us the structure of the world? This lengthy study aims to address these questions by setting Poincaré’s philosophy within its historical context and by examining in detail Poincaré’s developing views about the status and role of conventions in science and the status and (...) role of relations in science. It is argued that Poincaré was a neither a rampant conventionalist nor a pure structuralist. But he was both a conventionalist and a relationist, aiming to delineate a position which allowed room for both freely, but not arbitrarily, chosen constitutive principles of science and the acquisition of objective, though, relational knowledge of the natural world. (shrink)

The highly ordered neuronal projections from the retina to the tectum mesencephali (optic tectum) in several vertebrate groups have been intensively studied. Several hypotheses so far have been proposed, suggesting mechanisms to explain the topographical and biochemical specificity of the retinotectal projections during ontogeny. In the present paper we compare the main hypotheses of retinotectal development with respect to the nature of specificity envisaged, the activity-dependence versus inheritance criterium and the strategy of argument, in casu the descriptive versus interferential type (...) of argument. Matching of the current developmental hypotheses and mechanisms for elimination or persistance of contralateral, respectively ipsilateral connections, is attempted with respect to the known neuroanatomical connectivity data in the amphibian optic tectum and with respect to the symmetry relations between ipsilateral and contralateral connection patterns described in amphibians and other vertebrate groups. Local mechanisms influencing the survival potential of synaptic contacts between retinal afferents and tectal neurons are probably essential for generating global symmetry patterns. Finally, a global topological approach is discussed with respect to its applicability in the amphibian retinotectal projection system. Basic assumptions of topological modeling appear to rely on anatomical and functional properties of the visual system like left-right symmetry, dichotomy, (absence of) convergence and segregation of fibers and neurons into columnar information units. It is concluded however, that more neuroanatomical, physiological and ultrastructural data are needed to establish a formalized operation model of the amphibian retinotectal system. (shrink)

Beaucoup de « géomètres » du XIXe siècle - Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, et autres - ont joué un rôle important dans la discussion sur les fondements des mathématiques. Mais, contrairement aux idées d'Euclide, ils n'ont pas identifié «l'espace physique» avec« l'espace de nos sens». Partant de notre expérience dans l'espace, ils ont cherché à identifier les propriétés les plus importantes de l'espace et les ont posées à la (...) base de la géométrie. C'est sur la connaissance active de l'espace que les axiomes de la géométrie ont été élaborés ; ils ne pouvaient donc pas être a priori comme ils le sont dans la philosophie kantienne. En outre, pendant la dernière décade du siècle, certains mathématiciens italiens - De Paolis, Gino Fano, Pieri, et autres - ont fondé le concept de nombre sur la géométrie, en employant des résultats de la géométrie projective. Ainsi, on fondait l'arithmétique sur la géométrie et non l'inverse, comme David Hilbert a cherché à faire quelques années après, sans succès. (shrink)

Le conventionnalisme géométrique de Poincaré est bien connu ; les axiomes de la géométrie sont des conventions, le problème de la vérité de la géométrie n’a pas de sens et on doit le remplacer par celui de la commodité de la géométrie. Le conventionnalisme géométrique de Poincaré est associé à une théorie psycho-physio-logico-mathématique de la genèse de la géométrie et de l’espace : Je me suis demandé quel est le véritable caractère des...

I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyze the kinds of arguments offered by Jules Hoüel in 1860-1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami’s seminal papers, showing that Beltrami was much more concerned with the existence (...) of non-Euclidean objects than he was with the formal consistency of non-Euclidean geometries. The final step towards rigorous consistency proofs is taken in the 1880s by Henri Poincaré. It is the formal conception of geometry, stripping the geometric primitive terms of their usual meanings, that allows the introduction of a modern fully rigorous consistency proof. (shrink)

We argue that current constructive approaches to the special theory of relativity do not derive the geometrical Minkowski structure from the dynamics but rather assume it. We further argue that in current physics there can be no dynamical derivation of primitive geometrical notions such as length. By this we believe we continue an argument initiated by Einstein.