Scientific Conventionalism

I analyse in detail the construction of asymptotic surfaces in Sections 16–19 of Poincaré, also known as the prize paper. There are two prime reasons for doing so. Firstly, this part of the prize paper contains an interesting argumentative strategy, which I call Poincaré׳s gestalt switch. Secondly, it has been claimed that the prize paper contains one of the first descriptions of chaotic motion. I will argue that the latter claim is false, although both the gestalt switches and the graphical (...) representation which Poincaré chose for the asymptotic surfaces might well have provided the inspiration for later works in chaos theory. (shrink)

David Stump has recently argued that Pierre Duhem can be interpreted as a virtue epistemologist. Stump’s claims have been challenged by Milena Ivanova on the grounds that Duhem’s ‘epistemic aims’ are more modest than those of virtue epistemologists. I challenge Ivanova’s criticism of Stump by arguing that she not distinguish between ‘reliabilist’ and ‘responsibilist’ virtue epistemologies. Once this distinction is drawn, Duhem clearly emerges as a ‘virtue-responsibilist’ in a way that complements Ivanova’s positive proposal that Duhem’s ‘good sense’ reflects a (...) conception of the ‘ideal scientist’. I support my proposal that Duhem is a ‘virtue-responsibilist’ by arguing that his rejection of the possibility of our producing a ‘perfect theory’ reflects the key responsibilist virtue of ‘intellectual humility’.Keywords: David Stump; Good sense; Humility; Milena Ivanova; Pierre Duhem; Virtue epistemology. (shrink)

I discuss two subjects in Samir Okasha’s excellent book, Evolution and the Levels of Selection. In consonance with Okasha’s critique of the conventionalist view of the units of selection problem, I argue that conventionalists have not attended to what realists mean by group, individual, and genic selection. In connection with Okasha’s discussion of the Price equation and contextual analysis, I discuss whether the existence of these two quantitative frameworks is a challenge to realism.

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. 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. 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. (shrink)

This is a book of wide-ranging scope, as the title suggests. First, it canvasses a broad selection of topics—from electromagnetism and quantum mechanics to Husserl’s phenomological constitution of logic, from Russell and Wittgenstein to Hartry Field. Second, its aims are broad. The author describes the book both as a “rational reconstruction of Poincaré’s position” and as a “treatise on modern epistemology”. The former description is somewhat misleading in that, together with Zahar’s stated aim of both “clarifying and of then reconciling (...) Poincaré’s various theses about the foundations of mathematics and the natural sciences”, it might give the reader hope that all of these theses might be shown to be part of one unified position. In fact, though, Poincaré’s philosophy of physics and his philosophy of mathematics turn out to be fundamentally different. Zahar attributes to Poincaré a “structural realist” view of physics and a “quasi-Kantian” constructivist view of mathematics. It’s not entirely clear, though, why the considerations adduced in favor of structural realism in physics can’t be carried over to the case of mathematics. More might have been said to explain this divergence, perhaps for example by developing the contrast in the introduction between the empirical testability of scientific hypotheses and the intuitive self-evidence of mathematical theorems. (shrink)

Drawing on themes important in moral and political philosophy, much of the scholarship on the constitutional law of privacy in the United States distinguishes between privacy understood as a person's control over information and privacy understood as a person's ability to make autonomous decisions. For example, Katz v. United States established the framework for analyzing whether police activity constituted a “search” subject to the Fourth Amendment's requirement that the police either obtain a warrant before conducting a search or otherwise act (...) reasonably. The defendant was a professional gambler who knew enough about police techniques to use a public telephone to make his business calls. Police agents attached a listening device to the outside of the phone booth, and sought to use the recordings against the defendant. The Supreme Court agreed with the defendant that the Fourth Amendment had been violated. Justice John Marshall Harlan's influential concurring opinion asserted that a person's privacy, in the sense of control over information, depended on two factors: “that a person have exhibited an actual expectation of privacy and, second, that the expectation be one that society is prepared to recognize as ‘reasonable.’” Fourth Amendment cases like Katz involve informational control; they define the circumstances under which the government may acquire information from or about a person without first obtaining the person's agreement. In contrast, cases like Griswold v. Connecticut, which barred the state from making it a criminal offense to use contraceptives, and Roe v. Wade, which restricted the state's power to prohibit or regulate abortions, used the language of privacy rights to protect a much broader interest in autonomous decision-making. Seeing these cases and related ones through lenseees provided by moral and political philosophy, scholars have attempted to describe what a morally sound constitutional law of privacy would be, and the broadest sense, dworkinian. That is, they seek to provide an account of privacy with two characteristics: it is broadly consistent with the relevant constitutional decisions, and it is the most morally attractive account possible that satisfies the requirement of consistency with the decisions. (shrink)

In his account of probable reasoning, Poincaré used the concept, or at least the language, of conventions. In particular, he claimed that the prior probabilities essential for inverse probable reasoning are determined conventionally. This paper investigates, in the light of Poincaré's well known claim about the conventionality of metric geometry, what this could mean, and how it is related to other views about the determination of prior probabilities. Particular attention is paid to the similarities and differences between Poincaré's conventionalism as (...) it applies to probabilities and de Finetti's subjectivism. The aim of the paper is to suggest that in accounts of the development of ideas about probable reasoning, particularly those customarily described as Bayesian, Poincaré's discussion deserves more attention than it has so far received. (shrink)

We discuss in this paper the question of the scope of the principle of tolerance about languages promoted in Carnap's The Logical Syntax of Language and the nature of the analogy between it and the rudimentary conventionalism purportedly exhibited in the work of Poincaré and Hilbert. We take it more or less for granted that Poincaré and Hilbert do argue for conventionalism. We begin by sketching Coffa's historical account, which suggests that tolerance be interpreted as a conventionalism that allows us (...) complete freedom to select whatever language we wish—an interpretation that generalizes the conventionalism promoted by Poincaré and Hilbert which allows us complete freedom to select whatever axiom system we wish for geometry. We argue that such an interpretation saddles Carnap with a theory of meaning that has unhappy consequences, a theory we believe he did not hold. We suggest that the principle of linguistic tolerance in fact has a more limited scope; but within that scope the analogy between tolerance and geometric conventionalism is quite tight. (shrink)

This book contains twenty-two papers by K. Ajdukiewicz, an outline of his memoir and philosophical evolution by J. Giedymin, and a bibliography of Ajdukiewicz’s works compiled by T. Czezowski. In the colorful introductory paper, Giedymin characterizes the personality of the famous Polish philosopher-logician as a person open not only to philosophical investigations but also to contemplation of the beauty contained in music, literature, and nature. The sketch of Ajdukiewicz’s scientific activity presents him as an excellent teacher, open-minded in understanding different (...) viewpoints but simultaneously as an independent and uncompromising thinker. (shrink)

In attempting to assess the legacy of Paul Feyerabend's philosophical work, matters are complicated by the fact that there was a change in his basic orientation towards the philosophy of science around the end of the 1960s. Here I shall indicate one aspect of Feyerabend's divided legacy. My main aims are to sketch the principal themes in his (fairly extensive but little-known) 1990s output, to situate that later output insofar as it bears on the realism/antirealism debate, and (rather precipitously, perhaps) (...) to identify what I take to be the single common premise of his entire philosophical work. (shrink)

The book Poincaré, Philosopher of Science – Problems and Perspectives, edited by María de Paz and Robert DiSalle, is the result of various colloquia and conferences organized by the Portuguese project bearing the same name. The project, initiated by University of Lisbon, brought together scholars of many different countries to speak about the three main philosophical facets of Henri Poincaré: as a philosopher of science in general, as a philosopher of mathematics, and as a philosopher of physics.

Carnap suggests that philosophy can be construed as being engaged solely in conceptual engineering. I argue that since many results of the sciences can be construed as stemming from conceptual engineering as well, Carnap’s account of philosophy can be methodologically naturalistic. This is also how he conceived of his account. That the sciences can be construed as relying heavily on conceptual engineering is supported by empirical investigations into scientific methodology, but also by a number of conceptual considerations. I present a (...) new conceptual consideration that generalizes Carnap’s conditions of adequacy for analytic–synthetic distinctions and thus widens the realm in which conceptual engineering can be used to choose analytic sentences. I apply these generalized conditions of adequacy to a recent analysis of scientific theories and defend the relevance of the analytic–synthetic distinction against criticisms by Quine, Demopoulos, and Papineau. (shrink)

W pierwszej połowie XX wieku przyjęło się upatrywać w poglądach H. Poincarégo i P. Duhema przykładów antyrealistycznego stanowiska odnośnie do nauki i jej teorii. Etykietka ta przylgnęła do tych autorów tak mocno, że coraz częstszym dzisiaj głosom tych, którzy sprzeciwiają się takiemu szufladkowaniu ich filozofii, trudno jest przebić się do głównego nurtu dyskusji filozoficznych. W artykule wskazuję, że odczytywanie poglądów obu francuskich autorów jako antyrealistycznych nie znajduje potwierdzenia w ich własnych wypowiedziach. Przeciwnie, ich prace dostarczają mocnych świadectw na rzecz upatrywania (...) w nich prekursorów współczesnych wyrafinowanych stanowisk realistycznych. (shrink)

This book defends the constructivist view of science, namely, the view that scientific theories are mental constructions in the mind of the scientist, rather than the realist view that scientific theories are accounts of what nature itself is like. To prove this point, evolution theory is contrasted with "creation science" as two paradigms or extremely divergent theories, each of which, as a mental construct, explains the data or facts of the natural world equally well. Contents: Realism vs. Constructivism; Meaning and (...) Reference in the Natural Sciences; The Role of Paradigm in the Creationism Controversy; Science As Mental Construction. (shrink)

Contemporary science seems to be caught in a strange predicament. On the one hand, it holds a firm and reasonable commitment to a healthy naturalistic methodology, according to which explanations of natural phenomena should never overstep the limits of the natural itself. On the other hand, contemporary science is also inextricably and now inevitably dependent on ever more complex technologies, especially Information and Communication Technologies, which it exploits as well as fosters. Yet such technologies are increasingly “artificialising” or “denaturalising” the (...) world, human experiences and interactions, as well as what qualifies as real. So the search for the ultimate explanation of the natural seems to rely upon, and promote, the development of the artificial, seen here as an instantiation of the non-natural. In this article, I would like to try and find a way out of this apparently strange predicament. I shall argue that the naturalisation of our knowledge of the world is either philosophically trivial, or mistaken. First, I shall distinguish between different kinds of naturalism. Second, I shall remind the reader that the kinds of naturalism that are justified today need to be protected and supported pragmatically, but they are no longer very interesting conceptually. We know how to win the argument. We just have to keep winning it. Whereas the kind of naturalism that is still interesting today is now in need of revision in order to remain acceptable. Such a kind of naturalism may be revised on the basis of a realistic philosophy of information, according to which knowing is a constructive activity, through which we do not merely represent the phenomena we investigate passively, but create more or less correct informational models of them, proactively and interactively. I shall conclude that the natural is in itself artefactual, and that the information revolution is disclosing a tension not between the natural and the non-natural, but a deeper one between a user’s and a producer’s interpretation of knowledge. The outcome is a philosophical view of knowledge and science in the information age that may be called constructionist and a revival of philosophy as a classic, foundationalist enterprise. (shrink)

To consider Pierre Duhem’s conception of natural classification as the aim of physical theory, along with his instrumentalist view on its nature, sets up an inconsistency in his philosophy of science which has not yet been solved. This paper argues that to solve it we have to take Duhem on his own terms and that a solution can only be found by interpreting his philosophy as an articulated system which necessarily involves the following connections: 1. The association of natural classification (...) to the thesis of historical continuity as an essential condition to the possibility of assigning a goal to the evolution of physical theory, 2. The connection of Pascal’s esprit de finesse to Duhem’s conception of analogy as a heuristic criterion to the conception of hypotheses that are able to lead physical theory to an end that aims to approach the real structure of the world. (shrink)

The new book by Professor David J. Stump explores and develops the theories of the a priori, which are rarely considered in contemporary epistemology and philosophy of science: the theories of pragmatic and functional a priori, proposed in the early XX century by Clarence Irving Lewis and Arthur Pap. The author begins with the analysis of «constitutive elements of science» and Henri Poincare's conventionalism. He consistently and historically examines the approaches towards the theories of the a priori within the philosophy (...) of science in the XX-XXI centuries, and also develops his own original approach to a priori based on the philosophy of science. (shrink)

Poincaré’s conventionalism has thoroughly transformed both the philosophy of science and the philosophy of mathematics. In the former it gave rise to new insights into the complexities of scientific method, in the latter to a new account of the nature of (so-called) necessary truth. Not only proponents of conventionalism, such as the logical positivists, were influenced by Poincaré, but also outspoken critics of conventionalism, such as Quine, Putnam, and (as I will argue) Wittgenstein, were deeply inspired by conventionalist ideas. Indeed, (...) during the twentieth century, most philosophers of science and mathematics engaged in dialogue with conventionalism. As is often the case with complex ideas, there is no consensus about the meaning of conventionalism in general and Poincaré’s original version of it in particular. Nonetheless, notions such as underdetermination (of theory), empirical equivalence (of incompatible theories), implicit definition, holism, and conceptual relativity, all of which can be linked to Poincaré’s writings, have become central to philosophy. In tracing the flow of Poincaré’s ideas through the philosophical space of the twentieth century, this article emphasizes not only the stimulus provided by his actual views but also the effects of misreading and unjustified appropriation. (shrink)

Abstract Artificial language philosophy (also called ‘ideal language philosophy’) is the position that philosophical problems are best solved or dissolved through a reform of language. Its underlying methodology—the development of languages for specific purposes—leads to a conventionalist view of language in general and of concepts in particular. I argue that many philosophical practices can be reinterpreted as applications of artificial language philosophy. In addition, many factually occurring interrelations between the sciences and philosophy of science are justified and clarified by the (...) assumption of an artificial language methodology. (shrink)

Up until recently social scientists took it for granted that their task was to account for the social world as objectively as possible: they were realists in practice if not always in their methodological sermons. This situation started to change in the 1960s, when a number of antirealist philosophies made inroads into social studies. -/- This paper examines critically the following kinds of antirealism: subjectivism, conventionalism, fictionism, social constructivism, relativism, and hermeneutics. An attempt is made to show that these philosophies (...) are false and are causing serious damage to social studies. -/- Next the subjective interpretation of probability is analyzed as a case of subjectivism. An approach to the subjective perception of justice is sketched as an example of the objective study of subjective experience. -/- Finally, the three main varieties of realism — naive, critical, and scientific — are outlined. It is argued that the scientific attitude involves scientific realism, which is put in practice even by scholars who, like Weber and Simmel, called themselves antirealists. (shrink)

Rudolf Carnap's essay "Empiricism, Semantics, and Ontology" is traditionally interpreted as an expression of either the analytic/synthetic distinction or verificationism. However, Carnap's fundamental aim---the repudiation of both nominalism and Platonism---cannot be accommodated by either interpretation. I interpret ESO as a renunciation of first-philosophical metaphysics, understood as an inquiry into what there is that transcends empirical science and constrains what sorts of entities a legitimate science can countenance. Carnap saw such constraints as metaphysical prejudices dressed up as ontological insights, and wrote (...) ESO in order to protect science from their malign influence. The repudiation of first philosophy and advocacy of the autonomy and authority of science is naturalism, in at least one sense of the term. So ESO advocates naturalism. ;This is surprising, since Carnap's most famous opponent, Quine, is also the most famous advocate of naturalism. Quine thought that Carnap was tying to enjoy the benefits of quantifying over abstracta while denying their existence. This is the maneuver Quine's criterion of ontological commitment was designed to block. But Carnap's purpose was not to satisfy nominalistic scruples. It was, rather, to show that empiricism does not imply nominalism, and therefore that such scruples are superfluous. Quine, in assuming that Carnap was subject to such scruples, has painted Carnap as Carnap's own antagonist. ;The verificationist interpretation of ESO also misconstrues Carnap's intent. It sees Carnap's overall philosophical project as the defense of radical empiricism and the refutation of scepticism. But the purpose of ESO is not the refutation of scepticism; it is the repudiation of first-philosophical metaphysics. Carnap was not trying to secure the epistemic credentials of scientific doctrine. He was trying to protect science from the imposition of metaphysical prejudice. ;After rejecting these two interpretations and offering mine, I turn to the impact that Carnap's views would have on the realism debate in the philosophy of science. Carnap's attitude toward this debate resembles Arthur Fine's "Natural Ontological Attitude" . Fine's own exposition of NOA, however, is difficult to interpret, a situation that is improved if we set NOA within a broadly Carnapian philosophical orientation. (shrink)

Duhem is often described as an anti-realist or instrumentalist. A contrary view has recently been expressed by Martin (1991) (Pierre Duhem: Philosophy and History in the Work of a Believing Physicist (La Salle, IL: Open Court)), who suggests that this interpretation makes it difficult to understand the vantage point from which Duhem argues in La science allemande (1915) that deduction, however impeccable, cannot establish truths unless it begins with truths. In the same spirit, the present paper seeks to establish that (...) Duhem is at any rate not the kind of anti-realist he is often presented as being, and that his views are like those Quine sees fit to call realist. An interpretation of Duhem's views on explanation and precision in science, and their bearing on the epistemological status of theory, is advanced which leads naturally into his critique of conventionalism. His attitude towards atomism, which should not be judged from a post-1925 perspective, is considered part of the unified view he strove after and appropriately called Duhem's physicalism, standing in contrast to the kind of reductionist conception usually associated with atomism. (shrink)

The following study aims to articulate the key problems, doctrines, concepts and contributions of the conventionalist philosophers. Following the preliminary clarifications, the main body of this dissertation will proceed to a critical and analytical survey of key conventionalist philosophers and their contribution to the development of the convention­ alist outlook. This study will conclude with a brief statement about some of the important contributions to epistemology that can be traced to the work of conventionalists.

The thesis of the conventionality of simultaneity in the special theory of relativity has been the subject of controversy for over fifty years Unfortunately, debates about this thesis have sometimes been marred by a failure to clearly distinguish different conventionalist theories. In my dissertation I evaluate, clarify, and carefully distinguish a number of different conventionalist theories, and thus clear up some of the confusion surrounding the thesis of the conventionality of simultaneity . In particular, I examine the following conventionalist theories. (...) ;According to the definitional theory of principles, there are some important scientific "laws" which apparently state facts, but which in reality are true by definition. I show that the most notable attempts, to establish that some important scientific laws were actually "definitions in disguise" were not successful. ;According to the theory of conventional reference, there are some words which have meanings which do not uniquely determine their respective references. For example, Reichenbach claimed that the meaning of "simultaneity" did not uniquely determine its reference. I show in my dissertation that if Reichenbach were correct about the meaning of "simultaneity" then his argument would be sound, but that there are good reasons for doubting the correctness of Reichenbach's views about the meaning of "simultaneity". ;Closely related to the theory of conventional reference was Reichenbach's theory of coordinative definitions. According to the theory of coordinative definitions, if a word's meaning failed to uniquely determine its reference, some sentences in the theory must be used solely to fix the reference of the word. Reichenbach proposed a coordinative definition of "simultaneity", but I argue in my dissertation that even if one accepts Reichenbach's views about the meaning of "simultaneity", his views about the coordinative definition of "simultaneity" are not substantiated. ;According to the theory of intertranslatability, there are apparently incompatible scientific theories which nonetheless "say the same thing", in some intuitive sense. Such theories are said to be intertranslatable. For example, according to Winnie there are theories which seem to be incompatible with the standard version of the special theory of relativity, but which are actually intertranslatable with it. After examining a number of proposed criteria for intertranslatability, I select an adequate one. I use this criterion to show that Winnie's claim is true, but trivial, since the proposed "alternatives" to the standard version of the special theory of relativity are merely the same covariant theory expressed in different coordinate systems. ;Finally, according to the theory of conventional relations, there are some relations which are conventional because they are not intrinsic . Malament demonstrated that if symmetric causal connectability is the only intrinsic spacetime relation, then standard simultaneity is not a conventional relation, but every non-standard simultaneity relation is conventional. I demonstrate that if an asymmetric causal connectability relation is intrinsic, then not only is standard simultaneity not conventional, there are also an infinitude of non-conventional non-standard simultaneity relations. (shrink)

This paper construes various positions in the philosophy of science and the philosophy of law as responses to the problem of underdetermination in science and in law. We begin by drawing a close analogy between the successive approaches to this problem in the two fields. In particular, we stress the analogy between conventionalism as a philosophy of science and legal realism as a philosophy of law, and between Putnam's and Dworkin's critiques of these positions. We then challenge the Putnam-Dworkin strategy, (...) arguing that their attempts to combat underdetermination are unsuccessful. We are thus led to scepticism regarding the outlook underlying the celebrated maxim, “ruled by law, not by men”. (shrink)

This article focuses on the conventions that sustain social interaction and argues that they are central to Simon's decision-making theory. Simon clearly identifies two kinds of coordination by convention: behavioral mores that shape human actions, and shared mental models that govern human perceptions. This article argues that Poincaré–Carnap's conventionalism provides powerful support for Simon's theory; it contends that this theory offers a more convincing account of decision and coordination than Lewis' concept of convention. Simon's approach to applying conventionalist logic to (...) social interaction emphasizes the normative role played by mental models in solving coordination problems and considers rationality in terms of both cognitive and moral considerations. By connecting conventional phenomena to social identifications, Simon stresses the resulting complexity of coordination problems. (shrink)

Between 1906 and 1911, as a response to Betrand’s Russell’s review of La Science et l’Hypothèse, Henri Poincaré launched an attack on the movement to formalise the foundations of mathematics reducing it to logic. The main point is the following: the universality of logic is based on the idea that their truth is independent of any context including epistemic and cultural contexts. From the free context notion of truth and proof it follows that, given an axiomatic system, nothing new can (...) follow. One of the main strategies of Poincaré’s solution to this dilemma is based on the notions of understanding and of grasping the architecture of the propositions of mathematics. According to this view mathematic rigour does not reduce to “derive blindly” without gaps from axioms,mathematical rigour is, according to Poincaré, closely linked to the ability to grasp the architecture of mathematics and contribute to an extension of the meaning embedded in structures that constitute the architecture of mathematical propositions. The focus of my paper relates precisely to the notion of architecture and to the notion of understanding. According to my reconstruction, Poincaré’s suggestions could be seen as pointing out that understanding is linked to reason not only within a structure but reasoning about the structure. (shrink)

In the frame of the celebration of the century of the publication that gave way to the special theory of relativity, a semblance of the discussions generated from the philosophical implications that derive from the possibility of accepting non-euclidian frames for our space of representation. Poncaré’s argument is exposed in defense of geometrys principle of relativity and the criticism formulated by Hans Reichenbach is discussed.

Résumé Partant du principe que la philosophie de la connaissance de Poincaré est cohérente, j’essaie de faire voir que son conventionnalisme en géométrie et en physique n’est qu’une conséquence de son intuitionnisme. Après avoir rappelé, dans la première section, ce qu’est l’intuitionnisme et décrit ce que l’intuitionnisme de Poincaré a de spécifique, je montre, dans la deuxième section, comment celui-ci retentit sur la conception de l’espace. Dans la troisième section, j’applique les conclusions précédemment établies à la question très controversée de (...) la découverte de la relativité restreinte en renvoyant dos à dos les historiens : il n’a rien manqué à Poincaré pour découvrir la relativité restreinte, car, cette théorie étant incompatible avec son intuitionnisme, il n’avait aucune raison d’y adhérer.Taking for granted that Poincaré’s epistemology is consistent, I attempt to show that his geometrical and physical conventionalism is no more than a consequence of his intuitionism. After having rehearsed the issues defining intuitionism and describing what is particular to Poincaré’s version in the first section of the paper, I show, in the second section, how Poincaré’s intuitionism influenced his conception of space. In the last section, I apply these now established conclusions to a very contested issue, the discovery of the special theory of relativity. Rejecting the view of historians on both sides of the issue, I argue that Poincaré had everything he would have needed to discover the special theory of relativity, but that since this theory is incompatible with his intuitionism, he had no reason to adopt it. (shrink)