Scientific Conventionalism

I provide a compact reformulation of Carnap’s conditions of adequacy for the analytic and the synthetic component of a theory and show that, contrary to arguments by Winnie and Demopoulos, Carnap’s conditions of adequacy need not be supplemented by another condition. This has immediate implications for the analytic component of reduction sentences.

I motivate “Origin Conventionalism”—the view that which facts about one’s origins are essential to one’s existence in part depend on our person-directed attitudes. One important upshot of the view is that it offers a novel and attractive solution to the Nonidentity Problem. The Nonidentity Problem typically assumes that the sperm-egg pair from which a person originates is essential to that person’s existence; if so, then for many future persons that come into existence under adverse conditions, had those conditions not been (...) realized, the individuals wouldn't have existed. This is problematic since it delivers the counter-intuitive conclusion that it’s not wrong to bring about such adverse conditions since they don’t harm anyone. Origin Conventionalism, in contrast, holds that whether a person’s sperm-egg origin is essential to their existence depends on their person-directed attitudes. I argue that this provides a unique and attractive way of preserving the intuition that the actions in the ‘nonidentity cases’ are morally wrong because of the potential harm done to the individuals in question. (shrink)

In what sense is the direction of time a matter of convention? In 'The Direction of Time', Hans Reichenbach makes brief reference to parallels between his views about the status of time’s direction and his conventionalism about geometry. In this article, I: (1) provide a conventionalist account of time direction motivated by a number of Reichenbach’s claims in the book; (2) show how forwards and backwards time can give equivalent descriptions of the world despite the former being the ‘natural’ direction (...) of time; and (3) argue that this offers an important middle-ground position between existing realist and antirealist accounts of the direction of time. (shrink)

In his refreshingly non-parochial book There Are No Such Things as Theories, Steven French develops an ontology and an account of representation for the Partial Structures View in the philosophy of science as a competitor to the logical empiricists’ Received View. I argue that formally and practically, the two views are on a par, and that French just needs to take a few more steps with his ontology and account of representation to arrive at the logical empiricists’ positions.

In this paper I argue that the positivist–conventionalist interpretation of the Restricted Principle of Relativity is flawed, due to the positivists’ own understanding of conventions and their origins. I claim in the paper that, to understand the conventionalist thesis, one has to diambiguate between three types of convention; the linguistic conventions stemming from the fundamental role of mathematical axioms, the conventions stemming from the coordination betweeh theoretical statements and physical, observable facts or entities, and conventions that are made possible by (...) possible revisions to theory. I claim that it is not possible to interpret the Principle of Relativity as based on one of these three types of convention. This renders the conventionalist interpretation of the Principle of Relativity untenable. The paper is part of a larger project that aims to understand the philosophical significance of the Principle of Relativity. (shrink)

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)

La vida en el laboratorio. La construcción social de los hechos científicos (Latour y Woolgar, 1979) sostiene que los hechos y las entidades cuya existencia ha sido establecida por la ciencia no son descubrimientos sino “construcciones sociales” llevadas a cabo por los científicos mediante “versiones” o “explicaciones ordenadas” al establecer acuerdos (“cierres de controversias”). Se sostiene, siguiendo la terminología de la filosofía de la ciencia actual, que este argumento es una forma de antirrealismo científico lingüístico, tesis sustentada también por autores (...) como Richad Rorty, Nelson Goodman, Thomas Kuhn y Ludwik Fleck, que es inconsistente y que confunde niveles de lenguaje, porque al referirse metalingüísticamente a las teorías, “versiones” o descripciones científicas no diferencia entre cosas metafísicamente diferentes: la existencia (o la inexistencia) de una entidad o un hecho, y la creencia compartida o la descripción de la existencia (o la inexistencia) de esa entidad o ese hecho. Ello lo lleva a cometer el error categorial de atribuir características del lenguaje (como la de explicar o la de ser usado) a cosas que no son lingüísticas (como la naturaleza o un hecho). Si bien tanto la versión de Latour y Woolgar como las demás no diferencian entre que un conjunto de personas crean que existe lo que la ciencia afirma y las propias afirmaciones de la ciencia sobre lo que existe, ambas cosas ocurren en la realidad social, por lo que el argumento constructivista –tal como el de Goodman de que una constelación ha sido creada mediante una versión, el de Kuhn de que “los conceptos” “conforman el mundo al que se aplican” o el de que los hechos y las teorías no son categóricamente separables, el de Fleck de que la sífilis no existe independientemente de las representaciones lingüísticas de la medicina o el de Rorty de que el color de la piel de un dinosaurio depende de la descripción científica sobre él, por ejemplo-, en la medida en que niega la existencia independiente de esos hechos y entidades no es más que una forma actual de lo que se llamó idealismo metafísico, en la que no se considera como entidad primitiva las “ideas” o estados de conciencia sino hechos de sociedad humana como las afirmaciones y los significados científicos y las creencias que generan en las personas. (shrink)

This chapter discusses the roles of ether and electrons in relativity theory. One of the most radical moves made by Albert Einstein was to dismiss the ether from electrodynamics. His fellow physicists felt challenged by Einstein’s view, and they came up with a variety of responses, ranging from enthusiastic approval, to dismissive rejection. Among the naysayers were the electron theorists, who were unanimous in their affirmation of the ether, even if they agreed with other aspects of Einstein’s theory of relativity. (...) The eventual success of the latter theory (circa 1911) owed much to Hermann Minkowski’s idea of four-dimensional spacetime, which was portrayed as a conceptual substitute of sorts for the ether. (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)

Recent controversy over whether the Vienna Circle can provide a model for today’s political turn in the philosophy of science indicates the need to clarify just what is meant by the term political philosophy of science. This paper finds fourteen different meanings of the term, including both descriptive and normative usages, having to do with the roles of political values in the sciences, the political consequences and significance of the sciences and scientific modes of thought, and political processes within the (...) sciences. These different senses are exemplified by the history of nineteenth century French philosophy of science, including Comte and Renouvier, as well as twentieth century logical positivists such as Neurath and more recent philosophers of science such as Kitcher and Longino. The paper also addresses the issue of how there could be a positivist political philosophy of science, given positivisms’ questioning of values, and considers Renouvier’s social contract approach to a political philosophy of science more promising than either Comte’s naturalism or the logical positivists’ non-cognitivism. (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)

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)

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)

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

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. (shrink)

As reflexões metodológicas de Poincaré sobre a modelação mecânica dos fenômenos, as teorias físicas, a hierarquização das leis e a evolução do seu estatuto e sistema são susceptíveis de uma leitura kantiana que exibe a função constitutiva das matemáticas e a função reguladora dos princípios de conveniência e dos princípios da física, correspondendo estes a uma importante etapa na evolução das teorias físicas. The methodological reflections of Poincaré on the mechanical modeling of phenomena, physical theories, the hierarchy of laws and (...) the evolution of their status and system are illuminated by a Kantian reading that displays the constitutive function of mathematics and the regulative function of principles of convenience and of the principles of physics, these corresponding to an important step in the evolution of physical theories. (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.

Nous reproduisons ici, avec l’aimable autorisation de la Hofbibliothek Aschaffenburg, la courte correspondance inédite entre Dingler et Henri Poincaré. Cette correspondance, conservée aux Archives Dingler dans la Hofbibliothek Aschaffenburg, consiste en trois documents : un brouillon en allemand de la main de Dingler, sa traduction française par une autre plume, mais avec des corrections ef...

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)

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)

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)

Este texto introduz a tradução do discurso de intitulado "Sobre os números transfinitos" ("Über transfinite Zahlen"), proferido por Henri Poincaré em 27 de abril de 1909, na Universidade de Göttingen. Após uma breve apresentação do pensamento do autor acerca dos fundamentos da aritmética, procura-se citar os aspectos mais relevantes da chamada crise dos fundamentos da matemática, para então introduzir a reformulação do conceito de predicatividade aventada no referido discurso sobre números transfinitos, contribuição compreendida como um recurso teórico necessário para a (...) superação dos paradoxos relativos à teoria dos conjuntos. Com isso, pretende-se evidenciar o papel central do texto publicado nesta edição para o desenvolvimento da concepção matemática de Henri Poincaré. This article provides an introduction to the translation of the lecture entitled "On transfinite numbers" ("Über transfinite Zahlen"), given by Henri Poincaré at the University of Göttingen on April 27, 1909. Following a short presentation of Poincaré's views on the foundations of arithmetic, it identifies the aspects of the so-called crisis of the foundations of mathematics that are most relevant for understanding his reconstruction of the concept of predicativity, which is intended to be a theoretical resource that may overcome the paradoxes of set theory. In doing so, the article highlights the central role of this text in the process of maturation of Poincaré's views on the foundations of mathematics. (shrink)

No presente artigo, procuramos mostrar, por intermédio de numerosos exemplos, que a distinção lógica operada por Pierre Duhem entre a física e a metafísica não impossibilita que, do ponto de vista histórico, o autor reconheça a existência de um entrosamento profícuo a cingir as duas áreas do saber. Distinguimos três níveis possíveis de interação entre a física e a metafísica, porque acreditamos que ele aceita (a) que o físico trabalha constantemente movido por ambições metafísicas não autorizadas pela rigorosa lógica, (b) (...) que os sistemas metafísicos contribuíram para muitos dos progressos das teorias físicas, em especial, para o nascimento da ciência moderna e (c) que podemos identificar tradições metafísicas de pesquisa duradouras que se mostraram mais férteis do que algumas tradições positivas. In this article, we aim to show, by means of several examples, that Pierre Duhem's logical distinction operated by Pierre Duhem between physics and metaphysics does not prevent him, from a historical perspective, recognizing that there can be a fruitful interplay between the two fields of knowledge. We distinguish three possible levels of interaction that we believe Duhem accepts between physics and metaphysics: (a) that the physicist works constantly moved by metaphysical ambitions not authorized by rigorous logic; (b) that the metaphysical systems have contributed to the progress of many physical theories and, especially, to the birth of modern science, and; (c) that we can identify long-lasting metaphysical traditions of research which have shown themselves to be more fertile than the positivist traditions. (shrink)

Against Thomas Mormann's argument that differential topology does not support Carnap's conventionalism in geometry we show their compatibility. However, Mormann's emphasis on the entanglement that characterizes topology and its associated metrics is not misplaced. It poses questions about limits of empirical inquiry. For Carnap, to pose a question is to give a statement with the task of deciding its truth. Mormann's point forces us to introduce more clarity to what it means to specify the task that decides between competing hypotheses (...) and in what way such a task may be both in practice and/or in principle impossible to carry out. (shrink)

Henri Poincaré was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to (...) society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world. (shrink)

This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations, and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune with the (...) physical geometry underlying the Einstein-Hilbert general theory of relativity developed more than two decades later. (shrink)

Cette étude montre que les réflexions épistémologiques de Poincaré émergèrent dans le cadre de ses recherches scientifiques et qu’elles furent en partie inspirées par sa lecture de savants philosophes comme Helmholtz et surtout Maxwell. Elle donne une analyse systématique des textes philosophiques publiés par Poincaré vers 1900, au moment où il juge que la physique des principes constitue le sommet de l’évolution des théories. Enfin, elle met en rapport certaines de ses thèses sur la physique avec l’Analytique et la Dialectique (...) transcendantales kantiennes.This study shows that the epistemological reflections of Poincaré emerged as part of his scientific researches and they were partly inspired by his reading of Helmholtz and especially Maxwell. It provides a systematic analysis of philosophical texts published by Poincaré about 1900, where he finds that the physics of principles is the culmination of the evolution of theories. Finally, it brings together some of his theses on physics with Kant’s Transcendental Analytic and Dialectic. (shrink)

This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations , and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune with (...) the physical geometry underlying the Einstein-Hilbert general theory of relativity developed more than two decades later. (shrink)

The historical variation of scientific knowledge has lent itself to the development of historical epistemology, which attempts to historicize the origin and establishment of knowledge claims. The questions I address in this paper revolve around the historicity of the objects of those claims: How and why do new scientific objects appear? What exactly comes into being in such cases? Do scientific objects evolve over time and in what ways? I put forward and defend two theses: First, the ontology of science (...) is so rich and variegated that there are no universally valid answers to these questions. Second, we need a pluralist account of scientific objects, a pluralist metaphysics that can do justice to their rich diversity and their various modes of being and becoming. I then focus on hidden objects, which are supposed to be part of the permanent furniture of the universe, and I discuss their birth and historicity: They emerge when various phenomena coalesce as manifestations of a single hidden cause and their representations change over time. Finally, I examine the conditions under which an evolving representation may still refer to the same object and I illustrate my argument drawing upon the early history of electrons. (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)

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)

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.

Arthur Pap was not quite a Logical Empiricist. He wrote his dissertation in philosophy of science under Ernest Nagel, and he published a textbook in the philosophy of science at the end of his tragically short career, but most of his work would be classified as analytic philosophy. More important, he took some stands that went against Logical Empiricist orthodoxy and was a persistent if friendly critic of the movement. Pap diverged most strongly from Logical Empiricism in his theory of (...) a “functional a priori” in which fundamental principles of science are hardened into definitions and act as criteria for further inquiry. Pap was strongly influenced by the pragmatists C. I. Lewis and John Dewey in developing this alternative theory of a priori knowledge. Using Poincaré’s conventionalism as a springboard, Pap attempted to substantiate these views with examples from physics, and this was his largest foray into philosophy of science topics. Pap, as well as Lewis and Dewey, developed an alternative theory of the a priori in the 1950s that never quite took hold, despite the fact that their views are very intriguing and similar to Michael Friedman’s recent work on the constitutive a priori. (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)

W. V. Quine famously argues that though all knowledge is empirical, mathematics is entrenched relative to physics and the special sciences. Further, entrenchment accounts for the necessity of mathematics relative to these other disciplines. Michael Friedman challenges Quine’s view by appealing to historicism, the thesis that the nature of science is illuminated by taking into account its historical development. Friedman argues on historicist grounds that mathematical claims serve as principles constitutive of languages within which empirical claims in physics and the (...) special sciences can be formulated and tested, where these mathematical claims are themselves not empirical but conventional. For Friedman, their conventional, constitutive status accounts for the necessity of mathematics relative to these other disciplines. Here I evaluate Friedman’s challenge to Quine and Quine’s likely response. I then show that though we have reason to find Friedman’s challenge successful, his positive project requires further development before we can endorse it. (shrink)