The violation of Bell’s inequality has shown that quantum theory and relativity are in tension: reality is nonlocal. Nonetheless, many have argued that GRW-type theories are to be preferred to pilot-wave theories as they are more compatible with relativity: while relativistic pilot-wave theories require a preferred slicing of space-time, foliation-free relativistic GRW-type theories have been proposed. In this paper I discuss various meanings of ‘relativistic invariance,’ and I show how GRW-type theories, while being more relativistic in one sense, are less (...) relativistic in another. If so, the initial claim that GRW-type theories have a greater compatibility with relativity is unwarranted: both type of theories violate relativity, one way or another. (shrink)

Philosophy Compass, Volume 17, Issue 4, April 2022.

It has been claimed, recently, that the fact that all the non-gravitational fields are locally Poincaré invariant and that these invariances coincide, in a certain regime, with the symmetries of the spacetime metric is miraculous in general relativity. In this paper I show that, in the context of GR, it is possible to account for these so-called miracles of relativity. The way to do so involves integrating the realisation that the gravitational field equations impose constraints on the behaviour of matter (...) in a novel interpretation of the equivalence principle, which dictates the determination of local inertial frames through gravitational interaction. This proposed explanation of the miracles can also deal with the problematic cases for attempts at explaining them in the context of the standard geometrical perspective on relativity theory. (shrink)

In this dissertation, I present a novel account of the components that have a peculiar epistemic role in our scientific inquiries, since they contribute to establishing a form of coordination. The issue of coordination is a classic epistemic problem concerning how we justify our use of abstract conceptual tools to represent concrete phenomena. For instance, how could we get to represent universal gravitation as a mathematical formula or temperature by means of a numerical scale? This problem is particularly pressing when (...) justification for using these abstract tools comes, in part or entirely, from knowledge which is not independent from them, thus leading to threats of circularity. Achieving coordination between some abstract conceptual tools and the concrete phenomena that they are supposed to represent is usually a complex process, which involves several epistemic components. Some of these components eventually provide stable conditions for applying those abstract representations to concrete phenomena. It is in this sense of providing certain conditions of applicability that different philosophical traditions, as well as some contemporary reappraisals, view these components as constitutive or a priori. In this work, I present a new gradualist, contextualist, and relational approach to understand these constitutive components of scientific inquiry. It is gradualist inasmuch as the degree to which some component is constitutive depends on three quantifiable features: quasi-axiomaticity, generative potential, and empirical shielding. Since the quantification of these three features impinges on the history and practice of using these components in a scientific context, my approach is a contextualist one. Finally, my approach is relational in a double sense: first, it identifies ordinal relationships among epistemic components with respect to their constitutive character; second, these relationships are relative to a scientific framework of inquiry. After introducing my account and a classic example of constitutively a priori principles, i.e., Friedman’s (2001) analysis of Newtonian mechanics, I turn to my own case studies to demonstrate the advantages of my approach. Firstly, I discuss Okasha’s (2018) view of endogenization as a pervasive theoretical strategy in evolutionary biology and suggest that the constitutive character of the core Darwinian principles progressively increases with endogenization. Secondly, I apply a conceptual distinction between two varieties or scopes of coordination – general coordination and coordination in measurement – to Ohm’s work on electrical conductivity. This distinction allows me to pinpoint to what extent components along different dimensions (e.g., instrumentation, measurement, theorising, etc.) were constitutive of the forms of coordination which Ohm relied on. Thirdly, I discuss the epistemic function of the Hardy-Weinberg principle in the history and practice of population genetics. I assess this principle in terms of my account and identify approximation and stability as two components that are highly constitutive, in that they contribute to justifying its use in population genetics. Finally, applying my account to these case studies enables me to identify at least three qualitatively different types of constitutive components: domain-specific theoretical principles, material components, and domain-independent assumptions underlying reasoning abilities. In the light of my results, I draw some general conclusions on epistemic justification and scientific knowledge. (shrink)

The following article describes a pilot study on the possible integration of digital historiography into teaching practice. It focuses on Émilie Du Châtelet’s considerations of space and time against the background of Leibniz’s program of analysis situs. Historians have characterized philosophical controversies on space and time as a dichotomy between the absolute and relational concepts of space and time. In response to this, the present case study pursues two aims: First, it shows that the common portrayal simplifies the complex pattern (...) of change and the semantic shift from absolute-relational concepts of space and time to invariance and conservation principles. Second, against this background, I present the Online Reading Guide on Émilie Du Châtelet’s Foundations of Physics, a teaching and research project designed to help navigate Du Châtelet’s Institutions physiques. This project makes Du Châtelet’s important text visible to a broad audience and allows for a more critical and deeper view on classical topics of the history of philosophy and science in a more accessible way than traditional introductions. (shrink)

In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...) any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space–time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained. (shrink)

In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information-theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub’s conjecture that QT should be interpreted as a theory about information, by examining whether his information-theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub’s theses will also serve to investigate, more in general, whether other approaches succeed in defending the claim that (...) QT is about quantum information. First of all, I argue that Bub’s interpretation of QT as a principle theory fails to fully explain quantum non-locality. Secondly, I argue that a constructive interpretation, where the quantum state is interpreted ontically as information, also fails at providing a full explanation of quantum correlations. Finally, while epistemic interpretations might succeed in this respect, I argue that such a success comes at the price of rejecting some in between the most basic scientific standards of physical theories. (shrink)

Isaac Newton is best known as a mathematician and physicist. He invented the calculus, discovered universal gravitation and made significant advances in theoretical and experimental optics. His master-work on gravitation, the Principia, is often hailed as the crowning achievement of the scientific revolution. His significance for philosophers, however, extends beyond the philosophical implications of his scientific discoveries. Newton was an able and subtle philosopher, working at a time when science was not yet recognized as an activity distinct from philosophy. He (...) engaged with the work of Rene Descartes and G.W. Leibniz, and showed sensitivity to the work of John Locke, Francis Bacon, Pierre Gassendi and Henry More, to name just a few. In his time, Newton was not perceived as a scientific outsider, but as an active and knowledgeable participant in philosophical debates.... (shrink)

Newton began his Principia with three Axiomata sive Leges Motus. We offer an interpretation of Newton’s dual label and investigate two tensions inherent in his account of laws. The first arises from the juxtaposition of Newton’s confidence in the certainty of his laws and his commitment to their variability and contingency. The second arises because Newton ascribes fundamental status both to the laws and to the bodies and forces they govern. We argue the first is resolvable, but the second is (...) not. However, the second tension shows that Newton conceives laws as formal causes of bodies and forces. This neo-Aristotelian conception goes missing in Kantian accounts of laws, as well as accounts that stress laws’ grounding in powers and capacities. (shrink)

Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities cannot be smaller than the derived and so cannot ‘compose’ them in (...) any ordinary sense, would a formal derivation actually show the physical reality of localized entities? We address these questions via a survey of a range of theories of quantum gravity, and generally sketch how they may be answered positively. (shrink)

This is a defense of Kant against the allegedly neglected alternative in his formulation of transcendental idealism. What sets it apart from the contributions of others who have spoken for Kant in this regard is the construction of a general interpretive framework — a reconstruction of the one Kant provides for transcendental idealism — as opposed to the development of an ad hoc defensive strategy for refuting the charges. Hence, comprehensive clarification instead of pointed rebuttal. The difference is between focusing (...) on the text and focusing on the problem. No doubt, doing both is not only possible but also required, as the problem is supposed to be in the text, but the point is that it is not there, and further, that we need not go anywhere else to show that it is not there. Thus, the approach is constructive rather than defensive, or more accurately, constructive as well as defensive. And the construction rests on what Kant actually said rather than on what he might have meant or on what he should have said instead. (shrink)

Galileo’s dictum that the book of nature “is written in the language of mathematics” is emblematic of the accepted view that the scientific revolution hinged on the conceptual and methodological integration of mathematics and natural philosophy. Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated, and that philosophical controversies (...) about the implications of mathematization cannot be understood in isolation from broader social developments related to the status and practice of mathematics in various commercial, political, and academic institutions. (shrink)

This essay aims to provide a self-contained introduction to time in relativistic cosmology that clarifies both how questions about the nature of time should be posed in this setting and the extent to which they have been or can be answered empirically. The first section below recounts the loss of Newtonian absolute time with the advent of special and general relativity, and the partial recovery of absolute time in the form of cosmic time in some cosmological models. Section II considers (...) the beginning and end of time in a broader class of models in which there is not an analog of Newtonian absolute time. As we will see, reasonable physical assumptions imply that the universe is finite to the past, and Section III turns to consideration of the “beginning” itself. We critically review conventional wisdom that a “singularity” reveals flaws in general relativity and briefly assess ways of avoiding the singularity. (shrink)

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. 1 Introduction2 The Hole Argument3 Limits of Spacetimes4 Pointless Constructions5 The Debate between Substantivalists and Relationalists6 Existence and Physicality: An Embarassment of Spacetime Structures7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics. (shrink)

On 11thOctober 2007, at the first international conference on Integrated History and Philosophy of Science (&HPS1) hosted by the Center for Philosophy of Science in Pittsburgh, Ernan McMullin (University of Notre Dame) portrayed a rather gloomy scenario concerning the current relationship between history and philosophy of science (HPS), on the one hand, and mainstream philosophy, on the other hand, as testified by a significant drop in the presence of HPS papers at various meetings of the American Philosophical Association (APA).

The basic principles of dispositional essentialism do not require that the fundamental spatiotemporal relations are dispositional in nature. Nevertheless, Bird (who defends dispositional monism) argues that they possess dispositional essences in virtue of the fact that the obtaining of these relations can be characterised by the satisfaction of a certain counterfactual. In this paper I argue that his suggestion fails, and so, despite his attempt, the case of the spatiotemporal relations remains the ‘big bad bug’ for the thesis of dispositional (...) monism. (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)

On an influential view, Newton's mechanics is built into Kant's very theory of exact knowledge. However, Newtonian dynamics had serious explanatory limits already known by 1750. Thus, we might worry that Kant's Analytic is too narrow to ground enough exact knowledge. In this paper, I draw on Enlightenment dynamics to show that Kant's notion of determinate objecthood is sufficiently broad, non-trivial, and still relevant to the present.

This essay examines Friedman's recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman's characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman's thesis is defensible.

The Oxford Handbook of the History of Physics brings together cutting-edge writing by more than twenty leading authorities on the history of physics from the seventeenth century to the present day. By presenting a wide diversity of studies in a single volume, it provides authoritative introductions to scholarly contributions that have tended to be dispersed in journals and books not easily accessible to the general reader. While the core thread remains the theories and experimental practices of physics, the Handbook contains (...) chapters on other dimensions that have their place in any rounded history. These include the role of lecturing and textbooks in the communication of knowledge, the contribution of instrument-makers and instrument-making companies in providing for the needs of both research and lecture demonstrations, and the growing importance of the many interfaces between academic physics, industry, and the military. (shrink)

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) ones. (shrink)

Scholars have long recognized that Newton regarded Descartes as his principal philosophical interlocutor when composing the first edition of Philosophiae Naturalis Principia Mathematica in 1687. The arguments in the Scholium on space and time, for instance, can profitably be interpreted as focusing on the conception of space and motion in part two of Descartes's Principles of Philosophy (1644). What is less well known, however, is that this Cartesian conception, along with Descartes's attempt to avoid Galileo's fate in 1633, serves as (...) an essential background to understanding Newton's own (poorly understood) view of the theological implications of his theory of space and motion. In particular, after withdrawing Le Monde from publication in 1633 because of its Copernican leanings, Descartes later introduced what some regard as a “fudge factor” into the theory of motion in the Principles: from an ordinary perspective the earth does move; but from a philosophical one, it does not. This background indicates the novelty and originality of Newton's own attempt to explicate how scriptural passages concerning the motions of the heavenly bodies can be reconciled with the philosophical views he developed during the 1680s. New evidence from archival sources and correspondence supports this argument, shedding light on the Scholium and on Newton's conception of philosophy's relation to theology. (shrink)

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

Commentators attempting to understand the empirical method that Isaac Newton applies in his Mathematical Principles of Natural Philosophy (1687) are forced to grapple with the thorny issue of how to reconcile Newton's rejection of hypotheses with his appeal to absolute space. On the one hand, Newton claims that his experimental philosophy does not rely on claims that are assumed without empirical evidence, and on the other hand, Newton appeals to an absolute space that, by his own characterization, does not make (...) any impressions on our senses. Howard Stein (1967, 2002) has offered an insightful strategy for reconciling this apparent contradiction and suggested a way to enhance our understanding of Newton's 'empiricism' such that absolute space can be preserved as a legitimate part of Newton's experimental project. Recently, Andrew Janiak (2008) has posed a worthy challenge to Stein's empirical reading of Newton and directed our attention to the metaphysical commitments that underlie the experimental philosophy of Newton's Principia . Although Stein and Janiak disagree on the degree to which Newton's empiricism influences his natural philosophy, both agree and clearly show that an adequate treatment of Newton's empiricism cannot be divorced from consideration of Newton's views on God and God's relationship to nature. (shrink)

This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial (...) hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors. (shrink)

This paper investigates the question of, and the degree to which, Newton’s theory of space constitutes a third-way between the traditional substantivalist and relationist ontologies, i.e., that Newton judged that space is neither a type of substance/entity nor purely a relation among such substances. A non-substantivalist reading of Newton has been famously defended by Howard Stein, among others; but, as will be demonstrated, these claims are problematic on various grounds, especially as regards Newton’s alleged rejection of the traditional substance/accident dichotomy (...) concerning space. Nevertheless, our analysis of the metaphysical foundations of Newton’s spatial theory will strive to uncover its unique and innovative characteristics, most notably, the distinctive role that Newton’s “immaterialist” spatial ontology plays in his dynamics. (shrink)

According to Minkoswki, Einstein's special theory of relativity reveals that ‘space by itself, and time by itself are doomed to fade away into mere shadows’. But perceptual experience represents objects as instantiating shapes like squareness — properties of ‘space by itself’. Thus, STR seems to threaten the veridicality of shape experience. In response to this worry, some have argued that we should analyze the contents of our spatial experiences on the model of traditional secondary qualities. On this picture—defended in recent (...) work by Chalmers —an experience of squareness just represents whatever property usually causes such experiences. This view salvages the veridicality of shape experience, but leaves the nature of the properties we perceive outside our ken. I argue that such a move is unwarranted: STR is compatible with the idea that shape experience acquaints us with the spatial character of our world. In defending this claim, I propose a view on which shape experience presents familiar Euclidean spatial properties veridically, while implicitly representing those properties as instantiated in a particular manner — namely, relative to our own frame of reference. (shrink)

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to figure in (...) a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

I discuss the three distinctions “absolute and relative”, “true and apparent”, and “mathematical and common”, for the specific case of time in Newton’s Principia. I argue that all three distinctions are needed for the project of the Principia and can be understood within the context of that project without appeal to Newton’s wider metaphysical and theological commitments. I argue that, within the context of the Principia, the three claims that time is absolute rather than relative, true rather than apparent, and (...) mathematical rather than common, are to be evaluated with respect to the needs of, and relative to the success of, the project of the Principia. I claim that Newton is thereby offering a new, and empirical, philosophy of time. (shrink)

The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states – the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious "collapse of the wave (...) function" by relating it to a sudden change in the epistemic situation of the observer registering a measured result. On the other hand, his remarks on quantum probabilities as "potentia" or "objective tendencies" are difficult to reconcile with such a reading. The accounts that are attributed to Heisenberg by the different possible readings considered are subjected to closer scrutiny; at the same time, their respective virtues and problems are discussed. _German_ Diese Arbeit untersucht mögliche Lesarten von Heisenbergs späten Bemerkungen über die Natur von Quantenzuständen. Insbesondere wird die Frage diskutiert, ob Heisenberg als Vertreter der epistemischen Auffassung von Quantenzuständen gelten kann – der Idee, dass Quantenzustände nicht Beschreibungen der objektiven Eigenschaften von Quantensystemen sind sondern die epistemischen Beziehungen von Beobachtern zu diesen Systemen widerspiegeln. Einerseits erscheint es plausibel, dass Heisenberg dieser Sichtweise zustimmt, wenn man sich ansieht, wie er den berüchtigten,,Kollaps der Wellenfunktion" verteidigt, indem er ihn mit einer plötzlichen Änderung in der Kenntnis des ein Messergebnis registrierenden Beobachters in Zusammenhang bringt. Andererseits sind seine Bemerkungen über quantenmechanische Wahrscheinlichkeiten als,,Potentia" oder,,objektive Tendenzen" mit einer solchen Lesart nur schwer in Einklang zu bringen. Die Positionen, die Heisenberg den verschiedenen möglichen Lesarten zufolge vertritt, werden eingehenden Untersuchungen unterzogen; gleichzeitig werden ihre jeweiligen Vorzüge und Probleme diskutiert. (shrink)

The present paper offers some remarks on the significance of first order model theory for our understanding of theories, and more generally, for our understanding of the “structuralist” accounts of the nature of theoretical knowledge that we associate with Russell, Ramsey and Carnap. What is unique about the presentation is the prominence it assigns to Craig’s Interpolation Lemma, some of its corollaries, and the manner of their demonstration. They form the underlying logical basis of the analysis.

This paper has two goals. (i) I explore the limits of the mathematical theory of spacetime (more generally, differential geometry) as an analytical tool for interpreting early modern thought. While it dramatically clarifies some issues, it can also lead to misunderstandings of some figures, and is a very poor tool indeed for others - Leibniz in particular. (ii) I will show how to blunt a very influential argument against a relational conception of spacetime - the view that the properties and (...) relations of bodies exhaust the spatiotemporal. (shrink)

Philosophy Compass, Volume 17, Issue 10, October 2022.

In this article, we explore the heuristic power of the theoretical distinction between framework and interaction theories applied to the case of General Relativity. According to the distinction, theories and theoretical elements can be classified into two different groups, each with clear ontological, epistemic and functional content. Being so, to identify the group to which a theory belongs would suffice to know a priori its prospects and limitations in these areas without going into a detailed technical analysis. We make the (...) exercise here with General Relativity, anticipate its ontological, epistemic and functional content and show afterwords that such expectations are justified in this case, being consistent with formal issues of General Relativity. With this, we attempt to make a case for the use of the distinction as a powerful tool for scientific and philosophical analysis. (shrink)

The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of (...) particular sciences. A fruitful approach to these problems combines the study of scientific detail with the kind of conceptual analysis that is characteristic of the modern analytic tradition. Such an approach is shared by these contributors: some primarily known as analytic philosophers, some as philosophers of science, but all deeply aware that the problems of analysis and interpretation link these fields together. (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)

In this paper I argue that physics is, always was, and probably always will be voiceless with respect to tense and passage, and that, therefore, if, as I believe, tense and passage are the essence of time, physics’ contribution to our understanding of time can only be limited. The argument, in a nutshell, is that if "physics has no possibility of expression for the Now", to quote Einstein, then it cannot add anything to the study of tense and passage, and (...) specifically, cannot add anything to the debate between deniers and affirmers of the existence or reality of tense and passage. Since relativity theory did not equip physics with a new language with which to speak of tense and passage, I draw the further conclusion that relativity theory has not generated the revolution to our conception of time that is attributed to it. In the last section I discuss the motivations behind the continued but misguided attempts to integrate tense into a relativistic setting, and assess the manners in which relativity theory has nevertheless enhanced, albeit indirectly, our understanding of tense and passage. (shrink)

This paper compares Newton’s and Descartes’s conceptions of the complex relationship between physics and metaphysics.

We consider an approach to some philosophical problems that I call the Method of Conceptual Articulation: to recognize that a question may lack any determinate answer, and to re-engineer concepts so that the question acquires a definite answer in such a way as to serve the epistemic motivations behind the question. As a case study we examine “Galileo’s Paradox”, that the perfect square numbers seem to be at once as numerous as the whole numbers, by one-to-one correspondence, and yet less (...) numerous, being a proper subset. I argue that Cantor resolved this paradox by a method at least close to that proposed—not by discovering the true nature of cardinal number, but by articulating several useful and appealing extensions of number to the infinite. Galileo was right to suggest that the concept of relative size did not apply to the infinite, for the concept he possessed did not. Nor was Bolzano simply wrong to reject Hume’s Principle (that one-to-one correspondence implies equal number) in the infinitary case, in favor of Euclid’s Common Notion 5 (that the whole is greater than the part), for the concept of cardinal number (in the sense of “number of elements”) was not clearly defined for infinite collections. Order extension theorems now suggest that a theory of cardinality upholding Euclid’s principle instead of Hume’s is possible. Cantor’s refinements of number are not the only ones possible, and they appear to have been shaped by motivations and fruitfulness, for they evolved in discernible stages correlated with emerging applications and results. Galileo, Bolzano, and Cantor shared interests in the particulate analysis of the continuum and in physical applications. Cantor’s concepts proved fruitful for those pursuits. Finally, Gödel was mistaken to claim that Cantor’s concept of cardinality is forced on us; though Gödel gives an intuitively compelling argument, he ignores the fact that Euclid’s Common Notion is also intuitively compelling, and we are therefore forced to make a choice. The success of Cantor’s concept of cardinality lies not in its truth (for concepts are not true or false), nor its uniqueness (for it is not the only extension of number possible), but in its intuitive appeal, and most of all, its usefulness to the understanding. (shrink)

This paper addresses and proposes to resolve a longstanding problem in the philosophy of physics: whether and in what sense Albert Einstein’s Chasing the Light thought experiment was significant in the development of the theory of special relativity. Although Einstein granted this thought experiment pride of place in his 1949 Autobiographical Notes, philosophers and physicists continue to debate about what, if anything, the experiment establishes. I claim that we ought to think of Chasing the Light as Einstein’s first attempt to (...) problematize the very idea of the electromagnetic ether frame, and that it thereby contributed to his eventual adoption of one of special relativity’s two foundational axioms: the “light postulate”. This interpretation requires the assumption that Einstein had presupposed special relativity’s other axiom, the “principle of relativity”, when initially considering Chasing the Light. This argument is novel insofar as it provides evidence that such a presupposition by Einstein is both conceptually and historically plausible. Moreover, this paper directly challenges John D. Norton’s compelling claim that Chasing the Light is best understood as a refutation of emission theories of light propagation; while both interpretations of the experiment are conceptually coherent, I argue that the interpretation found in this paper is supported more straightforwardly by historical evidence. (shrink)

Recent debates in philosophy of science have witnessed the rise of two major proposals. On the one hand, regarding the conceptual structure of scientific theories, some believe that they exhibit constitutive elements. The constitutive elements of a theory are the components that play the role of laying the foundations of empirical meaningfulness, and whose acceptance is prior to empirical research. On the other hand, as for the nature of scientific knowledge and its relation to nature, perspectival realism has pursued a (...) middle ground in classic debates between realism and antirealism, by assuming that although knowledge is always situated both historically and culturally, scientific statements have truth values and constitute genuine claims about a mind-independent world. In this paper, I argue that these two lines of research are not only compatible but complement each other, and provide a common view of science. I contend that a theoretical perspective is a set of constitutive elements where models and representations may develop, and stress that both constitutivism and perspectivism have numerous shared characteristics, such as their vindication of the historicity of scientific knowledge, their recognition of human epistemic limits, and a very similar conception of truth. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation (...) of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invari-ance, a misconception that in turn sheds more shadows than light on our understand-ing of the explanatory nature and power of Einstein’s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and uni-directional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers. (shrink)

Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as (...) Poincaré, Helmholtz or Hausdorff. However, they clearly failed to give a plausible account of General Relativity. Thus the point-coincidence/hole argument cannot be interpreted as Leibnizian indiscernibility argument, but must be considered as an indiscernibility argument of a new kind. Weyl's analysis of Leibniz's and Einstein's indiscernibility arguments is used to support this claim. (shrink)

Eino Kaila's thought occupies a curious position within the logical empiricist movement. Along with Hans Reichenbach, Herbert Feigl, and the early Moritz Schlick, Kaila advocates a realist approach towards science and the project of a “scientific world conception”. This realist approach was chiefly directed at both Kantianism and Poincaréan conventionalism. The case in point was the theory of measurement. According to Kaila, the foundations of physical reality are characterized by the existence of invariant systems of relations, which he called structures. (...) In a certain sense, these invariant structures, he maintained, are constituted in the act of measuring. By “constitution”, however, Kaila meant neither the dependency of the objects of measurement on a priori concepts (or Kantian categories) nor their being effected by conventional stipulations in a Poincaréan sense. He held that invariant structures are, quite literally, real: they exist prior to and independently of our theoretical capacity. By executing measurements, invariant structures are detected and objectively determinable by laws of nature. (shrink)

We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining (...) these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our "Principle of general tovariance" states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our "Equivalence principle" states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos. (shrink)