The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics. We will also show that if we distinguish a class (...) of observers in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent. Furthermore, we show that classical kinematics is definitionally equivalent to classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with “Ether” is definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, wee xplicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no “Ether”, accompanied by a redefinition of the concepts of time and space. (shrink)

In this article, I examine whether or not the Hamiltonian and Lagrangian formulations of classical mechanics are equivalent theories. I do so by applying a standard for equivalence that was recently introduced into philosophy of science by Halvorson and Weatherall. This case study yields three general philosophical payoffs. The first concerns what a theory is, while the second and third concern how we should interpret what our physical theories say about the world. 1Introduction 2When Are Two Theories Equivalent? 3Preliminaries on (...) Classical Mechanics 3.1Hamiltonian mechanics 3.2Lagrangian mechanics 4Are Hamiltonian and Lagrangian Mechanics Equivalent Theories? 4.1Tangent bundle versus cotangent bundle 4.2Tangent bundle versus symplectic manifold 4.3Lagrangian vector field versus Hamiltonian vector field 5Conclusion Appendix. (shrink)

In the literature over the Ramsey-sentence approach to structural realism, there is often debate over whether structural realists can legitimately restrict the range of the second-order quantifiers, in order to avoid the Newman problem. In this paper, I argue that even if they are allowed to, it won’t help: even if the Ramsey sentence is interpreted using such restricted quantifiers, it is still an implausible candidate to capture a theory’s structural content. To do so, I use the following observation: if (...) a Ramsey sentence did encode a theory’s structural content, then two theories would be structurally equivalent just in case they have logically equivalent Ramsey sentences. I then argue that this criterion for structural equivalence is implausible, even where frame or Henkin semantics are used. (shrink)

I argue that, in order for us to be justified in believing that two theories are metaphysically equivalent, we must be able to conceive of them as unified into a single theory, which says nothing over and above either of them. I propose one natural way of precisifying this condition, and show that the quantifier variantist cannot meet it. I suggest that the quantifier variantist cannot meet the more general condition either, and argue that this gives the metaphysical realist a (...) way to rule out theses like quantifier variance without appealing to fundamentality, grounding, or "levels" of reality. (shrink)

I critically examine the semantic view of theories to reveal the following results. First, models in science are not the same as models in mathematics, as holders of the semantic view claim. Second, when several examples of the semantic approach are examined in detail no common thread is found between them, except their close attention to the details of model building in each particular science. These results lead me to propose a deflationary semantic view, which is simply that model construction (...) is an important component of theorizing in science. This deflationary view is consistent with a naturalized approach to the philosophy of science. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

Based on archival material from the Carnap and FeiglArchives, this paper re-examines Carnap's approach tothe issue of scientific realism in the 1950s and theearly 1960s. It focuses on Carnap's re-invention ofthe Ramsey-sentence approach to scientific theoriesand argues that Carnap wanted to entertain a genuineneutral stance in the realism-instrumentalism debate.Following Grover Maxwell, it claims that Carnap'sposition may be best understood as a version of`structural realism'. However, thus understood,Carnap's position faces the challenge that Newmanraised against Russell's structuralism: the claim thatthe knowledge of (...) the unobservable is limited to itspurely structural characteristics is eitheruninformative or unsustainable. (shrink)

Model theoretic considerations purportedly show that a certain version of structural realism, one which articulates the nvtion of structure via Ramsey sentences, is in fact trivially true. In this paper we argue that the structural realist is by no means forced to Ramseyfy in the manner assumed in the formal proof. However, the structural realist's reprise is short-lived. For, as we show, there are related versions of the model theoretic argument which cannot be so easily blocked by the structural realist. (...) We examine various ways in which the structural realist may respond, and conclude that the best way of blocking the model theoretic argument involves formulating his Ramseyfied theories using intensional operators. Introduction The model theoretic arguments On Ramseyfying away predicates The model theoretic argument bites back Restricting the second order quantifiers 5.1 Naturalness 5.2 Intrinsic 5.3 Qualitative 5.4 Contingent and causal Intensional operators and relations between properties Conclusion. (shrink)

Structural realism has been proposed as an epistemological position interpolating between realism and sceptical anti-realism about scientific theories. The structural realist who accepts a scientific theory thinks that is empirically correct, and furthermore is a realist about the ‘structural content’ of . But what exactly is ‘structural content’? One proposal is that the ‘structural content’ of a scientific theory may be associated with its Ramsey sentence (). However, Demopoulos and Friedman have argued, using ideas drawn from Newman's earlier criticism of (...) Russell's structuralism, that this move fails to achieve an interesting intermediate position between realism and anti-realism. Rather, () adds little content beyond the instrumentalistically acceptable claim that the theory is empirically adequate. Here, I formulate carefully the crucial claim of Demopoulos and Friedman, and show that the Ramsey sentence () is true just in case possesses a full model which is empirically correct and satisfies a certain cardinality condition on its theoretical domain. This suggests that structural realism is not a position significantly different from the anti-realism it attempts to distinguish itself from. Introduction Technical framework Ramsification Empirical adequacy Ramsification empirical adequacy + cardinality constraint Conclusion. (shrink)

An essay review of Michael Weisberg's Simulation and Similarity.

Several recent authors identify structural realism about scientific theories with the claim that the content of a scientific theory is expressible using its Ramsey sentence. Many of these authors have also argued that so understood, the view collapses into empiricist anti-realism, since an argument originally proposed by Max Newman in a review of Bertrand Russell’s The analysis of matter demonstrates that Ramsey sentences are trivially satisfied, and cannot make any significant claims about unobservables. In this paper I argue against both (...) of these claims. Structural realism and Ramsey sentence realism are, in their most defensible versions, importantly different doctrines, and neither is committed to the premises required to demonstrate that they collapse into anti-realism.Keywords: Ramsey sentence; Structural realism; Structuralism; Scientific realism. (shrink)

Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.

In recent papers Hans Halvorson has offered a critique of the semantic view of theories, showing that theories may be the same although the corresponding sets of models are different and, conversely, that theories may be different although the corresponding sets of models are the same. This critique will be assessed, first, as it pertains to issues concerning scientific models in the empirical sciences and, second, independent of any concern with empirical science.

ZusammenfassungUnter den nichtlogischen Konstanten der Wissenschaftssprache werden zwei Arten unterschieden, die Beobachtungsterme und die theoretischen Terme . Die letzteren werden nicht durch Definitionen eingeführt, sondern durch Postulate zweier Arten, nämlich theoretische Postulate, zum Beispiel Grundgesetze der Physik, und Korrespondenzpostulate, die die theoretischen Terme mit Beobachtungstermen verbinden. Wie schon Hilbert gezeigt hat, können in dieser Weise sowohl die Mathematik als auch die theoretische Physik als ungedeutete Kalküle aufgestellt werden. Es wird hier kurz erklärt, dass durch diesen Aufbau auch den mathematischen Termen (...) eine Bedeutung beigelegt wird. Die theoretischen Terme erhalten durch die Korrespondenzpostulate wenigstens eine unvollständige Deutung. Es wird gezeigt, wie die Unterscheidung von analytischen und synthetischen Sätzen auch für die theoretische Sprache definiert werden kann.Among the non‐logical constants of the language of science two kinds are distinguished, the observation terms and the theoretical terms . The latter terms are introduced, not by definitions, but by postulates of two kinds, theoretical postulates, e.g., basic laws of physics, and correspondence postulates which connect the theoretical terms with observation terms. As Hilbert has explained, both mathematics and theoretical physics can in this way be constructed in the form of uninterpreted calculi. It is here briefly indicated that by this method of construction also the mathematical terms have meanings assigned to them. The theoretical terms obtain at least an incomplete interpretation by means of the correspondence postulates. It is shown how the distinction between analytic and synthetic sentences can be defined also for the theoretical language. (shrink)

In this article, I give a counterexample to a claim made in that empirically equivalent theories can often be regarded as theoretically equivalent by treating one as having surplus structure, thereby overcoming the problem of underdetermination of theory choice. The case I present is that of Lorentz's ether theory and Einstein's theory of special relativity. I argue that Norton's suggestion that surplus structure is present in Lorentz's theory in the form of the ether state of rest is based on a (...) misunderstanding of the role that the ether plays in Lorentz's theory, and that in general, consideration of the conceptual framework in which a theory is embedded is vital to understanding the relationship between different theories. (shrink)

The purported fact that geometric theories formulated in terms of points and geometric theories formulated in terms of lines are “equally correct” is often invoked in arguments for conceptual relativity, in particular by Putnam and Goodman. We discuss a few notions of equivalence between first-order theories, and we then demonstrate a precise sense in which this purported fact is true. We argue, however, that this fact does not undermine metaphysical realism.

Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...) analyzed according to this theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with quantum theory simply evaporate.Bohr's ... approach to atomic problems ... is really remarkable. He is completely convinced that any understanding in the usual sense of the word is impossible. Therefore the conversation is almost immediately driven into philosophical questions, and soon you no longer know whether you really take the position he is attacking, or whether you really must attack the position he is defending. (shrink)

For simplicity, most of the literature introduces the concept of definitional equivalence only for disjoint languages. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to non-disjoint languages and they show that their generalization is not equivalent to intertranslatability in general. In this paper, we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce another formalization of definitional equivalence due to Andréka and Németi which is equivalent to the Barrett–Halvorson (...) generalization in the case of disjoint languages. We show that the Andréka–Németi generalization is the smallest equivalence relation containing the Barrett–Halvorson generalization and it is equivalent to intertranslatability, which is another definition for definitional equivalence, even for non-disjoint languages. Finally, we investigate which definitions for definitional equivalences remain equivalent when we generalize them for theories in non-disjoint languages. (shrink)

What is it reasonable to believe about our most successful scientific theories such as the general theory of relativity or quantum mechanics? That they are true, or at any rate approximately true? Or only that they successfully ‘save the phenomena’, by being ‘empirically adequate’? In earlier work I explored the attractions of a view called Structural Scientific Realism (hereafter: SSR). This holds that it is reasonable to believe that our successful theories are (approximately) structurally correct (and also that this is (...) the strongest epistemic claim about them that it is reasonable to make). In the first part of this paper I shall explain in some detail what this thesis means and outline the reasons why it seems attractive. The second section outlines a number of criticisms that have none the less been brought against SSR in the recent (and as we shall see, in some cases, not so recent) literature; and the third and final section argues that, despite the fact that these criticisms might seem initially deeply troubling (or worse), the position remains viable. (shrink)

Glymour and Quine propose two different formal criteria for theoretical equivalence. In this paper we examine the relationships between these criteria.

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

There is good reason to suppose that our best physical theories are false: In addition to its own internal problems, the standard formulation of quantum mechanics is logically incompatible with special relativity. I will also argue that we have no concrete idea what it means to claim that these theories are approximately true.