Interpretation is commonly used in mathematical logic to compare different theories and identify cases where two theories are for almost all intents and purposes the same. Similar techniques are used in the comparison between alternative logics although the links between these approaches are not transparent. This paper generalizes theoretical comparison techniques to the case of logical comparison using an extremely general approach to semantics that provides a very generous playing field upon which to make our comparisons. In particular, we (...) aim to develop the useful idea that interpretations should determine inner models. (shrink)

This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.

In this paper the system IL for relative interpretability is studied.

I argue that, contrary to the recent claims of physicists and philosophers of physics, general relativity requires no interpretation in any substantive sense of the term. I canvass the common reasons given in favor of the alleged need for an interpretation, including the difficulty in coming to grips with the physical significance of diffeomorphism invariance and of singular structure, and the problems faced in the search for a theory of quantum gravity. I find that none of them shows (...) any defect in our comprehension of general relativity as a physical theory. I conclude by comparing general relativity with quantum mechanics, a theory that manifestly does stand in need of an interpretation in an important sense. Although many aspects of the conceptual structure of general relativity remain poorly understood, it suffers no incoherence in its formulation as a physical theory that only an ‘interpretation’ could resolve. *Received November 2007; revised February 2009. †To contact the author, please write to: Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected] . When science starts to be interpretive it is more unscientific even than mysticism. (D. H. Lawrence, “Self‐Protection”). (shrink)

A proof is given, at a greater level of generality than previous 'no-go' theorems, of the impossibility of formulating a modal interpretation that exhibits 'serious' Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.

The existence of probability in the sense of the frequency interpretation, i.e., probability as “long term relative frequency,” is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous results regarding relative frequency and probability in quantum mechanics. The ontology of the Everett interpretation in the Heisenberg picture is also discussed.

The article investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of general relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative space-times, all of which are compatible with a given initial data set.

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set of possessed properties that is supposed to be rich enough to account for the classical-like behavior of macroscopic systems, but sufficiently (...) restricted so as to avoid the no-hidden-variables theorems. But, as recent no-go theorems suggest, current modal interpretations are incompatible with relativity. In this paper, we suggest a strategy for circumventing these theorems. We then show how this strategy could naturally be integrated in a relational version of the modal interpretation, where quantum-mechanical states assign relational rather than intrinsic properties. (shrink)

Maddy gave a semi-formal account of restrictiveness by defining a formal notion based on a class of interpretations and explaining how to handle false positives and false negatives. Recently, Hamkins pointed out some structural issues with Maddy's definition. We look at Maddy's formal definitions from the point of view of an abstract interpretation relation. We consider various candidates for this interpretation relation, including one that is close to Maddy's original notion, but fixes the issues raised by Hamkins. Our (...) work brings to light additional structural issues that we also discuss. (shrink)

In 1986 David Gauthier proposed an arbitration scheme for two player cardinal bargaining games based on interpersonal comparisons of players’ relative concessions. In Gauthier’s original arbitration scheme, players’ relative concessions are defined in terms of Raiffa-normalized cardinal utility gains, and so it cannot be directly applied to ordinal bargaining problems. In this paper I propose a relative benefit equilibrating bargaining solution for two and n-player ordinal and quasiconvex ordinal bargaining problems with finite sets of feasible basic agreements (...) based on the measure of players’ ordinal relative individual advantage gains. I provide an axiomatic characterization of this bargaining solution and discuss the conceptual relationship between RBEBS and ordinal egalitarian bargaining solution proposed by Conley and Wilkie. I show the relationship between the measurement procedure for ordinal relative individual advantage gains and the measurement procedure for players’ ordinal relative concessions, and argue that the proposed arbitration scheme for ordinal games can be interpreted as an ordinal version of Gauthier’s arbitration scheme. (shrink)

In the publication is considered the religious factor in political terrorism. Is analyzed the basic causes of the religious terrorism. The author found s that religious terrorism in itspurest form does not exist, because each act of terrorism has political or economic basis and only is covered religion to justify their goals.

What makes an interpretation good? This question defines an area where the concerns of philosophers and literary theorists coincide. One sort of response, which stresses the relativity of interpretation to the interests, purposes, and background beliefs of interpreters, increasingly commands the attention of both groups, though it is hard to get past one’s initial reaction, favorable or not, to the accompanying displays of rhetorical plumage. In this essay I shall try to do just that, in the hope of (...) seeing what the relativity of interpretation consists in and whether it need lead to the consequences that make some people pine for universal constraints and determinate meanings. (shrink)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in (...) the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)

There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I (...) illustrate this claim by examining the interpretative consequences of a particular technical move in canonical quantum gravity. (shrink)

The paper (given in the section on "Recent work in the History of Philosophy of Science) discusses the method and some of the results of the doctoral dissertation on philosophical interpretations of Einstein's special and general theories of relativity, submitted to the Dept. for History of Science, Univ. of Hamburg, in 1989, also published by Birkhauser, Basel, in 1990. It is claimed that many of the gross oversimplifications, misunderstandings and misinterpretations occurring in more than 2500 texts about the theories of (...) relativity written by scientists, philosophers, and laymen contemporary to Einstein can in fact serve as a clue to a better understanding of the general process by which philosophical interpretations are formed. Another very important source for answering the question of how misinterpretations are formed are hitherto unpublished documents in the estates of physicists and philosophers of that time, including apart from Einstein himself: Bergson, Bridgman, Carnap, Cassirer, Metz, Meyerson, Petzoldt, Reichenbach, Schlick and Vaihinger. (shrink)

During Einstein’s lifetime, the special and general theories of relativity were quite frequently interpreted by philosophers. Most of these interpretations actually were misinterpretations. Even today interpretative statements about relativity theory are often false or highly misleading. Why is this so? In my Ph.D. dissertation (Hentschel 1990a), I analyzed (mis)interpretations by 10 different philosophical schools active in the early twentieth century which widely differed in their approaches, emphasis and blind spots. Many of these interpreters – including philosophers of high standing such (...) as Ernst Cassirer, Moritz Schlick or Joseph Petzoldt – had studied the theory intensely and many even had close contact with Einstein himself or with one of the members of his “protective belt” of close friends and allies. Rather than declaring all of these (mis)interpreters as either luminaries or idiots (which would be implausible, if not downright silly), I show structurally how these misunderstandings arose and why they were kind of unavoidable, even for highly qualified and often well-informed interpreters. More popular texts about relativity theory were often second-order interpretations of these first-order accounts, thus multiplying the first-order errors of misinterpretations. I will give a few characteristic examples but my focus will rather be on structural characteristics of these misinterpretations. I will discuss how to analyze them historically by means of interpretational frames. A link will also be made to Ludwik Fleck’s thesis that socially and cognitively stabilized “thought collectives” (“Denkkollektive”) exert strong constraints on human thinking and interpretation (“Denkzwang”). My concept of interpretational frames is one method to formalize and analyze the complex interrelations between different assumptions and inferences within such a frame of thinking (“Denkstil”). Semantic frames and word clouds are also discussed as alternative approaches but both are discarded as unsuitable for the purpose of reconstructing interpretative frames. (shrink)

This paper is a summary of my doctoral dissertation on philosophical interpretations of Einstein’s special and general theories of relativity, submitted to the Dept. for History of Science, Univ. of Hamburg, in 1989, which was recently published in the Series Science Networks at Birkäuser.2 After a brief overview of its content I will focus on a discussion of the method employed to analyse philosophical interpretations of a physical theory.My analysis is based- firstly on about 2500 contemporary published texts about the (...) theories of relativity written both by scientists and philosophers. These texts have not been of particular interest to historians or philosophers of science up to now; this is understandable from the fact that many of diem contain gross oversimplifications, misinterpretations and incorrect statements about the theories of relativity. (shrink)

A recent ontological modification of Cramer’s Transactional Interpretation, called “Possibilist Transactional Interpretation” or PTI, is extended to the relativistic domain. The present interpretation clarifies the concept of ‘absorption,’ which plays a crucial role in TI. In particular, in the relativistic domain, coupling amplitudes between fields are interpreted as amplitudes for the generation of confirmation waves by a potential absorber in response to offer waves, whereas in the nonrelativistic context CW are taken as generated with certainty. It is (...) pointed out that solving the measurement problem requires venturing into the relativistic domain in which emissions and absorptions take place; nonrelativistic quantum mechanics only applies to quanta considered as ‘already in existence’, and therefore cannot fully account for the phenomenon of measurement, in which quanta are tied to sources and sinks. (shrink)

Fragmentalism was first introduced by Kit Fine in his ‘Tense and Reality’. According to fragmentalism, reality is an inherently perspectival place that exhibits a fragmented structure. The current paper defends the fragmentalist interpretation of the special theory of relativity, which Fine briefly considers in his paper. The fragmentalist interpretation makes room for genuine facts regarding absolute simultaneity, duration and length. One might worry that positing such variant properties is a turn for the worse in terms of theoretical virtues (...) because such properties are not involved in physical explanations and hence theoretically redundant. It will be argued that this is not right: if variant properties are indeed instantiated, they will also be involved in straightforward physical explanations and hence not explanatorily redundant. Hofweber and Lange, in their ‘Fine’s Fragmentalist Interpretation of Special Relativity’, object that the fragmentalist interpretation is in tension with the right explanation of the Lorentz transformations. It will be argued that their objection targets an inessential aspect of the fragmentalist framework and fails to raise any serious problem for the fragmentalist interpretation of special relativity. (shrink)

Ordinary language contains groups of related predicates with different arities. Interpreting utterances that appear to contain an n-place predicate by using an n+m-place predicate to dissolve merely apparent disagreements and other misunderstandings is an established practice in everyday discourse. This paper aims to present hermeneutical maxims to guide and evaluate these interpretations through arity raising. In interpreting utterances by using a higher-place predicate, we should use only expressions that their authors themselves reasonably could have used and which would have been (...) suitable to achieve their supposed purposes. The goal is to achieve a charitable, accurate reading that also maximizes the text's transparency to improve our understanding of it. (shrink)

Recent no go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate that current modal interpretations are incompatible with relativity. In this paper we propose strategies for how to circumvent these theorems. We further show how these strategies can be developped into new modal interpretations in which the properties of systems are in general either holistic or relational. We explicitly write down an outline of dynamics for these properties which does not pick out a preferred foliation of (...) spacetime. (shrink)

The axiomatic approaches of quantum mechanics and relativity theory are compared with approaches in which the theories are thought to describe readings of certain measurement operations. The usual axioms are shown to correspond with classes of ideal measurements. The necessity is discussed of generalizing the formalisms of both quantum mechanics and relativity theory so as to encompass more realistic nonideal measurements. It is argued that this generalization favours an empiricist interpretation of the mathematical formalisms over a realist one.

In “Tense and Reality”, Kit Fine () proposed a novel way to think about realism about tense in the metaphysics of time. In particular, he explored two non-standard forms of realism about tense, arguing that they are to be preferred over standard forms of realism. In the process of defending his own preferred view, fragmentalism, he proposed a fragmentalist interpretation of the special theory of relativity, which will be our focus in this paper. After presenting Fine's position, we will (...) raise a problem for his fragmentalist interpretation of STR. We will argue that Fine's view is in tension with the proper explanation of why various facts obtain. We will then consider whether similar considerations also speak against fragmentalism in domains other than STR, notably fragmentalism about tense. (shrink)

The problem of motion in general relativity is about how exactly the gravitational field equations, the Einstein equations, are related to the equations of motion of material bodies subject to gravitational fields. This article compares two approaches to derive the geodesic motion of matter from the field equations: the ‘T approach’ and the ‘vacuum approach’. The latter approach has been dismissed by philosophers of physics because it apparently represents material bodies by singularities. I argue that a careful interpretation of (...) the approach shows that it does not depend on introducing singularities at all and that it holds at least as much promise as the T approach. (shrink)

The process of ‘logical differentiation’ was introduced by Peirce in 1870. Directly analogous to mathematical differentiation, it uses logical terms instead of mathematical variables. Here, this mysterious process receives new interpretations which serve to clarify Peirce’s use of logical terms. I introduce the logical terms, the operation of multiplication, the logical analogy to the binomial theorem, infinitesimal relatives, the concepts of numerical coefficients and the number associated with each term. I also analyse the algebraic development of ‘logical differentiation’ and consider (...) in depth one application of the process. (shrink)

A recent ontological variant of Cramer’s Transactional Interpretation, called “Possibilist Transactional Interpretation” or PTI, is extended to the relativistic domain. The present interpretation clarifies the concept of ‘absorption,’ which plays a crucial role in TI (and in PTI). In particular, in the relativistic domain, coupling amplitudes between fields are interpreted as amplitudes for the generation of confirmation waves (CW) by a potential absorber in response to offer waves (OW), whereas in the nonrelativistic context CW are taken as (...) generated with certainty. It is pointed out that solving the measurement problem requires venturing into the relativistic domain in which emissions and absorptions take place; nonrelativistic quantum mechanics only applies to quanta considered as ‘already in existence’ (i.e., ‘free quanta’), and therefore cannot fully account for the phenomenon of measurement, in which quanta are tied to sources and sinks. (shrink)

The incongruence between quantum theory and relativity theory is traced to the probability interpretation of the former. The classical continium interpretation of ψ removes the difficulty. How quantum properties of matter and light, and in particular the radiative problems, like spontaneous emission and Lamb shift, may be accounted in a first quantized Maxwell-Dirac system is discussed.

The Theory of Relativity has been portrayed as a theory that redefined the way we look at the cosmos, enabling us to unlock the reality we live in. Its proponents are constantly reminding us of how Einstein managed to reveal the true nature of the universe with his groundbreaking theory, which has been proved multiple times until now. Yet, philosophy of science teaches us that no theory has any privileged connection with what we call reality per se. The role of (...) science is to formulate models of the cosmos we see and not to try to interpret or reveal reality. This paper tries to show how this holds true even for the famous relativity theory, by showing specific objections to the connection of the theory with the Holy Grail of philosophers. By analyzing various subjects related to the theory, from the twins’ paradox to the GPS satellites, this paper illustrates that relativity is much less connected to reality than what we would like to think. At the end, what Einstein’s theory provides is nothing more than a way to formalize the interactions of the world but without being able to make any claims whatsoever regarding the ‘reality’ of its conclusions. (shrink)

Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton, Arntzenius and Myrvold demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of property composition. Based on these interpretations, we consider (...) strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems. (shrink)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in (...) the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)

In this essay, we explore the various aspects of hermeneutic relativity that have rarely been explicitly discussed. Our notion of “hermeneutic relativity” can be seen as an extension, with significant revisions, of Gadamer’s notion of Vorurteil. It refers to various choices and constraints of the interpreter, including beliefs concerning the best way of doing philosophy, what criteria are to be used to evaluate competing interpretations, and so on. The interpreter cannot completely eliminate the guidance and constraint originating from his/her “background.” (...) However, in principle the interpreter can “choose” to be guided by other constraints. Hence, we speak of “choices” or “commitments.” Hermeneutic relativity is the major cause for the variation of competing interpretations. (shrink)

In the established space-time coordinate-transformation (STCT) interpretation of special relativity theory, relativistic changes are consequent upon the Lorentz transformation of coordinate clocks and rods between relatively moving systems. In the proposed alternative interpretation, relativistic changes occur only in association with physical interactions, and are direct alterations in the variables of the observed system. Since space-time and momentum-energy are conjugate four-vectors, transformation of a space or time variable of a system is to be expected only if there is a (...) concomitant transformation of the corresponding momentum or energy variable. The Lorentz invariance of the scalar entropy functionS supports the interaction interpretation; timet=f(S) of a macroscopic, entropy clock should give a Lorentz-invariant time measure, and an illustrative entropy clock is discussed. Noninteracting physical processes may be called Clausius processes, in contrast to Lorentz processes for which there is interaction and associated Lorentz transformation. Changes of energy and frequency, withE=hv, are instances of the parallel relativistic transformations. Likewise, the variation with velocity in decay time of mesons follows directly from the relativistic energy transformation of decay products; this relationship is shown for muons by a simple calculation with β-decay theory. (shrink)

The interaction interpretation of special relativity theory (elaborated in Part I) is discussed in relation to quantum theory. The relativistic transformations (Lorentz processes) of physical variables, on the interaction interpretation, are observation-interaction dependent, just as are the physical values (eigenvalues) of systems described by quantum-theoretic state functions; a common, basic structure of the special relativity and quantum theories can therefore be presented. The constancy of the light speed is shown to follow from interaction-transformations of frequency and wavelength variables. (...) A parallelism is suggested between, on the one hand, the Lorentz-Clausius distinction for relativistic transformations, and, on the other, the distinction between observation-dependent and observation-independent natural processes. The empirical study of rates of macroscopic clocks can provide a critical test of the interaction interpretation and of a possible extension to gravitational time changes; the role of time as prior determinant of natural process is at issue. The Hafele-Keating observations are of general relativity effects on clocks in accelerated motion. (shrink)

In this essay I offer an interpretative reading of the first chapter in the two canonical works, the Zhuang-zi and the Lao-zi, and argue that there is an inner connection between the first chapters of the two books. My presupposition is that what Zhuang-zi has argued in "Xiao Yao You" is the theme of the relativity of the position of the human world, which is in accord with the mystery of Dao presented at the beginning of the Lao-zi. Therefore, there (...) are two opposite directions running in the Daoist philosophy in Lao-zi and Zhuang-zi: the first one is from this world (worlds) to Dao; the second one is from Dao to the worlds. While the first emphasizes the relativity of the point of views of the worldly beings, the second shows the mystery of Dao. This can be seen as a hermeneutical circle. (shrink)

Scholars who engage with texts that were written by George Herbert Mead (e.g., 1925e.g., 1926e.g., 1929e.g., 1932e.g., 1938) in the latter half of the 1920s are faced with the task of comprehending Mead’s interpretation of relativity theory and also understanding why relativity theory was considered by Mead to have such profound implications for his own philosophy. As several scholars of Mead’s work have explained (e.g., Joas 1997; Martin 2007; Rosenthal and Bourgeois 1991), Mead was a realist. Mead opposed psychophysical (...) dualism (Cook 1979) and both the behaviorist and the idealist implications that could follow from such a dualism. He wanted to explain human conduct in terms of the self-determination of human .. (shrink)

This article examines instances of the pu relative construction in Modern Greek in which the semantic role of the head is underspecified by the syntax. Such cases include sentences whose nominal head corresponds to some complement of the relative clause predicate and sentences in which the head does not have any sort of syntactic relationship with the relative. The latter, which are characteristic of oral, informal discourse, have been completely ignored in the previous literature, which has defined (...) relatives on the basis of exclusively structural criteria. It is argued that a unified account of the pu-construction (including gapped and gapless relatives) can be achieved if we analyze it as a conventional instruction for a particular kind of conceptual integration. Semantic and pragmatic factors influencing successful construal (one which leads to the construction of a unique blend) are systematically examined. The lack of a clear cut-off point in acceptability for such utterances tallies with the conclusion reached here, namely that the constraints governing such uses are constraints on interpretability. (shrink)

A geometric interpretation of gravitation is given using general relativity. The law of gravitation is taken in the formR 44=0, whereR 44is the component of the contracted Riemann-Christoffel (Ricci) tensor representing the curvature of time. The remaining curvature components of the contracted Riemann-Christoffel tensor may or may not vanish. All that is required in addition toR 44=0 is that the Gaussian curvatureR be nowhere infinite. The conditionR 44=0 yields a nonlinear wave equation. One of the static degenerate solutions represents (...) the gravitational field surrounding a static gravitational point singularity. It is found that for this solution, the three famous predictions of general relativity are obtained in the weak-field approximation. In addition, it is found that there is a correction to the Kepler period of revolution for an orbit. (shrink)