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 (...) class='Hi'>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 this article we critically examine the principle of equivalence of care in prison medicine. First, we provide an overview of how the principle of equivalence is utilized in various national and international guidelines on health care provision to prisoners. Second, we outline some of the problems associated with its applications, and argue that the principle of equivalence should go beyond equivalence to access and include equivalence of outcomes. However, because of the (...) particular context of the prison environment, third, we contend that the concept of “health” in equivalence of health outcomes needs conceptual clarity; otherwise, it fails to provide a threshold for healthy states among inmates. We accomplish this by examining common understandings of the concepts of health and disease. We conclude our article by showing why the conceptualization of diseases as clinical problems provides a helpful approach in the delivery of health care in prison. (shrink)

The philosophy of physics literature contains conflicting claims on the heuristic significance of general covariance. Some authors maintain that Einstein's general relativity distinguishes itself from other theories in that it must be generally covariant, for example, while others argue that general covariance is a physically vacuous and trivial requirement applicable to virtually any theory. Moreover, when general covariance is invested with heuristic significance, that significance as a rule is assigned to so-called “active” general covariance, underwritten by the principle of (...) background independence, rather than to general covriance as Einstein understood it. While agreeing with the latter group of commentators that general covariance indeed carries heuristic significance, I argue that a background independent theory need not be generally covariant and that instead the Principle of Equivalence as Einstein understood it provides the key to understanding the heuristic power of general covariance as a “mathematical sieve” for determining the gravitational field law. However, heuristic significance accrues to general covariance only indirectly, by its encompassing the relativity of frames underwritten by Einstein's principle of equivalence. (shrink)

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The principle of “equivalence of care” in prison medicine is a principle by which prison health services are obliged to provide prisoners with care of a quality equivalent to that provided for the general public in the same country. It is cited in numerous national and international directives and recommendations.The principle of equivalence is extremely relevant from the point of view of normative ethics but requires adaptation from the point of view of applied ethics. From (...) a clinical point of view, the principle of equivalence is often insufficient to take account of the adaptations necessary for the organization of care in a correctional setting. The principle of equivalence is cost-effective in general, but has to be overstepped to ensure the humane management of certain special cases. (shrink)

General relativity is the exact theory of gravity which has been experimentally found to be correct with extremely high accuracy. One of the most surprising predictions of the general theory is that time runs slow in a gravitational field. Its proof formally comes from Schwarzschild metric which is a solution of Einstein field equation for a spherically symmetric mass. However, as Einstein field equation is too complex, attempts have been made earlier to derive gravitational time dilation by direct use of (...) principle of equivalence and special theory of relativity. But, this objective has been accomplished partially till date as the resulting expression agrees with the exact expression only upto first order. In this paper, by using principle of equivalence and special relativity, we present a thought experiment which helps us to derive an expression that exactly matches with the expression for gravitational time delay. (shrink)

BackgroundThe principle of equivalence in prison health has been established for nearly four decades. It seeks to ensure that prisoners have access to the same level of healthcare as members of society at large, which is entrenched within the international legal framework and England’s national health policies.AimsThis study examined how key policymakers interpret and implement the principle of equivalence in English prisons. It also identified opportunities and threats associated with the application of the principle.MethodsIn total, (...) 30 policymakers took part in this research. These participants engaged in policymaking activities and occupied positions of authority in the prison field.ResultsDespite the policymakers’ consensus on the importance of the equivalence principle, there was a varying degree of understanding regarding what constitutes ‘equivalence’. Participants described how the security culture impedes prisoners’ access to healthcare services. Additionally, the increasing size and complexity of the prison population, coupled with a diminishing level of resources, reduce the level of care being provided in prisons and thus compromise implementation of equivalence in English prisons.ConclusionsInconsistent interpretation of equivalence, the prevailing security drive, increasing numbers and health complexities of prisoners and fiscal austerity threaten the implementation of equivalence in English prisons. This research calls for new guidance on how to interpret and implement equivalence, along with measures to educate prison governors and staff on the prison rehabilitation value, ensure greater investment in prison health and consider alternatives to imprisonment to future-proof the principle of equivalence in the English prison system. (shrink)

We review from a historical and a didactic point of view the Equivalence Principle, which was considered by Einstein as the corner stone of his new theory of Gravitation: the General Relativity. Before and after the enormous success of his theory, this principle was the subject of studies and discussions. Still today, after more than one century, the debate about its interpretation, application and generalization is very fertile. Einstein soon understood the revolutionary significance of his idea and (...) defined it as “the happiest thought of my life”. (shrink)

We discuss the main ideas that lie at the foundations of the approximating Hamiltonian method (AHM) in statistical mechanics. The principal constraints for model Hamiltonians to be investigated by AHM are considered along with the main results obtainable by this method. We show how it is possible to enlarge the class of model Hamiltonians solvable by AHM with the help of an example of the BCS-type model.

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFγs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFγs that is associated with the PLLI. Next we (...) give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent. (shrink)

We show that the axiom of choice AC is equivalent to the Vector Space Kinna-Wagner Principle, i.e., the assertion: “For every family [MATHEMATICAL SCRIPT CAPITAL V]= {Vi : i ∈ k} of non trivial vector spaces there is a family ℱ = {Fi : i ∈ k} such that for each i ∈ k, Fiis a non empty independent subset of Vi”. We also show that the statement “every vector space over ℚ has a basis” implies that every infinite (...) well ordered set of pairs has an infinite subset with a choice set, a fact which is known not to be a consequence of the axiom of multiple choice MC. (shrink)

We show that Bounded Forcing Axioms (for instance, Martin's Axiom, the Bounded Proper Forcing Axiom, or the Bounded Martin's Maximum) are equivalent to principles of generic absoluteness, that is, they assert that if a $\Sigma_1$ sentence of the language of set theory with parameters of small transitive size is forceable, then it is true. We also show that Bounded Forcing Axioms imply a strong form of generic absoluteness for projective sentences, namely, if a $\Sigma^1_3$ sentence with parameters is forceable, then (...) it is true. Further, if for every real x, $x^{\sharp}$ exists, and the second uniform indiscernible is less than $\omega_2$ , then the same holds for $\Sigma^1_4$ sentences. (shrink)

The following is a foundationalist exercise based upon a single observation or postulate distinguishing one’s knowledge of information versus one’s knowledge of one’s former unknowing of that information. This postulate is titled the “principle of implicit ignorance.” Utilizing this postulate, several theorems are constructed including the equivalence to Hume’s thesis regarding the absence of knowledge of a necessary connection. The postulate is then negated, demonstrating equivalence to Kant’s thesis regarding the presence of synthetic a priori statements. The (...) final result is a single general epistemic postulate that brokers between the two respective positions. Because both systems are the result of this general principle, rejecting the results of one system necessarily forces one into the contrary position. (shrink)

The aim of this paper is twofold: First, to present an examination of the principles underlying gauge field theories. I shall argue that there are two principles directly connected to the two well-known theorems of Emmy Noether concerning global and local symmetries of the free matter-field Lagrangian, in the following referred to as "conservation principle" and "gauge principle". Since both these express nothing but certain symmetry features of the free field theory, they are not sufficient to derive a (...) true interaction coupling to a new gauge field. For this purpose it is necessary to advocate a third, truly empirical principle which may be understood as a generalization of the equivalence principle. The second task of the paper is to deal with the ontological question concerning the reality status of gauge potentials in the light of the proposed logical structure of gauge theories. A nonlocal interpretation of topological effects in gauge theories and, thus, the non-reality of gauge potentials in accordance with the generalized equivalence principle will be favoured. (shrink)

The principle of indifference (hereafter ‘Poi’) says that if one has no more reason to believe A than B (and vice versa ), then one ought not to believe A more than B (nor vice versa ). Many think it’s demonstrably false despite its intuitive plausibility, because of a particular style of thought experiment that generates counterexamples. Roger White ( 2008 ) defends Poi by arguing that its antecedent is false in these thought experiments. Like White I believe Poi, (...) but I find his defense unsatisfactory for two reasons: it appeals to false premises, and it saves Poi only at the expense of something that Poi’s believers likely find just as important. So in this essay I defend Poi by arguing that its antecedent does hold in the relevant thought experiments, and that the further propositions needed to reject Poi are false. I play only defense in this essay; I don’t argue that Poi is true (even though I think it is), but rather that one popular refutation is faulty. In showing this, I also note something that has to my knowledge gone unnoticed: given some innocuous-looking assumptions the denial of Poi is equivalent to a version of epistemic permissivism , and Poi itself is equivalent to a version of epistemic uniqueness. (shrink)

The Principle of Context and the Principle of Compositionality only conflict when they are construed as claims about the origin of meanings. I will clarify this point by means of an historical survey into the treatment that PCtxt receives in Frege's Grundlagen and in Wittgenstein's Tractatus. I will argue that Frege actually introduces non-equivalent formulations of PCtxt generating an unstable notion of meaning when related with PCmp. The Tractatus solves this imbalance by assuming both the contextuality and the (...) compositionality at the very core of the notion of meaning, thus by ruling out the claim of two separated —sensitive to collision— principles. My thesis is that in the stage of development of the Tractatus, Wittgenstein found a way to meet and fit together the tensions between PCtxt and PCmp emerging in Frege´s philosophy of language and detected by latter commentators. (shrink)

The kinematical principle of Equal Passage Times (EPT) was introduced by Winnie in his 1970 derivation of the relativistic coordinate transformations compatible with arbitrary synchrony conventions in one-dimensional space. In this paper, the claim by Winnie and later Giannoni that EPT is a direct consequence of the relativity principle is questioned. It is shown that EPT, given Einstein's 1905 postulates, is equivalent to the relativistic (synchrony independent) clock retardation principle, and that for standard synchrony it reduces to (...) an isotropy condition for contraction (and dilation) effects. (shrink)

Reid's principle of credulity may be interpreted as equivalent to a principle of charity, due to the nature of three beliefs it implies concerning the interlocutors, which are held by the person who attempts to acquire their language: They are telling truth in the sense that they are saying what they really think, perceive, feel, believe; they are veracious in the sense that what they say is objectively true; they use language consistently. This interpretation relies on Reid's straightforward (...) remarks on his principle of credulity and on his view of two related correspondences: One correspondence is between the principle of credulity and the principle of veracity. The other is between these two principles and the principles that create the ‘language of nature’ and guide us in our efforts to unravel it. (shrink)

After discussing the limitations inherent to all set-theoretic reflection principles akin to those studied by A. Lévy et. al. in the 1960s, we introduce new principles of reflection based on the general notion of Structural Reflection and argue that they are in strong agreement with the conception of reflection implicit in Cantor’s original idea of the unknowability of the Absolute, which was subsequently developed in the works of Ackermann, Lévy, Gödel, Reinhardt, and others. We then present a comprehensive survey of (...) results showing that different forms of the new principle of Structural Reflection are equivalent to well-known large cardinal axioms covering all regions of the large-cardinal hierarchy, thereby justifying the naturalness of the latter. (shrink)

Łukasiewicz distinguishes three formulations of the principle of contradiction in Aristotle’s works: ontological, logical, and psychological. The first two formulations are equivalent though not synonymous, but neither of them is equivalent to the psychological one, which expresses not a principle but only an empirical law. Furthermore, the principle of contradiction is neither a simple and ultimate law nor is it necessary for conducting an inference, because the syllogism is independent of it. The further explanation of this concept (...) leads Łukasiewicz to formulate the idea of a non-Aristotelian logic, that is, a logic operating without the principle of contradiction. If the principle of contradiction shall be valid, it must be proved. A proof can be supplied only on the basis of a definition of object, as something that cannot have and not have the same property at the same time. However, this definition does not hold for all objects, i.e., for contradictory objects. In virtue of its ontological character the Aristotelian principle of contradiction is then different from that of symbolic logic. (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)

This paper formulates generalized versions of the general principle of relativity and of the principle of equivalence that can be applied to general abstract spaces. It is shown that when the principles are applied to the Hilbert space of a quantum particle, its law of coupling to electromagnetic fields is obtained. It is suggested to understand the Aharonov-Bohm effect in light of these principles, and the implications for some related foundational controversies are discussed.

Łukasiewicz distinguishes three formulations of the principle of contradiction in Aristotle’s works: ontological, logical, and psychological. The first two formulations are equivalent though not synonymous, but neither of them is equivalent to the psychological one, which expresses not a principle but only an empirical law. Furthermore, the principle of contradiction is neither a simple and ultimate law nor is it necessary for conducting an inference, because the syllogism is independent of it. The further explanation of this concept (...) leads Łukasiewicz to formulate the idea of a non-Aristotelian logic, that is, a logic operating without the principle of contradiction. If the principle of contradiction shall be valid, it must be proved. A proof can be supplied only on the basis of a definition of object, as something that cannot have and not have the same property at the same time. However, this definition does not hold for all objects, i.e., for contradictory objects. In virtue of its ontological character the Aristotelian principle of contradiction is then different from that of symbolic logic. (shrink)

This article improves two existing theorems of interest to neologicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic. The improved theorem states that if an equivalence relation E is defined without nonlogical vocabulary, then the bicardinal slice of any equivalence class—those equinumerous elements of the equivalence class with equinumerous complements—can have one of only three profiles. The improvements to Fine’s theorem allow (...) for an analysis of the well-behaved models had by an abstraction principle, and this in turn leads to an improvement of Walsh and Ebels-Duggan’s relative categoricity theorem. (shrink)

The axiomatic bases of Special Relativity Theory (SRT) are thoroughly re-examined from an operational point of view, with particular emphasis on the status of Einstein synchronization in the light of the possibility of arbitrary synchronization procedures in inertial reference frames. Once correctly and explicitly phrased, the principles of SRT allow for a wide range of “theories” that differ from the standard SRT only for the difference in the chosen synchronization procedures, but are wholly equivalent to SRT in predicting empirical facts. (...) This results in the introduction, in the full background of SRT, of a suitable synchronization gauge. A complete hierarchy of synchronization gauges is introduced and elucidated, ranging from the useful Selleri synchronization gauge (which should lead, according to Selleri, to a multiplicity of theories alternative to SRT) to the more general Mansouri–Sexl synchronization gauge and, finally, to the even more general Anderson–Vetharaniam–Stedman’s synchronization gauge. It is showed that all these gauges do not challenge the SRT, as claimed by Selleri, but simply lead to a number of formalisms which leave the geometrical structure of Minkowski spacetime unchanged. Several aspects of fundamental and applied interest related to the conventional aspect of the synchronization choice are discussed, encompassing the issue of the one-way velocity of light in inertial and rotating reference frames, the global positioning system (GPS)’s working, and the recasting of Maxwell equations in generic synchronizations. Finally, it is showed how the gauge freedom introduced in SRT can be exploited in order to give a clear explanation of the Sagnac effect for counter-propagating matter beams. (shrink)

In this paper, the author analyzes critically some of the ideas found in Karel Lambert's recent book, Meinong and the Principle of Independence (Cambridge: Cambridge University Press, 1983). Lambert attempts to forge a link between the ideas of Meinong and the free logicians. The link comes in the form of a principle which, Lambert says, these philosophers adopt, namely, Mally's Principle of Independence, which Mally himself later abandoned. Instead of following Mally and attempting to formulate the (...) class='Hi'>principle in the material mode as the claim that an object can have properties without having any sort of being, Lambert formulates the principle in the formal mode, as (something equivalent to) the rejection of the traditional constraint on the principle of predication. The principle of predication is that a formula of the form Fa' is true iff the general term F' is true of the object denoted by the object term a'. The traditional constraint on this predication principle is that for the sentence Fa' to be true, not only must the object term have a denotation, but it must also denote an object that has being. According to Lambert, the free logicians violate this constraint by suggesting that Fa' can be true even if the object term has no denotation, whereas Meinong violates this constraint by proposing Fa' can be true even when the object term denotes an object that has no being. Lambert then tries to `vindicate' the Principle of Independence, thereby justifying both the work of the free logicians and Meinong. (shrink)

Fiscal equivalence in the public administration of justice requires local police and courts to be financed exclusively by the populations that benefit from their services. Within a polycentric framework, broad based taxation to achieve fiscal equivalence is a desirable principle of public finance because it conceptually allows for the provision of justice to be determined by constituent’s preferences, and increases the political accountability of service providers to constituents. However, the overproduction of justice services can readily occur when (...) the benefits of the justice system are not enjoyed equally. Paradoxically, the same properties that make fiscal equivalence desirable by imposing restraint and control between constituents and local government also create internal pressures for agents of the state to engage in predatory, revenue-generating behavior. (shrink)

The equivalence principle, being one of the building blocks of general relativity, seems to be crucial for analysis of quantum effects in gravity. In this paper we consider the relation between the equivalence principle and the consistency of quantum information processing in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame. We show that without the equivalence principle the looped (...) quantum evolution cannot be unitary and looses its consistency. For this reasoning the equivalence principle is formulated in terms of the gauge transformations and is analyzed for particles acquiring an appropriate phase associated with the action over the looped path. In consequence, to keep consistency of quantum operations in gravitational field, it is required to keep a quantum variant of the equivalence principle. This proves importance of the quantized version of this fundamental gravitational principle for quantum information processing. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are (...) often seen as part of the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist of (...) an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations. (shrink)

Two thought experiments are discussed which suggest, first, a geometric interpretation of the concept of a (say, vector) potential (i.e., as a kinematic quantity associated with a transformation between moving frames of reference suitably related to the problem) and, second, that, in a quantum treatment one should extend the notion of the equivalence principle to include not only the equivalence of inertial forces with suitable “real” forces, but also the equivalence of potentials of such inertial forces (...) and the potentials of suitable real forces. The two types of cancellation are physically independent of each other, because of the Aharonov-Bohm effect. Finally, we show that the latter effect itself can be understood “geometrically” as a kinematic effect arising upon the transformation between the two reference frames. (shrink)

In recent years, the principle of equivalence has been accepted in many countries as the standard against which healthcare provision for prisoners should be measured. There are several ways in which this principle can be interpreted, but current policy in the UK and elsewhere seems to focus on the measurement and achievement of equivalence in the process of healthcare provision. We argue that it is not appropriate to apply this interpretation to all aspects of prisoner healthcare, (...) as it does not necessarily address the challenges inherent to the prisoner population and prison setting. Consequently equivalence of health outcomes should also be considered alongside processes in the interests of providing healthcare in prison that is equivalent to that outside prison. (shrink)

A generalized version of Martin's axiom, called BACH, is shown to be equivalent to one of its combinatorial consequences, a generalization of P(c).

The equivalence principle has constituted one of the cornerstones of discussions in the foundations of spacetime theories over the past century. However, up to this point the principle has been considered overwhelmingly only within the context of relativistic physics. In this article, we demonstrate that the principle has much broader, super-theoretic significance: to do so, we present a unified framework for understanding the principle in its various guises, applicable to both relativistic and Newtonian contexts. We (...) thereby deepen significantly our understanding of the role played by the equivalence principle in a broad class of spacetime theories. (shrink)

Central to the discourse ethics advanced by Jürgen Habermas is a principle of universalization (U) amounting to a dialogical equivalent of Kant's Categorical Imperative. Habermas has proposed that ?U? follows by material implication from two premises: (1) what it means to discuss whether a moral norm ought to be . adopted and (2) what those involved in argumentation must suppose of themselves if they are to consider a consensus they reach as rationally motivated. To date, no satisfactory derivation of (...) ?U? from these two premises has been presented. Thus the present study attempts to show how one can, without begging the question, arrive at ?U? by assuming a suitable explication of these two premises, supplemented with a fairly innocuous assumption about the context of discourse. If the argument is sound, then ?U? brings both deontological and consequentialist intuitions together with a notion of solidarity that requires an intersubjective account of insight. (shrink)

We consider the restriction of classical principles like Excluded Middle, Markov’s Principle, König’s Lemma to arithmetical formulas of degree 2. For any such principle, we find simple mathematical statements which are intuitionistically equivalent to it, provided we restrict universal quantifications over maps to computable maps.