Interpretations of Einstein’s Equation E = mc 2

Interpretations of Einstein’s equation differ primarily concerning whether E = mc² entails that mass and energy are the same property of physical systems, and hence whether there is any sense in which mass is ever ‘converted’ into energy (or vice versa). In this paper, I examine six interpretations of Einstein’s equation and argue that all but one fail to satisfy a minimal set of conditions that all interpretations of physical theories ought to satisfy. I argue that we should prefer the interpretation of Einstein’s equation that holds that mass and energy are distinct properties of physical systems. This interpretation also carries along the view that while most cases of ‘conversion’ are not genuine examples of mass being ‘converted’ into energy (or vice versa), it is possible that the there are such ‘conversions’ in the sense that a certain amount of energy ‘appears’ and an equivalent of mass ‘disappears’. Finally, I suggest that the interpretation I defend is the only one that does not blur the distinction between what Einstein called ‘principle’ and ‘constructive’ theories. This is philosophically significant because it emphasizes that explanations of Einstein’s equation and the ‘conversion’ of mass and energy must be top‐down explanations.     

Projective Explanation: How Theories Explain Empirical Data in Spite of Theory-Data Incommensurability

In scientific explanations, the explanans theory is sometimes incommensurable with the explanandum empirical data. How is this possible, especially when the explanation is deductive in nature? This paper attempts to solve the puzzle without relying on any particular theory of reference. For us, it is rather obvious that the geometric idea of projection plays a key role in Kepler’s explanation of Tycho Brahe’s empirical data. We discover that a similar mechanism operates in theoretic explanations in general. In short, all theoretic explanations are “projective” explanations. If so, there should be no logical reason why explanans theories cannot be incommensurable with explanandum data. For illustration, we analyse Einstein’s explanation of the results of the Michelson–Morley experiment in some detail.     

Teleological principles in science

In the search for elementary particles, such principles are used as Gell‐mann's that ‘anything which is possible is compulsory’. This is an example of a teleological principle according to which the scientist tries to realize in science the kind of world that he desires on prior emotional grounds. Mendeleev's classical discovery of the Periodic Law and Table of Elements was thus guided by his mystical values. A mechanistic anti‐teleologist such as Jacques Loeb was indeed a crypto‐teleologist who wished science to fulfil his radical, socialistic aims. Hoyle's ‘perfect cosmological principle’ projected conservative values, while such conceptions as Oppenheimer's ‘catastrophic collapse’, and Mach's Principle likewise had their teleological bases. Anti‐mystical and individualistic values inspired Bridgman's operationism. A ‘perfect operational principle’ would stipulate that every imaginable state of affairs would be operationally differentiable from others. Teleological principles are essential to the functioning of sciences; in the Theory of Theories, the principle of plenitude may hold: that for every mode of theory, there is some segment of reality for which it provides the best explanation. Naturalistic accounts of basic teleological principles seem inadequate.     

The only X and Y principle

In this paper, I consider the validity and proper formulation of the only‐x‐and‐y principle, which states, roughly, that whether a later individual, y, is numerically identical to an earlier individual, x, can depend only on facts about x and y and the relationships between them. In the course of my investigation, I distinguish between two classes of physical entities?–?those that exist in a ‘real’ sense, and those that exist in a mere Cambridge sense. This distinction is grounded in Peter Geach's distinction between ‘real’ and mere Cambridge change. I argue in favor of a modified version of the only‐x‐and‐y principle?–?the qualified only‐x‐and‐y principle?–?which applies to entities that exist in a ‘real’ sense, but not to mere Cambridge entities. It is also argued that the plausibility of the qualified only‐x‐and‐y principle has more to do with facts about the nature of causality than with intuitions we have about existence or numerical identity. I finish by considering some traditional objections to the only‐x‐and‐y principle, and conclude that they do not succeed in refuting the qualified only‐x‐and‐y principle.     

Noumenalism and Einstein's argument for the existence of God

Einstein argued in his latter years that the intelligibility of the world was in the nature of a miracle, and that in no way could one have expected a priori such a high degree of order; this is why he rejected the atheist, positivist standpoint, and believed in a Spinozist God. Einstein's argument, however, is essentially a form of the ‘argument from design’ for a personal God based on the existence of beautiful, mathematically simple laws of nature; that physical order is a unique, improbable alternative compared to the infinite number of chaotic universes that might have existed. Einstein, in his early manhood, was a Humean, but in later years, as he moved toward Spinoza, from phenomenalism to noumenalism, he clearly rejected Hume's restriction of probable inferences to observed sequences. Darwin's arguments against biological design did not apply to Einstein's argument, because the laws of physics are not the outcome of any cumulative struggle for existence and natural selection. Perhaps the beautiful simplicity of basic physical laws helps account for the fact that relatively more physicists than biologists or psychologists hold to a theistic standpoint. Einstein's finite universe would have seriously weakened the argument that life, though infinitely improbable, would have been realized in an infinite world. But in any case, Einstein would have regarded ‘emergence’ theories of life as irrational. In accordance with the principle of identity of Emile Meyerson, the epistemologist whom he most respected, it would have followed that the occurrence of consciousness and intelligence was grounded in a God with those attributes, and that theism was consequently the basis for scientific knowledge.     

The “concept of time” and the “being of the clock”: Bergson, Einstein, Heidegger, and the interrogation of the temporality of modernism

The topic to be addressed in this paper, that is, the distinction between the “concept” of time and the being of the clock, divides into two parts: first, in the debate between Albert Einstein and Henri Bergson, one discovers the ground for the diverging concepts of time characterized by physics in its opposing itself to philosophy. Bergson’s durée or “duration” in opposition to Einstein’s ‘physicist’s time’ as ‘public time,’ one can argue, sets the terms for Martin Heidegger’s extending, his ontological analysis of Da-sein, as human being-in-the-world. Second, in this the ‘concept of time’ gives way to the analysis of the ‘being of the clock.’ What is this being of the clock that makes evident the fundamental temporality of Da-sein? This question is rehearsed in Division Two of Being and Time. My claim is that the fundamental insight into the nature of time revealed by the encounter between Bergson and Einstein is that time extemporizes itself. Temporality “is” not a being but a process that temporalizes itself, precisely because it “is not.”     

Basic‐Know And Super‐Know

Sometimes a proposition is ‘opaque’ to an agent: (s)he doesn't know it, but (s)he does know something about how coming to know it should affect his or her credence function. It is tempting to assume that a rational agent's credence function coheres in a certain way with his or her knowledge of these opaque propositions, and I call this the ‘Opaque Proposition Principle’. The principle is compelling but demonstrably false. I explain this incongruity by showing that the principle is ambiguous: the term ‘know’ as it appears in the principle can be interpreted in two different ways, as either basic‐know or super‐know. I use this distinction to construct a plausible version of the principle, and then to similarly construct plausible versions of the Reflection Principle and the Sure‐Thing Principle.     

Einstein,his theories,and his aesthetic considerations

This article deals with the question whether aesthetic considerations affected Einstein in formulating both his theories of relativity. The opinions of philosophers and historians alike are divided on this matter. Thus, Gerald Holton supports the view that Einstein employed aesthetic considerations in formulating his theory of special relativity whereas Jim Shelton opposes it, one of his reasons being that Einstein did not mention such considerations. The other theory, namely, that of general relativity, is discussed by John D. Norton. He asserts that the successful completion of this theory was due to Einstein's adherence to mathematical simplicity resulting from experience, as Einstein himself stated, and not from an aesthetic drive, to which he did not refer. The present work attempts to overcome this deficiency indirectly by investigating Einstein's aesthetic awareness and its consequences for his work. It is found that this awareness was imbedded in his perception of nature and is linked to the criteria (such as simplicity) that guided him in formulating his theories. The conclusion thus reached is that aesthetic considerations did play a role in Einstein's endeavour, contrary to the assertions of Shelton and Norton.     

Intrinsic Explanation and Field’s Dispensabilist Strategy

Abstract

Hartry Field defended the importance of his nominalist reformulation of Newtonian Gravitational Theory, as a response to the indispensability argument, on the basis of a general principle of intrinsic explanation. In this paper, I argue that this principle is not sufficiently defensible, and can not do the work for which Field uses it. I argue first that the model for Field’s reformulation, Hilbert’s axiomatization of Euclidean geometry, can be understood without appealing to the principle. Second, I argue that our desires to unify our theories and explanations undermines Field’s principle. Third, the claim that extrinsic theories seem like magic is, in this case, really just a demand for an account of the applications of mathematics in science. Finally, even if we were to accept the principle, it would not favor the fictionalism that motivates Field’s argument, since the indispensabilist’s mathematical objects are actually intrinsic to scientific theory.     

Neuromythology of Einstein’s brain

The idea that the brain of the great physicist Albert Einstein is different from “average” brains in both cellular structure and external shape is widespread. This belief is based on several studies examining Einstein’s brain both histologically and morphologically. This paper reviews these studies and finds them wanting. Their results do not, in fact, provide support for the claim that the structure of Einstein’s brain reflects his intellectual abilities.     

Parts, classes and Parts of Classes: an anti-realist reading of Lewisian mereology

This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean (and Gentzenian) rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology with class theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has to be when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis—which is central to his marriage of class theory with mereology—as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR. This is the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual.     

Constructing the collective unconscious

Abstract: Innovative attempts at collating Jungian analytical psychology with a range of ‘post‐modern’ theories have yielded significant results. This paper adopts an alternative strategy: a Lacanian vantage point on Jungian theory that eschews an attempt at reconciling Jung with post‐structuralism. A focused Lacanian gaze on Jung will establish an irreducible tension between Jung's view of archetypes as factors immanent to the psyche and a Lacanian critique that lays bare the contingent structures and mechanisms of their constitution, unveiling the supposed archetypes’a posteriori production through the efficacy of a discursive field. Theories of ideology developed in the wake of Lacan provide a powerful methodological tool allowing to bring this distinction into focus. An assembly of Lacan's fragmentary accounts of Jung will be supplemented with an approach to Jungian theory via ?i?ek's Lacan‐oriented theory of the signifying mechanism underpinning ‘ideology’. Accordingly, the Jungian archetype of the self, which is considered in some depth, can begin to be seen in a new light, namely as a ‘master signifier’, not only of Jung's academic edifice, but also —and initially—of the discursive strategies that establish his own subjectivity. A discussion of Jung's approach to mythology reveals how the ‘quilting point’ of his discourse comes to be coupled with a correlate in the Real, a non‐discursive ‘sublime object’ conferring upon archetypes their fascinating aura.     

MORAL FACTS AND SUITABLY INFORMED SUBJECTS: A REPLY TO DENHAM

The nature of moral facts, and their relationship to rationality, imagination and sentiment, have been central and pressing issues in recent moral philosophy. In this paper, I discuss and criticise a meta‐ethical theory put forward by Alison Denham, which views moral facts as being constituted by the responses of ideal, empathetic agents. I argue that Denham's account is radically unstable, in that she has given us an account of the nature of such agents which is inconsistent with an independently plausible principle relating to concept acquisition. I go on to discuss one line of defence that Denham might employ, but argue that taking such a line entails abandoning what she takes to be an important advantage of her account over rival ideal‐observer theories such as Michael Smith’s.     

Talking at cross-purposes: how Einstein and the logical empiricists never agreed on what they were disagreeing about

By inserting the dialogue between Einstein, Schlick and Reichenbach into a wider network of debates about the epistemology of geometry, this paper shows that not only did Einstein and Logical Empiricists come to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but also that in their lifelong interchange, they never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his ”measuring rod objection” against Weyl. On the contrary, Logical Empiricists, though carefully analyzing the Einstein–Weyl debate, tried to interpret Einstein’s epistemology of geometry as a continuation of the Helmholtz–Poincaré debate by other means. The origin of the misunderstanding, it is argued, should be found in the failed appreciation of the difference between a “Helmholtzian” and a “Riemannian” tradition. The epistemological problems raised by General Relativity are extraneous to the first tradition and can only be understood in the context of the latter, the philosophical significance of which, however, still needs to be fully explored.     

Variations on the concept of traumatism: Traumatism,traumatic, trauma1

In this paper, the author outlines Freud's fundamental hypotheses concerning the concept of traumatism, then goes on to differentiate three notions (French being a particularly apposite language for such a venture): ‘traumatism’, ‘traumatic’ (in a substantive sense) and ‘trauma’. These three terms correspond to the three turning points in Freud's theory with respect to the concept of traumatism (1895‐97, 1920, 1938). The author evokes also the developments that are due to Ferenczi, particularly in his later writings (1928‐33), where he defi ned and discussed the question of ‘trauma’ in contemporary clinical practice; the author goes on to explore the different variations on this theme as regards mental functioning. He then defi nes, from a metapsychological point of view, the differences between ‘traumatisms’ that have been ‘worked over by secondary processes’, organised and governed by the pleasure‐unpleasure principle (‘traumatism’) and ‘early’ or ‘primary traumatisms’, which interfere with the process of binding the instinctual drives (‘trauma’); states of mind infl uenced by a traumatic imprint (‘traumatic’) are looked upon as belonging to both categories of the above mentioned traumatisms. The author illustrates his hypotheses with a clinical example.     

The Foundations of Capability Theory: Comparing Nussbaum and Gewirth

This paper is written from a perspective that is sympathetic to the basic idea of the capability approach. Our aim is to compare Martha Nussbaum’s capability theory of justice with Alan Gewirth’s moral theory, on two points: the selection and the justification of a list of central capabilities. On both counts, we contend that Nussbaum’s theory suffers from flaws that Gewirth’s theory may help to remedy. First, we argue that her notion of a (dignified) human life cannot fulfill the role of a normative criterion that Nussbaum wants it to play in selecting capabilities for her list. Second, we question whether Nussbaum’s method of justification is adequate, discussing both her earlier self-validating argumentative strategy and her more recent adherence to the device of an overlapping consensus. We conclude that both strategies fail to provide the capabilities theory with the firm foundation it requires. Next, we turn to Gewirth’s normative theory and discuss how it can repair these flaws. We show how his theory starts from a fundamental moral principle according to which all agents have rights to the protection of the necessary preconditions of their agency. Gewirth’s justification of this principle is then presented, using a version of a transcendental argument. Finally, we explicitly compare Nussbaum and Gewirth and briefly demonstrate what it would mean for Nussbaum to incorporate Gewirthian elements into her capabilities theory of justice.     

“心为太极”说在朱子学中的诠释

朱子在《易学启蒙》中曾引用邵雍“心为太极”之说。此说与朱子学的固有观念似乎相矛盾。但“心为太极”说在朱子学的框架内至少曾出现如下三种理解:朱子本人以“心”为易图的中心方位来解释“太极虚中之象”的“环中说”;在朱子后学中具有广泛影响的禀赋说;现代学者所揭示出的“境界说”。三种说法并不矛盾,“环中说”背后所体现的是“太极不离阴阳”的活动性原则,它与“禀赋说”所代表的实体性原则相辅相成,二者的统一就是“境界说”。此外,“心为太极”还有一层工夫的含义,对于提示学者在自家身上体贴太极观念具有重要的意义。     

On field's argument for substantivalism

In this article I subject to criticism Field's argument, according to which field theory takes space‐time to be à substance since it ascribes field properties to space‐time points. There is petitio principii error made in this reasoning because Field does not give any justification for his controversial assumption that fields are properties of space‐time points. What is more, I suggest, Field's interpretation of field theory is incompatible with the way this theory is understood and utilized by its users, namely scientists. My criticism is based on the assumption that one cannot propose an ontology of a given scientific theory, at the same time imposing on it an interpretation which clashes with the interpretation current among its users. I also suggest that in order to establish the ontology of a scientific theory one should also take into account the way it has been constructed. According to this criterion, field theory does indeed take space‐time to be a substance.