When involved in a disagreement, a common reaction is to tell oneself that, given that the information about one’s own epistemic standing is clearly superior in both amount and quality to the information about one’s opponent’s epistemic standing, one is justified in one’s confidence that one’s view is correct. In line with this natural reaction to disagreement, some contributors to the debate on its epistemic significance have claimed that one can stick to one’s guns by relying in part on information (...) about one’s first-order evidence and the functioning of one’s cognitive capacities. In this article, I argue that such a manoeuvre to settle controversies encounters the problem that both disputants can make use of it, the problem that one may be wrong about one’s current conscious experience, and the problem that it is a live possibility that many of one’s beliefs are the product of epistemically distorting factors. I also argue that, even if we grant that personal information is reliable, when it comes to real-life rather than idealized disagreements, the extent of the unpossessed information about one’s opponent’s epistemic standing provides a reason for doubting that personal information can function as a symmetry breaker. (shrink)

There are basically four options to which state the limiting instant in a change from one state to its opposite belongs – only the first, only the second, both or none. This situation is usually referred to as the limit decision problem since all of these options seem troublesome: The first two alleged solutions are asymmetric and thus need something to ground this asymmetry in ; while the last two options leave the realm of classical logic. I argue that including (...) the debate about dispositions enables new options for solutions to the temporal limit decision problem. Metaphysical considerations function as a symmetry-breaker and thus remove the need for a non-classical solution. Dispositions bring about the changes in the world, so they constitute the metaphysical background for the instant of change. In particular, I argue that according to the triadic process account of dispositions, the limiting instant belongs to the second interval and only the second interval. (shrink)

James Henry Collin recently developed a new symmetry breaker favouring the ontological argument’s possibility premiss over that of the reverse ontological argument. The symmetry breaker amounts to an undercutting defeater for the reverse possibility premiss based on Kripkean cases of a posteriori necessity. I argue, however, that symmetry re-arises in two forms. First, I challenge the purported asymmetry in epistemic entitlements to the original and reverse possibility premisses. Second, relevantly similar Kripkean cases equally undercut the (...) original possibility premiss. (shrink)

What is the rational response to disagreement with an epistemic peer? Some say the steadfast response of holding on to your own belief can be rational; others argue that some degree of conciliation is always rationally required. I argue that only an epistemological externalist about rationality—someone who holds that the rationality of a belief is partly constituted by factors outside a subject’s cognitive perspective—can defend the steadfast view. Or at least that this is so in the kinds of idealized cases (...) of peer disagreement that take center stage in the current debate about disagreement. The argument has three steps. First, I show how rationality internalism motivates conciliationism: in view of the mutually recognized internal epistemic symmetry between peers, it would be arbitrary for either peer to hold on to her own belief. Second, I strengthen this line of thought by considering various proposed ‘symmetry breakers’ that appear to introduce a relevant asymmetry between peers, which could be used to defend the rationality of a steadfast response. I argue that none of these alleged symmetry breakers can help internalists. Third, I show how externalism does have the resources to defend steadfastness and expose how extant defenses of steadfastness implicitly rely on externalist intuitions. (shrink)

It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite. In the present paper, we show that, even given a dynamic theory of time, the cardinality of an endless series of events, each of which will occur, is the same as that of a beginningless series of events, each of which has occurred. Both are denumerably infinite. So if an endless series of events is (...) possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite. What would be required to rebut our argument is a symmetry breaker – something that motivates treating the past relevantly differently to the future. We consider several attempts to provide a symmetry breaker and show that none of them is successful. (shrink)

Does having an initially high level of justified confidence in a belief vindicate remaining steadfast in the face of disagreement? According to one prominent view in the literature, namely Jennifer Lackey's justificationist position, the answer is yes so long as one also has personal information that provides a symmetry-breaker. In this article, I raise a problem for the justificationist view. On the most straightforward reading of the justificationist position, personal information always provides a symmetry-breaker in a (...) peer dispute over a belief in which one has high justified confidence. However, this position is implausibly strong because it renders epistemically permissible a dogmatic attitude in a relevant set of peer disagreements. Alternatively, weaker readings of the view fail to provide a perspicuous account of when high justified confidence matters in a disagreement. (shrink)

This Element engages with the epistemic significance of disagreement, focusing on its skeptical implications. It examines various types of disagreement-motivated skepticism in ancient philosophy, ethics, philosophy of religion, and general epistemology. In each case, it favors suspension of judgment as the seemingly appropriate response to the realization of disagreement. One main line of argument pursued in the Element is that, since in real-life disputes we have limited or inaccurate information about both our own epistemic standing and the epistemic standing of (...) our dissenters, personal information and self-trust can rarely function as symmetry breakers in favor of our own views. (shrink)

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the (...) empiricist view of science as a construction of models to represent the phenomena. (shrink)

Philosophical semantics requires an ontology that includes negative as well as positive states of affairs as truth-makers and truth-breakers. Theories that try to do without negative states of affairs while interpreting propositional truth as positive correspondence with existent states of affairs are inherently inadequate and incomplete. A semantics and ontology of negative states of affairs can also do justice to positive states of affairs, since the iterated negative state of affairs that a negative state of affairs exists describes a positive (...) state of affairs, but the iterated positive state of affairs that a positive state of affairs exists never describes a negative state of affairs. Negative states of affairs are not only essential to semantics, but to a complete description of the world; they include phenomena of presence in absence and the metaphysics of gaps, lacks, holes and interstitia. The conceivability of an empty or null universe as consisting of nothing but negative states of affairs recalls a famous problem of Parmenides. (shrink)

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent. A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is (...) no such concept. The present paper arrives at a cautiously pessimistic conclusion. (shrink)

Annotation "Fearful Symmetry" brings the incredible discoveries of contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how today's theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, the book describes the majestic sweep and accomplishments of twentieth-century physics. In the end, we stand in awe before the grand vision of modern physics--one of the greatest chapters (...) in the intellectual history of humankind. (shrink)

We investigate Maker–Breaker games on graphs of size $\aleph _1$ in which Maker’s goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the game on the axiomatic framework. Relating to this, we prove that there is a winning strategy for Maker in the $K_{\omega,\omega _1}$ -game under ZFC+MA+ $\neg $ CH and a winning strategy for Breaker under ZFC+CH. We prove a similar result for the $K_{\omega _1}$ -game. (...) Here, Maker has a winning strategy under ZF+DC+AD, while Breaker has one under ZFC+CH again. (shrink)

Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and (...) philosophy of science, the volume is a valuable reference for students and researchers. (shrink)

Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such (...) as Curie's principle), and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic. (shrink)

A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson is (...) speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

To this day, a hundred and fifty years after Mendeleev's discovery, the overal structure of the periodic system remains unaccounted for in quantum-mechanical terms. Given this dire situation, a handful of scientists in the 1970s embarked on a quest for the symmetries that lie hidden in the periodic table. Their goal was to explain the table's structure in group-theoretical terms. We argue that this symmetry program required an important paradigm shift in the understanding of the nature of chemical elements. (...) The idea, in essence, consisted of treating the chemical elements, not as particles, but as states of a superparticle. We show that the inspiration for this came from elementary particle physics, and in particular from Heisenberg's suggestion to treat the proton and neutron as different states of the nucleon. We provide a careful study of Heisenberg's last paper on the nature of elementary particles, and explain why the Democritean picture of matter no longer applied in modern physics and a Platonic symmetry-based picture was called for instead. We show how Heisenberg's Platonic philosophy came to dominate the field of elementary particle physics, and how it found its culmination point in Gell-Mann's classification of the hadrons in the eightfold way. We argue that it was the success of Heisenberg's approach in elementary particle physics that sparked the group-theoretical approach to the periodic table. We explain how it was applied to the set of chemical elements via a critical examination of the work of the Russian mathematician Abram Ilyich Fet the Turkish-American physicist Asim Orhan Barut, before giving some final reflections. (shrink)

the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..

If the tiles of a mosaic are arranged symmetrically, then the image those tiles constitute must be symmetric as well. This paper formulates and defends the general principle at work in this case: roughly, that a symmetry cannot ground an asymmetry. It is argued that the principle supports strong objections to four metaphysical views: qualitativism, relationalism, the tenseless or ‘B’ theory of time, and comparativism. A response to these objections is developed which appeals to fragmentalism, the view that reality (...) contains facts which are incompatible with one another. But fragmentalism might be thought too bizarre to tolerate, and if it is, then the objections developed in this paper may well be fatal. (shrink)

Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of (...) the laws of nature, the relationships between mathematics, physical theory, and the world, and the extent to which mathematics suggests new physics.This entry begins with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern science. It then turns to the application of this concept to physics, distinguishing between two different uses of symmetry: symmetry principles versus symmetry arguments. It mentions the different varieties of physical symmetries, outlining the ways in which they were introduced into physics. Then, stepping back from the details of the various symmetries, it makes some remarks of a general nature concerning the status and significance of symmetries in physics. (shrink)

The classical field theories that underlie the quantum treatments of the electromagnetic, weak, and strong forces share a peculiar feature: specifying the initial state of the field determines the evolution of some degrees of freedom of the theory while leaving the evolution of some others wholly arbitrary. This strongly suggests that some of the variables of the standard state space lack physical content-intuitively, the space of states of such a theory is of higher dimension than the corresponding space of genuine (...) physical possibilities. The structure of such theories can helpfully be characterized in terms of the action of symmetry groups on their space of states; and the conceptual problems surrounding their strange behavior can be sharpened in light of the observation that it is usually possible to eliminate the redundant variables associated with these symmetries-which turn out to be precisely those variables whose evolution is unconstrained by the dynamical laws of the theory. This paper discusses this approach, uses it to frame questions about the interpretation of classical gauge theories, and to reflect (pessimistically) on our prospects of reaching satisfactory answers to these questions. (shrink)

I examine the link between extensionality principles of classical mereology and the anti‐symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti‐symmetry. I examine the notions of proper parthood, weak supplementation and non‐well‐foundedness. By rejecting anti‐symmetry, the anti‐extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non‐extensional mereology in which anti‐symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non‐anti‐symmetric mereology recaptures (...) all of the structure of classical mereology. (shrink)

Fearful Symmetry brings the incredible discoveries of contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how today's theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, the book describes the majestic sweep and accomplishments of twentieth-century physics. In the end, we stand in awe before the grand vision of modern physics--one of the greatest chapters in (...) the intellectual history of humankind. (shrink)

The widely held picture of dynamical symmetry as surplus structure in a physical theory has many metaphysical applications. Here, I focus on its relevance to the question of which quantities in a theory represent fundamental natural properties.

Symmetries in physics are a guide to reality. That much is well known. But what is less well known is why symmetry is a guide to reality. What justifies inferences that draw conclusions about reality from premises about symmetries? I argue that answering this question reveals that symmetry is an epistemic notion twice over. First, these inferences must proceed via epistemic lemmas: premises about symmetries in the first instance justify epistemic lemmas about our powers of detection, and only (...) from those epistemic lemmas can we draw conclusions about reality. Second, in order to justify those epistemic lemmas, the notion of symmetry must be defined partly in epistemic terms. 1 Symmetry-to-Reality Reasoning1.1 A rough introduction to symmetry1.2 The symmetry-to-reality inference1.3 Two questions1.4 Two answers1.5 Preliminary clarifications2 Against Redundancy2.1 Redundancy2.2 Is absolute velocity redundant?2.3 Some redundancies3 Against Objectivity4 From Symmetry to Detection4.1 The epistemic approach4.2 The Occamist norm4.3 From symmetry to detection5 The Meaning of ‘Symmetry’5.1 A framework5.2 Formal definitions5.3 Ontic definitions6 Epistemic Definitions6.1 Taking observation seriously6.2 How things look6.3 Observation sentences6.4 Observational equivalence7 Symmetry as an Epistemic Notion 7.1 Observational equivalence and metaphysics7.2 The Occamist norm revisted7.3 Consequences8 Conclusion. (shrink)

In an earlier Dissecting Bioethics contribution, Debra J. H. Mathews, Joseph J. Fins, and Eric Racine challenge standard ways of thinking about the therapeutic misconception in the context of consent for research participation. They propose that instead of demanding “rational congruence” between how researchers and participants conceive of a given protocol, we should accept a less stringent standard of “reasonable coherence.” While Mathews, Fins, and Racine (MFR) provide some important insights, their proposal needs refinement. There is room for a wide (...) but not unlimited range of participant hopes and motivations. However, their model of reasonable coherence is too weak a standard for whether participants have adequate understanding of the scientific goals of a protocol. By the time participants are recruited for medical research, the goals of the protocol, having been set and agreed to through accepted scientific processes, are no longer open for alternate interpretations. This paper discusses this and other objections to MFR’s proposal. It then suggests that a concept of “deal breakers” might be useful in this context. (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

A survey of the main themes and arguments concerning symmetry and invariance in physics and philosophy of physics.

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These (...) predictions were made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for the framework that generated them. I shall attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a considerably high (philosophical) price. (shrink)

Many important explanations in physics are based on ideas and assumptions about symmetries, but little has been said about the nature of such explanations. This chapter aims to fill this lacuna, arguing that various symmetry explanations can be naturally captured in the spirit of the counterfactual-dependence account of Woodward, liberalized from its causal trappings. From the perspective of this account symmetries explain by providing modal information about an explanatory dependence, by showing how the explanandum would have been different, had (...) the facts about an explanatory symmetry been different. Furthermore, the authors argue that such explanatory dependencies need not be causal. (shrink)

Given its importance in modern physics, philosophers of science have paid surprisingly little attention to the subject of symmetries and invariances, and they have largely neglected the subtopic of symmetry breaking. I illustrate how the topic of laws and symmetries brings into fruitful interaction technical issues in physics and mathematics with both methodological issues in philosophy of science, such as the status of laws of physics, and metaphysical issues, such as the nature of objectivity.

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

The relevance of symmetry to today's physics is a widely acknowledged fact. A significant part of recent physical inquiry – especially the physics concerned with investigating the fundamentalbuilding blocks of nature – is grounded on symmetry principles andtheir many and far-reaching consequences. But where these symmetries come from and what their real meaning is are open questions, at the center of a developing debate among physicists and philosophers of science. To tackle the problems arising in considering the (...) class='Hi'>symmetry issue is the main purpose of this paper. Starting with briefly recalling the bases for the discussion – how symmetry enters and operates in physics, its special effectiveness in the quantum domain and the many relevant functions it performs (Sections 1–3), the paper then focus on the general interpretative questions that arise and the sorts of answers that have been given (Section 4). (shrink)

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler–DeWitt cosmology. Furthermore, the local symmetry principle—and corresponding observables—of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of (...) the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity. (shrink)

Imagine that we are on a train playing with some mechanical systems. Why can’t we detect any differences in their behavior when the train is parked versus when it is moving uniformly? The standard answer is that boosts are symmetries of Newtonian systems. In this paper, I use the case of a spring to argue that this answer is problematic because symmetries are neither sufficient nor necessary for preserving its behavior. I also develop a new answer according to which boosts (...) preserve the relational properties on which the behavior of a system depends, even when they are not symmetries. (shrink)

It is often said in physics that if two models of a theory are related by a symmetry, then the two models provide (or could provide) two different representations of the very same situation, alike the case of two maps of different color for the very same city. It is also said that the situations represented by two models of a theory are indiscernible in some ways when the models in question are related by a symmetry of the (...) theory, just like the situation in the interior of the cabin of a train when the train is at rest in the station is empirically indiscernible from the situation in the interior when the train is moving uniformly (in classical mechanics, these two situations are represented by two models related by a boost). In recent years, philosophers of physics have focused a lot of attention in developing various principles that aim to elucidate these and similar remarks on symmetries, models, physical equivalence, and representation that are widespread in physics practice. The goal of the current article is to provide a critical review of these principles, and suggest a new framework for thinking about these kinds of questions. One important upshot of the paper is that questions of indiscernibility, and questions of the representational capacity of models, must be distinguished from one another. (shrink)

Many have thought that symmetries of a Lagrangian explain the standard laws of energy, momentum, and angular momentum conservation in a rather straightforward way. In this paper, I argue that the explanation of conservation laws via symmetries of Lagrangians involves complications that have not been adequately noted in the philosophical literature and some of the physics literature on the subject. In fact, such complications show that the principles that are commonly appealed to to drive explanations of conservation laws are not (...) generally correct without caveats. I hope here to give a clearer picture of the relationship between symmetries and conservation laws in Lagrangian mechanics via an examination of the bearing that results in the inverse problem in the calculus of variations have on this topic. (shrink)

We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries. Overall, the account meshes well with standard treatments of symmetries. But the distinction between the common core and the dual theories prompts a distinction between three kinds of symmetry: which we call ‘stipulated’, ‘accidental’ and ‘proper’.

Professional boundaries are an important aspect of social work theory and praxis – yet it is an underexplored topic within the research literature. Research often explores specific types of professional boundary issue rather than exploring social workers’ boundary stories or boundary narratives. In contrast, this qualitative study explored UK social workers’ broader understanding and experience of professional boundaries. This paper will examine one of the research themes – Humour as a boundary breaker. By using humour, social workers were able (...) to break down the boundaries that often impede effective practice. Participants also used humour to build connections with service users, colleagues and other professionals. Nonetheless, there were various aspects of this practice that raised serious issues related to power, prejudice and discrimination. This theme is important to explore because of how relevant it was for participants’ practice and because humour is also an underexplored topic within the social work literature. (shrink)

Although symmetry has been discussed in terms of a major law of perceptual organization since the early conceptual efforts of the Gestalt school (Wertheimer, Metzger, Koffka and others), the first quantitative measurements testing for effects of symmetry on processes of Gestalt formation have seen the day only recently. In this study, a psychophysical rating study and a “foreground”-“background” choice response time experiment were run with human observers to test for effects of bilateral symmetry on the perceived strength (...) of figure-ground in triangular Kanizsa configurations. Displays with and without bilateral symmetry, identical physically-specified-to-total contour ratio, and constant local contrast intensity within and across conditions, but variable local contrast polarity and variable orientation in the plane, were presented in a random order to human observers. Configurations with bilateral symmetry produced significantly stronger figure-ground percepts reflected by greater subjective magnitudes and consistently higher percentages of “foreground” judgments accompanied by significantly shorter response times. These effects of symmetry depend neither on the orientation of the axis of symmetry, nor on the contrast polarity of the physical inducers. It is concluded that bilateral symmetry, irrespective of orientation, significantly contributes to the, largely sign-invariant, visual mechanisms of figure-ground segregation that determine the salience of figure-ground in perceptually ambiguous configurations. (shrink)

Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. In this (...) overview we review the current state of affairs on both the philosophy and the physics side. In particular, we focus on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, we determine a set of yet to be answered questions to clarify the status of gauge symmetries. (shrink)

This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes this analogy: (...) in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. (shrink)

SYMMETRY IN PHYSICS: FROM PROPORTION AND HARMONY TO THE TERM OF METALENGUAJE -/- Ruth Castillo Universidad Central de Venezuela -/- The revolutionary changes in physics require a careful exploration of the way in which concepts depend on the theoretical structure in which they are immerse. A historical reconstruction allows us to show how the notion of symmetry evolves from the definition as proportion and harmony to its consideration within the language of contemporary physics, as a linguistic meta-theoretical requirement (...) in physical theories. In contemporary terms, symmetry is a fundamental category of research to which the usual categories of the natural sciences can be reduce in: space, time, causality, interaction, matter, strength, etc ... Thus, symmetry is a concept with different meanings: heuristically symmetric models inspire scientists in the search for solutions to different problems. Methodologically, symmetric structures are use to make theories, laws with invariant properties. A description of nature in terms of symmetric structures and symmetry ruptures seems to be the proper way to describe the complexity of reality. (shrink)

Here I respond to Anthony Brueckner and John Martin Fischer’s “The Evil of Death: A Reply to Yi.” They developed an influential strategy in defense of the deprivation account of death’s badness against the Lucretian symmetry problem. The core of their argument consists in the claim that it is rational for us to welcome future intrinsic goods while being indifferent to past intrinsic goods. Previously, I argued that their approach is compatible with the evil of late birth insofar as (...) an earlier birth would have generated more goods in the future. In reply, Brueckner and Fischer argue that my critique fails to appreciate an important aspect of their thought experiment, which aims only to show that the deprivation of past goods per se is not bad for us. Thus, purportedly, my critique poses no threat to their view. Here I argue that since the deprivation account explains the evil of death with recourse to how one’s life would have fared had one lived longer, it ought to respond to the symmetry problem with reference to how one’s life would have fared had one been born earlier. However, it is not generally true that the life one would have had with an earlier birth is not preferable to one’s actual life, because in many cases such a life would contain more future goods. (shrink)

Cognitive tests show that identity and symmetry reflect intellect. 'Guess of other guess' creates various symmetries, while only one is right: 'absolute symmetry', which can be outvoted by the majority. Prejudices result from differences between ME (my identity) and others. Unbiased judgement is symmetrical, always in the middle: neither in favor, nor against ME. Intelligence reduces prejudices, but the lack of opportunities can counterbalance it. That's why type of bias differs in various groups: people from war zones, people (...) in therapy, artists, etc.. "The law of values' equity" is a symmetrical principle redefining utility in economics, when people equate all their values. E.g. 2 children averagely rich, is better than one child rich and another poor. If 'a' is an average richness, and 'x' is a difference in richness, and Utility multiplies all values, then: a * a > (a - x) * (a + x), which is: a² > a² - x². It does not however imply egalitarianism, as it is still better to have both children rich than both average or poor. (shrink)

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.

The structural approach to alternatives :669–690, 2007; Fox and Katzir in Nat Lang Semant 19:87–107, 2011; Katzir in Semantics, pragmatics and the case of scalar implicatures, Palgrave Macmillan, London, pp 40–71, 2014) is the most developed attempt in the literature at solving the symmetry problem of scalar implicatures. Problematic data with indirect and particularised scalar implicatures have however been raised :249–270, 2015). To address these problems, Trinh and Haida proposed to augment the theory with the Atomicity Constraint. Here we (...) show that this constraint falls short of explaining minimal variants of the original problems, and moreover that it runs into trouble with the inferences of sentences involving gradable adjectives like full and empty. We furthermore discuss how the structural approach suffers at times from the problem of ‘too many lexical alternatives’ pointed out by Swanson :31–36, 2010), and at other times from the opposite problem of ‘too few lexical alternatives’. These three problems epitomise the challenge of constructing just enough alternatives under the structural approach to solve the symmetry problem in full generality. Finally, we also sketch another recent attempt at solving the symmetry problem, Bergen et al., 2016), which is based on relative informativity and complexity. We argue that Bergen et al. do not provide a general solution to the symmetry problem either, by pointing to some of the open problematic cases that remain for this approach as well. We conclude that while important progress has been made in the theory of alternatives for scalar implicatures in the last few years, a full solution to the symmetry problem has not yet been attained. (shrink)