I argue that the contemporary interplay of cosmology and particle physics in their joint effort to understand the processes at work during the first moments of the big bang has important implications for understanding the nature of lawhood. I focus on the phenomenon of spontaneous symmetry breaking responsible for generating the masses of certain particles. This phenomenon presents problems for the currently fashionable Dretske-Tooley-Armstrong theory and strongly favors a rival nomic ontology of causal powers.

We argue the thesis that if (1) a physical process is mathematically representable by a Cauchy sequence; and (2) we accept that there can be no infinite processes, i.e., nothing corresponding to infinite sequences, in natural phenomena; then (a) in the absence of an extraneous, evidence-based, proof of `closure' which determines the behaviour of the physical process in the limit as corresponding to a `Cauchy' limit; (b) the physical process must tend to a discontinuity (singularity) which has not been reflected (...) in the Cauchy sequence that seeks to describe the behaviour of the physical process. We support our thesis by mathematical models of the putative behaviours of (i) a virus cluster; (ii) an elastic string; and (iii) a Universe that recycles from Big Bang to Ultimate Implosion, in which parity and local time reversal violation, and the existence of `dark energy' in a multiverse, need not violate Einstein's equations and quantum theory. We suggest that the barriers to modelling such processes in a mathematical language that seeks unambiguous communication are illusory; they merely reflect an attempt to ask of the language chosen for such representation more than it is designed to deliver. (shrink)

At the heart of chemistry lies the periodic system of chemical elements. Despite being the cornerstone of modern chemistry, the overall structure of the periodic system has never been fully understood from an atomic physics point of view. Group-theoretical models have been proposed instead, but they suffer from several limitations. Among others, the identification of the correct symmetry group and its decomposition into subgroups has remained a problem to this day. In an effort to deepen our limited understanding of the (...) periodic law, we have extended the traditional Lie algebraic framework to account for the peculiar degeneracy structure of the periodic system. Starting from the four-dimensional hidden symmetry and accidental degeneracy of the hydrogen atom, as first revealed by Fock in 1935, our research has mainly focussed on the way this SO(4) symmetry of the Coulomb potential gets broken in the periodic system as a consequence of the transformation of the hydrogenic (n, l) filling order to the Madelung (n+l, n) order due to electronic repulsions, relativistic effects and spin-orbit couplings. In this PhD dissertation, a new left-step format of the periodic table is first proposed on the basis of the Madelung rule. Following the particle physics tradition, the chemical elements are then considered as various states of some 'atomic matter', which is described by a non-compact spectrum-generating dynamical Lie group. The chemical elements are shown to form a basis for a single infinite-dimensional degeneracy space of the SO(4,2) ⊗ SU(2) group. An explanation for the period doubling is then proposed in terms of a particular symmetry breaking of the SO(4,2) group to the anti de Sitter SO(3,2) group. The Madelung rule is rationalised on the basis of nonlinear Lie algebras which reflect the screening of the Coulomb hole. This opens new perspectives for a symmetry-based understanding of how the periodic law emerges from its quantum mechanical foundations, and holds the future promise of complementing our current phenomenological approach by a direct atomic physics approach. (shrink)

The answer to some of the longstanding issues in the 20th century theoretical physics, such as those of the incompatibility between general relativity and quantum mechanics, the broken symmetries of the electroweak force acting at the subatomic scale and the missing mass of Higgs particle, and also those of the cosmic singularity and the black matter and energy, appear to be closely related to the problem of the quantum texture of space-time and the fluctuations of its underlying geometry. (...) Each region of space landscape seem to be filled with spacetime weaved and knotted networks, for example, spacetime has immaterial curvature and structures, such as topological singularities, and obeys the laws of quantum physics. Thus, it is filled with potentialparticles, pairs of virtual matter and anti-matter units, and potential properties at the quantum scale. For example, quantum entities (like fields and particles) have both wave (i.e., continuous) and particle (i.e., discrete) properties and behaviors. At the quantum level (precisely, the Planck scale) of space-time such properties and behaviors could emerge from some underlying (dynamic) phase space related to some field theory. Accordingly, these properties and behaviors leave their signature on objects and phenomena in the real Universe. In this paper we consider some conceptual issues of this question. (shrink)

Ruetsche ([2011]) argues that the occurrence of unitarily inequivalent representations in quantum theories with infinitely many degrees of freedom poses a novel interpretational problem. According to Ruetsche, such theories compel us to reject the so-called ideal of pristine interpretation; she puts forward the ‘coalescence approach’ as an alternative. In this paper I offer a novel defence of the coalescence approach. The defence rests on the claim that the ideal of pristine interpretation already fails before one considers the peculiarities of QM∞: (...) there are pre-QM∞ parallels to coalescence. Despite this departure from pristinism, the ‘modest’ view that emerges poses no threat to scientific realism. (shrink)

A primary argument against the badness of death (known as the Symmetry Argument) appeals to an alleged symmetry between prenatal and posthumous nonexistence. The Symmetry Argument has posed a serious threat to those who hold that death is bad because it deprives us of life’s goods that would have been available had we died later. Anthony Brueckner and John Martin Fischer develop an influential strategy to cope with the Symmetry Argument. In their attempt to break the symmetry, they claim that (...) due to our preference of future experiential goods over past ones, posthumous nonexistence is bad for us, whereas prenatal nonexistence is not. Granting their presumption about our preference, however, it is questionable that prenatal nonexistence is not bad. This consideration does not necessarily indicate their defeat against the Symmetry Argument. I present a better response to the Symmetry Argument: the symmetry is broken, not because posthumous nonexistence is bad while prenatal nonexistence is not, but because (regardless as to whether prenatal nonexistence is bad) posthumous nonexistence is even worse. (shrink)

The evil God challenge is an argumentative strategy that has been pursued by a number of philosophers in recent years. It is apt to be understood as a parody argument: a wholly evil, omnipotent and omniscient God is absurd, as both theists and atheists will agree. But according to the challenge, belief in evil God is about as reasonable as belief in a wholly good, omnipotent and omniscient God; the two hypotheses are roughly epistemically symmetrical. Given this symmetry, thesis belief (...) in an evil God and belief in a good God are taken to be similarly preposterous. In this paper, we argue that the challenge can be met, suggesting why the three symmetries that need to hold between evil God and good God – intrinsic, natural theology and theodicy symmetries – can all be broken. As such, we take it that the evil God challenge can be met. (shrink)

Significant variations in the way objects appear across different viewing conditions pose a challenge to the view that they have some true, determinate color. This view would seem to require that we break the symmetry between multiple appearances in favor of a single variant. A wide range of philosophical and non-philosophical writers have held that the symmetry can be broken by appealing to daylight viewing conditions—that the appearances of objects in daylight have a stronger, and perhaps unique, claim to (...) reveal their true colors. In this note we argue that, whatever else its merits, this appeal to daylight is not a satisfactory answer to the problem posed by perceptual variation. (shrink)

> Context • The alleged dichotomy between mind and matter is pervasive. Therefore, the attempt to explain mat- ter in terms of mind (idealism) is often considered a mirror image of that of explaining mind in terms of mat- ter (mainstream physicalism), in the sense of being structurally equivalent despite being reversely arranged. > Problem • I argue that this is an error arising from language artifacts, for dichotomies must reside in the same level of abstraction. > Method • I (...) show that, because matter outside mind is not an empirical observation but rather an explanatory model, the epistemic symmetry between the two is broken. Consequently, matter and mind cannot reside in the same level of abstraction. > Results • It then becomes clear that attempting to explain mind in terms of matter is epistemically more costly than attempting to explain matter in terms of mind. > Implications • The qualities of experience are suggested to be not only epistemically, but also ontologically primary. > Constructivist content • I high- light the primacy of perceptual constructs over explanatory abstraction on both epistemic and ontic levels. > Key words • Idealism, physicalism, pancomputationalism, anti-realism, hard problem of consciousness, epistemic symmetry, explanatory abstraction, levels of abstraction. (shrink)

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)

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)

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)

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)

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)

The modal ontological argument (MOA) proceeds from God’s possible existence to God’s actual existence. A prominent objection to the MOA is that it suffers from a symmetry problem: an exactly parallel modal ontological argument can be given for God's non-existence. Several attempts have been made to break the symmetry between the arguments. This draft is a mostly comprehensive survey of those attempts. -/- The draft was initially written as a supplement to the 2024 Summer edition of the SEP entry on (...) Ontological Arguments. However, the draft is not included in the SEP entry. (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.

Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. To this (...) end, we exploit a neural network metric in the output of a biologically inspired Self- Organizing Map Quantization Error (SOM-QE). Shape pairs with perfect geometry mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within and/or across the shapes in a given pair produce, as shown here, a longer choice response time (RT) for “yes” responses relative to symmetry. These data are consistently mirrored by the variations in the SOM-QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data. (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)

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)

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)

In addressing the Lucretian symmetry problem, the content-based approach attends to the difference between the contents of the actual life and those of relevant possible lives of a person. According to this approach, the contents of a life with an earlier beginning would substantially differ from, and thus be discontinuous with, the contents of the actual life, whereas the contents of a life with the same beginning but a later death would be continuous with the contents of the actual life. (...) In this paper, I examine two versions of the content-based approach: the identity account and the preference account. The identity account holds that, in the sense of identity which is relevant to the evil of nonexistence, the subject of the actual life, though identical to the person in the life with a later death, is distinct from the subject of the life with an earlier beginning. The preference account maintains that, given one’s attachments to actual particulars, a life with an earlier beginning is not rationally preferable to one’s actual life, whereas a life with a later death is. I argue that each version of the content-based approach is implausible, while discussing some of the complications that face each of them. (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)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations that (...) are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

In this paper I contend that the 'superfluity' of triangles is only apparent; all those specified are indeed required for the smallest sub-units, so long as the symmetry of the final body to be constructed is taken into account at earlier stages.

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)

There are many possible definitions of “technology” and I will discuss some of these in this book. However, in this introduction let me use a definition of Svante Lindqvist who defines technology very intuitively as “those activities, directed towards the satisfaction of human wants, which produce change in the material world.” He says also “the distinction between human “wants” and more limited human “needs” is crucial, for we do not use technology only to satisfy our essential material requirements.” Consequently, from (...) this perspective, a technology that is “broken” could be defined as those activities, directed towards the satisfaction of human wants that are intended to produce changes in the material world that either do not manage to satisfy these wants or do not produce changes in the material world, or both. This is the third edition, updated October 2015. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. 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 (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “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)

I critically examine the assumption that the theoretical structure that varies under theoretical symmetries is redundant and should be eliminated from a metaphysical picture of the universe, following a ‘symmetry to reality’ inference. I do so by analysing the status of coordinate change symmetries taking a pragmatic approach. I argue that coordinate systems function as indexical devices, and play an important pragmatic role for representing concrete physical systems. I examine the implications of considering this pragmatic role seriously, taking (...) what I call a perspectivist stance. My conclusion is that under a perspectivist stance, all symmetries (including local gauge symmetries) potentially have a direct empirical status: they point to dynamical aspects that are invariant under changes of operationalisation, and they constitute a guide not to reality, but to nomology and kinship. (shrink)

Path-dependence offers a promising way of understanding the role historicity plays in explanation, namely, how the past states of a process can matter in the explanation of a given outcome. The two main existing accounts of path-dependence have sought to present it either in terms of dynamic landscapes or branching trees. However, the notions of landscape and tree both have serious limitations and have been criticized. The framework of causal networks is both more fundamental and more general that that of (...) landscapes and trees. Within this framework, I propose that historicity in networks should be understood as symmetry breaking. History matters when an asymmetric bias towards an outcome emerges in a causal network. This permits a quantitative measure for how path-dependence can occur in degrees, and offers suggestive insights into how historicity is intertwined both with causal structure and complexity. (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)

This is a study of the correspondence between Forms and particulars in Plato. The aim is to determine whether they exhibit an ontological symmetry, in other words, whether there is always one where there is the other. This points to two questions, one on the existence of things that do not have corresponding Forms, the other on the existence of Forms that do not have corresponding things. Both questions have come up before. But the answers have not been sufficiently sensitive (...) to the intricacies of the questions. Nor have they been adequately resourceful with what little evidence there is in the original sources. The intention here is to make up for that deficiency, not just with better answers but also with better insight into the questions. (shrink)

A prima facie plausible and widely held view in epistemology is that the epistemic standards governing the acquisition of testimonial knowledge are stronger than the epistemic standards governing the acquisition of perceptual knowledge. Conservatives about testimony hold that we need prior justification to take speakers to be reliable but recognise that the corresponding claim about perception is practically a non-starter. The problem for conservatives is how to establish theoretically significant differences between testimony and perception that would support asymmetrical epistemic standards. (...) In this paper I defend theoretical symmetry of testimony and perception on the grounds that there are no good reasons for taking these two belief forming methods to have significant theoretical differences. I identify the four central arguments in defence of asymmetry and show that in each case either they fail to establish the difference that they purport to establish or they establish a difference that is not theoretically significant. (shrink)

This paper outlines a defense of hybrid contingentism: that it is contingent which individuals there are, but not contingent what properties there are. Critics pursue two main lines of complaint. First, that the hybrid contingentist’s treatment of haecceitistic properties is metaphysically mysterious, and second, that hybrid contingentism involves an unjustified asymmetry in the associated modal logic. I suggest that these complaints may be too quick, at least in the setting of higher-order metaphysics. It is not at all obvious whether and (...) to what extent we should expect particular "symmetries" across the orders, and so whether (as Williamson (2013) argues) “the default preference is for a uniform metaphysics, on which being is contingent at all orders or none.”. (shrink)

On the broken myth in the philosophy of religion and theology Abstract. The article deals with the concept of broken myth, thus named by the German theologian and philosopher Paul Tillich (1886 - 1965). The thesis related to this concept is that all religions, including Christianity, use a mythical language. This language is expressing moral truths and metaphysical intuitions, but not the objective facts and states of affairs that may provide knowledge. The broken myth does not imply (...) the rejection of myth as a mere untruth, but rather its split into untruth, which is the garment of the story understood literally, and truth, which is (although not always and to varying degrees) a moral and spiritual inspiration. The broken myth is self-aware, but not discredited. The author formulates six reasons that can speak in favor of such view. He believes that its acceptance by the community of believers can be very difficult, so the traditional discourse of faith, in which one understands literally credo articles (including the notions of mystery and analogy), must be considered not as an anachronism, but as an autonomous partner of dialogue. -/- . (shrink)

Recently, there has been an increased interest in employing model-based definitions of actual causation in legal inquiry. The formal precision of such approaches promises to be an improvement over more traditional approaches. Yet model-based approaches are viable only if suitable models of legal cases can be provided, and providing such models is sometimes difficult. I argue that causal-model-based definitions benefit legal inquiry in an indirect way. They make explicit the causal assumptions that need to be made plausible to defend a (...) particular claim of actual causation. My argument concerns the analysis of legal cases involving a combination of double prevention and causal redundancy. I show that discussions among legal theorists about such cases sometimes suffer from ambiguous assumptions about the causal structure. My account illustrates that causal models can act as a heuristic tool for clarifying such assumptions, and that causal models provide a framework for more accurate analyses of legal cases involving complex causal structure. (shrink)

Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail. The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion and (...) the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality. (shrink)

Noether's Theorem produces the configuration (and symmetry) for everything in Nature.

Mathematically, gauge theories are extraordinarily rich --- so rich, in fact, that it can become all too easy to lose track of the connections between results, and become lost in a mass of beautiful theorems and properties: indeterminism, constraints, Noether identities, local and global symmetries, and so on. -/- One purpose of this short article is to provide some sort of a guide through the mathematics, to the conceptual core of what is actually going on. Its focus is on (...) the Lagrangian, variational-problem description of classical mechanics, from which the link between gauge symmetry and the apparent violation of determinism is easy to understand; only towards the end will the Hamiltonian description be considered. -/- The other purpose is to warn against adopting too unified a perspective on gauge theories. It will be argued that the meaning of the gauge freedom in a theory like general relativity is (at least from the Lagrangian viewpoint) significantly different from its meaning in theories like electromagnetism. The Hamiltonian framework blurs this distinction, and orthodox methods of quantization obliterate it; this may, in fact, be genuine progress, but it is dangerous to be guided by mathematics into conflating two conceptually distinct notions without appreciating the physical consequences. (shrink)

This article examines the British colonial theft of Indigenous sovereignty and the particular obstacles that it presents to establishing just social relations between the colonizer and the colonized in settler states. In the first half, I argue that the particular nature of the crime of sovereign theft makes apologies and reparations unsuitable policy tools for reconciliation because Settler societies owe their very existence to the abrogation of Indigenous sovereignties. Instead, Settler states ought to return sovereignty to the land’s Indigenous peoples. (...) In the second half of this paper, I take up some of the practical questions of how this might be done and anticipate a number of objections. Giving up sovereignty would not mean dispossessing the millions of colonists who currently reside in these countries of their homes and property – but it does mean rethinking the constitutional makeup of a country and how that serves to benefit the different peoples who make their homes there. (shrink)

Recognition of the plasticity of development — from gene expression to neuroplasticity — is increasingly undermining the traditional distinction between structure and function, or anatomy and behavior. At the same time, dynamic systems theory — a set of tools and concepts drawn from the physical sciences — has emerged as a way of describing what Maurice Merleau-Ponty calls the “dynamic anatomy” of the living organism. This article surveys and synthesizes dynamic systems models of development from biology, neuroscience, and psychology in (...) order to propose an integrated account of growth, learning, and behavior. Key to this account is the concept of self-differentiation or symmetry-breaking. I argue that development can be understood as a cascade of symmetry-breaking events brought about by the ongoing interactions of multiple, nested, nonlinear dynamic systems whose self-organizing behaviors gradually alter their own anatomical conditions. I begin by introducing the concept of symmetry-breaking as a way of understanding anatomical development. I then extend this approach to motor development by arguing that the organism’s behavior grows along with its body, like a new organ. Finally, I argue that the organism’s behavior and its world grow together dialectically, each driving the other to become more complex and asymmetrical through its own increasing asymmetry. Thus development turns out to be a form of cognition or sense-making, and cognition a form of development. (shrink)

One of the most influential arguments against the claim that computers can think is that while our intentionality is intrinsic, that of computers is derived: it is parasitic on the intentionality of the programmer who designed the computer-program. Daniel Dennett chose a surprising strategy for arguing against this asymmetry: instead of denying that the intentionality of computers is derived, he endeavours to argue that human intentionality is derived too. I intend to examine that biological plausibility of Dennett’s suggestion and show (...) that Dennett’s argument for the claim that human intentionality is derived because it was designed by natural selection is based on the misunderstanding of how natural selection works. (shrink)

Today, there is a family of celebrated police strategies that teach the importance of cracking down on petty crime and urban nuisance as the key to effective crime control. Under the “broken windows” appellation, this strategy is linked in the public mind with New York City and the alleged successes of its police department in reducing the rate of crime over the past two decades. This paper is critical of such order maintenance approaches to policing: I argue that infringements (...) of civil liberty by such departments could be reduced if the departments looked at law more as a good to be served for its own sake and less as an instrument for the promotion of order. In other words, a shot of legalism is the correct medicine to reduce police misconduct that pierces the law’s protections of citizen freedom. -/- This Article contributes to the critical literature on broken windows policing by reassessing the work of the famous Harvard scholar (James Q. Wilson) who fathered it. The Article takes Wilson’s work and turns it on its head, drawing very different prescriptive conclusions than he did himself. (shrink)

Many philosophers have wrongly assumed that there is an asymmetry between the problem of induction and the logocentric predicament (the justification of deductive inferences). This paper will show that the demand for justification, for the very inferences that are required for justification, is deeply problematic. Using a Wittgensteinian approach, I will argue that justification has an internal relation with deductive and inductive inferences. For Wittgenstein, two concepts are internally related if my understanding of one is predicated on my understanding of (...) the other. Separating the two concepts so that one can be applied to the other is then a misunderstanding of role that these concepts play. (shrink)

Mathematicians, physicists, and philosophers of physics often look to the symmetries of an object for insight into the structure and constitution of the object. My aim in this paper is to explain why this practice is successful. In order to do so, I present a collection of results that are closely related to (and in a sense, generalizations of) Beth’s and Svenonius’ theorems.

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)

Physicists routinely claim that the fundamental laws of physics are 'time symmetric' or 'time reversal invariant' or 'reversible'. In particular, it is claimed that the theory of quantum mechanics is time symmetric. But it is shown in this paper that the orthodox analysis suffers from a fatal conceptual error, because the logical criterion for judging the time symmetry of probabilistic theories has been incorrectly formulated. The correct criterion requires symmetry between future-directed laws and past-directed laws. This criterion is formulated and (...) proved in detail. The orthodox claim that quantum mechanics is reversible is re-evaluated. The property demonstrated in the orthodox analysis is shown to be quite distinct from time reversal invariance. The view of Satosi Watanabe that quantum mechanics is time asymmetric is verified, as well as his view that this feature does not merely show a de facto or 'contingent' asymmetry, as commonly supposed, but implies a genuine failure of time reversal invariance of the laws of quantum mechanics. The laws of quantum mechanics would be incompatible with a time-reversed version of our universe. (shrink)

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some (...) detail. However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory. (shrink)

When beliefs are quantified as credences, they are related to each other in terms of closeness and accuracy. The “accuracy first” approach in formal epistemology wants to establish a normative account for credences based entirely on the alethic properties of the credence: how close it is to the truth. To pull off this project, there is a need for a scoring rule. There is widespread agreement about some constraints on this scoring rule, but not whether a unique scoring rule stands (...) above the rest. The Brier score equips credences with a structure similar to metric space and induces a “geometry of reason.” It enjoys great popularity in the current debate. I point out many of its weaknesses in this article. An alternative approach is to reject the geometry of reason and accept information theory in its stead. Information theory comes fully equipped with an axiomatic approach which covers probabilism, standard conditioning, and Jeffrey conditioning. It is not based on an underlying topology of a metric space, but uses a non-commutative divergence instead of a symmetric distance measure. I show that information theory, despite initial promise, also fails to accommodate basic epistemic intuitions; and speculate on its remediation. (shrink)

From his earliest work forward, phenomenologist Maurice Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own intrinsic sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up (...) Merleau-Ponty’s ontology as the basis for a new, “enactive” approach to cognitive science, synthesizing it with concepts from dynamic systems theory and Francisco Varela’s theory of autopoiesis. However, Thompson does not quite succeed in resolving the ambiguities in Merleau-Ponty’s account of form. This article builds on an indication from Thompson in order to propose a new account of form as asymmetry, and of the genesis of form in nature as symmetry-breaking. These concepts help us to escape the antinomies of Modern thought by showing how nature is the autoproduction of a sense which can only be known by an embodied perceiver. (shrink)