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)

Understanding the events that led to the emergence of the bilaterians is a daunting task, impaired by the huge evolutionary gap separating us from the pre‐Cambrian. During gastrulation, the expression of the transcription factor Brachyury is remarkably well conserved around the blastopore of bilaterians and cnidarians. Only the bilaterian Brachyury proteins, however, share a distinctive N‐terminal sequence not found in outgroups such as cnidarians, sponges or placozoans. We now know that, in vertebrates, this N‐terminal domain confers specific transcriptional activity, by (...) recruiting Smad1, the first identified co‐factor for Brachyury. Smad1 is an effector of the BMP pathway, and has been isolated in bilaterians and cnidarians. Here, I propose that the protein–protein interaction between Brachyury and Smad1 represents an evolutionary novelty of the Urbilateria. The gain of the N‐terminal domain might have been selected to spatially modulate the activity of Brachyury, thereby facilitating the establishment of bilateral symmetry during gastrulation movements. BioEssays 28: 413–420, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

The standard explanation for the origin of bilateral symmetry is that it conferred an advantage over radial symmetry for directed locomotion. However, recent developmental and phylogenetic studies suggest that bilateral symmetry may have evolved in a sessile benthic animal, predating the origin of directed locomotion. An evolutionarily feasible alternative explanation is that bilateral symmetry evolved to improve the efficiency of internal circulation by affecting the compartmentalization of the gut and the location of major (...) ciliary tracts. This functional design principle is illustrated best by the phylum Cnidaria where symmetry varies from radial to tetraradial, biradial and bilateral. In the Cnidaria, bilateral symmetry is manifest most strongly in the internal anatomy and the disposition of ciliary tracts. Furthermore, the bilaterally symmetrical Cnidaria are typically sessile and, in those bilaterally symmetrical cnidarians that undergo directed locomotion, the secondary body axis does not bear a consistent orientation to the direction of locomotion as it typically does in Bilateria. Within the Cnidaria, the hypothesized advantage of bilateral symmetry for internal circulation can be tested by experimental analysis and computer modeling of fluid mechanics. The developmental evolution of symmetry within the Cnidaria can be further explored through comparative gene expression studies among species whose symmetry varies. BioEssays 27:1174–1180, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

Plants are considered as archetypes of the ramification phenomenon but numerous elementary processes occur in the elaboration of the shaping of each species. This paper aims to identify the part ascribed to different mechanisms in the morphogenesis of a Thallophyte, the red alga Antihamnion plumula.Agonistic-antagonistic models (Bernard-Weil, 1988) can be applied to this alga whose thallus includes two different kinds of whorls, pleuridian and cladomian. In each whorl the agonistic and antagonistic effects are expressed by the full development (S) of (...) the two branches and by their symmetry rate (R) respectively. Variations in S and R show the existence of particular pleuridian whorls having an intermediary dissymmetry and a rhythmic arrangement similarly to that of the cladomian whorls. A unilateral change of the system (removal of a lateral cladome) induces a transitory destabilisation mainly manifested by the stimulating ascendant flow throughout the thallus. (shrink)

Population-level asymmetry may be maintained, not by an “evolutionarily stable strategy” pitting a dominant bias against its nondominant opposite, but rather by a genetically based system pitting a directional bias against the absence of any such bias. Stability is then achieved through a heterozygotic advantage, maintaining balanced polymorphism. This model may better capture the fundamental trade-off between lateralization and bilateral symmetry.

Whether designing animals, insects, or plants, Nature draws upon symmetry and periodicity to play a fundamental role in defining the body plan. When implemented with the proper chemical mechanisms, these principles guide our bodies from single-celled embryos to bilaterally symmetric creatures with intricate periodic structures, such as the spine and rib cage. The properties of symmetry and periodicity also appear to be fundamental to visual perception. We will show that this is no coincidence, but is a consequence of (...) the fact that these properties are generated by the same underlying phenomenon, standing wave patterns formed from harmonic resonances. The symmetry in life forms arises from chemical harmonic resonances, whereas the symmetry in visual perception arises from harmonic resonances in the visual system. We will show that harmonic resonances have very interesting properties for the representation of geometrical form that make them eminently suitable for encoding geometric form for body plans as well as for visual perception. In particular, we will show that by being simultaneously invariant to perspective transformation and robust to deformation, such resonant representations have fundamental advantages over more traditional techniques. (shrink)

A specific mapping mechanism is defined as the basic unit of “Biological Memory”. This mechanism must account for the characteristic frequency patterns in the organic world, where future probability is a function of past experience. The conditions for the function of biological memory are analysed. It is found that asymmetry, and irreversibility as a consequence of complexity, are the basic principles of memory function. The essential asymmetries in genetic memory are pointed out, and the problem of bilateral symmetry (...) in a basically asymmetrical organization is briefly outlined.Complexity is defined in terms of symmetry. The thermodynamic arrow of time and the biological arrow of time are discussed in relation to elementarity and complexity with their specific types of repeatabilities: non-accumulative in the first case and accumulative as a result of “copy-reproduction” by memory in the second case. The application of terminology from Information Theory and Thermodynamics to Memory Mechanics is critically considered.The immediate and inevitable consequences of memory function are shown to be irreversible expansion and irreversible, unpredictable diversification, leading to growing complexity and size on all but the sub-molecular levels of biological structure. (shrink)

It is hypothesized that human faces judged to be attractive by people possess two features—averageness and symmetry—that promoted adaptive mate selection in human evolutionary history by way of production of offspring with parasite resistance. Facial composites made by combining individual faces are judged to be attractive, and more attractive than the majority of individual faces. The composites possess both symmetry and averageness of features. Facial averageness may reflect high individual protein heterozygosity and thus an array of proteins to (...) which parasites must adapt. Heterozygosity may be an important defense of long-lived hosts against parasites when it occurs in portions of the genome that do not code for the essential features of complex adaptations. In this case heterozygosity can create a hostile microenvironment for parasites without disrupting adaptation. Facial bilateral symmetry is hypothesized to affect positive beauty judgments because symmetry is a certification of overall phenotypic quality and developmental health, which may be importantly influenced by parasites. Certain secondary sexual traits are influenced by testosterone, a hormone that reduces immunocompetence. Symmetry and size of the secondary sexual traits of the face (e.g., cheek bones) are expected to correlate positively and advertise immunocompetence honestly and therefore to affect positive beauty judgments. Facial attractiveness is predicted to correlate with attractive, nonfacial secondary sexual traits; other predictions from the view that parasite-driven selection led to the evolution of psychological adaptations of human beauty perception are discussed. The view that human physical attractiveness and judgments about human physical attractiveness evolved in the context of parasite-driven selection leads to the hypothesis that both adults and children have a species-typical adaptation to the problem of identifying and favoring healthy individuals and avoiding parasite-susceptible individuals. It is proposed that this adaptation guides human decisions about nepotism and reciprocity in relation to physical attractiveness. (shrink)

The flowers of the primitive angiosperm plants were radially symmetrical (actinomorphic). Flowers with bilateral symmetry (zygomorphic) evolved in several clades independently as an adaptation to specialized methods of pollination and played an important role in the diversification of flowering plants. In the model species Antirrhinum majus (snapdragon), the related genes CYCLOIDEA (CYC) and DICHOTOMA (DICH) are key in the development of this trait. This raises the question of whether they played a role in the evolution of floral (...) class='Hi'>bilateral symmetry. To address this, the evolution of CYC in relation to the evolution of zygomorphy is being investigated. Phylogenetic and functional analyses of CYC‐like genes are being carried out in groups either closely related to Antirhinum or in families where zygomorphy evolved as an independent event. In addition, the origin of zygomorphy is being studied by comparing the function of CYC‐like genes in species with zygomorphic flowers with their function in species with radially symmetrical flowers. BioEssays 26:1175–1184, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

Metazoa are one of the great monophyletic groups of organisms. They comprise several major groups of organisms readily recognizable based on their anatomy. These major groups include the Bilateria (animals with bilateral symmetry), Cnidaria (jellyfish, corals and other closely related animals), Porifera (sponges), Ctenophores (comb jellies) and a phylum currently made up of a single species, the Placozoa. Attempts to systematize the relationships of these major groups as well as to determine relationships within the groups have been made (...) for nearly two centuries. Many of the attempts have led to frustration, because of a lack of resolution between and within groups. Other attempts have led to “a new animal phylogeny”. Now, a study by Dunn et al.,1 using the expresssed sequence tag (EST) approach to obtaining high‐throughput large phylogenetic matrices, presents an “even newer” animal phylogeny. There are two major aspects of this study that should be of interest to the general biological community. First, the methods used by the authors to generate their phylogenetic hypotheses call for close examination. Second, the relationships of animal taxa in their resultant trees also prompt further discussion. BioEssays 30:1043–1047, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

In 1891 Cambridge biologist William Bateson (1861–1926) announced his idea that the symmetrical segmentation in living organisms resulted from energy peaks of some vibratory force acting on tissues during morphogenesis. He also demonstrated topographically how folding a radially symmetric organism could produce another with bilateral symmetry. Bateson attended many lectures at the Cambridge Philosophical Society and viewed mechanical models prepared by eminent physicists that illustrated how vibrations affected materials. In his subsequent research, Bateson utilized analogies and metaphors based (...) upon his observations of nature to build a thought model on the effects of vibrations on living tissue, because he realized that the chemistry and biology of his day lacked technologies to perform actual experiments on the subject. He concluded the production of organic segmentation was both a chemical and mechanical phenomenon. By the time of his death Bateson had incorporated new ideas about embryonic organizer regions to suggest a center from which a rhythmic force emanated and then produced the observed repetitive segmentation as a common feature in living organisms. (shrink)

I BEGIN WITH A PUZZLE of sorts. Time is one; space is two—at least two. Time comes always already unified, one time. Thus we say “What time is it now?” and not “Which time is it now?” We do not ask, “What space is it?” Yet we might ask: “Which space are we in?”. Any supposed symmetry of time and space is skewed from the start. If time is self-consolidating—constantly gathering itself together in coherent units such as years or (...) hours or semesters or seasons— space is self-proliferating. Take, for example, the dimensionality of space. One dimension in space is represented by a point or a line, whose radically reduced format mocks the extensiveness of cosmic space. Two dimensions, as in a plane figure, also falls far short of our sense that space spreads out indefinitely far beyond the perceiving subject. Only with three dimensions do we begin to approach an adequation between the structure and the sense of space. For then the subject is surrounded by something sufficiently roomy in which to live and move. Indeed, as Aristotle, Kant, and Merleau-Ponty all remark, the three-dimensionality of space directly reflects our bodily state, that is, the fact that as upright beings three perpendicular planes implicitly meet and intersect in us. Even here, proliferation abounds: our bilateral symmetry means that each dimension is doubled: one vertical plane bifurcates into “up” and “down,” the other vertical plane into “front” and “back,” and the horizontal plane into “right” and “left.” Thus subject-centered space is triple, only to be redoubled. Further, if we think of spatiality not as body-based but as locatory—as determined by landmarks and other locales in the environment—the proliferation is more striking still. There are the four cardinal directions, which themselves split easily into the thirty two points of a compass. Nor need we be so arithmetically well-rounded. Even apart from fancy mathematical models of n –dimensional space, and recent technological instantiations of virtual space, there is no end to the number or ways in which we can be oriented in space—in accordance with what Deleuze and Guattari call “the variability, the polyvocity of directions” by which we can move in any given spatial scene. Beyond direction, however, is place. Heidegger remarks that “space has been split up into places.” The fact is that we continually find ourselves immersed in a multiplex spatial network whose nodal points are supplied by particular places. If space is infinitely large, place is indefinitely many. (shrink)

I BEGIN WITH A PUZZLE of sorts. Time is one; space is two—at least two. Time comes always already unified, one time. Thus we say “What time is it now?” and not “Which time is it now?” We do not ask, “What space is it?” Yet we might ask: “Which space are we in?”. Any supposed symmetry of time and space is skewed from the start. If time is self-consolidating—constantly gathering itself together in coherent units such as years or (...) hours or semesters or seasons— space is self-proliferating. Take, for example, the dimensionality of space. One dimension in space is represented by a point or a line, whose radically reduced format mocks the extensiveness of cosmic space. Two dimensions, as in a plane figure, also falls far short of our sense that space spreads out indefinitely far beyond the perceiving subject. Only with three dimensions do we begin to approach an adequation between the structure and the sense of space. For then the subject is surrounded by something sufficiently roomy in which to live and move. Indeed, as Aristotle, Kant, and Merleau-Ponty all remark, the three-dimensionality of space directly reflects our bodily state, that is, the fact that as upright beings three perpendicular planes implicitly meet and intersect in us. Even here, proliferation abounds: our bilateral symmetry means that each dimension is doubled: one vertical plane bifurcates into “up” and “down,” the other vertical plane into “front” and “back,” and the horizontal plane into “right” and “left.” Thus subject-centered space is triple, only to be redoubled. Further, if we think of spatiality not as body-based but as locatory—as determined by landmarks and other locales in the environment—the proliferation is more striking still. There are the four cardinal directions, which themselves split easily into the thirty two points of a compass. Nor need we be so arithmetically well-rounded. Even apart from fancy mathematical models of n –dimensional space, and recent technological instantiations of virtual space, there is no end to the number or ways in which we can be oriented in space—in accordance with what Deleuze and Guattari call “the variability, the polyvocity of directions” by which we can move in any given spatial scene. Beyond direction, however, is place. Heidegger remarks that “space has been split up into places.” The fact is that we continually find ourselves immersed in a multiplex spatial network whose nodal points are supplied by particular places. If space is infinitely large, place is indefinitely many. (shrink)

According to Greimas, the semiotic square is far more than a heuristic for semantic and literary analysis. It represents the generative “deep structure” of human culture and cognition which “define the fundamental mode of existence of an individual or of a society, and subsequently the conditions of existence of semiotic objects” (Greimas & Rastier 1968: 48). The potential truth of this hypothesis, much less the conditions and implications of taking it seriously (as a truth claim), have received little attention in (...) the literature. In response, this paper traces the history and development of the logical square of opposition from Aristotle to Greimas and beyond, to propose that the relations modelled in these diagrams are embodied relations rooted in gestalt memories of kinesthesia and proprioception from which we derive basic structural awareness of opposition and contrast such as verticality, bilaterality, transversality, markedness and analogy. To make this argument, the paper draws on findings in the phenomenology of movement (Sheets-Johnstone 2011a, 2011b, 2012, Pelkey 2014), recent developments in the analysis of logical opposition (Beziau & Payette 2008), recent scholarship in (post)Greimasian semiotics (Corso 2014, Broden 2000) and prescient insights from Greimas himself (esp. 1968, 1984). The argument of the paper is further supported through a visual and textual content analysis of a popular music video, both to highlight relationships between the semiotic square and mundane cultural ideologies and to show how these relationships might be traced to the marked symmetries of bodily movement. In addition to illustrating the enduring relevance of Greimasean thought, the paper further illustrates the neglected relevance that embodied chiasmus holds for developments in anthropology, linguistics and the other cognitive sciences. (shrink)

The early evolutionary history of echinoderms was reconstructed on the basis of structural-functional considerations and application of the quasi-engineering approach of ‘Konstruktions-Morphologie’. According to the presented evolutionary scenario, a bilaterally symmetrical ancestor, such as an enteropneust-like organism, became gradually modified into a pentaradial echinoderm by passing through an intermediate pterobranch-like stage. The arms of a pentaradial echinoderm are identified as hydraulic outgrowths from the central coelomic cavity of the bilateral ancestor which developed due to a shortening of the body (...) in length but widening in the diameter. The resulting pentaradial symmetry is a consequence of mechanical laws that dictate minimal contact surface areas among hydraulic pneumatic entities. These developed in the coelomic cavity (metacoel) in the bilaterally symmetrical ancestor, when from the already U-shaped mesentery with the intestinal tract two additional U-shaped bows developed directly or subsequently. During the subsequent development tensile chords of the mesentery ‘sewed’ the gut with the body wall first in three and secondly in five ‘seams’. During the direct development five ‘seams’ between tensile chords and body wall developed straightly. These internal tensile chords subdivide the body coelom into five hydraulic subsystems (‘pneus’), which eventually arrange in a pentaradial pattern. The body could then enlarge only between the tensile chords, which means that five hydraulic bulges developed. These bulges initially supported the tentacles and finally each of them enclosed the tentacle until only the feather-like appendages of the tentacles projected over the surface. The tentacles with their feathers were transformedinto the ambulacral system, and the bulges become the arms. These morphological transformations were accompanied and partly determined by specific histological modifications, such as the development of mutable connective tissues and skeletal elements that fused to ossicles and provided shape stabilization in form of a calcareous skeleton in the body wall. The organism resulted was an ancestral echinoderm (‘Ur-Echinoderm’) with an enlarged metacoel, stabilized by hydraulic pressure working againsta capsule of mutable connective tissue, skeletal elements and longitudinal muscles. In regard to these reconstructions, the body structure of echinoderms can be understood as a hydraulic skeletal capsule. (shrink)

In the last few years, an understanding has emerged of the developmental mechanism for the consistent internal left–right structure, termed situs, that characterises vertebrate anatomy. This involves largely vertebrate‐conserved (i.e. ‘phylotypic’) gene expression cascades that encode ‘leftness’ and ‘rightness’ in appropriate tissues either side of the embryo's midline soon after gastrulation. Recent evidence indicates that the initial, directional symmetry breaking that initiates these cascades utilises mechanisms that are conserved or at least closely related in different vertebrate types. I describe (...) a scenario whereby the capacity for directional modification of an otherwise bilateral body plan can be viewed as an adaptive innovation rather closely connected with vertebrate origins, enabling optimal ‘design’ for very active lifestyles. But an alternative scenario, while retaining the view that situs and indeed other vertebrate functional lateralisations are deeply adaptive, proposes that they originated in the co‐optation of left–right developmental information inherited from a very early stage in metazoan diversification. It is proposed that a remote chordate ancestor lost its original or ‘ur‐bilaterian’ symmetry to pass through an altogether non‐symmetrical stage, and that the vertebrate dorsoventral midline plane is not descended from that original one. I review the considerable evidence in favour of this scenario, and discuss its wider implications for directional asymmetries across the Metazoa. BioEssays 26:413–421, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

There is renewed interest in how the different body plans of extant phyla are related. This question has traditionally been addressed by comparisons between vertebrates and Drosophila. Fortunately, there is now increasing emphasis on animals representing other phyla. Pentamerally symmetric echinoderms are a bilaterian metazoan phylum whose members exhibit secondarily derived radial symmetry. Precisely how their radially symmetric body plan originated from a bilaterally symmetric ancestor is unkown, however, two recent papers address this subject. Peterson et al.(1) propose a (...) hypothesis on evolution of the anteroposterior axis in echinoderms, and Arenas-Mena et al.(2) examine expression of five posterior Hox genes during development of the adult sea urchin. BioEssays 23:211–214, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

The mechanisms responsible for the fine tuning of development, where the wildtype phenotype is reproduced with high fidelity, are not well understood. The difficulty in approaching this problem is the identification of mutant phenotypes indicative of a defect in these fine‐tuning control mechanisms. Evolutionary biologists have used asymmetry as a measure of developmental homeostasis. The rationale for this was that, since the same genome controls the development of the left and right sides of a bilaterally symmetrical organism, departures from (...) class='Hi'>symmetry can be used to measure genetic or environmental perturbations. This paper examines the relationship between asymmtry and resistance to organophosphorous insecticides in the Australian sheep blowfly, Lucilia cuprina. A resistance gene, Rop‐1, which encodes a carboxylesterase enzyme, also confers a significant increase in asymmetry. Continued exposure of resistant populations to insecticide has selected a dominant suppressor of the asymmetry phenotype. Genetic evidence indicates that the modifier is the L. cuprina Notch homologue. (shrink)

Fluctuating asymmetry (FA) is small deviations from perfect symmetry in normally bilaterally symmetrical traits. We examined the relationship between FA of five body traits (ear height, length of three digits, and ankle circumference) and self-reported scores of physical and verbal aggression in a sample of 90 boys aged 10 to 15 years. The relationships between FA and scores of aggression (particularly physical aggression) were found to be negative; in other words, the most symmetrical boys showed highest aggression. One trait (...) (ankle circumference) showed the characteristics of “ideal” FA—parametric mean of zero and a normal distribution. Mean asymmetries calculated from six repeated measures of ankle FA in 30 subjects taken over a period of five months showed strong negative associations with scores of physical aggression which were independent of age, height, and weight.It is argued that soft tissue “cyclical” FA (as opposed to “fixed” bony FA) is dependent on the secretion of hormones: for example, cortisol. Causal associations between behavioral traits such as aggresion and hormones will lead to similar correlations between FA and behavior. (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)

The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) (...) negative introduction and elimination rules, and (ii) positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality (not referring to truthtables), using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible. (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..

This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination (...) rules from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguish it from Francez's. (shrink)

The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: negative introduction (...) and elimination rules, and positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality, using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible. (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)

Rumfitt has given two arguments that in unilateralist verificationist theories of meaning, truth collapses into correct assertibility. In the present paper I give similar arguments that show that in unilateral falsificationist theories of meaning, falsehood collapses into correct deniability. According to bilateralism, meanings are determined by assertion and denial conditions, so the question arises whether it succumbs to similar arguments. I show that this is not the case. The final section considers the question whether a principle central to Rumfitt's first (...) argument, ‘It is assertible that if and only if it is assertible that it is assertible that ’, is one that bilateralists can reject, and concludes that they cannot. It follows that the logic of assertibility and deniability, according to a result by Williamson, is the little known modal logic K4 studied by Sobociński. The paper ends with a plaidoyer for bilateralists to adopt this logic. (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)

In this short paper I note that a key metatheorem does not hold for the bilateralist inferential framework: harmony does not entail consistency. I conclude that the requirement of harmony will not suffice for a bilateralist to maintain a proof theoretic account of classical logic. I conclude that a proof theoretic account of meaning based on the bilateralist framework has no natural way of distinguishing legitimate definitional inference rules from illegitimate ones (such as those for tonk). Finally, as an appendix (...) to the main argument, I propose an alternative non-bilateral formal solution to the problem of providing a proof-theoretic account of classical logic. (shrink)

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)

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)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral proof (...) rules has a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (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)

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)

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)

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)

This paper provides a proof-theoretic account of imperative logical consequence by generalising Greg Restall’s multiple conclusion bilateralism for declarative logic. According to imperative bilateralism, a sequent Γ ⊢ Δ is valid iff jointly commanding all the imperatives Φ ∈ Γ and prohibiting all the imperatives Ψ ∈ Δ clashes. This account has three main virtues: (1) it provides a proof-theoretic account of imperatives; (2) it does not rely on the controversial notion of imperative inference; and (3) it is neutral regarding (...) cognitivism about imperatives. (shrink)

The paper introduces the formula structure of poly-sequents, allowing the expression of poly-positions: positions with any number of stances, of which bilateralism and trilateralism are special cases. The paper also puts forward the view that s-coherence of such poly-positions can be defined inferentially, without appealing to their validity under interpretations of the object language.

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)

We examine the short-term and long-term impact of bilateral agreements on migrant workers’ vulnerability during their employment in Israel. To do so, we developed the Vulnerability Index of Migrant Workers based on five dimensions: poor working conditions, poor living conditions, poor safety conditions, low wages, and dependence on migration costs. We focus on migrant workers arriving in Israel from two different countries, employed in two different sectors of the economy. Data was gathered through a survey conducted among workers arriving (...) from both countries before and after the implementation of the bilateral agreements. The study revealed that after the implementation of bilateral agreements, the working, living and safety conditions of migrant workers remained poor or even worsened. For Thai workers, there was a slight improvement in the working and living conditions in the short term after the bilateral agreement, but they worsened in the long run. The total Index of Vulnerability of both groups showed improvement due to the dramatic decrease in dependence on migration costs, despite the deterioration in some working and living conditions and the reduction in migrant workers’ relative wages. (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.

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)

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)

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)

Ian Rumfitt (2000) developed a bilateralist account of logic in which the meaning of the connectives is given by conditions on asserted and rejected sentences. An additional set of inference rules, the coordination principles, determines the interaction of assertion and rejection. Fernando Ferreira (2008) found this account defective, as Rumfitt must state the coordination principles for arbitrary complex sentences. Rumfitt (2008) has a reply, but we argue that the problem runs deeper than he acknowledges and is in fact related to (...) the challenge of establishing proof-theoretic harmony. We motivate a distinctively bilateral criterion for harmony and show how the bilateralist can meet it. This also resolves Ferreira's complaint. (shrink)