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)
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)
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)
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)
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)
Science frequently gives us multiple, compatible ways of solving the same problem or formulating the same theory. These compatible formulations change our understanding of the world, despite providing the same explanations. According to what I call "conceptualism," reformulations change our understanding by clarifying the epistemic structure of theories. I illustrate conceptualism by analyzing a typical example of symmetry-based reformulation in chemical physics. This case study poses a problem for "explanationism," the rival thesis that differences in understanding require ontic explanatory (...) differences. To defend conceptualism, I consider how prominent accounts of explanation might accommodate this case study. I argue that either they do not succeed, or they generate a skeptical challenge. (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)
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)
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.
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)
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)
Bertrand Russell famously argued that causation is not part of the fundamental physical description of the world, describing the notion of cause as “a relic of a bygone age”. This paper assesses one of Russell’s arguments for this conclusion: the ‘Directionality Argument’, which holds that the time symmetry of fundamental physics is inconsistent with the time asymmetry of causation. We claim that the coherence and success of the Directionality Argument crucially depends on the proper interpretation of the ‘ time (...)symmetry’ of fundamental physics as it appears in the argument, and offer two alternative interpretations. We argue that: if ‘ time symmetry’ is understood as the time -reversal invariance of physical theories, then the crucial premise of the Directionality Argument should be rejected; and if ‘ time symmetry’ is understood as the temporally bidirectional nomic dependence relations of physical laws, then the crucial premise of the Directionality Argument is far more plausible. We defend the second reading as continuous with Russell’s writings, and consider the consequences of the bidirectionality of nomic dependence relations in physics for the metaphysics of causation. (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)
It is widely held that one can be responsible for doing something that one was unable to avoid doing. This paper focuses primarily on the question of whether one can be responsible for not doing something that one was unable to do. The paper begins with an examination of the account of responsibility for omissions offered by John Martin Fischer and Mark Ravizza, arguing that in many cases it yields mistaken verdicts. An alternative account is sketched that jibes with and (...) explains judgments about a variety of omissions cases, including intentional omissions as well as simple failures to act. (shrink)
Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress (...) that symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not just processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions. (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)
In this paper I prove that holistic coherentism is logically equivalent to the conjunction of symmetry and quasi-transitivity of epistemic support and a condition on justified beliefs. On the way I defend Tom Stoneham from a criticism made by Darrell Rowbottom and prove a premiss of Stoneham’s argument to be an entailment of coherentism.
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)
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)
Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully (...) satisfactory. This is a symmetry argument in line with Curie’s first principle. Further, I argue that this same feature of group theory helps to explain the ‘unreasonable’ effectiveness of mathematics in physics, and that it reduces the philosophical significance that has been attributed to the objectivity of gauge symmetries. (shrink)
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.
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)
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)
Helen Frowe has recently objected to Michael Tooley’s famous Moral Symmetry Principle, which is meant to show that in themselves killing and letting die are morally equivalent. I argue that her objection is not compelling but a more compelling objection is available. Specifically, Tooley’s rebuttal of a proposed counter-example to his Moral Symmetry Principle has two problematic implications. First, it undercuts the very principle itself. If we reject the proposed counter-example, then any instance of the Moral Symmetry (...) Principle will actually demonstrate the moral in-equivalence of killing and letting die. Second, it commits us to the view, which Tooley wishes to avoid, that we are just as obligated to refrain from doing wrong as we are to prevent others from doing the same. I conclude with a brief discussion of a more general concern regarding Tooley’s basic strategy. My focus here is quite narrow. My claims, if plausible, only show that the Moral Symmetry Principle is unsound and thus cannot serve as a basis for the view that killing and letting die are morally equivalent. (shrink)
The notion of space is one of the most discussed within classical physics concepts. The works of Copernicus and Galileo, as well as Gassendi´s ideas led to Newton to regard it as substance. This conception of space, allows the notion of symmetry is present in an indirect or implied, within the laws of physics, formed through the notions of equivalence and balance. The aim of this study is to identify the symmetry, through such notions, under the study of (...) indistinction between the repose state and the state of uniform translational movement known as the law of inertia. The philosophical approach is framed in the link between these notions and the problem of indistinguishability between states of different movement. We will discuss first the conception of space Telesio and Gassendi that led Newton to his absolutist conception of space. The conception of space and its relationship with Newton symmetry is the second part of our work. As a third part present linking of the Newtonian space with notions of balance, symmetry and equivalence. Subsequently they give our conclusions. (shrink)
Many instances of parental enhancement are objectionable on egalitarian grounds because they unnecessarily amplify one kind of asymmetry of power between parents and children. Because children have full moral status, we ought to seek egalitarian relationships with them. Such relationships are compatible with asymmetries of power only to the extent to which the asymmetry is necessary for (1) advancing the child's level of advantage up to what justice requires or (2) instilling in the child morally required features. This is a (...) ground to oppose parental enhancements whose purpose is either to merely satisfy parents' preferences or to confer on the child advantages above and beyond what the child is owed by justice. (shrink)
Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of (...) class='Hi'>symmetry is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. (shrink)
The philosophy of mind concerns much about how novelty occurs in the world. The very recent progress in this field inspired by quantum mechanics indicates that symmetry restoration occurs in the mind at the moment when new creative thought arises. Symmetry restoration denotes the moment when one’s cognition leaves ordinary internalized mental schemes such as conceptual categories, heuristics, subjective theories, conventional thinking, or expectations. At this moment, fundamentally new, original thought may arise. We also predict that in older (...) age, symmetry restoration is less likely to occur as internalized mental schemes become more rigid in the elderly. Furthermore, the present study demonstrates that symmetry restoration may occur not only individually, in one’s mind, but also collectively, during collaborative creative activities, e.g. during small-group brainstorming sessions or creative improvisational performances. The possibility of collective symmetry restoration interacts well with the ideas in the field of relational ontology. Relational ontology highlights an important ontological role of relations. The ontological primacy is not given to individual entities, as in traditional metaphysics, but to relational structures and transformative relational processes (interactions). When accepting this assumption, we cannot imagine the situation when the actor’s mind could act absolutely independently and leave all of its relations as assumed in the compatibilist theory of free will. We argue that creative free action can be performed even in the case when the actor is entangled within their material, environmental, and social relational structures. (shrink)
In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the (...) Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)
The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave function describing (...) a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)
This review is a critical discussion of three main claims in Debs and Redhead’s thought-provoking book Objectivity, Invariance, and Convention. These claims are: (i) Social acts impinge upon formal aspects of scientific representation; (ii) symmetries introduce the need for conventional choice; (iii) perspectival symmetry is a necessary and sufficient condition for objectivity, while symmetry simpliciter fails to be necessary.
Under semantic monism I understand the thesis “The Good is said in one way” and under semantic pluralism the antithesis “The Good is said in many ways”. Plato’s Socrates seems to defend a “semantic monism”. As only one sun exists, so the “Good” has for Socrates and Plato only one reference. Nevertheless, Socrates defends in the Philebus a semantic pluralism, more exactly trialism, of “beauty, symmetry and truth” . Therefore, metaphorically speaking, there seem to exist not only one sun, (...) but three suns. If the platonic Socrates defends a semantic monism on the one hand and pluralism on the other, how can we unite his pluralism with his monism? My thesis is that the three references are “qualities” of the one single reference, or again, speaking metaphorically, “side suns” of the single sun. In the following, I propose first an exegesis of Plato’s last written word on the Good in Phil. 65 A 1-5 by dividing it into five sentences. Second, I ask a philosophical question on this monism and the corresponding hierarchy of values. (shrink)
ABSTRACT This article is a response to 'Fear of death and the symmetry argument', in this issue. In that article, the author discusses the above Lucretian symmetry argument, and proposes a view that justifies the existing asymmetry in our attitudes towards birth and death. I begin by distinguishing this symmetry argument from a different one, also loosely inspired by Lucretius, which also plays a role in the article. I then describe what I take to be the author's (...) solution to the original symmetry argument and explain why I am unpersuaded by it. (shrink)
This chapter starts with a simple conventional presentation of time reversal in physics, and then returns to analyse it, rejects the conventional analysis, and establishes correct principles in their place.
A descriptive role is suggested for uracil as a temporal divide in the immediate aspects of metabolism verses long term maintained genetic transmission. In particular, details of the mechanism of excision repair of uracil from DNA based on differential parameters of spatial distortion of the planar uracil molecule within the DNA helix verses RNA, when viewed in analogy to a proposed model for space involving the substitution of the act of mirroring for the element of time in processes and a (...) descending complexity of structure with time of evolution, suggest the possibility that negative selection against decreased lifetime is the singular motive force of natural selection. The geometry of the Mobius strip, as it has a plane of mirroring symmetry, a twist able to account for torque in nature, an inversion of inside and out seen in biological structures, and an endless surface that can be accommodated to an atemporal account of physical processes is employed in a holistic model to elaborate a negative selection opposing death as zero volume or the logical existence of physical constraint to volumes that is represented as the ubiquitous inability of witnessing objects of any type to witness simultaneously both a self reflection and the reflection of self reflection. A role for uracil and its’ physical structure, in a model in which both are evolved from the mirroring of events of the witnessing of energies, is elaborated in which temporal aspects such as those entailed in existing models of natural evolution are considered inappropriate in perspectives that are oriented positively towards a successful comprehension of processes; focus is placed instead upon the geometry and arrangement of physical spaces. (shrink)
For Tarski talk about the truth in a language, and not generate contradictions, it requires doing it from a different language with greater expressive power: the metalanguage. So, a metalanguage is a language that is used to talk about another language. In scientific language this distinction is very important. In physics, the notion of symmetry is shown through the language used within physical theories. In this way, through algebraic language ─automorphism─ we shown the symmetry ─invariancia, order, equilibrium─ finding (...) (within the language of these theories) the use of the notion sometimes as a principle and sometimes as argument. The distinction in use of the notion of symmetry, on the part of physics, allows us to glimpse symmetry as a term of the metalanguage. Through a brief historical reconstruction ─from the Greeks to present time─ we show the notion of symmetry as a metalanguage term distinguishing the use ─principle and argument─ that physics makes of the concept. Keywords: symmetry, automorphism, principle, argument. (shrink)
For Tarski talk about the truth in a language, and not generate contradictions, it requires doing it from a different language with greater expressive power: the metalanguage. So, a metalanguage is a language that is used to talk about another language. In scientific language this distinction is very important. In physics, the notion of symmetry is shown through the language used within physical theories. In this way, through algebraic language ─automorphism─ we shown the symmetry ─invariancia, order, equilibrium─ finding (...) (within the language of these theories) the use of the notion sometimes as a principle and sometimes as argument. The distinction in use of the notion of symmetry, on the part of physics, allows us to glimpse symmetry as a term of the metalanguage. Through a brief historical reconstruction ─from the Greeks to present time─ we show the notion of symmetry as a metalanguage term distinguishing the use ─principle and argument─ that physics makes of the concept. (shrink)
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)
The leaders of the Scientific Revolution were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.
What would it be for a process to happen backwards in time? Would such a process involve different causal relations? It is common to understand the time-reversal invariance of a physical theory in causal terms, such that whatever can happen forwards in time can also happen backwards in time. This has led many to hold that time-reversal symmetry is incompatible with the asymmetry of cause and effect. This article critiques the causal reading of time reversal. First, I argue that (...) the causal reading requires time-reversal-related models to be understood as representing distinct possible worlds and, on such a reading, causal relations are compatible with time-reversal symmetry. Second, I argue that the former approach does, however, raise serious sceptical problems regarding the causal relations of paradigm causal processes and as a consequence there are overwhelming reasons to prefer a non-causal reading of time reversal, whereby time reversal leaves causal relations invariant. On the non-causal reading, time-reversal symmetry poses no significant conceptual nor epistemological problems for causation. _1_ Introduction _1.1_ The directionality argument _1.2_ Time reversal _2_ What Does Time Reversal Reverse? _2.1_ The B- and C-theory of time _2.2_ Time reversal on the C-theory _2.3_ Answers _3_ Does Time Reversal Reverse Causal Relations? _3.1_ Causation, billiards, and snooker _3.2_ The epistemology of causal direction _3.3_ Answers _4_ Is Time-Reversal Symmetry Compatible with Causation? _4.1_ Incompatibilism _4.2_ Compatibilism _4.3_ Answers _5_ Outlook. (shrink)
Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of (...) time the ”niches” which constitute the boundary conditions on selec- tion. More generally, by the mathematical unprestatability of the ”phase space”, no laws of mo- tion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound concep- tual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of symmetries as invariant preserving transformations will allow us to under- stand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of ”enablement”. Life lives in a web of enablement and radical emergence. This will restrict causal analyses to differential cases. Mutations or other causal differ- ences will allow us to stress that ”non conservation princi- ples” are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as sym- metries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to ”extended criticality” as a conceptual frame for a better understanding of the living state of matter. (shrink)
The classical arguments for scepticism about the external world are defended, especially the symmetry argument: that there is no reason to prefer the realist hypothesis to, say, the deceitful demon hypothesis. This argument is defended against the various standard objections, such as that the demon hypothesis is only a bare possibility, does not lead to pragmatic success, lacks coherence or simplicity, is ad hoc or parasitic, makes impossible demands for certainty, or contravenes some basic standards for a conceptual or (...) linguistic scheme. Since the conclusion of the sceptical argument is not true, it is concluded that one can only escape the force of the argument through some large premise, such as an aptitude of the intellect for truth, if necessary divinely supported. (shrink)
Death can be bad for an individual who has died, according to the “deprivation approach,” by depriving that individual of goods. One worry for this account of death’s badness is the Lucretian symmetry argument: since we do not regret having been born later than we could have been born, and since posthumous nonexistence is the mirror image of prenatal nonexistence, we should not regret dying earlier than we could have died. Anthony Brueckner and John Martin Fischer have developed a (...) response to the Lucretian challenge by arguing that it is rational to have asymmetric attitudes toward posthumous and prenatal nonexistence. Recently, Jens Johansson has criticized the Brueckner/Fischer position, claiming that it is irrelevant whether it is actually rational to care about future pleasures but not past pleasures. What matters, according to Johansson, is whether it would be rational for us to care about past pleasures had we come into existence earlier. In this paper, I add to the conversation between Johansson and Brueckner/Fischer by suggesting a way to defend the latter side’s position in a way that has not yet been suggested. I do this by considering a suggestion of Johansson’s for interpreting the Brueckner/Fischer position and by arguing that Johansson’s worry for the position I consider is actually incoherent. (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)
Chrisoula Andreou says procrastination qua imprudent delay is modeled by Warren Quinn’s self-torturer, who supposedly has intransitive preferences that rank each indulgence in something that delays his global goals over working toward those goals and who finds it vague where best to stop indulging. His pair-wise choices to indulge result in his failing the goals, which he then regrets. This chapter argues, contra the money-pump argument, that it is not irrational to have or choose from intransitive preferences; so the agent’s (...) delays are not imprudent, not instances of procrastination. Moreover, the self-torturer case is intelligible only if there is no vagueness and if the agent’s preferences are transitive. But then he would delay only from ordinary weakness of will. And when it is vague where best to stop indulging, rational agents would use symmetry-breaking techniques; so, again, any procrastination would be explained by standard weakness of will, not vagueness. (shrink)
From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.
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