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)

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)

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.

UNOFFICIAL ABSTRACT It is not clear (to me at least) whether certain metaphysical questions really demand explanation. In this article I propose an argument for why fundamental laws of nature (of a form similar to those of the Standard Model) would welcome an explanation. The argument relies on Curie's first principle and on a feature of the current laws of particle physics. I also argue that this feature allows us to understand the ``unreasonable'' effectiveness of mathematics in physics (5.2) and (...) to demistify any objectivity of these laws vindicated by ontic structural realists (5.3). -/- ABSTRACT 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)

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)

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)

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)

Symmetries have a crucial role in today’s physics. In this thesis, we are mostly concerned with time reversal invariance (T-symmetry). A physical system is time reversal invariant if its underlying laws are not sensitive to the direction of time. There are various accounts of time reversal transformation resulting in different views on whether or not a given theory in physics is time reversal invariant. With a focus on quantum mechanics, I describe the standard account of time reversal and compare (...) it with my alternative account, arguing why it deserves serious attention. Then, I review three known ways to T-violation in quantum mechanics, and explain two unique experiments made to detect it in the neutral K and B mesons. (shrink)

Pointing to broad symmetries between the idea that God is omniscient, omnipotent and all-good, and the idea that God is omniscient, omnipotent but all-evil, the evil-God challenge raises the question of why theists should prefer one over the other. I respond to this challenge by drawing on a recent theory in epistemology, pragmatic encroachment, which asserts that practical considerations can alter the epistemic status of beliefs. I then explore some of the implications of my argument for how we do (...) philosophy of religion, arguing that practical and contextual as well as alethic considerations are properly central to the discipline. (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 main intent of this thesis is to defend that the laws of nature are better thought as transcendent universals, such as platonic governism suggests, and that they are metaphysically necessary in a strong way, such as the heterodox version of such platonism defends. With this intention, we sustain that physical symmetries are essential consequences of the laws of nature – what solves the challenge of symmetries – thus being metaphysically necessary, without being governist's necessitation laws. First, we (...) will show what laws of nature are and the reasons to reject other metaphysical theories and to accept platonic governism. Soon after, we will present the challenge of symmetries and the reasons to prefer the platonic governist answer over dispositionalist, regularist, aristotelic (governism), counterfatualist and primitivist ones. At last, we will define what is the metaphysical necessity, argue for the strong metaphysical necessity of laws and their consequences, and show why the reasons for the contingency or weak necessity of laws are bad theoretical paths. (shrink)

I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled way (...) of knowing when to stop second-guessing oneself. Peer disagreement is treated as a special case where one doubts oneself because of news that an intellectual equal disagrees. This framework, and variants of it, imply that the typically stated belief that an equally reliably peer disagrees is incoherent, and thus that pure rationality constraints without further substantive information cannot give an answer as to what to do. The framework also shows that treating both ourselves and others as thermometers in the disagreement situation does not imply the Equal Weight view. (shrink)

The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that (...) conservation laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. (shrink)

In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely that the (...) following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world. (shrink)

Clark and Shackel have recently argued that previous attempts to resolve the two-envelope paradox fail, and that we must look to symmetries of the relevant expected-value calculations for a solution. Clark and Shackel also argue for a novel solution to the peeking case, a variant of the two-envelope scenario in which you are allowed to look in your envelope before deciding whether or not to swap. Whatever the merits of these solutions, they go beyond accepted decision theory, even contradicting (...) it in the peeking case. Thus if we are to take their solutions seriously, we must understand Clark and Shackel to be proposing a revision of standard decision theory. Understood as such, we will argue, their proposal is both implausible and unnecessary. (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws (the role of determining local inertial structure). I raise two complications for this approach. First, our spacetime concept seems to have the structure of a cluster concept, which means that Knox's inertial criteria for spacetime cannot succeed with complete generality. Second, the notion of metaphysical fundamentality may feature in the spacetime concept, in which case spacetime functionalism may be uninformative (...) in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

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

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

Non-Humean accounts of the metaphysics of nature posit either laws or powers in order to account for natural necessity and world-order. We argue that such monistic views face fundamental problems. On the one hand, neo-Aristotelians cannot give unproblematic power-based accounts of the functional laws among quantities offered by physical theories, as well as of the place of conservation laws and symmetries in a lawless ontology; in order to capture these characteristics, commitment to governing laws is indispensable. On the other (...) hand, ontologies that entirely exclude some kind of power ascription to worldly entities face what we call the Governing Problem: such ontologies do not have the resources to give an adequate account of how laws play their governing role. We propose a novel dualist model, which, we argue, has the resources to solve the difficulties encountered by its two dominant competitors, without inheriting the problems of either view. According to the dualist model, both laws and powers are equally fundamental and irreducible to each other, and both are needed in order to give a satisfactory account of the nomological structure of the world. The dualist model constitutes thus a promising alternative to current monistic views in the metaphysics of science. (shrink)

The general theory of relativity was developed using as a nucleus a principle of symmetry: the principle of general covariance. Initially, Einstein saw the principle of general covariance as an extension of the principle of relativity in classical mechanics, and in SR. For Einstein, the principle of general covariance was a crucial postulate in the development of GR. The freedom of the GR diffeomorphism (the invariance of the form of the laws under transformations of the coordinates depending on the arbitrary (...) functions of space and time) is a "local" spacetime symmetry, as opposed to the "global" spacetime symmetries of the SR (which depend instead on the constant parameters ). DOI: 10.13140/RG.2.2.30854.32326. (shrink)

It’s possible to accept or to reject a promise. According to a new proposal by Abraham Roth, accepting a promise involves intending that the promisee perform the promised action. According to Roth, this view is supported by rational symmetries between promissory acceptance and intention. Here, I show how these symmetries actually generate two problems for the view.

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. The gauge interactions (...) are uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances. (shrink)

Ontic Structural Realism, as pivotal position in philosophy of science and metaphysics, defends the idea that the world is ultimately constituted of real physical structures. French (2014) regards physical symmetries as the foundational structure of a world without objects. On the other hand, Ladyman and Ross (2007) hold that the world is essentially made of non-redundant informational structure. I argue in this paper that these two positions are by no means incompatible, for instance by interpreting French’s physical symmetries (...) as real structures both encompassing and compressing every piece of information (Kolmogorov complexity) within the world. (shrink)

As we have seen in the transition form Part I to Part II of this book, the inductive riskiness of doxastic methods applied in testimonial uptake or prescribed as exemplary of religious faith, helpfully operationalizes the broader social scientific, philosophical, moral, and theological interest that people may have with problems of religious luck. Accordingly, we will now speak less about luck, but more about the manner in which highly risky cognitive strategies are correlated with psychological studies of bias studies and (...) human cognitive ecology. Chapter Four is concerned with connections between psychological study of biases and heuristics, and the comparative study of fundamentalism. The first section looks at work by psychologists and philosophers on our bias blind spot. Later sections ask, ‘In what ways might biases and heuristics play a special role in aiding our understanding of, and response to, fundamentalist orientation?’. The judgments we make in ignorance of our own biases Montaigne calls our importunate presumptions, and he suggests a host of practical factors that make them appealing. Montaigne, as I discuss in the first section, associates many of our errors with one or another kind of presumption, often about our similarity or differences from others, or from God. Our obvious psychographic diversity, and the polemical ground dynamics involved in our ‘culture wars’ are compounded on the agential side by the invisibility of our biases to ourselves. A number of person and social biases are described that plausibly affect all of our beliefs in domains of controversial views, religious views included. The second section continues to study of how etiological symmetry (similar patterns of belief-uptake) gives rise to religious contrariety (diverse narratives and theologies) in testimonial faith traditions, and what the implications of this are for philosophy of religion, generally, and for an improved comparative study of fundamentalism, in particular. Utilizing the work of philosophers such as Rachel Fraser and psychologists such as Emily Pronin and her co-authors, I offer a four-step genealogical account for how etiological symmetry so easily gives rise to religious contrariety. This account begins with the narrative nature of testimony in the Abrahamic family of religions, and how narrative content confounds our “source monitoring.” My genealogy also introduces what I term biased-closure inferences (BCI) as one of the key enablers of religious exclusivism and absolutism. These are the seemingly ‘logical’ but actually very self-serving inferences people often make, inferences from their own belief being true, to any belief contrary to it being false. Those who claim unique truth, epistemic access, and/or virtue and religious value for the home religion are no exception to the broad pertinence of bias studies across domains of controversial view. The proximate causes of belief are all that we can study, and in these there may be significant etiological symmetries. Yet those groups themselves, especially to the extent that they are exclusivist, are tunnel-visioned on claims of doctrinal uniqueness: on content differences of a theological sort. Comparative philosophy is met with the puzzlement that symmetric or essentially similar doxastic strategies should give rise not just to cognitive diversity, but to what we can call polarized or polemical contrariety, contrariety of a kind where each view adamantly rejects all others. Arguably, the more that theologies offer explanations of a counter-inductive sort, or profess counter-inductive thinking as exemplary of faith, the better evidential ground there for inferring that bias involved in the acquisition or maintenance of beliefs. This provides more substance to the question of when censure, and etiological challenges to faith-based beliefs are philosophically well-motivated. (shrink)

The fact that physical laws often admit certain kinds of space-time symmetries is often thought to be problematic for substantivalism --- the view that space-time is as real as the objects it contains. The most prominent alternative, relationism, avoids these problems but at the cost of giving abstract objects (rather than space-time points) a pivotal role in the fundamental metaphysics. This incurs related problems concerning the relation of the physical to the mathematical. In this paper I will present a (...) version of substantivalism that respects Leibnizian theses about space-time symmetries, and argue that it is superior to both relationism and the more orthodox form of substantivalism. (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)

Modal idealism is a Theory of Everything, based on metaphysical abstractions of the physical principles of hidden symmetries, entanglement, and quantum field theory, considered in the context of the Many Worlds Interpretation of quantum mechanics. These abstractions are used to extend the scope of existing philosophical positions on idealism, consciousness and possible world semantics, to rationally explain the fundamental mysteries of our existence. While it conceptually aligns with the Many Minds Interpretation of quantum mechanics, modal idealism posits a more (...) comprehensive characterization of the mind, and thereby addresses many of the objections to MMI and MWI. Consequently, it can provide unequivocal, logical answers to our most enduring existential questions. To demonstrate the explanatory power of modal idealism, this article will present seven of our most meaningful physical and metaphysical questions, enumerate the principles of this framework, and use them to rationally answer these questions. (shrink)

The author has established a mathematical theory about the system of freedom in which components of freedom are ruled by the largest freedom principle, explaining how one invariant reality can be equated with the dynamical universe. Freedom as a whole is the reality, and components of freedom show variable phenomena and become a dynamic system. In freedom, component equality leads to sequence equality; therefore, various sequences coexist in the system. Because there are incompatible sequences for any sequence, the interior of (...) freedom cannot be a static sequence. In order for the system to be a whole, there must be some connecting sequences between any two sequences. Then, at every part of freedom, it is always possible to find a group of three independent sequences that, for most components, is located inside. For the sequence group, there is a sequence through which most components flow in and out. The most abundant three - sequence group and most abundant connecting sequence correspond to the space - time structure. Other incompatible sequences correspond to particles, and interactions between these sequences correspond to interactions between particles. The interactions have some symmetries similar to those in physics, such as SU (3) AND SU (2)×U (1), thus proving the feasibility of the hypothesis: the universe is equivalent with the system of freedom. (shrink)

“Free will” puzzles are failed attempts to make freedom fit into forms of science. The failures seem puzzling because of widespread beliefs that forms of science describe and control everything. Errors in such beliefs are shown by reconstruction of forms of “platonic science” that were invented in ancient Greece and that have developed into modern physics. Like platonic Ideas, modern Laws of Physics are said to exercise hegemonic control through eternal, universal principles. Symmetries, rigidity and continuity are imposed through (...) linear forms that have been abstracted from geometry and indifference. Static and quasi-static forms presume placid equilibrium conditions and relaxation processes. Such forms, based on empty space, fail to describe actual material transformations that occur during the making of steel or the generation of snowflakes. They also fail to describe muscular movements and related bodily feelings of persons and animals that have actual life. Limitations of platonic science are overcome by means of new forms with the character of time, such as “beats” and saccadic, jumpy forms. New technologies of action and freedom generate and control temporal forms in proposed device models of brains and muscles. Some temporal forms have critical moments of transformation, resembling moments when persons exercise freedom, e.g., a moment of overtaking during a footrace or a moment of decision by a jury during a civil trial. (shrink)

The naive idea of a mimesis between theory and experiments, a concept still lasing in many epistemologies, is here substituted by a more sophisticated mathematical methexis where theoretical physics is a system of production of formal structures under strong mathematical constraints, such as global and local symmetries. Instead of an ultimate “everything theory”, the image of physical theories here proposed is a totality of interconnected structures establishing the very conditions of its “thinkability” and the relations with the experimental domain.

n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, (...) we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness. (shrink)

After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple proposed the Raven Paradox. Then, Carnap used the increment of logical probability as the confirmation measure. So far, many confirmation measures have been proposed. Measure F proposed by Kemeny and Oppenheim among them possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on (...) the semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, measures b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. Furthermore, it is still not easy to use b*, F, or another measure to clarify the Raven Paradox. For this reason, measure c* similar to the correct rate is derived. Measure c* supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the Raven Paradox. An example indicates that measures F and b* are helpful for diagnosing the infection of Novel Coronavirus, whereas most popular confirmation measures are not. Another example reveals that all popular confirmation measures cannot be used to explain that a black raven can confirm “Ravens are black” more strongly than a piece of chalk. Measures F, b*, and c* indicate that the existence of fewer counterexamples is more important than more positive examples’ existence, and hence, are compatible with Popper’s falsification thought. (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.

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 paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by (...) presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach. (shrink)

Traditionally Ψ is used to stand in for both the mathematical wavefunction (the representation) and the quantum state (the thing in the world). This elision has been elevated to a metaphysical thesis by advocates of the view known as wavefunction realism. My aim in this paper is to challenge the hegemony of the wavefunction by calling attention to a little-known formulation of quantum theory that does not make use of the wavefunction in representing the quantum state. This approach, called Lagrangian (...) quantum hydrodynamics (LQH), is not an approximation scheme, but rather a full alternative formulation of quantum theory. I argue that a careful consideration of alternative formalisms is an essential part of any realist project that attempts to read the ontology of a theory off of the mathematical formalism. In particular, I show that LQH undercuts the central presumption of wavefunction realism and falsifies the claim that one must represent the many-body quantum state as living in a 3n-dimensional configuration space. I conclude by briefly sketching three different realist approaches one could take toward LQH, and argue that both models of the quantum state should be admitted. When exploring quantum realism, regaining sight of the proverbial forest of quantum representations beyond the Ψ is just the first step. (shrink)

“The universe is expanding, not contracting.” Many statements of this form appear unambiguously true; after all, the discovery of the universe’s expansion is one of the great triumphs of empirical science. However, the statement is time-directed: the universe expands towards what we call the future; it contracts towards the past. If we deny that time has a direction, should we also deny that the universe is really expanding? This article draws together and discusses what I call ‘C-theories’ of time — (...) in short, philosophical positions that hold time lacks a direction — from different areas of the literature. I set out the various motivations, aims, and problems for C-theories, and outline different versions of antirealism about the direction of time. (shrink)