In the context of a parametric theory (with the time being a dynamical variable) we consider here the coupling between the quantum vacuum and the background gravitation that pervades the universe (unavoidable because of the universality and long range of gravity). We show that this coupling, combined with the fourth Heisenberg relation, would break the parametric invariance of the gravitational equations, introducing thus a difference between the marches of the atomic and the astronomical clocks. More precisely, they (...) would be progressively and adiabatically desynchronized with respect to one another in such a way that the latter would lag behind the former. This would produce a discrepancy between gravitational theory and observations, which use astronomical and atomic time respectively. It turns out that this result, surprising at it might be, is fully compatible with current physics, since it does not conflict with any known physical law or principle. We argue that this phenomenon must be studied, since it could have cosmological consequences. (shrink)

A theory is presented in which a field depends not only on spacetime coordinates xμ, but also on a Lorentz-invariant parameter τ. Such a theory is conceptually and technically simple and manifestly covariant at every step. The generator of evolution and the generator of spacetime translations and Lorentz transformations are obtained in a straightforward way. In the quantized theory the Heisenberg equation of motion is written in a covariant form and is equivalent to the field equation. The equal τ commutator (...) between the field and its canonically conjugate momentum is just proportional to the spacetime δ function. Finally comparison with the conventional field theory is done, and it is found that the expectation value of the momentum operator in the on shell states is the same. (shrink)

We wish to determine the correct partial differential equation(s) for describing a relativistic particle. A physical foundation is presented for using a parametrized wave equation with the general form $$i\frac{{\partial \psi }}{{\partial s}} = K\psi$$ where s is the invariant evolution parameter. Several forms have been proposed for the generator K of evolution parameter translations. Of the proposed generators, only the generator K 2 which is proportional to the inner product P μ P μ of fourmomentum operators can be derived (...) from first principles, notably a probabilistic basis. Although experimental tests must be made to establish the validity of K 2,we conclude that K 2 is the leading theoretical candidate for the form of a generator of evolution parameter translations. (shrink)

We consider several game versions of the cardinal invariants \, \ and \. We show that the standard proof that parametrized diamond principles prove that the cardinal invariants are small actually shows that their game counterparts are small. On the other hand we show that \ and \ are both relatively consistent with ZFC, where \ and \ are the principal game versions of \ and \, respectively. The corresponding question for \ remains open.

By using finite support iteration Suslin c.c.c forcing notions we construct several models which satisfy some ♢-like principles while other cardinal invariants are larger than ω1.

The purpose of this paper is to review relativistic quantum theories with an invariant evolution parameter. Parametrized relativistic quantum theories (PRQT) have appeared under such names as constraint Hamiltonian dynamics, four-space formalism, indefinite mass, micrononcausal quantum theory, parametrized path integral formalism, relativistic dynamics, Schwinger proper time method, stochastic interpretation of quantum mechanics and stochastic quantization. The review focuses on the fundamental concepts underlying the theories. Similarities as well as differences are highlighted, and an extensive bibliography is provided.

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The (...) anomalies include neutrino oscillations, non-locality, and gravity.The two key QFT assumptions that are altered in PRD are the following: fields depend on space and time; and interactions between fields are local. Locality and non-locality refer to the correlation of particles with space-like separation. A local theory does not allow the existence of greater than light speed correlations, while a non-local theory does. PRD is a non-local theory that allows fields to depend on space, time and an invariant evolution parameter. A formulation of PRD is presented together with applications that can be directly compared to results from the conventional paradigm. (shrink)

We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical dynamics of the system and must therefore be deemed inappropriate. We propose a new strategy for consistently quantizing systems with a relational notion of time that does capture the full classical dynamics of the system and allows for evolution parametrized by an equitable internal (...) clock. This proposal contains the minimal temporal structure necessary to retain the ordering of events required to describe classical evolution. In the context of shape dynamics (an equivalent formulation of general relativity that is locally scale invariant and free of the local problem of time) our proposal can be shown to constitute a natural methodology for describing dynamical evolution in quantum gravity and to lead to a quantum theory analogous to the Dirac quantization of unimodular gravity. (shrink)

Recent work in parametrized relativistic quantum theory (PRQT) has shown that oscillations between mass states are predicted by an alternative formulation of relativistic quantum theory that uses an invariant evolution parameter. A PRQT model of flavor transitions is compared to the standard model. The resulting PRQT expression for the probability of survival of an incident neutrino differs significantly from the standard neutrino oscillation model. Neutrino oscillation measurements provide an experimental testing ground for two theories that are based on fundamentally different (...) concepts of temporal evolution. (shrink)

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the de Broglie-Proca (...) non-gauge formulation observable A_{\mu} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_{\mu} + \partial_{\mu} \phi, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{\mu\nu} has the gauge equivalent X^A,_{\mu} g^{\mu\nu} X^B,_{\nu}. The Poisson bracket of X^A,_{\mu} g^{\mu\nu} X^B,_{\nu} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + \Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{\mu\nu} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence. (shrink)

The skewness of a distribution, a poorly-defined term, is conventionally deemed to be invariant under linear transformations. A comparison is made of three criteria of it: the sign of odd central moments; the several relationships of the mean, the median and the mode; and asymmetry proper which is the set of ratios of the probability densities of all pairs of points equidistant above and below some arbitrary point, usually the principal mode. Some useful general relationships are discussed. The skeness of (...) convolutions is briefly discussed. A class of distributions is identified for which the skewness of the minimum ofk competing processes is independent ofk. It has importance in the parametric study of survivorship. (shrink)

An exponential $\exp $ on an ordered field $$. The structure $$ is then called an ordered exponential field. A linearly ordered structure $$ is called o-minimal if every parametrically definable subset of M is a finite union of points and open intervals of M.The main subject of this thesis is the algebraic and model theoretic examination of o-minimal exponential fields $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp = 1$. This study (...) is mainly motivated by the Transfer Conjecture, which states as follows:Any o-minimal exponential field $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp =1$ is elementarily equivalent to $\mathbb {R}_{\exp }$.Here, $\mathbb {R}_{\exp }$ denotes the real exponential field $$, where $\exp $ denotes the standard exponential $x \mapsto \mathrm {e}^x$ on $\mathbb {R}$. Moreover, elementary equivalence means that any first-order sentence in the language $\mathcal {L}_{\exp } = \{+,-,\cdot,0,1, <,\exp \}$ holds for $$ if and only if it holds for $\mathbb {R}_{\exp }$.The Transfer Conjecture, and thus the study of o-minimal exponential fields, is of particular interest in the light of the decidability of $\mathbb {R}_{\exp }$. To the date, it is not known if $\mathbb {R}_{\exp }$ is decidable, i.e., whether there exists a procedure determining for a given first-order $\mathcal {L}_{\exp }$ -sentence whether it is true or false in $\mathbb {R}_{\exp }$. However, under the assumption of Schanuel’s Conjecture—a famous open conjecture from Transcendental Number Theory—a decision procedure for $\mathbb {R}_{\exp }$ exists. Also a positive answer to the Transfer Conjecture would result in the decidability of $\mathbb {R}_{\exp }$. Thus, we study o-minimal exponential fields with regard to the Transfer Conjecture, Schanuel’s Conjecture, and the decidability question of $\mathbb {R}_{\exp }$.Overall, we shed light on the valuation theoretic invariants of o-minimal exponential fields—the residue field and the value group—with additional induced structure. Moreover, we explore elementary substructures and extensions of o-minimal exponential fields to the maximal ends—the smallest elementary substructures being prime models and the maximal elementary extensions being contained in the surreal numbers. Further, we draw connections to models of Peano Arithmetic, integer parts, density in real closure, definable Henselian valuations, and strongly NIP ordered fields.Parts of this thesis were published in [2–5].Abstract prepared by Lothar Sebastian KrappE-mail: [email protected]: https://d-nb.info/1202012558/34. (shrink)

Relativistic quantum mechanics has been formulated as a theory of the evolution ofevents in spacetime; the wave functions are square-integrable functions on the four-dimensional spacetime, parametrized by a universal invariant world time τ. The representation of states with spin is induced with a little group that is the subgroup of O(3, 1) leaving invariant a timelike vector nμ; a positive definite invariant scalar product, for which matrix elements of tensor operators are covariant, emerges from this construction. In a previous study (...) a second-order equation was introduced similar to the second-order Dirac equation, based on a quadratic function of two operators which are the self-adjoint parts, in this new scalar product, of γμpμ. It is shown in this paper that one of these operators, in fact the one from which the gyromagnetic moment is obtained, can be used to construct a first-order equation. The corresponding quantum theory is somewhat analogous to Dirac's spinor form; the Hamilton equations appear to describe dynamical degrees of freedom in a spacelike hyperplane orthogonal to nμ (in Dirac's theory the motion appears to be lightlike). It is shown that the integration over nμ required by unitarity results in timelike motion (as in the expectation value of Dirac's α). Explicit forms are obtained for the wave functions and currents for free motion. The general form of the theory is written for the (five-dimensional) pre-Maxwell fields required by gauge invariance. (shrink)

Relational reasoning is a higher-order executive function that involves the ability to perceive meaningful patterns within a body of seemingly unrelated information. In this study, the ability of 749 fourth (Mage= 10), sixth (Mage= 12), eighth (Mage= 14), and tenth graders (Mage= 16) to identify meaningful relational patterns was investigated. This general cognitive ability was assessed by means of the Test of Relational Reasoning-Junior (TORRjr), a 32-item measure organized into four 8-item scales that assess analogical, anomalous, antinomous, and antithetical reasoning. (...) Students’ performance on the TORRjr was analyzed using confirmatory factor analysis, measurement invariance test, and non-parametric median-based analyses. The confirmatory factor analysis supported that the higher-order factor model was the best fit for the TORRjr data for the Korean students. The measurement was determined to be invariant by gender but variant across grade levels. The non-parametric analysis resulted in an asymptotic (a constant increasing up to grade 6 and then a level off witnessed from grades 8 to 10) development pattern in overall relational reasoning across the grades. In comparison to analogy and anomaly, antinomy and antithesis scores were more fully developed by grade 8 and that level of performance was maintained at grade 10. The TORRjr appeared to be a viable measure for the Korean samples up to approximately 15 years of age. The significance of these findings for research and instructional practice are discussed. (shrink)

. With an overall objective of establishing association between air pollutants and incidence of respiratory diseases, the environmental professionals and medical practitioners have made significant contribution, using statistical mechanics in modelling epidemiological data, population characteristics, and pollution parameters. Broadly speaking, the studies have shown that the increase in vehicular traffic has been one of the causes of respiratory diseases. However, the WHO Centre for Environment and Health, Europe in its 2005 document states: “There is little evidence for a causal relationship (...) between asthma prevalence/incidence and air pollution in general, though the evidence is suggestive of a causal association between the prevalence/incidence of asthma symptoms and living in close proximity to traffic”. Decision making process in a real world is invariably based on perceptions which are expressed in words or may be in numeric terms and not in probability terms. In the paper, we made an attempt to model the perceptions of experienced pulmonologists in arriving at their combined degree of belief/plausibility/ignorance for all the possible combinations of identified respiratory diseases, using evidence theory and fuzzy relational calculus without collecting sizeable parametric data accumulated over a period of years. Tightening pollution norms by the regulatory authorities is an overall objective of the global efforts on greenhouse gases reduction in general, and air pollution mitigation in particular. The concept of solar battery operated electric vehicles for road transport is advocated, initially for two/three wheelers, and extending it to four wheelers, especially in the developing countries. (shrink)

In a mathematical perspective, neighborhood models for modal logic are generalized quantifiers, parametrized to points in the domain of objects/worlds. We explore this analogy further, connecting generalized quantifier theory and modal neighborhood logic. In particular, we find interesting analogies between conservativity for linguistic quantifiers and the locality of modal logic, and between the role of invariances in both fields. Moreover, we present some new completeness results for modal neighborhood logics of linguistically motivated classes of generalized quantifiers, and raise new types (...) of open problem. With the bridges established here, many further analogies might be explored between the two fields to mutual benefit. (shrink)

The earliest formulation of the Higgs naturalness argument has been criticized on the grounds that it relies on a particular cutoff-based regularization scheme. One response to this criticism has been to circumvent the worry by reformulating the naturalness argument in terms of a renormalized, regulator-independent parametrization. An alternative response is to deny that regulator dependence poses a problem for the naturalness argument, because nature itself furnishes a particular, physically correct regulator for any effective field theory in the form of that (...) EFT’s physical cutoff, together with an associated set of bare parameters that constitute the unique physically preferred “fundamental parameters” of the EFT. Here, I argue that both lines of defense against the initial worry about regulator dependence are flawed. I argue that reformulation of the naturalness argument in terms of renormalized parameters simply trades dependence on a particular regularization scheme for dependence on a particular renormalization scheme, and that one or another form of scheme dependence afflicts all formulations of the Higgs naturalness argument. Concerning the second response, I argue that the grounds for suspending the principle of regularization or renormalization scheme independence in favor of a physically preferred parametrization are thin; the assumption of a physically preferred parametrization, whether in the form of bare “fundamental parameters” or renormalized “physical parameters,” constitutes a theoretical idle wheel in generating the confirmed predictions of established EFTs, which are invariably scheme-independent. I highlight certain features of the alternative understanding of EFTs, and the EFT-based approach to understanding the foundations of QFT, that emerges when one abandons the assumption of a physically preferred parametrization. I explain how this understanding departs from several dogmas concerning the mathematical formulation and physical interpretation of EFTs in high-energy physics. (shrink)

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting (...) with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential. (shrink)

A manifestly covariant relativistic statistical mechanics of a system of N indistinguishable events with motion in space-time parametrized by an invariant “historical time” τ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperangular variables. All the characteristic averages are calculated. Expressions for the pressure and the energy density are found, and the relativistic equation of state is obtained. Validity criteria are defined. (...) The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles. Anti-events are introduced; for an event-anti-event system the equation of state p, ρ ∝ T 6 is found, which gives the value of the sound velocity c 2 = 0.20, in agreement with the “realistic” equation of state suggested by Shuryak for hot hadronic matter. (shrink)

A fundamental problem in the construction of local electromagnetic interactions in the framework of relativistic wave equations of Klein-Gordon or Dirac type is discussed, and shown to be resolved in a relativistic quantum theory of events described by functions in a Hilbert space on the manifold of space-time. The relation, abstracted from the structure of the electromagnetic current, between sequences of events, parametrized by an evolution parameter τ (“historical time”), and the commonly accepted notion of particles is reviewed. As an (...) illustration of these ideas, a perturbative calculation is made for photon emission from a charged two-body system in which the electromagnetic field is quantized in the usual way. The result is in essential agreement with calculations in which the charged particles are treated in the framework of nonrelativistic quantum mechanics, and provides them with a relativistic interpretation. In particular, we obtain a relativistically invariant form of the Bohr radiation condition. (shrink)

We consider the relativistic statistical mechanics of an ensemble of N events with motion in space-time parametrized by an invariant “historical time” τ. We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses to find approximate dynamical equations for the kinetic state of any nonequilibrium system, to the relativistic case, and obtain a manifestly covariant Boltzmann- type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation (...) is then used to prove the H-theorem for evolution in τ. In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential V(q), where q is an invariant distance in the Minkowski space-time. The two- body correlations are taken to have the support in a relative O(2, 1)-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit. (shrink)

The formulation of manifestly covariant relativistic statistical mechanics as the description of an ensemble of events in spacetime parametrized by an invariant proper-time τ is reviewed. The linear and cubic mass spectra, which result from this formulation (the latter with the inclusion of anti-events) as the actual spectra of an individual hadronic multiplet and hot hadronic matter, respectively, are discussed. These spectra allow one to predict the masses of particles nucleated to quasi-levels in such an ensemble. As an example, the (...) masses of the ground-state mesons and baryons are considered; the results are in excellent agreement with the measured hadron masses. Additivity of inverse Regge slopes is established and shown to be consistent with available experimental data on the D meson and Λc baryon production. (shrink)

This paper describes how the entire universe might be considered an eigenstate determined by classical limiting conditions within it. This description is in the context of an approach in which the path of each relativistic particle in spacetime represents a fine-grained history for that particle, and a path integral represents a coarse-grained history as a superposition of paths meeting some criteria. Since spacetime paths are parametrized by an invariant parameter, not time, histories based on such paths do not evolve in (...) time but are rather histories of all spacetime. Measurements can then be represented by orthogonal states that correlate with specific points in such coarse-grained histories, causing them to decohere, allowing a consistent probability interpretation. This conception is applied here to the analysis of the two slit experiment, scattering and, ultimately, the universe as a whole. The decoherence of cosmological states of the universe then provides the eigenstates from which our “real” universe can be selected by the measurements carried out within it. (shrink)

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

I argue that in order to apply the most common type of criteria for logicality, invariance criteria, to natural language, we need to consider both invariance of content—modeled by functions from contexts into extensions—and invariance of character—modeled, à la Kaplan, by functions from contexts of use into contents. Logical expressionsshould be invariant in both senses. If we do not require this, then old objections due to Timothy McCarthy and William Hanson, suitably modified, demonstrate that content invariant expressions (...) can display intuitive marks of non-logicality. If we do require this, we neatly avoid these objections while also managing to demonstrate desirable connections of logicality to necessity. The resulting view is more adequate as a demarcation of the logical expressions of natural language. (shrink)

In this work, we question the ability of existing ranking-based semantics to capture persuasion settings, emphasising in particular the phenomena of procatalepsis and of fading. Some widely accepted principles of ranking-based semantics are incompatible with a faithful treatment of these phenomena, which means that no existing ranking-based semantics can capture these two principles together. This motivates us to introduce a new parametrized ranking-based semantics based on the notion of propagation which extends the existing propagation semantics 139–150) by adding an additional (...) parameter allowing us to gradually decrease the impact of arguments when the length of the path between two arguments increases. We show that this parameter gives the possibility of choosing if one wants to satisfy the property Void Precedence or not and to control the scope of the impact of the arguments. We also propose an experiment to show that the new semantics remains stable when this parameter varies and an axiomatic evaluation to compare it with existing ranking-based semantics in the literature. (shrink)

Many philosophers are baffled by necessity. Humeans, in particular, are deeply disturbed by the idea of necessary laws of nature. In this paper I offer a systematic yet down to earth explanation of necessity and laws in terms of invariance. The type of invariance I employ for this purpose generalizes an invariance used in meta-logic. The main idea is that properties and relations in general have certain degrees of invariance, and some properties/relations have a stronger degree (...) of invariance than others. The degrees of invariance of highly-invariant properties are associated with high degrees of necessity of laws governing/describing these properties, and this explains the necessity of such laws both in logic and in science. This non-mysterious explanation has rich ramifications for both fields, including the formality of logic and mathematics, the apparent conflict between the contingency of science and the necessity of its laws, the difference between logical-mathematical, physical, and biological laws/principles, the abstract character of laws, the applicability of logic and mathematics to science, scientific realism, and logical-mathematical realism. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as (...) part of the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

Graphical displays of simple moving geometrical figures have been repeatedly used to study the attribution of animacy in human observers. Yet little is known about the relevant movement characteristics responsible for this experience. The present study introduces a novel parametric research paradigm, which allows for the experimental control of specific motion parameters and a predictable influence on the attribution of animacy. Two experiments were conducted using 3D computer animations of one or two objects systematically introducing variations in the following (...) aspects of motion: directionality, discontinuity and responsiveness. Both experiments further varied temporal kinematics. Results showed that animacy experience increased with the time a moving object paused in the vicinity of a second object and with increasing complexity of interaction between the objects . The experience of animacy could be successfully modulated in a parametric fashion by the systematic variation of comparably simple differential movement characteristics. (shrink)

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the (...) invariance criterion is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force. (shrink)

Eino Kaila's thought occupies a curious position within the logical empiricist movement. Along with Hans Reichenbach, Herbert Feigl, and the early Moritz Schlick, Kaila advocates a realist approach towards science and the project of a “scientific world conception”. This realist approach was chiefly directed at both Kantianism and Poincaréan conventionalism. The case in point was the theory of measurement. According to Kaila, the foundations of physical reality are characterized by the existence of invariant systems of relations, which he called structures. (...) In a certain sense, these invariant structures, he maintained, are constituted in the act of measuring. By “constitution”, however, Kaila meant neither the dependency of the objects of measurement on a priori concepts (or Kantian categories) nor their being effected by conventional stipulations in a Poincaréan sense. He held that invariant structures are, quite literally, real: they exist prior to and independently of our theoretical capacity. By executing measurements, invariant structures are detected and objectively determinable by laws of nature. (shrink)

Invariance criteria are widely accepted as a means to demarcate the logical vocabulary of a language. In previous work, I proposed a framework of “semantic constraints” for model theoretic consequence which does not rely on a strict distinction between logical and nonlogical terms, but rather on a range of constraints on models restricting the interpretations of terms in the language in different ways. In this paper I show how invariance criteria can be generalized so as to apply to (...) semantic constraints on models. Some obviously unpalatable semantic constraints turn out to be invariant under isomorphisms. I shall connect our discussion to known counterexamples to invariance criteria for logical terms, and so the generalization will also shed light on the current existing debate on logicality. I analyse the failure of invariance to fulfil its role as a criterion for logicality, and argue that invariance conditions should best be thought of as merely methodological meta-constraints restricting the ways the model-theoretic apparatus should be used. (shrink)

This paper considers the parametric control to the Lorenz system by state feedback. Based on the solutions of the generalized Sylvester matrix equation, the unified explicit parametric expression of the state feedback gain matrix is proposed. The closed loop of the Lorenz system can be transformed into an arbitrary constant matrix with the desired eigenstructure. The freedom provided by the parametric control can be fully used to find a controller to satisfy the robustness criteria. A numerical simulation (...) is developed to illustrate the effectiveness of the proposed approach. (shrink)

In Bermúdez 2013 I argued against David Lewis’s well-known and widely accepted claim that Newcomb’s problem and the prisoner’s dilemma are really notational variants of a single problem. Mark Walker’s paper in this journal takes issue with my argument. In this note I show how Walker’s criticisms are misplaced. The problems with Walker’s argument point to more general and independently interesting conclusions about, first, the relation between deliberation and decision and, second, the differences between the prisoner’s dilemma, which is a (...) strategic choice problem, and Newcomb’s problem, which is a parametric choice problem. (shrink)

The structural-parametric synthesis of neural networks of deep learning, in particular convolutional neural networks used in image processing, is considered. The classification of modern architectures of convolutional neural networks is given. It is shown that almost every convolutional neural network, depending on its topology, has unique blocks that determine its essential features, Residual block, Inception module, ResNeXt block. It is stated the problem of structural-parametric synthesis of convolutional neural networks, for the solution of which it is proposed to (...) use a genetic algorithm. The genetic algorithm is used to effectively overcome a large search space: on the one hand, to generate possible topologies of the convolutional neural network, namely the choice of specific blocks and their locations in the structure of the convolutional neural network, and on the other hand to solve the problem of structural-parametric synthesis of convolutional neural network of selected topology. The most significant parameters of the convolutional neural network are determined. An encoding method is proposed that allows to repre- sent each network structure in the form of a string of fixed length in binary format. After that, several standard genetic operations were identified, i.e. selection, mutation and crossover, which eliminate weak individuals of the previous generation and use them to generate competitive ones. An example of solving this problem is given, a database of patients with thyroid disease was used as a training sample. (shrink)

A series of experiments was performed in which subjects indicated whether two four-dot patterns were the same, although possibly viewed from different directions, or different, paired at random. Analyses of responses times and error rates suggest that the subjects' performance in this affine matching task is based on non-accidental properties such as convexity, parallelism, collinearity, and proximity, rather than on real affine invariants such as the ratio of triangular areas.

The dual character of invariance under transformations and definability by some operations has been used in classical works by, for example, Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves could be characterized in terms of invariance. In this article, we generalize a correspondence due to Krasner between invariance under groups of permutations and definability in L∞∞ so as to cover the cases that are of interest in the logicality debates, getting McGee’s (...) theorem about quantifiers invariant under all permutations and definability in pure L∞∞ as a particular case. We also prove some optimality results along the way, regarding the kinds of relations which are needed so that every subgroup of the full permutation group is characterizable as a group of automorphisms. (shrink)

The article considers possible issues connected with using contemporary systematic methods in studying human existence during the crisis stages of life. We suggest that the role of science, art and culture in human life be considered as a way to overcome crises. The system-parametric method developed by Avenir Uyemov allows us to explore the nature of human creativity. This method is based on the dual definition of a system, which may represent any object. When an object is defined, the (...) concept, structure and substrate can be identified. This hierarchy constitutes integrity in the system. The use of such a system-parametric method in studying an object provides new perspectives, especially when it comes to arts and humanities. This paper endeavors to characterize the “creative human” system. The definitions of the “creative human” system used herein indicate that the two definitions are different, but yet still meet the complementarity principle. Both systems are characterized using first-order parameters. For an in-depth analysis, we can use second-order parameters: attributive and relational. In this study five attributive second-order system parameters were used to characterize “creative human” systems. (shrink)

The most compelling extant accounts of explanation casts all explanations as causal. Yet there are sciences, theoretical population biology in particular, that explain their phenomena by appeal to statistical, non-causal properties of ensembles. I develop a generalised account of explanation. An explanation serves two functions: metaphysical and cognitive. The metaphysical function is discharged by identifying a counterfactually robust invariance relation between explanans event and explanandum. The cognitive function is discharged by providing an appropriate description of this relation. I offer (...) examples of explanations from portfolio theory and population genetics that meet this characterisation. In each case the invariance relation holds between a statistical property of an ensemble and a change in structure of the ensemble. In neither case, however, does the statistical property cause the outcome it explains. There are genuine statistical, non-causal scientific explanations. (shrink)

In this article I assess the Invariance Principle, which states that only quantities that are invariant under the symmetries of our theories are physically real. I argue, contrary to current orthodoxy, that the variance of a quantity under a theory’s symmetries is not a sufficient basis for interpreting that theory as being uncommitted to the reality of that quantity. Rather, I argue, the variance of a quantity under symmetries only ever serves as a motivation to refrain from any commitment (...) to the quantity in question. (shrink)

Excerpts from Robert Nozick's "Invariances" Necessary truths are invariant across all possible worlds, contingent ones across only some.

Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.

The parametrized post-Newtonian (PPN) approximation is generalized to accommodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and (...) angularmomentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories. (shrink)