This French article aims at analyzing the Ricardian problem of an "invariable standard of value" in Ricardo's own terms. It is argued that Ricardo's commentators and modern followers have changed these terms significantly. The problem actually branches into two subproblems, i.e., that of "invariability" strictly, and that of "neutrality with respect to distribution". These subproblems do not matter to Ricardo to the same extent. He regards the latter (in various formulations recapitulated here) as a complication of the former, which is (...) the crucial one in his search for a "good" standard. This exemplifies precisely how Ricardo could theoretically focus on the production side of the economy at the expense of the distribution side. With these conclusions at hand, the paper can be critical of Marx's and Sraffa's interpretations of the Ricardian problem of the standard: respectively, because Marx's is simply incorrect, and because Sraffa's solved a problem that was unrelated to the original one in Ricardo. -/- -/- . (shrink)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a (...) classification of classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

In the social sciences, within the explanatory paradigm of structural individualism, a theory of action – like rational choice theory – models how individuals behave and interact at the micro level in order to explain macro observations as the aggregation of these individuals actions. A central epistemological issue is that such theoretical models are stuck in a dilemma between falsity of their basic assumptions and triviality of their explanation. On the one hand, models which have a great empirical success often (...) rest on unrealistic or even knowingly false assumptions; on the other hand, more complex models, with additional more realistic hypotheses, can (trivially) adapt to a wide range of situations and thus loose their explanatory power. Our purpose here is epistemological and consists in wondering to which extent demanding realistic assumptions in such cases is a relevant criterion with respect to the acceptance of a given explanatory model. Via an analogical reasoning with physics, we argue that this criterion seems too strong and actually irrelevant. General physical principles are not just idealized or unrealistic, they can also be formulated in many different yet equivalent ways which do not imply the same fundamental unobservable entities or phenomena. However, the classification of phenomena that such principles allow to highlight does not depend, at the end, on any particular formulation of these basic assumptions. This suggests that some hypotheses in theoretical models are actually not genuine empirical statements that could be independently tested but only substrates of modeling embodying a classification principle. Thus, we develop a structural invariance criterion that we then apply to rational choice models in the social sciences. We argue that this criterion allows to escape from the epistemological dilemma without condemning formal approaches like rational choice theory for their lack of realisticness nor being stuck to any antirealist viewpoint. (shrink)

We argue that traditional formulations of the reduction thesis that tie it to privileged relational operations do not suffice for Peirce’s justification of the categories and invite the charge of gerrymandering to make it come out as true. We then develop a more robust invariant formulation of the thesis, one that is immune to that charge, by explicating the use of triads in any relational operations. The explication also allows us to track how Thirdness enters the structure of (...) higher order relations and even to propose a numerical measure of it. Our analysis reveals new conceptual phenomena when negation or disjunction are used to compound relations. (shrink)

[ENGLISH] The present article is a contribution to the development of metrological structural realism. This position of philosophy of science goes back to Matthias Neuber, who introduces it as a third variation of the main structural realisms: epistemic structural realism and ontic structural realism. Here, Neuber attempts to tackle the problems of OSR and ESR while preserving their respective strengths. Of central importance to his approach, are the concepts of invariance, structure and, especially, measurement. Starting from Eino Kaila’s „non-linguistic, realist (...) account of logical empricism“, the present article investigates the necessity of yet another position of structural realism. The established structural realisms are examined for their strengths and weaknesses. Afterwards, the requirements on MSR are formulated in a way that extends beyond Neuber’s account. These requirements are of ontological, epistemological and metrological nature. -/- [DEUTSCH] Der vorliegende Aufsatz ist ein Beitrag zur Entwicklung des Metrologischen Strukturenrealismus. Diese Wissenschaftstheoretische Position geht auf Matthias Neuber zurück, der sie als dritte Spielart zwischen den großen Strukturenrealismen – dem Epistemischen Strukturenrealismus und dem Ontischen Strukturenrealismus – ansiedelt. Neuber versucht, die wissenschaftstheoretischen Probleme von ESR und OSR anzugehen, gleichzeitig aber ihre jeweiligen Stärken beizubehalten. Dabei sind die Konzepte der Invarianz, der Struktur und besonders der Messung von zentraler Bedeutung. Ausgehend von Eino Kailas „non-linguistic, realist account of logical empiricism“ untersucht der vorliegende Aufsatz die Notwendigkeit einer weiteren strukturenrealistischen Position. Dazu werden die etablierten Strukturenrealismen auf ihre Stärken und Schwächen hin untersucht. Es folgt eine Ausformulierung der Forderungen an den MSR, die über die Darstellung bei Neuber hinaus geht. Diese Forderungen sind ontologischer, epistemischer und metrologischer Natur. (shrink)

An axiomatization of the so-called Teleparallel Equivalent to General Relativity is presented. A set of formal and semantic postulates are elaborated from where the physical meaning of various key concepts of the theory are clarified. These concepts include those of inertia, Lorentz and diffeomorphism invariance, and reference frame. It is shown that Teleparallel Gravity admits a wider representation of space-time than General Relativity, allowing to define properties of the gravitational field such as energy and momentum that are usually considered problematic. (...) In this sense, although the dynamical equations of both theories are equivalent, their inequivalence from a physical point of view is demonstrated. Finally, the axiomatic formulation is used to compare Teleparallel Gravity with other theories of gravity based on absolute parallelism such as non-local and f(T) gravity. (shrink)

We summarize a new realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this (...) intuitive picture of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. Our interpretation—which we claim is ultimately compatible with Lorentz invariance—reformulates wave-function collapse in terms of an underlying interpolating dynamics, makes it possible to derive the Born rule from deeper principles, and resolves several open questions regarding ontological stability and dynamics. (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)

In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In particular, we show that (...) the propositional connectives that are definable in terms of Frege’s horizontal, negation, and conditional are exactly the connectives that fuse with the horizontal, and we show that the logical operators that are definable in terms of the horizontal, negation, the conditional, and identity are exactly the operators that are invariant with respect to permutations on the domain that leave the truth-values fixed. We conclude with some general observations regarding how Frege understood his logic, and how this understanding differs from modern views. (shrink)

Can the idea of a minimal proposition be successfully held? I will first formulate what the minimal proposition is in the minimalist’s mind, taking Emma Borg as the representative. What a minimalist seeks for a minimal proposition is the abstract and skeletal core meaning of a sentence, and this faith is founded on the notion of minimal word meaning—an atomic, code-like, conceptual thing. I show that the problem of this notion of minimal proposition lies in the three features, intuitive read-off, (...) invariantness, and truth-evaluability, that Borg ascribes to it. I shall argue, first, that positing a conceptual-like thing as the invariant minimal content of word cannot support the invariantness of the minimal proposition of a sentence, and second, that the skeletal content, as the minimal proposition of a sentence, is a grammatically analyzed product and thus is hardly truth evaluable. According to the analyses, the idea of a minimal proposition with these three features identified by minimalists cannot be maintained. (shrink)

State of nature theories have a long history and play a lively role in contemporary work. Theories of this kind share certain nontrivial commitments. Among these are commitments to inclusion of a Lockean proviso among the principles of justice and to an assumption of invariance of political principles across changes of circumstances. In this article I want to look at those two commitments and bring to light what I believe are some important difficulties they engender. For nonpattern state of nature (...) theories, the justness of a society is marked by the conformance of the society to procedural principles. Distributions of resources and the like have no particular import for questions of justice. Whatever may later result, so long as it came about in accordance with the rules determined by the principles of justice, is itself just. The Lockean proviso is one of the principles of justice governing property and other rights of nonpattern theories of justice. The proviso hangs as a "shadow" over the results of the operation of the other (usual) principles of justice. It is intended to remedy a complaint which arises when the positions of those no longer at liberty to use some resource are worsened (1) by no longer being able to use freely what they previously were free to use and (2) in such a way that they fall below a "baseline." Following Locke, a traditional formulation of the proviso is to allow acquisition just so long as there is "enough and as good" left over for others. Section I concerns the relation of the Lockean proviso to pattern and nonpattern principles of justice, demonstrating that a Lockean proviso turns a nonpattern into a pattern theory of justice. Section II is about the relation of the Lockean proviso to the ideas revealed by an examination of a state of nature, suggesting reasons to reject ideal theories of justice. (shrink)

Scientists working within a paradigm must play by the rules of the game of that paradigm in solving problems, and that is why incommensurability arises when the rules of the game change. If we deny the thesis of the priority of paradigms, then there is no good argument for the incommensurability of theories and thus for taxonomic incommensurability, because there is no invariant way to determine the set of results provable, puzzles solvable, and propositions cogently formulable under a given (...) paradigm. (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive (...) picture of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

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

It is a remarkable fact that all processes occurring in the observable universe are irre- versible, whereas the equations through which the fundamental laws of physics are formu- lated are invariant under time reversal. The emergence of irreversibility from the funda- mental laws has been a topic of consideration by physicists, astronomers and philosophers since Boltzmann's formulation of his famous \H" theorem. In this paper we shall discuss some aspects of this problem and its connection with the dynamics (...) of space-time, within the framework of modern cosmology. We conclude that the existence of cosmological horizons allows a coupling of the global state of the universe with the local events deter- mined through electromagnetic processes. (shrink)

In his article “Insight: Genesis and Ongoing Context,” Fred Crowe calls out Lonergan’s line “the diagram is more important than…is ordinarily believed” as the “philosophical understatement of the century.” Sixteen pages later he identifies elaborating an invariant cognitional theory to underlie generalized emergent probability and thus “the immanent order of the universe of proportionate being,” as “our challenge,” “but given the difficulty” he does not “see any prospect for an immediate answer.” Could this have something to do with the (...) lack of a comprehensive diagram of cognitional theory? Appendix A of The Boston College Lectures on Mathematical Logic and Existentialism offers diagrams of the dynamics of knowing and doing perhaps copied from Lonergan’s own blackboard work, but they do not distinguish explanatory and descriptive insights, let alone statistical insights, and do not illustrate the pull upwards or the fusing of routinized insights. Before we can effectively relate cognitional theory to generalized emergent probability, we must have an adequately rigorous and precise cognitional theory. I firmly believe in the truth of Lonergan’s fundamental insights, but in order to rigorously undergird generalized emergent probability there are many pertinent questions about his cognitional theory which must be asked and answered. In this paper I (1) review some of Lonergan’s attempts to diagram cognitional theory and discuss what insights they do and do not express, (2) elaborate and defend principles for making our formulations of insight into insight rigorous and clear, and (3) attempt to build up a diagram which makes full use of those principles in a maximally expressive way. (shrink)

In this essay I take the opportunity to recast some insights from my extensive study over the last decade of Wittgenstein’s remarks on music into a coherent and concise portrayal of Wittgenstein’s philosophical underpinning and upshots pertaining to his perception of the modern music scene in interwar Austria. The gist of the present essay is to show that, for better or for worse, Wittgenstein’s personal taste in music was powered by philosophical reasoning, which was organic to his philosophical development, and (...) that ultimately his philosophical attitude to the music scene of interwar Austria manifests a deeply probing gradation. I are argue that we can distinguish between four varieties of the absurd in the music of interwar Austria, according to Wittgenstein. First is the nonsensical absurd of the incapability of seeing that the nonsensicality of the form of progress is incomprehensible. This category pertains to music which straightforwardly tries to emulate the various maxims and formulations derived from the form of progress. Such nonsensically absurd music typifies progressive Romantic composers such as Richard Strauss, Max Reger, and the early Arnold Schoenberg. Second is the vacuous absurd of the incapability of seeing what the form of progress renders incomprehensible. This category pertains to music which denounces the predominantly nonsensical maxims and formulations of modernity, thus destining itself to keeping on groping for something which it cannot express. Such vacuously absurd music is best exemplified, in Wittgenstein’s mind, by Josef Labor. Third is the philosophical absurd of rendering what is incomprehensible (from the perspective of a cultured person) comprehensible within the same purview. For Wittgenstein, Mahler’s music betokens such incommensurability, evoking a relativist philosophical puzzle: whether cultural progress is real, and it is us who have been left behind, or whether culture has really been vanquished, and we are the only ones left to notice it. The very thought of an artwork of “a totally different sort” remains invariably hypothetical. Fourth is the praxeological absurd of giving rise to an auxiliary, praxeologically dislodged musical language, replacing the transparency of human gesture with exact rules of comprehensibility. From Wittgenstein’s perspective, the shunning of the expanse of lived experience in a musical language fit for the meaning-blind would be the inglorious spot assigned to Arnold Schoenberg’s vision of the music of the future. (shrink)

The algebra of transactions as fundamental measurements is constructed on the basis of the analysis of their properties and represents an expansion of the Boolean algebra. The notion of the generalized economic measurements of the economic “quantity” and “quality” of objects of transactions is introduced. It has been shown that the vector space of economic states constructed on the basis of these measurements is relativistic. The laws of kinematics of economic objects in this space have been analyzed and the stages (...) of constructing the dynamics have been formulated. In particular, the “principle of maximum benefit”, which represents an economic analog of the principle of least action in the classical mechanics, and the principle of relativity as the principle of equality of all possible consumer preferences have been formulated. The notion of economic interval between two economic objects invariant to the selection of the vector of consumer preferences has been introduced. Methods of experimental verification of the principle of relativity in the space of economic states have been proposed. (shrink)

ABSTRACT: Decision-theoretic approach and a nonlinguistic theory of norms are applied in the paper in an attempt to explain the nature of scientific rationality. It is considered as a normative system accepted by scientific community. When we say that a certain action is rational, we express a speaker’s acceptance of some norms concerning a definite action. Scientists can choose according to epistemic utility or other rules and values, which themselves have a variable nature. Rationality can be identified with a decision (...) to accept a norm. This type of decision cannot be reduced only to its linguistic formulation; it is an act of evolvement of the normative regulation of human behavior. Norms are treated as decisions of a normative authority: a specific scientific community is the normative authority in science. These norms form a system and they are absolutely objective in the context of individual scientists. There exists an invariant core in all the norms of rationality, accounting for their not being liable to change, as compared with the flexibility of legal norms. The acceptance of and abidance by these norms is of social importance – it affects the aims of the community. A norm only defines the common framework and principles of scientific problem-solving; its application is a matter of professional skills and creative approach to a particular problem. It is of no importance at all, if an agent’s cognitive abilities do not live up to the requirements of a norm. Such discrepancy can be compensated for by the fact that a scientist carries out work in a conceptual and normative framework established by a respective scientific community. (shrink)

This work is driven by the attempt to criticise Phenomenology with the help of Levinas. Similar to the Frankfurt School, he characterises it as a “vision of essences”. These eidetical essences are, and can never be fully absolute, not only because several movements of Hegelian Dialectics are refuted in submitting knowledge either to the imago of mere immanence, or to normative structures which are postulated as invariant like in certain versions of Neoplatonism, but because they function as an apriori (...) of an eternally unfinished and fragmented Lebenswelt. Maybe it is to harsh to compare Husserl to the neoscholastic readings of Descartes and to the formalist interpretations of Kant. Husserl is well aware of the kinaesthetic foundations of consciousness and, contrary to Heidegger, he even promotes Spinozism in a certain phase of his work which excels his adolescent fervour of Berkeley. Nevertheless, Husserl incorporates a subject-based, “monadic” transcendentalism, that paradoxically leads to the dissolution of subjective identity. Traditional reasoning itself is exfoliated to perfection in Heidegger afterwards. Husserl's halfhearted formalism ignores the materialist theory of the simulacrum by Lucretius. Heideggers philosophy widens this overseen aspect in calling the Eidos an Aussehen in referring to the Presocratics, but it despises any kind of method and finally flees in to poetry, maintaining its fatalist errors which it committed right form the start: this is why it gained the name of pseudo-concreteness. Cursed through a specific anti-sociological tendency caused by an anti-empiricist vision of history, their theories virtually (not conceptually) exclude the influences of society on philosophy: they are the end result of the era of Kulturkampf, in which idealism tried to battle positivism, naturalism and historicism. Husserl even defines this philosophical battle as the very struggle of existence. The formulation of the Eidos becomes performance. Aristotle used Eidos synonymous to genus and species. Hence the amplitudes of these philosophies foster the metaphysical standpoint of race, that got out of hand in the Nazi Era and even later on. The “topic” of blood and soil appears in Husserl's definition of Heimwelt and his Eurocentrism. Phenomenology is in no case to blame for National Socialism, and it has very little to to with its causes. My work simply tries to make the same analogy that Marx had made for Hegel. It tries to describe, how two leading philosophers of the German Bourgeoisie are reproducing the categories of their surrounding society without even really observing it. (shrink)

Since the 1950`s in Britain, and perhaps in the rest of the world, the term pluralism is almost invariably associated with the name of Isaiah Berlin and his formulation of ‘value pluralism’. The core idea is that values (but also, on some interpretations, ends, duties and obligations) are irreducibly plural and heterogeneous, and nevertheless objective (...).

Since the 1950`s in Britain, and perhaps in the rest of the world, the term pluralism is almost invariably associated with the name of Isaiah Berlin and his formulation of ‘value pluralism’. The core idea is that values (but also, on some interpretations, ends, duties and obligations) are irreducibly plural and heterogeneous, and nevertheless objective.

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the A(Si) and i,±1 N Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. In detail we (...) realize a bare bone skeleton of quantum mechanics recovering all the basic foundations of this theory on an algebraic framework. We give proof of the quantum like Heisenberg uncertainty relations using only the basic support of the Clifford algebra. In addition we demonstrate the well known phenomenon of quantum Mach Zender interference using the same algebraic framework, as well as we give algebraic proof of quantum collapse in some cases of physical interest by direct application of the theorem that we derive to elaborate the i,±1 N algebra. We also discuss the problem of time evolution of quantum systems as well as the changes in space location, in momentum and the linked invariance principles. We are also able to re-derive the basic wave function of standard quantum mechanics by using only the Clifford algebraic approach. In this manner we obtain a full exposition of standard quantum mechanics using only the basic axioms of Clifford algebra. We also discuss more advanced features of quantum mechanics. In detail, we give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR paradox only using the Clifford algebra. By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that, as it is well known, are interpreted as logical statements, following the basic von Neumann results. Von Neumann realized a matrix logic on the basis of quantum mechanics. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic. Therefore, it seems that we may conclude that quantum mechanics, as it appears when investigated by the Clifford algebra, is a two-faced theory in the sense that it looks from one side to “matter per se”, thus to objects but simultaneously also to conceptual entities. We advance the basic conclusion of the paper: There are stages of our reality in which we no more can separate the logic ( and thus cognition and thus conceptual entity) from the features of “matter per se”. In quantum mechanics the logic, and thus the cognition and thus the conceptual entity-cognitive performance, assume the same importance as the features of what is being described. We are at levels of reality in which the truths of logical statements about dynamic variables become dynamic variables themselves so that a profound link is established from its starting in this theory between physics and conceptual entities. Finally, in this approach there is not an absolute definition of logical truths. Transformations , and thus … “redefinitions”…. of truth values are permitted in such scheme as well as the well established invariance principles, clearly indicate . (shrink)

Background independence begins life as an informal property that a physical theory might have, often glossed as 'doesn't posit a fixed spacetime background'. Interest in trying to offer a precise account of background independence has been sparked by the pronouncements of several theorists working on quantum gravity that background independence embodies in some sense an essential discovery of the General Theory of Relativity, and a feature we should strive to carry forward to future physical theories. This paper has two goals. (...) The first is to investigate what a world must be like in order to be truly described by a background independent theory given extant accounts of background independence. The second is to argue that there are no non-empirical reasons to be more confident in theories that satisfy extant accounts of background independence than in theories that don't. The paper concludes by drawing a general moral about a way in which focussing primarily on mathematical formulations of our physical theories can adversely affect debates in the metaphysics of physics. (shrink)

The purpose of this paper is to argue that (1) that the hard problem of consciousness is concerned with subjective experience; (2) subjective experience arises from the measure of absolute quantities directly by our senses; (3) objective experience, on the other hand, arises from the measure of relative quantities which are invariant to perception; (4) only relative quantities can be shared with others; (5) consequently the hard problem is forever locked inside the head of each individual and can never (...) be discussed, explained or shared with another. (6) Accordingly, no theory can, in principle, be formulated to explain it. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties of (...) energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (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)

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

It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek, and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a (...) related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision- theoretic implications. -/- The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgments about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to nonmeasurable regions. (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)

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.

Some philosophers say that in special relativity, four-dimensional stuff is invariant in some sense that three-dimensional stuff is not. I show that this claim is false.

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)

What can rational deliberation indicate about belief? Belief clearly influences deliberation. The principle that rational belief is stake-invariant rules out at least one way that deliberation might influence belief. The principle is widely, if implicitly, held in work on the epistemology of categorical belief, and it is built into the model of choice-guiding degrees of belief that comes to us from Ramsey and de Finetti. Criticisms of subjective probabilism include challenges to the assumption of additive values (the package principle) (...) employed by defenses of probabilism. But the value-interaction phenomena often cited in such challenges are excluded by stake-invariance. A comparison with treatments of categorical belief suggests that the appeal to stake-invariance is not ad hoc. Whether or not to model belief as stake-invariant is a question not settled here. (shrink)

It is now standard to interpret symmetry-related models of physical theories as representing the same state of affairs. Recently, a debate has sprung up around the question when this interpretational move is warranted. In particular, Møller-Nielsen :1253–1264, 2017) has argued that one is only allowed to interpret symmetry-related models as physically equivalent when one has a characterisation of their common content. I disambiguate two versions of this claim. On the first, a perspicuous interpretation is required: an account of the models’ (...) common ontology. On the second, stricter, version of this claim, a perspicuous formalism is required in addition: one whose mathematical structures ‘intrinsically’ represent the physical world, in the sense of Field. Using Dewar’s :485–521, 2019) distinction between internal and external sophistication as a case study, I argue that the second requirement is decisive. This clarifies the conditions under which it is warranted to interpret symmetry-related models as physically equivalent. (shrink)

We explore depth substitution invariance, or hyperformalism, and extend known results in this realm to justification logics extending weak relevant logics. We then examine the surprising invariance of justifications over formulas and restrict our attention to the substitution of proofs in the original relevant logic. The results of this paper indicate that depth invariance is a recalcitrant feature of the logic and that proof structures in hyperformal logics are quite inflexible.

Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle (...) version of the Higgs mechanism. (shrink)

This note contains a corrective and a generalization of results by Borsboom et al. (2008), based on Heesen and Romeijn (2019). It highlights the relevance of insights from psychometrics beyond the context of psychological testing.

Relativity Theory by Albert Einstein has been so far littleconsidered by cognitive scientists, notwithstanding its undisputedscientific and philosophical moment. Unfortunately, we don't have adiary or notebook as cognitively useful as Faraday's. But physicshistorians and philosophers have done a great job that is relevant bothfor the study of the scientist's reasoning and the philosophy ofscience. I will try here to highlight the fertility of a `triangulation'using cognitive psychology, history of science and philosophy of sciencein starting answering a clearly very complex question:why (...) did Einstein discover Relativity Theory? Here we arenot much concerned with the unending question of precisely whatEinstein discovered, that still remains unanswered, for we have noconsensus over the exact nature of the theory's foundations. We are mainly interested in starting to answer the`how question', and especially the following sub-question: what were his goals and strategies in hissearch? I will base my argument on fundamental publications ofEinstein, aiming at pointing out a theory-specific heuristic, settingboth a goal and a strategy: covariance/invariance.The result has significance in theory formation in science, especiallyin concept and model building. It also raises other questions that gobeyond the aim of this paper: why was he so confident in suchheuristic? Why didn't many other scientists use it? Where did he keep? such a heuristic? Do we have any other examples ofsimilar heuristic search in other scientific problemsolving? (shrink)

A number of papers have applied the CNI model of moral judgments to investigate deontological and consequentialist response tendencies (Gawronski et al., 2017). A controversy has emerged concerning the methodological assumptions of the CNI model (Baron & Goodwin, 2020, 2021; Gawronski et al. 2020). In this paper, we contribute to this debate by extending the CNI paradigm with a skip option. This allows us to test an invariance assumption that the CNI model shares with prominent process-dissociation models in cognitive and (...) social psychology (Klauer et al., 2015). Like for these models, the present experiments found violations of the invariance assumption for the CNI model. In Experiment 2, we replicate these results and selectively influence the new parameter for the skip option. In addition, structural equation modeling reveals that previous findings for the relationship between gender and the CNI parameters are completely mediated by the association of gender with primary psychopathy. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

We often get evidence that bears on the reliability of some of our own first-order reasoning. The rational response to such “higher-order” evidence would seem to depend on a rational assessment of how reliable we can expect that reasoning to be, in light of the higher-order evidence. “Independence” principles are intended to constrain this reliability-assessment, so as to prevent question-begging reliance on the very reasoning being assessed. However, extant formulations of Independence principles tend to be vague or ambiguous, and coming (...) up with a tolerably precise formulation turns out to be tricky. This paper aims to make some progress toward developing a more precise Independence principle, and also to highlight some of the difficulties the project entails. The hope is to take a step toward understanding how rational belief is informed by evidence bearing on agents’ cognitive reliability. (shrink)

Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to (...) a well-ordered set after measurement and thus requires the axiom of choice. Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. (shrink)

A violation of procedure invariance in preference measurement is that the predominant or prominent attribute looms larger in choice than in a matching task. In Experiment 1, this so-called prominence effect was demonstrated for choices between pairs of options, choices to accept single options, and preference ratings of single options. That is, in all these response modes the prominent attribute loomed larger than in matching. The results were replicated in Experiment 2, in which subjects chose between or rated their preference (...) for pairs of options which were matched to be equally attractive either in the same session or 1 week earlier. On the basis of these and previous results, it is argued that the prominence effect is a reliable phenomenon. However, none of several cognitive explanations which have been offered appears to be completely viable. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

I provide a theory of causation within the causal modeling framework. In contrast to most of its predecessors, this theory is model-invariant in the following sense: if the theory says that C caused (didn't cause) E in a causal model, M, then it will continue to say that C caused (didn't cause) E once we've removed an inessential variable from M. I suggest that, if this theory is true, then we should understand a cause as something which transmits deviant (...) or non-inertial behavior to its effect. (shrink)

The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski- Grothendieck set theory TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies the existence (...) of inaccessible cardinals [1].Non-conservative extension of ZFC based on an generalized quantifiers considered in [4]. In this paper we look at a set theory NC_{∞^{#}}^{#},based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [5]-[8]. In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC_{∞^{}}^{} contains Aczel's anti-foundation axiom [9]. We present a new approach to the invariant subspace problem for Hilbert spaces. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace. Non-conservative extension based on set theory NC_{∞}^{#} of the model theoretical nonstandard analysis [10]-[12] also is considered. (shrink)

I argue that we should question the orthodox way of thinking about epistemological disjunctivism. I suggest that we can formulate epistemological disjunctivism in terms of states of seeing things as opposed to states of seeing that p. Not only does this alternative formulation capture the core aspects of epistemological disjunctivism as standardly formulated, it has two salient advantages. First, it avoids a crucial problem that arises for a standard formulation of epistemological disjunctivism—the basis problem. And second, it is (...) less committed than standard formulations are in the metaphysics of perception. (shrink)