Permutationinvariance is often presented as the correct criterion for logicality. The basic idea is that one can demarcate the realm of logic by isolating specific entities—logical notions or constants—and that permutationinvariance would provide a philosophically motivated and technically sophisticated criterion for what counts as a logical notion. The thesis of permutationinvariance as a criterion for logicality has received considerable attention in the literature in recent decades, and much of the debate is (...) developed against the background of ideas put forth by Tarski in a 1966 lecture (Tarski 1966/1986). But as noted by Tarski himself in the lecture, the permutationinvariance criterion yields a class of putative ‘logical constants’ that are essentially only sensitive to the number of elements in classes of individuals. Thus, to hold the permutationinvariance thesis essentially amounts to limiting the scope of logic to quantificational phenomena, which is controversial at best and possibly simply wrong. In this paper, I argue that permutationinvariance is a misguided approach to the nature of logic because it is not an adequate formal explanans for the informal notion of the generality of logic. In particular, I discuss some cases of undergeneration of the criterion, i.e. the fact that it excludes from the realm of logic operators that we have good reason to regard as logical, especially some modal operators. (shrink)
Physical theories continue to be interpreted in terms of particles. The idea of a particle required modification with the advent of quantum theory, but remains central to scientific explanation. Particle ontologies also have the virtue of explaining basic epistemic features of the world, and so remain appealing for the scientific realist. However, particle ontologies are untenable when coupled with the empirically necessary postulate of permutationinvariance—the claim that permuting the roles of particles in a representation of a physical (...) state results in a representation of the same physical state. I demonstrate that any theory which is permutation invariant in this sense is incompatible with a particle ontology. (shrink)
The idea that the world is made of particles — little discrete, interacting objects that compose the material bodies of everyday experience — is a durable one. Following the advent of quantum theory, the idea was revised but not abandoned. It remains manifest in the explanatory language of physics, chemistry, and molecular biology. Aside from its durability, there is good reason for the scientific realist to embrace the particle interpretation: such a view can account for the prominent epistemic fact that (...) only limited knowledge of a portion of the material universe is needed in order to make reliable predictions about that portion. Thus, particle interpretations can support an abductive argument from the epistemic facts in favor of a realist reading of physical theory. However, any particle interpretation with this property is untenable. The empirical adequacy of modern particle theories requires adoption of a postulate known as permutationinvariance — the claim that interchanging the role of two particles of the same kind in a dynamical state description results in a description of the identical state. It is the central claim of this essay that PI is incompatible with any particle interpretation strong enough to account for the epistemic facts. This incompatibility extends across all physical theories. To frame and motivate the inconsistency argument, I begin by fixing the relevant notion of particle. To single out those accounts of greatest appeal to the realist, I develop the logically weakest particle ontology that entails the epistemic fact that the world is piecewise predictable, an ontology I call ‘minimal atomism’. The entire series of scientific conceptions of the particle, from Newton’s mechanically interacting corpuscles to the ‘centers of force’ in classical field theories, all comport with MA. As long as PI is left out, even quantum mechanics can be viewed this way. To assess the impact of PI on this picture, I present a framework for rigorously connecting interpretations to physical theories. In particular, I represent MA as a set of formal conditions on the models of physical theories, the mathematical structures taken to represent states of the world. I also formulate PI — originally introduced as a postulate of non-relativistic quantum mechanics — in theory independent terms. With all of these pieces in hand, I am then able to present a proof of the inconsistency of PI and MA. In the second part of the essay, I survey responses to the inconsistency result open to the scientific realist. The two most plausible approaches involve abandoning particles in one way or another. The first alternative interpretation considered takes the property bearing objects of the world to be regions of space rather than particles. In this view, the properties once attributed to particles in quantum states are attributed instead to one or more regions of space. PI no longer obtains in this case, at least not as a statement about the permutation symmetry of property bearers. Rather, the new interpretation naturally imposes an analogous constraint on quantum states. The second major approach to evading the inconsistency result is to dispense with objects altogether. This is the recommendation of so-called ‘Ontic Structural Realism’. The central OSR thesis is that structure rather than entities are the basic ontological components of the world. OSR is intended to embrace the ‘miracle’ argument in favor of scientific realism while avoiding the pessimistic meta-induction. I demonstrate that one principal motivation for OSR based on the under-determination of interpretations in QM is actually dissolved by the incompatibility result. At the same time, I suggest reasons to think that OSR fares no better with respect to the pessimistic meta-induction than traditional realism does. Thus, while PI and MA may be incompatible, object ontologies remain the best option for the realist. (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.
The paper provides a new argument against the classical invariance criterion for logical terms: if all terms with a permutation invariant extension qualify as logical, then for any arbitrary true contingent sentence K of the meta-language, there would be a logically true object-language sentence 'φ' such that K follows from the sentence 'φ is true'. Thus, many logically true sentences would be a posteriori. To prevent this fatal consequence, we propose to alter the invariance criterion: not only (...) the term's extension, but also its semantic clause must satisfy certain invariance conditions. The paper ends with the observation that the new criterion makes explicit the dependency of the classification of terms into logical and non-logical ones at the different levels of the Tarskian hierarchy of languages. (shrink)
This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutationinvariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a proposal in response to one of those critiques via homomorphism invariance. That has (...) quite divergent characterization results depending on its formulation, one in terms of FOL, the other by Bonnay in terms of L∞,∞, both without equality. From that we move on to a survey of Bonnay’s work on similarity relations between structures and his results that single out invariance with respect to potential isomorphism among all such. Turning to the critique that calls for sameness of meaning of a logical operation across domains, the paper continues with a result showing that the isomorphism invariant operations that are absolutely definable with respect to KPU−Inf are exactly those definable in full FOL; this makes use of an old theorem of Manders. The concluding section is devoted to a critical discussion of the arguments for set-theoretical criteria for logicality. (shrink)
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)
In this paper I discuss some metaphysical consequences of an unorthodox approach to the problem of the identity and individuality of “indistinguishable” quantum particles. This approach is based on the assumption that the only admissible way of individuating separate components of a given system is with the help of the permutation-invariant qualitative properties of the total system. Such a method of individuation, when applied to fermionic compositions occupying so-called GMW-nonentangled states, yields highly implausible consequences regarding the number of distinct (...) components of a given composite system. I specify the problem in detail, and I consider several strategies of solving it. The preferred solution of the problem is based on the premise that spatial location should play a privileged role in identifying and making reference to quantum-mechanical systems. (shrink)
The ways in which space-time points and elementary particles are modeled share a curious feature: neither seems to specify which basic object has which properties. This chapter sketches the motivation for this claim and searches for an explanation for it. After reviewing several proposals, it argues for a view according to which objects occupy their place in a given relational structure essentially. This view, which is termed minimal structural essentialism, provides a metaphysical grounding for the physical equivalence of models related (...) by permutation. An interesting consequence of this position is that space-time points and elemental particles turn out to be individuals, albeit of a rather different sort than has traditionally been considered. (shrink)
In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence phi according to this permutation should not change our belief in the truth of phi. In this paper we study when a prior probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.
The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutationinvariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutationinvariance for such principles, (...) assessing the philosophical significance of each. (shrink)
Fine and Antonelli introduce two generalizations of permutationinvariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, (...) and the comparative lack of success in reconstructing areas of mathematics other than arithmetic based on non-invariant abstraction principles. (shrink)
The relation of global supervenience is widely appealed to in philosophy. In slogan form, it is explained as follows: a class of properties A supervenes on a class of properties B if no two worlds differ in the distribution of A-properties without differing in the distribution of B-properties. It turns out, though, that there are several ways to cash out that slogan. Three different proposals have been discussed in the literature. In this paper, I argue that none of them is (...) adequate. Furthermore, I present a puzzle that reveals a tension in our concept of global supervenience. (shrink)
There has been considerable recent philosophical debate over the implications of many particle quantum mechanics for the metaphysics of individuality (cf. Huggett ). In this paper I look at things from a rather different perspective: by investigating the significance of permutation symmetry. I consider how various philosophical positions link up to the physical postulate of the indistinguishability of permuted states-permutationinvariance-and how this postulate is used to explain quantum statistics. I offer an explanation of the statistics that (...) relies on the neglected parallel between permutations and covariant spatial transformation. And I explore the parallel, showing that a further kind of symmetry explains why permutations are invariant when spatial symmetries are not. (shrink)
In this article I expound an understanding of the quantum mechanics of so-called “indistinguishable” systems in which permutationinvariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This understand- ing has heterodox consequences for the understanding of the states of constituent systems in an assembly and for the notion of entanglement. It corrects widespread misconceptions about the inter-theoretic relations between quantum mechanics and both classical particle mechanics and quantum field theory. The (...) most striking of the heterodox consequences are: that fermionic states ought not always to be considered entangled; it is possible for two fermions or two bosons to be discerned using purely monadic quantities; and that fermions may always be so discerned. (shrink)
The problem of logical constants consists in finding a principled way to draw the line between those expressions of a language that are logical and those that are not. The criterion of invariance under permutation, attributed to Tarski, is probably the most common answer to this problem, at least within the semantic tradition. However, as the received view on the matter, it has recently come under heavy attack. Does this mean that the criterion should be amended, or maybe (...) even that it should be abandoned? I shall review the different types of objections that have been made against invariance as a logicality criterion and distinguish between three kinds of objections, skeptical worries against the very relevance of such a demarcation, intensional warnings against the level at which the criterion operates, and extensional quarrels against the results that are obtained. I shall argue that the first two kinds of objections are at least partly misguided and that the third kind of objection calls for amendment rather than abandonment. (shrink)
This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutationinvariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes (...) this analogy: in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. (shrink)
Ontic structuralism or ontic structural realism in the philosophy of physics can be broadly considered as an interpretative strategy providing a set of conceptual and metaphysical tools—or, more ambitiously, an ontological framework—in order to account for central features of current fundamental physics. This article aims to review the main structuralist interpretative moves in the context of our two best fundamental physical theories of matter and spacetime, namely, quantum theory and general relativity. We highlight in particular the structuralist understanding of (...) class='Hi'>permutationinvariance, entanglement and nonlocality in quantum theory, and of the dynamical features of spacetime, diffeomorphism invariance and background independence in general relativity. (shrink)
Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and (...) a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)
This paper argues for a different logical form for complex demonstratives, given that the quantificational account is correct. In itself that is controversial, but two aspects will be assumed. Firstly, there are arguments to believe that complex demonstratives have quantificational uses. Specifically, there are syntactic arguments. Secondly, a uniform semantics is preferable to a semantics of ambiguity. Given this, the proposed logical forms for complex demonstratives that are prevalent do not respect a fundamental property of quantifiers: permutationinvariance. (...) The reason for this is the attempt to retain, in the logical forms proposed, the strong intuitions of reference that uses of complex demonstratives display. The paper suggests that the directly referential intuitions surrounding complex demonstratives cannot be taken to be part of the semantics of the expression. There appears to be no need to do so, either. The paper defends the new logical form against various objections. (shrink)
How best to think about quantum systems under permutationinvariance is a question that has received a great deal of attention in the literature. But very little attention has been paid to taking seriously the proposal that permutationinvariance reflects a representational redundancy in the formalism. Under such a proposal, it is far from obvious how a constituent quantum system is represented. Consequently, it is also far from obvious how quantum systems compose to form assemblies, i.e. (...) what is the formal structure of their relations of parthood, overlap and fusion. In this paper, I explore one proposal for the case of fermions and their assemblies. According to this proposal, fermionic assemblies which are not entangled—in some heterodox, but natural sense of ‘entangled’—provide a prima facie counterexample to classical mereology. This result is puzzling; but, I argue, no more intolerable than any other available interpretative option. (shrink)
A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational PermutationInvariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.
The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin-statistics connection and the Symmetrization Postulate. In light of recent theories (such as q-deformed commutators) that allow for ‘small’ violations of the spin-statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that (...) class='Hi'>permutation symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles. 1 Introduction 2 Philosophical background 2.1 Important terminology 2.1.1 Identity 2.1.2 Indistinguishability 2.1.3 Indiscernibility 2.2 When are particles indistinguishable? 2.3 The Principle of the Identity of Indiscernibles and quantum mechanics 2.4 The Principle of the Identity of Indiscernibles and logic 2.5 Particle history 2.6 Transcendental individuality 3 Some quantum formalism 3.1 The Principle of PermutationInvariance and the Symmetrization Postulate 3.2 The configuration-space approach 3.3 Commutators and anticommutators, and identical particle statistics 3.4 Q-mutators 4 Identical particle statistics: a holistic point of view 5 Conclusions. (shrink)
Dissipative structures consisting of a few macrovariables arise out of a sea of reversible microvariables. Unexpected residual effects of the massive underlying reversibility, on the macrolevel, cannot therefore be excluded. In the age of molecular-dynamics simulations, explicit dissipative structures like excitable systems (“explicit observers”) can be generated in a computer from first reversible principles. A class of classical, 1-D Hamiltonian systems of chaotic type is considered which has the asset that the trajectorial behavior in phase space can be understood geometrically. (...) If, as natural, the number of particle types is much smaller than that of particles, the Gibbs symmetry must be taken into account. The permutationinvariance drastically changes the behavior in phase space (quasi-periodization). The explicit observer becomes effectively reversible on a short time scale. In consequence, his ability to measure microscopic motions is suspended in a characteristic fashion. Unlike quantum mechanics whose “holistic” nature cannot be transcended, the present holistic (internal-interface) effects—mimicking the former to some extent—can be understood fully in principle. (shrink)
This research examines business and psychology students’ attitude toward unethical behavior (measured at Time 1) and their propensity to engage in unethical behavior (measured at Time 1 and at Time 2, 4 weeks later) using a 15-item Unethical Behavior measure with five Factors: Abuse Resources, Not Whistle Blowing, Theft, Corruption, and Deception. Results suggested that male students had stronger unethical attitudes and had higher propensity to engage in unethical behavior than female students. Attitude at Time 1 predicted Propensity at Time (...) 1 accurately for all five factors (concurrent validity): If students consider it to be unethical, then, they are less likely to engage in that unethical behavior. Attitude at Time 1 predicted only Factor Abuse Resources for Propensity at Time 2. Propensity at Time 1 was significantly related to Propensity at Time 2. Attitude at Time 1, Propensity at Time 1, and Propensity at Time 2 had achieved configural and metric measurement invariance across major (business vs. psychology). Thus, researchers may have confidence in using these measures in future research. (shrink)
How should we understand the notion of moral objectivity? Metaethical positions that vindicate morality’s objective appearance are often associated with moral realism. On a realist construal, moral objectivity is understood in terms of mind-, stance-, or attitude-independence. But realism is not the only game in town for moral objectivists. On an antirealist construal, morality’s objective features are understood in virtue of our attitudes. In this paper I aim to develop this antirealist construal of moral objectivity in further detail, and to (...) make its metaphysical commitments explicit. I do so by building on Sharon Street’s version of “Humean Constructivism”. Instead of the realist notion of attitude-independence, the antirealist account of moral objectivity that I articulate centres on the notion of standpoint-invariance. While constructivists have been criticized for compromising on the issue of moral objectivity, I make a preliminary case for the thesis that, armed with the notion of standpoint-invariance, constructivists have resources to vindicate an account of objectivity with just the right strength, given the commitments of ordinary moral thought and practice. In support of this thesis I highlight recent experimental findings about folk moral objectivism. Empirical observations about the nature of moral discourse have traditionally been taken to give prima facie support to moral realism. I argue, by contrast, that from what we can tell from our current experimental understanding, antirealists can capture the commitments of ordinary discourse at least as well as realists can. (shrink)
The Desire-as-Belief thesis (DAB) states that any rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis's argument was based on an Invariance condition that itself is inconsistent with the (standard formulation of the) version of Bayesian decision theory that he assumed in his arguments against DAB. The aim (...) of this paper is to explore what impact the rejection of Invariance has on the DAB thesis. Without assuming Invariance, we first refute all versions of DAB that entail that there are only two levels of goodness. We next consider two theses according to which rational desires are intimately connected to expectations of (multi-levelled) goodness, and show that these are consistent with Bayesian decision theory as long as we assume that the contents of 'value propositions' are not fixed. We explain why this conclusion is independently plausible, and show how to construct such propositions. (shrink)
Since the time of Aristotle, metaphysics has been an ill-defined term. This paper defines it as a logically idempotent metalinguistic identity of reality which couples the two initial ingredients of awareness: perceptual reality (the basis of physics), and cognitive-perceptual syntax, a formalization of mind. The explanation has been reduced to a few very simple, clearly explained mathematical ingredients. This paper contains no assumptions or arguable assertions, and is therefore presented as an advanced formulation of logic which has been updated for (...) meaningful reference to the structure of reality at large. This structure, called the Cognitive-Theoretic Model of the Universe or CTMU, resolves the problems attending Cartesian dualism by replacing dualism with the mathematical property of self-duality, meaning (for reality-theoretic purposes) the quantum-level invariance of identity under permutation of objective and spatiotemporal data types. The CTMU takes the form of a global coupling or superposition of mind and physical reality in a self-dual metaphysical identity M:L<-->U, which can be intrinsically developed into a logico-geometrically self-dual, ontologically self- contained language incorporating its own medium of existence and comprising its own model therein. (shrink)
This study investigates measurement invariance of the 17-item-4-factor Love of Money Scale across gender and college major among university students in People’s Republic of China. Results revealed configural invariance across gender. Metric invariance across gender was not achieved based on chi-square change, but achieved based on fit indices change between unconstrained and constrained multi-group confirmatory factor analysis. Both configural invariance and metric invariance were achieved across college major. Results of this study suggest that the Love (...) of Money Scale, developed in the U.S., has achieved measurement invariance in this student sample in China. Future researchers will have some confidence in using this measurement when they examine the love of money in Chinese management and organizational studies. (shrink)
This chapter explores some issues having to do with the structure of the evidential reasoning we use to infer causal and lawful claims. It is argued that such reasoning always makes use of prior, causally, or nomologically committed information, thus undercutting various views that attempt to reduce causal and lawful claims to claims about regularities. A non-reductive account of laws and causes built around the notion of invariance is advanced as an alternative.
In this paper I attempt mainly to elucidate the claim, advanced by Woorward, that the key notion to characterize physical laws is that of invariance. I draw a distinction betwen two levels of invariance in order to elaborate that thesis. I maintain that distinctive marks of the nomic status of basic laws of physics are either that they hold invariantly, within a domain of applivation, or that they fulfill some principles of symmetry. The fomer mark relatesd to the (...) manner in which physical systems change invariantly whereas the latter concerns to the invariance of the laws themselves. This view contrats with the traditional philosophical thesis that physical laws are true universal statements with a necessary character which differentiate then from accidental true generalizations, which are contingent. (shrink)
This paper discusses a novel approach to singularities, based on a recent extension of general relativity that shows why singularities do not constitute a breakdown of physical laws: it is not only the case that physical laws are valid, but they also remain invariant at singularities. The paper describes this kind of invariance, and draws its consequences for our understanding of equivalence in general relativity. In particular, it points out that the difference between the metrics at singularities and those (...) outside of singularities is factual, rather than nomological, and that this justifies the extension of the principle of equivalence to singularities. (shrink)
In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi–Dirac statistics follows as a consequence of this coupling (...) while the Bose–Einstein follows by breaking it. In Sec. 5, the above approach is related to Pauli's original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch–Gordan coefficients and the experimental evidence respectively, is presented. (shrink)
This review is a critical discussion of three main claims in Debs and Redhead’s thought-provoking book Objectivity, Invariance, and Convention. These claims are: (i) Social acts impinge upon formal aspects of scientific representation; (ii) symmetries introduce the need for conventional choice; (iii) perspectival symmetry is a necessary and sufficient condition for objectivity, while symmetry simpliciter fails to be necessary.
The principle of functional invariance states that it is a natural law that conscious beings with the same functional organization have the same quality of conscious experience. A group of arguments in support of this principle are rejected, on the grounds that they establish at most only the weaker intra-subjective principle that any two stages in the life of a single conscious being that duplicate one another in terms of functional organization also duplicate one another in terms of quality (...) of phenomenal experience. (shrink)
An experiment aimed at detecting a DC voltage across a conductor induced by the steady magnetic field of a coil, carried out in 1998, provided a positive (although preliminary) evidence for such an effect, which might be interpreted as a breakdown of local Lorentz invariance. We repeated in 1999 the same experiment with a different experimental apparatus and a sensitivity improved by two orders of magnitude. The results obtained are discussed here in detail. They confirm the findings of the (...) previous experiment, and show, among the others, that the effect is independent of the direction of the current. A possible interpretation of the results is given in terms of a geometric description of the gravitational and the electromagnetic interactions by means of phenomenological, energy-dependent metrics. (shrink)
If p(x 1 ,...,x n ) and q(x 1 ,...,x n ) are two logically equivalent propositions then p(π (x 1 ),...,π (x n )) and q(π (x 1 ),...,π (x n )) are also logically equivalent where π is an arbitrary permutation of the elementary constituents x 1 ,...,x n . In Quantum Logic the invariance of logical equivalences breaks down. It is proved that the distribution rules of classical logic are in fact equivalent to the meta-linguistic (...) rule of universal substitution and that the more restrictive structure of the substitution group of Quantum Logic prevents us from defining truth in a classical fashion. These observations lead to a more profound understanding of the Logic of Quantum Mechanics and of the role that symmetry principles play in that theory. (shrink)
The first invariance principle, called “meaningfulness,” is germane to the common practice requiring that the form of a scientific law must not be altered by a change of the units of the measurement scales. By itself, meaningfulness does not put any constraint on the possible data. The second principle requires that the output variable is “order-invariant” with respect to any transformation (of one of the input variables) belonging to a particular family or class of such transformations which are characteristic (...) of the law. These principles are formulated as axioms of a theory. Taken together, meaningfulness and order-invariance axioms have strong consequences on the feasible theories. Three applications of our results are discussed in details, involving the Lorentz–FitzGerald contraction, Beer's law, and the Monomial laws, each of which is derived from three axioms implementing meaningfulness and order-invariance concepts. (An “initial condition” axiom is also used.) Not all scientific laws are order-invariant in the sense of this paper. An example is van der Waals' equation. (shrink)
The paper considers the "GR-desideratum", that is, the way general relativity implements general covariance, diffeomorphism invariance, and background independence. Two cases are discussed where 5-dimensional generalizations of general relativity run into interpretational troubles when the GR-desideratum is forced upon them. It is shown how the conceptual problems dissolve when such a desideratum is relaxed. In the end, it is suggested that a similar strategy might mitigate some major issues such as the problem of time or the embedding of quantum (...) non-locality into relativistic spacetimes. (shrink)
Scientific knowledge should not only be true, it should be as objective as possible. It should refer to a reality independent of any subject. What can we use as a criterion of objectivity? Intersubjectivity (i.e., intersubjective understandability and intersubjective testability) is necessary, but not sufficient. Other criteria are: independence of reference system, independence of method, non-conventionality. Is there some common trait? Yes, there is: invariance under some specified transformations. Thus, we say: A proposition is objective only if its truth (...) is invariant against a change in the conditions under which it was formulated. We give illustrations from geometry, perception, neurobiology, relativity theory, and quantum theory. Such an objectivist position has many advantages. (shrink)
The failed criterion of logical truth proposed by Carnap in the Logical Syntax of Language was based on the determinateness of all logical and mathematical statements. It is related to a conception which is independent of the specifics of the system of the Syntax, hints of which occur elsewhere in Carnap’s writings, and those of others. What is essential is the idea that the logical terms are invariant under reinterpretation of the empirical terms, and are therefore semantically determinate. A certain (...) objection to Carnap’s version of the invariance conception has been repeated several times in the literature. It is based on Gödel incompleteness, which is puzzling, since Carnap’s Syntax is otherwise quite careful to take account of Gödel. We show here that, in fact, the objection is invalid and is based on a confusion about determinacy. Sorting this out is worthwhile not only for the purpose of better understanding Carnap’s thinking in the Syntax, though. The invariance conception is also related to recent work in the philosophy of logic regarding “logicality”—the characterization of logical concepts—following a proposal of Tarski’s. It is even connected to some very recent developments in the foundations of mathematics. (shrink)
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 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)
Crisp is right to detect a clash between Dancy's leading formulation of holism about reasons and the phenomenon of invariance. Replying to Crisp on behalf of the particularist, I suggest a better formulation of holism modelled on a standard treatment in the philosophy of language of context-sensitive expressions. Key Words: context-sensitivity Crisp Dancy holism invariance particularism.
How does the visual system recognize images of a novel object after a single observation despite possible variations in the viewpoint of that object relative to the observer? One possibility is comparing the image with a prototype for invariance over a relevant transformation set. However, invariance over rotations has proven difficult to analyze, because it applies to some objects but not others. We propose that the invariant transformations of an object are learned by incorporating prior expectations with real-world (...) evidence. We test this proposal by developing an ideal learner model for learning invariance that predicts better learning of orientation dependence when prior expectations about orientation are weak. This prediction was supported in two behavioral experiments, where participants learned the orientation dependence of novel images using feedback from solving arithmetic problems. (shrink)
We give a derivation of exclusion principles for the elementary particles of the standard model, using simple mathematical principles arising from a set theory of identical particles. We apply the theory of permutation group actions, stating some theorems which are proven elsewhere, and interpreting the results as a heuristic derivation of Pauli's Exclusion Principle (PEP) which dictates the formation of elements in the periodic table and the stability of matter, and also a derivation of quark confinement. We arrive at (...) these properties by using a symmetry property of collections of the particles themselves as compared for example to the symmetry property of their wave function under interchange of two particles. (shrink)
Let M be a model of ZFAC (ZFC modified to allow a set of atoms), and let N be an inner model with the same set of atoms and the same pure sets (sets with no atoms in their transitive closure) as M. We show that N is a permutation submodel of M if and only if N satisfies the principle SVC (Small Violations of Choice), a weak form of the axiom of choice which says that in some sense, (...) all violations of choice are localized in a set. A special case is considered in which there exists an SVC witness which satisfies a certain homogeneity condition. (shrink)
The article presents an analysis of a mystical practice of letter permutation conceived as part of the practice of “kavannah” in prayer. This practice was articulated by a 13th century anonymous ecstatic kabbalist writing in Catalonia. The anonymous author draws on earlier sources in the kabbalah and Ashkenazi spirituality. The article explores the wider connection between ecstasy and ritual, particularly prayer in the earlier stages of Judaism and its development in medieval theology and kabbalah. The anonymous author describes a (...) unique permutation technique capable of inducing ecstatic experiences as part of the liturgical ritual. (shrink)
The Carssirer's conceptions of aprioricity, especially of synthetic a priori principles in exact sciences, is analysed. I consider his 'Marburg's' period, first of all his paper on Kant and modern mathematics. Cassirer defends the thesis on invariance principles as the modern variant of synthetic principles a priori. I analyze his arguments on the existence of apriori principles of science and compare his concept of aprioricity with holistic accounts of theories, 'semantic view of theories' and structural realism.