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)

We present a new approach to the invariant subspace problem for complex Hilbert spaces.This approach based on nonconservative Extension of the Model Theoretical NSA. 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.

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)

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)

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)

David Albert has recently argued that classical electromagnetic theory (EM) is not time reversal invariant (non-TRI), while David Malament rejects this argument and maintains the orthodox result, that EM is TRI. Both Albert's and Malament's arguments are analysed, and both are found wanting in certain respects. It is argued here that the result really depends on the choice of theoretical ontology choosen to interpret EM theory, and there is more than one plausible choice. Albert and Malament have choosen different (...) plausible ontologies; but neither shows that their choice of interpretation is definitive. Deeper principles about this choice are examined. The extension to EM theory with magnetic monopoles is also examined. It is concluded that, despite certain flaws in his account, Albert's analysis does reveal serious problems in the orthodox account, which Malament's response does not adequately address. (shrink)

The problem of rational theory-choice is the problem of whether choice of theory by a scientist may be objectively rational in the absence of an invariant scientific method. In this paper I offer a solution to the problem, but the solution I propose may come as something of a surprise. For I wish to argue that the work of the very authors who have put the rationality of such choice in question, Thomas Kuhn and Paul Feyerabend, contains all that (...) is needed to solve the problem. (shrink)

The nature of temporal experience is typically explained in one of a small number of ways, most are versions of either retentionalism or extensionalism. After describing these, I make a distinction between two kinds of temporal character that could structure temporal experience: A-ish contents are those that present events as structured in past/present/future terms, and B-ish contents are those that present events as structured in earlier-than/later-than/simultaneous-with relations. There are a few exceptions, but most of the literature ignores this distinction, and (...) silently assumes temporal experience is A-ish. I then argue that temporal character is not scale invariant, but rather that temporal experience is A-ish at larger scales, and B-ish at smaller scales. I then point out that this scale non-invariance opens the possibility of hybrid views. I clarify my own view as a hybrid view, according to which temporal experience is B-ish at small scales – and at this scale my trajectory estimation model applies – but A-ish at larger scales, and at the larger scale my TEM does not apply. I then motivate this hybrid position by first defending it against arguments that have tried to show that the TEM is untenable. Since the hybrid view has TEM as its small-scale component, it must address this objection. I then put pressure on the main alternative account, extentionalism, by showing that its proponents have not adequately dealt with the problem of temporal illusions. The result is a new theory motivated by i) explaining its virtues, ii) showing that objections to it can be met, and iii) showing that objections to its main competitors have not been met. (shrink)

The boundary problem is related to the binding problem, part of a family of puzzles and phenomenal experiences that theories of consciousness (ToC) must either explain or eliminate. By comparison with the phenomenal binding problem, the boundary problem has received very little scholarly attention since first framed in detail by Rosengard in 1998, despite discussion by Chalmers in his widely cited 2016 work on the combination problem. However, any ToC that addresses the binding problem must also address the boundary problem. (...) The binding problem asks how a unified first person perspective (1PP) can bind experiences across multiple physically distinct activities, whether billions of individual neurons firing or some other underlying phenomenon. To a first approximation, the boundary problem asks why we experience hard boundaries around those unified 1PPs and why the boundaries operate at their apparent spatiotemporal scale. We review recent discussion of the boundary problem, identifying several promising avenues but none that yet address all aspects of the problem. We set out five specific boundary problems to aid precision in future efforts. We also examine electromagnetic (EM) field theories in detail, given their previous success with the binding problem, and introduce a feature with the necessary characteristics to address the boundary problem at a conceptual level. Topological segmentation can, in principle, create exactly the hard boundaries desired, enclosing holistic, frame-invariant units capable of effecting downward causality. The conclusion outlines a programme for testing this concept, describing how it might also differentiate between competing EM ToCs. (shrink)

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. This (...) undecidability result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (shrink)

The well-known empiricist apories of the lawfulness of nature prevent an adequate philosophical interpretation of empirical science until this day. Clarification can only be expected through an immanent refutation of the empiricist point of view. My argument is that Hume’s claim, paradigmatic for modern empiricism, is not just inconsequent, but simply contradictory: Empiricism denies that a lawlike character of nature can be substantiated. But, as is shown, anyone who claimes experience to be the basis of knowledge (as the empiricist naturally (...) does), has, in fact, always already presupposed the lawfullness of nature, i.e. has assumed the ontology of a nature lawful in itself. If lawfulness is, more closely, understood as dependency on conditions, then the functional character of the laws of nature is involved with the consequence that verification is not to be taken as a mere repetition of measurements but as clarification of the conditional structure of the physical process. Furthermore the functionality of the laws of nature also includes a statement on their invariance (relative to certain transformations) and so their lawlikeness. This throws a new light on the problem of induction. Seen in this way it is hardly surprising that the notorious neglect of the functional aspect in empiricism has led to fundamental problems with the concept of the law of nature. (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)

Effective altruists either believe they ought to be, or strive to be, doing the most good they can. Since they’re human, however, effective altruists are invariably fallible. In numerous situations, even the most committed EAs would fail to live up to the ideal they set for themselves. This fact raises a central question about how to understand effective altruism. How should one’s future prospective failures at doing the most good possible affect the current choices one makes as an effective altruist? (...) This question is important to answer not only because every effective altruist will face this question due to typical human akrasia, but also because how the question is answered will determine just how demanding effective altruism can be. I argue that no matter how effective altruists answer this question, they will have to take on some commitments seemingly antithetical to their movement. More precisely, I argue that effective altruism is subject to a dilemma. Effective altruists’, at times, implicit actualist assumptions (i) commit them to conclusions seemingly antithetical to what typical effective altruists actually believe, as well as the spirit of the movement and (ii) undermine effective altruists’ arguments against moral offsetting and giving to charities close to the heart. Yet, effective altruists’, at times, implicit possibilist assumptions (iii) also commit them to conclusions seemingly antithetical to what typical effective altruists actually believe, as well as the spirit of the movement and (iv) undermine typical responses to demandingness worries for the normative conception of effective altruism. I argue that the best way out of the dilemma is to accept hybridism, though even hybridism won’t preserve every commitment of effective altruism. (shrink)

David Hume's famous riddle of induction implies a second problem related to the question of whether the laws and principles of nature might change in the course of time. Claims have been made that modern developments in physics and astrophysics corroborate the translational invariance of the laws of physics in time. However, the appearance of a new general principle of nature, which might not be derivable from the known laws of physics, or that might actually be a non-physical one (this (...) means completely independent of physical science) supports the notion that the course of nature can change in time. Here it is argued that natural selection satisfies the criteria that identify a general principle of nature which so far, appears to be non-derivable from the known laws of physics and therefore, it is likely that it arose in the course of time, thus leaving open again the quest for a true solution to Hume's second problem. (shrink)

The well-known empiricist apories of the lawfulness of nature prevent an adequate philosophical interpretation of empirical science until this day. Clarification can only be expected through an immanent refutation of the empiricist point of view. My argument is that Hume’s claim, paradigmatic for modern empiricism, is not just inconsequent, but simply contradictory: Empiricism denies that a lawlike character of nature can be substantiated. But, as is shown, anyone who claimes experience to be the basis of knowledge (as the empiricist naturally (...) does), has, in fact, always already presupposed the lawfullness of nature, i.e. has assumed the ontology of a nature lawful in itself. If lawfulness is, more closely, understood as dependency on conditions, then the functional character of the laws of nature is involved with the consequence that verification is not to be taken as a mere repetition of measurements but as clarification of the conditional structure of the physical process. Furthermore the functionality of the laws of nature also includes a statement on their invariance (relative to certain transformations) and so their lawlikeness. This throws a new light on the problem of induction. Seen in this way it is hardly surprising that the notorious neglect of the functional aspect in empiricism has led to fundamental problems with the concept of the law of nature. (shrink)

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity theorem (...) for second-order —these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic. (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)

We criticise Shepard's notions of “invariance” and “universality,” and the incorporation of Shepard's work on inference into the general framework of his paper. We then criticise Tenenbaum and Griffiths' account of Shepard (1987b), including the attributed likelihood function, and the assumption of “weak sampling.” Finally, we endorse Barlow's suggestion that minimum message length (MML) theory has useful things to say about the Bayesian inference problems discussed by Shepard and Tenenbaum and Griffiths. [Barlow; Shepard; Tenenbaum & Griffiths].

This is a non-technical version of "The Decision Problem for Effective Procedures." The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that the effectively calculable functions on natural numbers are exactly the general recursive functions), cannot be proved. However, it is logically provable from the notion of an (...) effective procedure--without reliance on any (partially) mathematical thesis or conjecture concerning effective procedures, such as the Church–Turing thesis--that the class of effective procedures is undecidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. The proof does not appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of such a procedure. Though this undecidability result itself is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure is, in fact, a decision procedure, i.e., effective—for example, that it invariably terminates with the correct verdict. (shrink)

On Hume’s account of motivation, beliefs and desires are very different kinds of propositional attitudes. Beliefs are cognitive attitudes, desires emotive ones. An agent’s belief in a proposition captures the weight he or she assigns to this proposition in his or her cognitive representation of the world. An agent’s desire for a proposition captures the degree to which he or she prefers its truth, motivating him or her to act accordingly. Although beliefs and desires are sometimes entangled, they play very (...) different roles in rational agency. In two classic papers (Lewis 1988, 1996), David Lewis discusses several challenges to this Humean picture, but ultimately rejects them. We think that his discussion of a central anti-Humean alternative – the desire-as-belief thesis – is in need of refinnement. On this thesis, the desire for proposition p is given by the belief that p is desirable. Lewis claims that ‘[e]xcept in trivial cases, [this thesis] collapses into contradiction’(Lewis 1996, p. 308). The problem, he argues, is that the thesis is inconsistent with the purportedly plausible requirement that one’s desire for a proposition should not change upon learning that the proposition is true; call this the invariance requirement. In this paper, we revisit Lewis’s argument. We show that, if one carefully distinguishes between non-evaluative and evaluative propositions, the desire-asbelief thesis can be rendered consistent with the invariance requirement. Lewis’s conclusion holds only under certain conditions: the desire-as-belief thesis conflicts with the invariance requirement if and only if there are certain correlations between non-evaluative and evaluative propositions. But when there are such correlations, we suggest, the invariance requirement loses its plausibility. Thus Lewis’s argument against the desire-as-belief thesis appears to be valid only in cases in which it is unsound. (shrink)

What would it be for a process to happen backwards in time? Would such a process involve different causal relations? It is common to understand the time-reversal invariance of a physical theory in causal terms, such that whatever can happen forwards in time can also happen backwards in time. This has led many to hold that time-reversal symmetry is incompatible with the asymmetry of cause and effect. This article critiques the causal reading of time reversal. First, I argue that the (...) causal reading requires time-reversal-related models to be understood as representing distinct possible worlds and, on such a reading, causal relations are compatible with time-reversal symmetry. Second, I argue that the former approach does, however, raise serious sceptical problems regarding the causal relations of paradigm causal processes and as a consequence there are overwhelming reasons to prefer a non-causal reading of time reversal, whereby time reversal leaves causal relations invariant. On the non-causal reading, time-reversal symmetry poses no significant conceptual nor epistemological problems for causation. _1_ Introduction _1.1_ The directionality argument _1.2_ Time reversal _2_ What Does Time Reversal Reverse? _2.1_ The B- and C-theory of time _2.2_ Time reversal on the C-theory _2.3_ Answers _3_ Does Time Reversal Reverse Causal Relations? _3.1_ Causation, billiards, and snooker _3.2_ The epistemology of causal direction _3.3_ Answers _4_ Is Time-Reversal Symmetry Compatible with Causation? _4.1_ Incompatibilism _4.2_ Compatibilism _4.3_ Answers _5_ Outlook. (shrink)

Pragmatic encroachment theories have a problem with evidence. On the one hand, the arguments that knowledge is interest-relative look like they will generalise to show that evidence too is interest-relative. On the other hand, our best story of how interests affect knowledge presupposes an interest-invariant notion of evidence. -/- The aim of this paper is to sketch a theory of evidence that is interest-relative, but which allows that ‘best story’ to go through with minimal changes. The core idea is (...) that the evidence someone has is just what evidence a radical interpreter says they have. And a radical interpreter is playing a kind of game with the person they are interpreting. The cases that pose problems for pragmatic encroachment theorists generate fascinating games between the interpreter and the interpretee. They are games with multiple equilibria. To resolve them we need to detour into the theory of equilibrium selection. I’ll argue that the theory we need is the theory of risk-dominant equilibria. That theory will tell us how the interpreter will play the game, which in turn will tell us what evidence the person has. The evidence will be interest-relative, because what the equilibrium of the game is will be interest-relative. But it will not undermine the story we tell about how interests usually affect knowledge. (shrink)

Mainstream analytic epistemology regards knowledge as the property of individuals, rather ‎than groups. Drawing on insights from the reality of knowledge production and dissemination ‎in the sciences, I argue, from within the analytic framework, that this view is wrong. I defend ‎the thesis of ‘knowledge-level justification communalism’, which states that at least some ‎knowledge, typically knowledge obtained from expert testimony, is the property of a ‎community and possibly none of its individual members, in that only the community or some ‎members (...) of it collectively possesses knowledge-level justification for its individual members’ ‎beliefs. I address several objections that individuals, qua individuals, have or are able to ‎acquire knowledge-level justification for all the beliefs they obtain from expert testimony. I ‎argue that the problem I identify with individualism is invariant under any specific account of ‎justification, internalist or externalist. ‎. (shrink)

Medical terminology collects and organizes the many different kinds of terms employed in the biomedical domain both by practitioners and also in the course of biomedical research. In addition to serving as labels for biomedical classes, these names reflect the organizational principles of biomedical vocabularies and ontologies. Some names represent invariant features (classes, universals) of biomedical reality (i.e., they are a matter for ontology). Other names, however, convey also how this reality is perceived, measured, and understood by health professionals (...) (i.e., they belong to the domain of epistemology). We analyze terms from several biomedical vocabularies in order to throw light on the interactions between ontological and epistemological components of these terminologies. We identify four cases: 1) terms containing classification criteria, 2) terms reflecting detectability, modality, uncertainty, and vagueness, 3) terms created in order to obtain a complete partition of a given domain, and 4) terms reflecting mere fiat boundaries. We show that epistemology-loaded terms are pervasive in biomedical vocabularies, that the “classes” they name often do not comply with sound classification principles, and that they are therefore likely to cause problems in the evolution and alignment of terminologies and associated ontologies. (shrink)

In a recent article, Erasmus, Brunet, and Fisher (2021) argue that Artificial Neural Networks (ANNs) are explainable. They survey four influential accounts of explanation: the Deductive-Nomological model, the Inductive-Statistical model, the Causal-Mechanical model, and the New-Mechanist model. They argue that, on each of these accounts, the features that make something an explanation is invariant with regard to the complexity of the explanans and the explanandum. Therefore, they conclude, the complexity of ANNs (and other Machine Learning models) does not make (...) them less explainable. In this reply, it is argued that Erasmus et al. left out one influential account of explanation from their discussion: the Unificationist model. It is argued that, on the Unificationist model, the features that makes something an explanation is sensitive to complexity. Therefore, on the Unificationist model, ANNs (and other Machine Learning models) are not explainable. It is emphasized that Erasmus et al.’s general strategy is correct. The literature on explainable Artificial Intelligence can benefit by drawing from philosophical accounts of explanation. However, philosophical accounts of explanation do not settle the problem of whether ANNs are explainable because they do not unanimously declare that explanation is invariant with regard to complexity. (shrink)

This paper discusses knowledge of opposites. In particular, attention is given to the linguistic notion of antonymy and how it represents oppositional relations that are commonly found in perception. The paper draws upon the long history of work on the formalisation of antonymy in linguistics and formal semantics, and also upon work on the perception of opposites in psychology, and an assessment is made of the main approaches. Treatments of these phenomena in linguistics and psychology posit that the principles of (...) minimal difference and invariance are centrally important. It will be suggested that the standard approach employing meaning postulates fails to capture the relevant notion of antonymy, in part because it is not informed by these principles, and in part due to a number of other problems with this kind of approach, many of which may be overcome by building in the central principles from the beginning. The paper also discusses the issue of whether we can know that opposites necessarily exclude each other and, if so, how. This issue is intertwined with what is known as the colour incompatibility problem that Wittgenstein wrangled with at various times during his life. The paper assesses various solutions to these problems including an approach that was first put forward by Jerrold J. Katz. The relation between this approach and the theory of determinables and determinates is also examined. A further development upon this approach is proposed and then applied to the case of the formalisation of antonymy. It is argued that this approach avoids the problems suffered by the main approaches discussed earlier in the paper. (shrink)

The Higgs mechanism is an essential but elusive component of the Standard Model of particle physics. Without it Yang‐Mills gauge theories would have been little more than a warm‐up exercise in the attempt to quantize gravity rather than serving as the basis for the Standard Model. This article focuses on two problems related to the Higgs mechanism clearly posed in Earman’s recent papers (Earman 2003, 2004a, 2004b): what is the gauge‐invariant content of the Higgs mechanism, and what does it (...) mean to break a local gauge symmetry? (shrink)

Recent research into the nature of self in artificial and biological systems raises interest in a uniquely determining immutable sense of self, a “metaphysical ‘I’” associated with inviolable personal values and moral convictions that remain constant in the face of environmental change, distinguished from an object “me” that changes with its environment. Complementary research portrays processes associated with self as multimodal routines selectively enacted on the basis of contextual cues informing predictive self or world models, with the notion of the (...) constant, per-vasive and invariant sense of self associated with a multistable attractor set aiming to ensure personal integrity against threat of disintegrative change. This paper proposes that an immutable sense of self emerges as a global attractor which can be described as a project ideal self-situation embodied in frontal medial processes during more or less normal adolescent development, and that thereafter serves to orient agency in the more or less free development of embodied potentials over the life course in effort to realize project conditions, phenomenally identified with the felt pull towards this end as purpose of and source of meaning in life. So oriented, life-long self-development aims to embody solutions to problems at different timescales depending on this embodied purpose, ultimately in the service of evolutionary processes securing organism populations against threats of disintegrative change over timespans far beyond that of the individual. After characterizing the target sense of self, research circling this target is briefly surveyed. Self as global project and developmental neural correlates are proposed. Then, the paper discusses some implications for research in biological and artificial systems. Building from earlier work in cognitive neurorobotics, discussion affirms the value of reinforcement rituals including prayer in metaphysical self-development, considers implications for value alignment and rights associated with free will in the context of artificial intelligence and robot religion, and concludes by emphasizing the importance of self-development toward project ideals as source of meaning in life in the current social-political environment. (shrink)

Purpose (metatask) of the present work is to attempt to give a glance at the problem of existential and anthropo- logical risk caused by the contemporary man-made civilization from the perspective of comparison and confronta- tion of aesthetics, the substrate of which is emotional and metaphorical interpretation of individual subjective values and politics feeding by objectively rational interests of social groups. In both cases there is some semantic gap pre- sent between the represented social reality and its representation in perception (...) of works of art and in the political doctrines as well. Methodology of the research is evolutionary anthropological comparativistics. Originality of the conducted analysis comes to the following: As the antithesis to biological and social reductionism in interpretation of the phenomenon of bio-power it is proposed a co-evolutionary semantic model in accordance with which the de- scribed semantic gap is of the substantial nature related to the complex module organization of a consistent and adaptive human strategy consisting of three associated but independently functional modules (genetic, cultural and techno-rational). Evolutionary trajectory of all anthropogenesis components including civilization cultural and so- cial-political evolution is identified by the proportion between two macro variables – evolutionary effectiveness and evolutionary stability (sameness), i.e. preservation in the context of consequential transformations of some invari- ants of Homo sapiens species specificity organization. It should be noted that inasmuch as in respect to human, some modules of the evolutionary (adaptive) strategy assume self-reflection attributes, it would be more correctly to state about evolutionary correctness, i.e. correspondence to some perfection. As a result, the future of human nature de- pends not only on the rationalist principles of ethics of Homo species (the archaism of Jurgen Habermas), but also on the holistic and emotionally aesthetic image of «Self». In conclusion it should be noted that there is a causal link between the development of High Hume (NBIC) technologies and the totality of the trend in the anthropological phenomenon of bio-power that permeates all the available human existence in modern civilization. As a result, there is a transformation of a contemporary social (man-made) risk in the evolutionary civilization risk. (shrink)

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the influences of three-dimensionality in the solar system stability and the origin of life on Earth are discussed. New constraints on space dimensionality and on its invariance in very large spatial and temporal scales are also stressed.

Neo‐Aristotelian ethical naturalism purports to show that moral evaluation of human action and character is an evaluation of natural goodness—a kind of evaluation that applies to living things in virtue of their nature and based on their form of life. The standard neo‐Aristotelian view defines natural goodness by way of generic statements describing the natural history, or the ‘characteristic’ life, of a species. In this paper, I argue that this conception of natural goodness commits the neo‐Aristotelian view to a problematic (...) anti‐individualism that results in the wrong assessment of individuals with uniquely adaptive adjustments. I then offer an alternative account of natural goodness that avoids this problem. Instead of relying on generic statements about a species, my account defines natural goodness based on counterfactual conditionals describing the modal properties of a single individual. I argue that this modal‐explanatory account gives a conception of natural goodness that is more intuitively plausible and better suited to capture the diversity and plasticity distinctive of life. (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)

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)

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect (...) if and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

When performing a skilled action—whether something impressive like a double somersault or something mundane like reaching for a glass of water—you exercise control over your bodily movements. Specifically, you guide their course. In what does that control consist? In this dissertation, I argue that it consists in attending to what you are doing. More specifically, in attending, agents harness their perceptual and perceptuomotor states directly and practically in service of their goals and, in doing so, settle the fine-grained manner in (...) which their bodies will move—details an intention alone leaves unsettled. This requires, among other things, that we reject views on which agents’ control is identical with their practical rationality. When all goes well, agents attentionally prioritize what is motivationally relevant to them to the exclusion of what would otherwise distract them from achieving their goals. However, sometimes agents attend distractedly—i.e., without prioritizing. As the aim of attention is to avoid distraction, this entails the possibility of defective attention. Defective attention, in turn, casts light on scenarios in which agents lose control over what they are doing, as when a skilled practitioner ‘chokes under pressure’. A complaint sometimes levelled against accounts, like mine, that claim to reduce agents’ control of their behaviour to that of causally efficacious mental states or events is that these accounts invariably deprive agents themselves of their rightful role in the generation of behaviour. This is the “Disappearing Agent Problem” for “reductive” or “event-causal” theories of action. I argue that, correctly understood, extant reductive theories do face a genuine Disappearing Agent Problem. However, it is a problem we solve by recognizing the role that conscious attention plays in making an action the agent’s own. Accordingly, I develop and defend an attentional account of action ownership. On this view, allocating conscious attention in service of your goals is sufficient for a kind of conscious perspective (“motivational perspective”), which, when active in controlling your behaviour, constitutes the behaviour as your own doing. As I explain, such perspective also contributes to explaining the subjective structure of your perceptual awareness of the world around you. (shrink)

SYMMETRY IN PHYSICS: FROM PROPORTION AND HARMONY TO THE TERM OF METALENGUAJE -/- Ruth Castillo Universidad Central de Venezuela -/- The revolutionary changes in physics require a careful exploration of the way in which concepts depend on the theoretical structure in which they are immerse. A historical reconstruction allows us to show how the notion of symmetry evolves from the definition as proportion and harmony to its consideration within the language of contemporary physics, as a linguistic meta-theoretical requirement in physical (...) theories. In contemporary terms, symmetry is a fundamental category of research to which the usual categories of the natural sciences can be reduce in: space, time, causality, interaction, matter, strength, etc ... Thus, symmetry is a concept with different meanings: heuristically symmetric models inspire scientists in the search for solutions to different problems. Methodologically, symmetric structures are use to make theories, laws with invariant properties. A description of nature in terms of symmetric structures and symmetry ruptures seems to be the proper way to describe the complexity of reality. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case (...) we ask the question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (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)

This thesis is a philosophical examination of the explanatory roles of diagnoses in psychiatry. In medicine, diagnoses normally serve as causal explanations of patients’ symptoms. Given that psychiatry is a discipline whose practice is shaped by medical traditions, it is often implied that its diagnoses also serve such explanatory functions. This is evident in clinical texts that portray psychiatric diagnoses as referring to diseases that cause symptoms. However, there are problems which cast doubt on whether such portrayals are justified. I (...) address these problems and examine whether psychiatric diagnoses provide explanations of symptoms. The first problem is conceptual. In diagnostic manuals, psychiatric diagnoses are defined by their symptoms. This suggests that invoking them as explanations of the symptoms amounts to circularity. I argue that this can be resolved with an appropriate conceptual framework that captures the complex semantic values of diagnostic terms and their different uses in clinical discourse. I put forward such a framework based on two-dimensional semantics. The second problem is ontological. Empirical research suggests that diagnostic categories in psychiatry do not correspond to invariant causal types, but are associated with variable combinations of diverse causes that interact across biological, psychological, and social levels. Given this heterogeneity, I argue that psychiatric diagnoses fall short of paradigmatic cases of causal explanation, but that some can still provide other sorts of useful causal explanatory information. The original contribution of this thesis is the illumination of the conceptual relations between diagnoses and symptoms. This philosophical work is important, because it can be brought to valuable application in modifying psychiatric practice. (shrink)

This paper argues against the claim that Frege is committed to an infinite hierarchy of senses. Carnap and Kripke, along with many others, argue the contrary; I expose where all such arguments go astray. Invariably these arguments assume (without citation) that Frege holds that sense and reference are always distinct. This is the fulcrum upon which the hierarchy is hoisted. The counter to this assumption is based on two important but neglected passages. The locution ‘indirect sense’ has no ontological significance (...) for Frege. It was just a ‘short expression’ (his term) to indicate that the customary relation between sign, sense, and reference is suspended in what he called the exception case of indirect context. Once the hierarchy is abandoned, the alleged problem of just what indirect sense is, as well as questions as to why Frege said so little about it and why he did not examine iterative indirect contexts are resolved. Of course, with no hierarchy, Davidson’s “unlearnability argument” turns out to be a non-starter. Some objections to my interpretation are considered and answered. Additionally, comparisons to Dummett’s one-level view of sense, which is similar to mine are made, as well as to some two-level views (Parsons and Skiba). (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)

In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy (...) seemingly reasonable symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips. (shrink)

Action-based theories of cognition place primary emphasis upon the role that agent-environment coupling plays in the emergence of psychological states. Prima facie, mental imagery seems to present a problem for some of these theories because it is understood to be stimulus-absent and thus thought to be decoupled from the environment. However, mental imagery is much more multifaceted than this “naïve” view suggests. Focusing on a particular kind of imagery, comparative mental imagery generation, this paper demonstrates that although such imagery is (...) stimulus-absent, it is also stimulus-sensitive. Exhibiting stimulus-sensitivity is sufficient for a process to qualify as coupled to the environment. The notion of variant coupling is explicated as the coupling of a cognizer’s perceptual system to variant environmental information. By demarcating the categories of stimulus-absent and stimulus-sensitive cognition, and variant and invariant coupling, this paper expands the conceptual apparatus of action-based theories, suggesting not only a way to address the problem that comparative mental imagery generation presents, but perhaps a way to account for other forms of imagery too. (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)

What is a moral argument? A straightforward answer is that a moral argument is an argument dealing with moral issues, such as the permissibility of killing in certain circumstances. I call this the thin sense of ‘moral argument’. Arguments that we find in normative and applied ethics are almost invariably moral in this sense. However, they often fail to be moral in other respects. In this article, I discuss four ways in which morality can be absent from moral arguments in (...) the thin sense. If these arguments suffer from an absence of morality in at least one of these ways, they are not moral arguments in what I will call the thick sense of ‘moral argument’. Because only moral arguments in the thick sense could possibly qualify as proper responses to moral problems, the absence of morality in thin arguments means that these arguments will fail to give us a reason to do whatever they claim that we ought to do, even if we see no independent reason to question the truth of the premises or the logical validity of the argument. (shrink)

This article takes a new idea, ‘normative behaviourism’, and applies it to global political theory, in order to address at least one of the problems we might have in mind when accusing that subject of being too ‘unrealistic’. The core of this idea is that political principles can be justified, not just by patterns in our thinking, and in particular our intuitions and considered judgements, but also by patterns in our behaviour, and in particular acts of insurrection and crime. The (...) problem addressed is ‘cultural relativism’, understood here not as a meta-ethical doctrine, but as the apparent ‘fact’ that people around the world have culturally varying intuitions and judgements of a kind that lead them to affirm different political principles. This is a problem because it seems to follow (1) that global agreement on any substantial set of political principles is impossible, and (2) that any political theory in denial of this ‘fact’ would be, for that reason, deeply unrealistic. The solution argued for here is that, if domestic political principles (i.e. principles intended to regulate a single state) could be justified by normative behaviourism, and in reference to culturally invariant behaviour, then an international system supportive of such principles is justifiable by extension. (shrink)

The original conception of atomism suggests “atoms”, which cannot be divided more into composing parts. However, the name “atom” in physics is reserved for entities, which can be divided into electrons, protons, neutrons and other “elementary particles”, some of which are in turn compounded by other, “more elementary” ones. Instead of this, quantum mechanics is grounded on the actually indivisible quanta of action limited by the fundamental Planck constant. It resolves the problem of how both discrete and continuous (even smooth) (...) to be described uniformly and invariantly in thus. Quantum mechanics can be interpreted in terms of quantum information. Qubit is the indivisible unit (“atom”) of quantum information. The imagery of atomism in modern physics moves from atoms of matter (or energy) via “atoms” (quanta) of action to “atoms” (qubits) of quantum information. This is a conceptual shift in the cognition of reality to terms of information, choice, and time. (shrink)

There is not as much resistance to COVID-19 mitigation as there seems, but there are structural features that make resistance seem worse than it is. Here we describe two ways that the problem seeming to be worse than it is can make it worse. First, visible hesitation to implement COVID-19 responses signals to the wider society that mitigation measures may not succeed, which undermines people’s conditional willingness to join in on those efforts. Second, our evaluations of others’ willingness to implement (...) these measures are informed by our attempts to mind-read them. Yet attempts to mind-read groups often mislead us, because groups invariably act from diverse motives whereas mind-reading works best when identifying relatively stable and consistent motivations. This means that a small minority of people refusing to implement measures can have an outsized prominence that prompts mind-reading to diagnose widespread hesitation. These two factors form a feedback loop with each other: we see some people’s hesitation, which prompts us to mind-read other people as being more uncertain about the responses than they actually are, which undermines our confidence in the responses, which in turn encourages others to mind-read this hesitation, which further undermines confidence. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the quantum state in (...) a way that adds no significant complexity to the best system and solves the ''supervenient-kind problem'' facing the original version of the Past Hypothesis. We call the resultant theory the Humean unification. It provides a unified explanation of time asymmetry and quantum entanglement. On this theory, what gives rise to time's arrow is also responsible for quantum phenomena. The new theory has a separable mosaic, a best system that is simple and non-vague, less tension between quantum mechanics and special relativity, and a higher degree of theoretical and dynamical unity. The Humean unification leads to new insights that can be useful to Humeans and non-Humeans alike. (shrink)

We analyze the possible implications of spacetime discreteness for the special and general relativity and quantum theory. It is argued that the existence of a minimum size of spacetime may explain the invariance of the speed of light in special relativity and Einstein’s equivalence principle in general relativity. Moreover, the discreteness of spacetime may also result in the collapse of the wave function in quantum mechanics, which may provide a possible solution to the quantum measurement problem. These interesting results might (...) have some important implications for a complete theory of quantum gravity. (shrink)