Concerns a problem posed, but not solved, by Frege in part III of his Grundgesetze. As a preliminary to defining ‘real number’, Frege attempts to analyse the notion of a quantitative domain. He was unaware of the previous attempt of Otto Holder to do this; it is remarked how much weaker Frege's assumptions were in deriving theorems than Holder's. Frege deals with groups on which there is a right‐invariant semilinear ordering, although he does not use this terminology. He is uncertain (...) whether it can be deduced that the ordering is also left‐invariant, and proves as much as possible without invoking the assumption that it is. The independence proof, due to Dr Peter Neumann, establishes that it could not be deduced. (shrink)

The coronavirus disease 2019 pandemic is altering dynamics in academia, and people juggling remote work and domestic demands – including childcare – have felt impacts on their productivity. Female authors have faced a decrease in paper submission rates since the beginning of the pandemic period. The reasons for this decline in women’s productivity need to be further investigated. Here, we analyzed the influence of gender, parenthood and race on academic productivity during the pandemic period based on a survey answered by (...) 3,345 Brazilian academics from various knowledge areas and research institutions. Productivity was assessed by the ability to submit papers as planned and to meet deadlines during the initial period of social isolation in Brazil. The findings revealed that male academics – especially those without children – are the least affected group, whereas Black women and mothers are the most impacted groups. These impacts are likely a consequence of the well-known unequal division of domestic labor between men and women, which has been exacerbated during the pandemic. Additionally, our results highlight that racism strongly persists in academia, especially against Black women. The pandemic will have long-term effects on the career progression of the most affected groups. The results presented here are crucial for the development of actions and policies that aim to avoid further deepening the gender gap in academia. (shrink)

Recognising and responding appropriately to emotions is critical to adaptive psychological functioning. Psychopathic traits (e.g. callous, manipulative, impulsive, antisocial) are related to differences in recognition and response when emotion is conveyed through facial expressions and language. Use of emotional music stimuli represents a promising approach to improve our understanding of the specific emotion processing difficulties underlying psychopathic traits because it decouples recognition of emotion from cues directly conveyed by other people (e.g. facial signals). In Experiment 1, participants listened to clips (...) of emotional music and identified the emotional content (Sample 1, N = 196) or reported on their feelings elicited by the music (Sample 2, N = 197). Participants accurately recognised (t(195) = 32.78, p <.001, d = 4.69) and reported feelings consistent with (t(196) = 7.84, p <.001, d = 1.12) the emotion conveyed in the music. However, psychopathic traits were associated with reduced emotion recognition accuracy (F(1, 191) = 19.39, p <.001) and reduced likelihood of feeling the emotion (F(1, 193) = 35.45, p <.001), particularly for fearful music. In Experiment 2, we replicated findings for broad difficulties with emotion recognition (Sample 3, N = 179) and emotional resonance (Sample 4, N = 199) associated with psychopathic traits. Results offer new insight into emotion recognition and response difficulties that are associated with psychopathic traits. (shrink)

For a long while Bayesian techniques in statistics in general, and decision theory in particular, were considered suspect at best, and to be avoided; but now along comes Jeffrey with a system of subjective probability and utility functions determined by the individual's preferences, and a strongly Bayesian approach to decision-making, and by so doing puts the whole matter in a new light and makes it quite important to reassess the prior rejection of Bayesian methods. There are twelve chapters, each with (...) exercises, which begin with the model of deliberation, progress though scaling and ranking desirability, preference and propositional attitudes, thence to probability and measurement of desirability, and finally to induction and confirmation. The author's theory bears some resemblances to that sketched by Ramsey, but it draws somewhat on the later work of Von Neumann and Morgenstern. The author examines probability as viewed both statically—when the agent's attitudes are constant—and dynamically-when desirability and, consequently, probability assignments change. This text is one of the small but growing library of works whose interest is induction and probability theory; in that library, it will occupy an important place.—P. J. M. (shrink)

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the (...) canonical momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a “mechanical” (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields. (shrink)

The macroscopic properties of a many-particle quantum system are revealed by an embedding of the macroscopic classical into the microscopic quantum description of the system. Such an embedding is based on the assumption that the experiments to which the classical theory applies may also be described quantum mechanically. It results from the existence of an injective trajectory observable. For photon quantum systems with a finite number of modes an embedding is explicitly constructed using the well- known phase space observable for (...) quantum systems of finite degrees of freedom. For the general case of photon quantum fields the existence of a phase space observable is shown which, restricted to a finite number of modes, coincides with the mentioned one. (shrink)

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the (...) concrete example of the C*-algebra M n (ℂ) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ℘(M n (ℂ)) of projections in M n (ℂ) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice $\mathcal{O}(\Sigma_{n})$ of functions from the poset $\mathcal{C}(M_{n}(\mathbb{C}))$ of all unital commutative C*-subalgebras C of M n (ℂ) to ℘(M n (ℂ)). The lattice $\mathcal{O}(\Sigma_{n})$ is essentially the (pointfree) topology of the quantum phase space Σ n , and as such defines a Heyting algebra. Each element of $\mathcal{O}(\Sigma_{n})$ corresponds to a “Bohrified” proposition, in the sense that to each classical context $C\in\mathcal{C}(M_{n}(\mathbb{C}))$ it associates a yes-no question (i.e. an element of the Boolean lattice ℘(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann. (shrink)

This volume collects P. M. S. Hacker's papers on Wittgenstein and related themes written over the last decade. Hacker provides comparative studies of a range of topics--including Wittgenstein's philosophy of psychology, conception of grammar, and treatment of intentionality--and defends his own Wittgensteinian conception of philosophy.

An axiomatic foundation of a quantum theory for microsystems in the presence of external fields is developed. The space-time structure is introduced by considering the invariance of the theory under a kinematic invariance group. The formalism is illustrated by the example of charged particles in electromagnetic potentials. In the example, gauge invariance is discussed.

The concept of consciousness has been the source of much philosophical, cognitive scientific and neuroscientific discussion for the past two decades. Many scientists, as well as philosophers, argue that at the moment we are almost completely in the dark about the nature of consciousness. Stuart Sutherland, in a much quoted remark, wrote that.

This paper is an examination of Donald Davidson's writings on the idea of a conceptual scheme--and idea which he famously rejects. O relevance in this is the notion of linguistic relativity and the famous Whorf-Sapir thesis.

The concept of normal is so familiar that it can be hard to imagine contemporary life without it. Yet the term entered everyday speech only in the mid-twentieth century. Before that, it was solely a scientific term used primarily in medicine to refer to a general state of health and the orderly function of organs. But beginning in the middle of the twentieth century, normal broke out of scientific usage, becoming less precise and coming to mean a balanced condition to (...) be maintained and an ideal to be achieved. In Normality, Peter Cryle and Elizabeth Stephens offer an intellectual and cultural history of what it means to be normal. They explore the history of how communities settle on any one definition of the norm, along the way analyzing a fascinating series of case studies in fields as remote as anatomy, statistics, criminal anthropology, sociology, and eugenics. Cryle and Stephens argue that since the idea of normality is so central to contemporary disability, gender, race, and sexuality studies, scholars in these fields must first have a better understanding of the context for normality. This pioneering book moves beyond binaries to explore for the first time what it does—and doesn’t—mean to be normal. (shrink)

The place of the emotions among the passions -- The analytic of the emotions I -- The analytic of the emotions II -- The dialectic of the emotions -- Pride, arrogance, and humility -- Shame, embarrassment, and guilt -- Envy -- Jealousy -- Anger -- Love -- Friendship -- Sympathy and empathy.

Argues that though Kant articulated but a single solution to the problem of taste, by establishing a capacity for a common sense, but expanded it by explaining why people can take the disinterested attitude required for a common sense by appealing to our supersensible, rational nature. Proposes a solution to provide a natural reading of the antinomy according to which it is both required for Kant's broader purposes and does not make his earlier deduction obsolete. Revised from a dissertation for (...) the University of Iowa (no date noted). Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

1. First person authority: the received explanation Over a wide range of psychological attributes, a mature speaker seems to enjoy a defeasible form of authority on how things are with him. The received explanation of this is epistemic, and rests upon a cognitive assumption. The speaker’s word is a authoritative because when things are thus-and-so with him, then normally he knows that they are. This is held to be because the speaker has direct and privileged access to the contents of (...) his consciousness by means of introspection, conceived as a faculty of inner sense. Like perceptual knowledge, introspective knowledge is held to be direct and non-evidential. Accordingly, the first-person utterances ‘I have a pain’, ‘I believe that p’, ‘I intend to V’ are taken to be descriptions of what is evident to inner sense. Many classical thinkers held such subjective knowledge to be not only immediate, but also infallible and indubitable. The challenge to the received conceptions came from Wittgenstein. He denied the cognitive assumption, arguing that it cannot be said of me at all (except perhaps as a joke) that I know that I am in pain. For what is that supposed to mean — except perhaps that I am in pain?1 If it makes no sense to say that one knows that one is in pain, then the epistemic explanation is a non-starter, since it explains the special authoritative status of a person’s avowal of pain by reference to the putative fact that the subject of pain knows, normally knows, or cannot but know, that he is in pain when he is. It is important to note that Wittgenstein did not mechanically generalize the case of pain across the whole domain of firstperson utterances. The case of pain constitutes only one pole of a range of such utterances. Avowals and averrals of belief and intention approximate the other pole, and require independent analysis and grammatical description. (shrink)

AB THE DIFFICULTIES RAISED BY "TRACTATUS" 3.263 AND ITS USE OF THE TERM "ERLAUTERUNG" ARE EXAMINED. LIGHT IS THROWN ON THE MATTER BY THE SYSTEMATIC USE OF THIS TERM BY FREGE IN HIS DISCUSSION OF UNDEFINABLES. RUSSELL'S VIEWS ON UNDEFINABLES ARE ALSO TOUCHED UPON. IT IS SUGGESTED THAT THE "TRACTATUS" CONCEPTION OF AN 'ELUCIDATION' CONFUSEDLY COMBINED THE INCOMPATIBLE ROLES OF EMPIRICAL STATEMENT AND GRAMMATICAL SENTENCE (AN OSTENSIVE DEFINITION).

The author clarifies the existential philosophy that is implicit in Kurt Goldstein's philosophy of organism (Goldstein, 1963; 1995). Situated in response to the growing trend that psychological phenomena are reducible to the nervous system, the author argues for the reverse: that the significance of nervous system activity can only be understood by viewing it as background to foreground performances. Like the organization of perception into meaningful figure-- ground Gestalts, the existential modes of embodiment, sociality, temporality, spatiality, and attunement are organized (...) together to accomplish foreground performances. It is only within this context that the activity of the nervous system may be understood as significant or insignificant. Speech is given as an example. The article concludes with a commentary on how the trend of reducing psychological phenomena to neurological phenomena has impaired our understanding of brain disorders and psychological disorders. (shrink)

The equation of the world with 'life' and 'life' with consciousness ramified into the baffling account Wittgenstein gave of the 'philosophical self '. The physical world, as Descartes argued, is made of material substance, and the mental world 'is liable to be imagined as gaseous, or rather, aethereal'. Conceiving of consciousness as a private realm populated by private experiences, one is bound to be puzzled at its evolutionary emergence. Consciousness is attributable to an organism as a whole, not to its (...) parts, no matter how complex. And it is attributable to the organism on the grounds of the behaviour of the organism, its exercise of its perceptual faculties, its susceptibility to sensation, and its voluntary action. A venerable tradition going back at least as far as Descartes conceived of consciousness as the immovable rock against which the waves of scepticism break. (shrink)

1. Naturalism Naturalism, it has been said, is the distinctive development in philosophy over the last thirty years. There has been a naturalistic turn away from the a priori methods of traditional philosophy to a conception of philosophy as continuous with natural science. The doctrine has been extensively discussed and has won considerable following in the USA. This is, on the whole, not true of Britain and continental Europe, where the pragmatist tradition never took root, and the temptations of scientism (...) in philosophy were less alluring. Contemporary American naturalism originates in the writings of Quine, the metaphysician of twentieth-century science. With extraordinary panache, he painted a largescale picture of human nature, of language and of the web of belief. I believe that in almost every major respect, it is, like the picture painted by Descartes, the great metaphysician of seventeenth-century science, mistaken. But it evidently appeals to the spirit of the times. So it is worthy of critical examination and careful refutation. I shall argue that the naturalistic turn is a cul-de-sac – a turn that is to be passed by if we are to keep to the highroad of good sense. Naturalism, like so many of Quine’s doctrines, was propounded in response to Carnap. As Quine understood matters, Carnap had been persuaded by Russell’s Our Knowledge of the External World that it is the task of philosophy to demonstrate that our knowledge of the external world is a logical construction out of, and hence can be reduced to, elementary experiences. Quine rejected the reductionism of Carnap’s Logischer Aufbau, and found the idealist basis uncongenial to his own dogmatic realist behaviourism, inspired by Watson and later reinforced by Skinner. The rejection of reductionism and ‘unregenerate realism’, Quine averred, were the sources of his naturalism (FME 72). What exactly was this? We can distinguish in Quine between three different but inter-related programmes for future philosophy: epistemological, ontological and philosophical naturalism. Naturalized epistemology is to displace traditional epistemology, transforming the investigation into ‘an enterprise within natural science’ (NNK 68) – a psychological enterprise of investigating how the ‘input’ of radiation, etc., impinging on the nerve endings of human beings can ‘ultimately’ result in an ‘output’ of our theoretical descriptions of the external world.. (shrink)

In this paper, we discuss an approach to ‘design for wow’ that focuses on the emotions that constitute a wow-experience. In this approach, the eliciting conditions of these emotions are used to define a product character with a high wow-impact. In addition to the approach, a measurable wow-index is introduced. First, a concept of wow is described in which wow is explained as a combination of fascination, pleasant surprise, and desire. The eliciting conditions of these three emotions are examined and (...) combined to a ‘wow-appraisal.’ This concept is applied in the design of a mobile telephone. A combination of qualitative and quantitative research methods was used to formulate concern themes relevant for the wow-appraisal. These themes were used to create a layered product character and a prototype of the final design. An evaluation study demonstrated that the product designed with this approach rated higher on the wow-index than alternative products. (shrink)

This chapter contains section titled: The Emergence of the Philosophers' Self The Illusion of the Philosophers' Self The Body The Relationship Between Human Beings and Their Bodies.

William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deeper twentieth-century subject. Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. His works are of enormous historical importance; they remain also a source of inspiration and information. The works of his contemporaries, such as Klein, Frobenius, Schur, have been published as also have the works of his (...) immediate successors such as Phillip Hall. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography. Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material. This is the first reference volume of Burnside's collected papers, enhanced by a series of critical essays on his work, and is important for group theorists and historians and philosophers of mathematics and fills the gap in this area of literature. (shrink)