Summary In this paper we examine the reaction of the Leiden low-temperature laboratory of Heike Kamerlingh Onnes to new ideas in quantum theory. Especially the contributions of Albert Einstein (1906) and Peter Debye (1912) to the theory of specific heat, and the concept of zero-point energy formulated by Max Planck in 1911, gave a boost to solid state research to test these theories. In the case of specific heat measurements, Kamerlingh Onnes's laboratory faced stiff competition from Walter Nernst's (...) Institute of Physical Chemistry in Berlin. In fact, Berlin got the better of it because Leiden lacked focus. After the liquefaction of helium in 1908, Kamerlingh Onnes transformed his laboratory into an international facility for low temperature research, and for this reason it was impossible to make headway with the specific heat measurements. In the case of zero-point energy, Leiden developed a magnetic research programme to test the concept. Initially the balance of evidence seemed to be tipping in favour of zero-point energy. After 1914, however, Leiden would desert the theory in fovour, of a concept from calssical physics. A curious move that illustrates Kamerlingh Onnes's discomfort with the new quantum theory. (shrink)

We consider the reduct to the module language of certain theories of fields with a non surjective endomorphism. We show in some cases the existence of a model companion. We apply our results for axiomatizing the reduct to the theory of modules of non principal ultraproducts of separably closed fields of fixed but non zero imperfection degree.

In this fourth paper in a series on stochastic electrodynamics (SED), the harmonic oscillator-zero-point field system in the presence of an arbitrary applied classical radiation field is studied further. The exact closed-form expressions are found for the time-dependent probability that the oscillator is in the nth eigenstate of the unperturbed SED Hamiltonian H 0 , the same H 0 as that of ordinary quantum mechanics. It is shown that an eigenvalue of H 0 is the average (...) energy that the oscillator would have if its wave function could be just the corresponding eigenstate. The level shift for each unperturbed eigenvalue is found and shown to be unobservable for a different reason than in the corresponding QED treatment. Perturbation theory is applied to the SED Schrödinger equation to derive first-order transition rates for spontaneous emission and resonance absorption. The results agree with those of quantum electrodynamics, but the mathematics is strikingly different. It is shown that SED demands discarding the ideas of quantized energies, photons, and completeness of the Schrödinger equation, Finally, an intuitive physical SED model is suggested for the photoeffect and for Clauser's (2) coincidence experiment. (shrink)

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation (...) reaction (RR) vector potential that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field. (shrink)

In this second paper in a series on stochastic electrodynamics the system of a charged harmonic oscillator (HO) immersed in the stochastic zero-point field is analyzed. First, a method discussed by Claverie and Diner and Sanchez-Ron and Sanz permits a finite closed form renormalization of the oscillator frequency and charge, and allows the third-order Abraham-Lorentz (AL) nonrelativistic equation of motion, in dipole approximation, to be rewritten as an ordinary second-order equation, which thereby admits a conventional phase-space description (...) and precludes the runaway solutions of the AL equation. Second, following several authors, a momentum is defined that reduces to the usual canonical momentum in the limit of no radiation reaction, and the statistical moments of the oscillator position and this momentum are calculated in closed form to all orders of the radiative corrections. As has been shown by many authors, the velocity second moment is unbounded; semiquantitative arguments are given to support the conjecture that the use of the point-particle dipole approximation is responsible for this divergence. Third, it is shown that, to zeroth order in the radiative corrections, the renormalized HO has the same expectation energy found by other authors, that of the quantum ground state. (shrink)

Over the past several years Haisch, Rueda, and others have made the claim that the origin of inertial reaction forces can be explained as the interaction of electrically charged elementary particles with the vacuum electromagnetic zero-point field expected on the basis of quantum field theory. After pointing out that this claim, in light of the fact that the inertial masses of the hadrons reside in the electrically chargeless, photon-like gluons that bind their constituent quarks, is untenable, (...) the question of the role of quantum zero-point fields generally in the origin of inertia is explored. It is shown that, although non-gravitational zero-point fields might be the cause of the gravitational properties of normal matter, the action of non-gravitational zero-point fields cannot be the cause of inertial reaction forces. The gravitational origin of inertial reaction forces is then briefly revisited. Recent claims critical of the gravitational origin of inertial reaction forces by Haisch and his collaborators are then shown to be without merit. (shrink)

This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This (...) postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned. (shrink)

This paper deals with an (otherwise classical) two-(non-interacting) particle system immersed in a common stochastic zero-point radiation field. The treatment is an extension of the one-particle case for which it has been shown that the quantum properties of the particle emerge from its interaction with the background field under stationary and ergodic conditions. In the present case we show that non-classical correlations—describable only in terms of entanglement—arise between the (nearby) particles whenever both of them resonate to (...) a common frequency of the field. For identical particles the entanglement becomes maximum and must be described by totally (anti)symmetric states. (shrink)

The present paper reveals (non-relativistic) quantum mechanics as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum or zero-point radiation field (zpf). This result provides a theoretical basis for understanding recent numerical experiments in which a statistical analysis of an atomic electron interacting with the zpf furnishes the quantum distribution for the ground state of the H atom. The action of the zpf on matter is essential within the present approach, but it is (...) the ergodic demand what ultimately leads to the matrix formulation of quantum mechanics. The paper thus represents a step forward in the quest for an elucidation of the fundamentals of quantum mechanics. (shrink)

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non-null escape rate over the potential barrier at low temperatures (T → 0). It (...) is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results. (shrink)

The two-point correlation functions of classical electromagnetic zero-point radiation fields are evaluated in four-vector notation. The manifestly Lorentz-covariant expressions are then shown to be invariant under scale transformations and under the conformal transformations of Bateman and Cunningham. As a preliminary to the electromagnetic work, analogous results are obtained for a scalar Gaussian random classical field with a Lorentz-invariant spectrum.

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant (...) class='Hi'>zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics. (shrink)

We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.

We consider quantum deformations of the real symplectic (or anti-De Sitter) algebra sp(4), ℝ ≅ spin(3, 2) and of its singleton and (4-dimensional) zero-mass representations. For q a root of −1, these representations admit finite-dimensional unitary subrepresentations. It is pointed out that Uq (sp(4, ℝ)), unlike Uq (su(2, 2)), contains Uq (sl 2 ) as a quantum subalgebra.

Can we make mistakes about what rationality requires? A natural answer is that we can, since it is a platitude that rational belief does not require truth; it is possible for a belief to be rational and mistaken, and this holds for any subject matter at all. However, the platitude causes trouble when applied to rationality itself. The possibility of rational mistakes about what rationality requires generates a puzzle. When combined with two further plausible claims – the enkratic principle, and (...) the claim that rational requirements apply universally – we get the result that rationality generates inconsistent requirements. One popular and attractive solution to the puzzle denies that it is possible to make rational mistakes about what rationality requires. I show why (contra Titelbaum (2015b), and Littlejohn (2015)) this solution is doomed to fail. (shrink)

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such (...) view. (shrink)

This book offers a detailed study of the political philosophies of Thomas Hobbes and Benedict de Spinoza, focussing on their concept of power as potentia, concrete power, rather than power as potestas, authorised power. The focus on power as potentia generates a new conception of popular power. Radical democrats–whether drawing on Hobbes's 'sleeping sovereign' or on Spinoza's 'multitude'–understand popular power as something that transcends ordinary institutional politics, as for instance popular plebsites or mass movements. However, the book argues that these (...) understandings reflect a residual scholasticism which Hobbes and Spinoza ultimately repudiate. Instead, on the book's revisionist conception, a political phenomenon should be said to express popular power when it is both popular (it eliminates oligarchy and encompasses the whole polity), and also powerful (it robustly determines political and social outcomes). Two possible institutional forms that this popular power might take are distinguished: Hobbesian repressive egalitarianism, or Spinozist civic strengthening. But despite divergent institutional proposals, the book argues that both Hobbes and Spinoza share the conviction that there is nothing spontaneously egalitarian or good about human collective existence. From this point of view, the book accuses radical democrats of pernicious romanticism; the slow, meticulous work of organizational design and maintenance is the true centre of popular power. Three minute video summary available via HPBin3. Extended discussion on The Political Theory Review podcast. First chapter open access available via Oxford Scholarship Online. Videos of book talks at National University of Singapore (Centre for Legal Theory) and Universidad de Buenos Aires (Instituto de Investigaciones Gino Germani) available via YouTube. (See links below.). (shrink)

This corrigendum concerns [, § ] on ordered difference existentially closed valued fields where we overlooked the problem of immediate extensions.

I argue for the unexceptionality of evidence about what rationality requires. Specifically, I argue that, as for other topics, one’s total evidence can sometimes support false beliefs about this. Despite being prima facie innocuous, a number of philosophers have recently denied this. Some have argued that the facts about what rationality requires are highly dependent on the agent’s situation and change depending on what that situation is like. (Bradley 2019). Others have argued that a particular subset of normative truths, those (...) concerning what epistemic rationality requires, have the special property of being ‘fixed points’—it is impossible to have total evidence that supports false belief about them. (Smithies 2012; Titelbaum 2015). Each of these kinds of exceptionality permits a solution to downstream theoretical problems that arise from the possibility of evidence supporting false belief about requirements of rationality. However, as I argue here, they incur heavy explanatory burdens that we should avoid. (shrink)

The paper distinguishes two approaches to understanding the representational content of sentences and intentional states, and its role in describing people, predicting and explaining their behavior, and so forth. It sets forth the case for one of these approaches, the “egocentric” one, initially on the basis of its ability to explain the near‐indefeasibility of ascriptions of content to our own terms (“‘dogs’ as I use it means dogs”), but more generally on the basis of its providing an attractive overall picture (...) of the descriptive and explanatory role of representational content. In doing this, the paper relates the egocentric view to an “immanent” or “deflationary” view of reference and truth conditions, and also to the view of reference‐talk and truth‐talk as anaphoric devices. It discusses the indeterminacy of content ascriptions to those in communities with radically different theories, a phenomenon that is unsurprising on the egocentric approach, and connects this to the thesis of the normativity of meaning. (It does all this in rather broad brush: many strands of the egocentric account will be familiar, and are the subject of familiar controversies; the point of the paper is less to address these controversies individually than to tie the strands together into what is hoped to be an appealing package.). (shrink)

The goal of this work is to compile the basic components for the construction of an electromagnetic field theory of consciousness that meets the standards of a fundamental theory. An essential cornerstone of the conceptual framework is the vacuum state of quantum electrodynamics which, contrary to the classical notion of the vacuum, can be viewed as a vibrant ocean of energy, termed zero-point field (ZPF). Being the fundamental substrate mediating the electromagnetic force, the ubiquitous ZPF constitutes (...) the ultimate bedrock of all electromagnetic phenomena. In particular, resonant interaction with the ZPF is critical for understanding rapidly forming, long-range coherent activity patterns that are characteristic of brain dynamics. Assuming that the entire phenomenal color palette is rooted in the vibrational spectrum of the ZPF and that each normal mode of the ZPF is associated with an elementary shade of consciousness, it stands to reason that conscious states are caused by the coupling of the brain to a particular set of normal modes selectively filtered from the full frequency spectrum of the ZPF. From this perspective, the brain is postulated to function as a resonant oscillator that couples to a specific range of ZPF modes, using these modes as a keyboard for the composition of an enormous variety of phenomenal states. Theoretical considerations suggest that the brain-ZPF interface is controlled by altering the concentrations of neurotransmitters, placing the detailed study of the neurotransmitter-ZPF interaction at the center of future research activities. (shrink)

The main goal of this article consists in addressing two fundamental issues of consciousness research and cognitive science, namely, the question of why declarative memory functions are inextricably linked with phenomenal awareness and the question of the physical basis of memory traces. The presented approach proposes that high-level cognitive processes involving consciousness employ a universal mechanism by means of which they access and modulate an omnipresent background field that is identified with the zero-point field (ZPF) specified (...) by stochastic electrodynamics, a branch of physics that deals with the universal principles underlying quantum systems. In addition to its known physical properties and memory capacities, the ZPF is hypothesized to be an immanently sentient medium. It is propounded that linking up to a particular field mode of the ZPF activates a particular phenomenal nuance, implying that the phase-locked coupling of a set of field modes, i.e., the formation of a so-called ZPF information state, constitutes an appropriate mechanism for the amalgamation of elementary shades of consciousness into a complex state of consciousness. Since quantum systems rest exactly on this mechanism, conscious memory processes in the brain are expected to differ from unconscious processes by the presence of the typical features of many-body quantum systems, particularly long-range coherence and attractor formation, which is supported by a huge body of empirical evidence. On this basis, the conceptual framework set out in this article paves the way for a new understanding of the brain as a write-read head interacting with the ZPF, leading to self-consistent interpretations of the neural correlates of memory formation and memory retrieval and explaining why these memory processes are closely intertwined with phenomenal awareness. In particular, the neural correlates suggest that the brain produces consciously perceived memory traces by writing sequences of information states into the ZPF and retrieves consciously experienced memory traces by reading sequences of information states from the ZPF. Using these theoretical foundations, altered states of consciousness and memory disorders can be traced back to impairments of the ZPF write-read mechanism. The mechanism should reveal itself through characteristic photon emissions, resulting in testable predictions. (shrink)

We describe classes of existentially closed ordered difference fields and rings. We show an Ax-Kochen type result for a class of valued ordered difference fields.

Argues that there are two reasons for ascribing to mental states, structures more fine-grained than the sets of possible world they represent: first, fine-grained structure enters naturally into the explanation of behaviour; second, fine-grained structure is needed in a theory of how those states represent the sets of possible worlds they represent. In connection with the first point, it is argued that Stalnaker’s attempt to use metalinguistic content to obviate the need of fine-grained structure cannot work. In connection with (...) the second point, it is argued that the systematicity in the assignment of content to mental states can be accommodated only by postulating a fine-grained structure for mental states. Also contains some discussion of doing without representational content, understood in the non-deflationary sense that Stalnaker assumes. (shrink)

Prompted by the centenary of the founding of Summerhill, in my contribution to this JOPE Suite on Democratic Education, I briefly explore both the admiring reciprocity and the subsidiary but significant differences of praxis between A.S. Neill and Alex Bloom, two remarkable pioneers of education in and for participatory democracy as a way of life. Because A.S. Neill's work is internationally renowned and Alex Bloom's has yet to re-establish the worldwide recognition it had in his own lifetime, my emphasis is (...) on the contribution of Alex Bloom, in large part because he is amongst the most radical pioneers of democratic education the UK state sector has ever known. To a significant degree, the aspirations and actualities of Bloom's work rebutted Neill's insistence that pioneers within the state sector of education could not innovate in ways that would significantly challenge the status quo. Indeed, Alex Bloom extended participatory democratic educational aspirations in ways which Neill did not. Most importantly, these not only entailed a commitment to community engagement, they did so in conditions of abject poverty and profound psychological trauma following the ravages of the Second World War London Blitz with its attendant evacuation and subsequent return to the ruins of their former homes.In the first section, I take as my starting point Alex Bloom's strongly supportive review of A.S. Neill's book The Problem Family and Neill's visit to Bloom's school in the East End of London, some five years later. Foregrounding the dialectic of practice and aspiration, I touch on some of the key issues that emerged for both Neill and Bloom at that time.Challenging Neill's later affirmation that the only significant freedom one can introduce into a state school is ‘a free attitude on the teacher's part, his or her being on the side of the child’ and his reported view that Bloom and others might be able to experiment in methods of teaching or ways of organising the timetable, ‘but not in methods of living’, the second section explores the nature and interrelationship of six key strands woven into the fabric of Alex Bloom's truly remarkable work that exemplified the grounded possibility and vibrant actuality of participatory democracy as a way of living and learning together that prefigures a more just, creative and caring form of human engagement.Locating the foundation of Alex Bloom's praxis within the 20th-century personalist philosophical tradition and its Adlerian psychological counterpart, the brief concluding section draws in particular on the work of John Macmurray who argues, as did Bloom in his own writing and his daily praxis, that ‘The first priority in education—if by education we mean learning to be human—is learning to live in personal relation to other people. Let us call it learning to live in community’. (shrink)

Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2.

This book helps understand Plato’s writings by describing the circumstances in which they were produced. The author begins with an account of Plato’s life and development and a brief analysis of some of the more difficult points arising from the criticism of Plato’s writings. The remainder of the work considers the total setting – political, literary and philosophical – in which Plato’s writings were produced. There are extensive appendices on the Platonic Epistles, Aristotle and the Theory of Ideas, and on (...) the post-Aristotelian tradition. The result is both a lucid account of Plato himself and a comprehensive view of culture in fifth century Greece. (shrink)

In her commentary of Field (1999), Hammerl (1999) has drawn attention to several interesting points concerning the issue of contingency awareness in evaluative conditioning. First, she comments on several contentious issues arising from Field's review of the evaluative conditioning literature, second she critiques the data from his pilot study and finally she argues the case that EC is a distinct form of conditioning that can occur in the absence of contingency awareness. With reference to these criticisms, this reply (...) attempts to address Hammerl's comments by exploring the issues of how awareness is defined, how it is best measured, and whether it is reasonable to believe that EC uniformly occurs in the absence of contingency awareness. The article concludes that the available evidence supports Field's proposition that EC is, in fact, Pavlovian learning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Response to the CommentariesLloyd FieldsAbstractIn this response, I address three points raised in the commentaries: the question of whether there is a legitimate formal use of “moral,” the claim that a certain sort of affective capacity is required for acquiring the capacity to form other-regarding moral beliefs, and the problem of how to show that psychopaths lack the capacity to form other-regarding moral beliefs. I maintain that there is (...) a use of “moral” according to which moral beliefs need not be rational. Regarding the affective capacity that Adshead identifies, I explain that I had not intended that such a capacity be constitutive of a moral belief, even an other-regarding one. I then try a new approach, in the light of Adshead’s commentary, to the third point addressed, according to which the psychopath is unable to form other-regarding moral beliefs because a causally necessary condition for doing so is absent in him.KeywordsMoral beliefs, moral understanding, personality disorder, empathy, incapacity, responsibilityThe criticisms offered in the three excellent commentaries on my paper raise deep and important issues. I agree with many of the points made and will respond to three key issues: (1) the question of whether there is a legitimate formal use of “moral”; (2) the claim that there is a certain sort of affective capacity that is required in order to form other-regarding moral beliefs; (3) the problem of how to show that psychopaths lack the capacity to form other-regarding moral beliefs.I concede that Duff establishes (Duff 1977) that the psychopath lacks moral understanding in Duff’s own content-based sense of “moral.” It is illuminating, however, to emphasize that in my formal sense a psychopath of the kind that I consider in my paper is capable of some degree of understanding of “moral” concepts. Unlike Duff, I do not build rationality into my account of moral principles. Hence, I can accommodate eccentric, irrational or even “crazy” moral beliefs like that of Duff’s split-infinitive fanatic. A person can have irrational factual beliefs; why not irrational moral beliefs?Adshead in her commentary attributes to me the claim that moral beliefs, including other-regarding beliefs, “result” in a disposition to experience certain emotions, and to have certain attitudes in certain situations. She then writes, “it is arguable that the disposition to experience certain emotions and have certain attitudes towards others could be critical to acquiring the capacity to have other-regarding beliefs.” There is only an apparent disagreement here. First, I intended to claim that a disposition to experience certain emotions, etc., is partly constitutive of having a moral belief, not a result of having one. Second, in specifying my third condition of having a moral belief, I had in mind such attitudes and emotions as approval, disapproval, indignation and remorse. Adshead identifies an affective capacity, aspects of which are the recognition of, empathy with, and sympathy with, another’s distress. This capacity seems to correspond more or less to what Rousseau described as “natural compassion” (Rousseau [End Page 291] 1973, 66–69), which arises prior to reflection and the use of reason, and which is exemplified by a mother’s responsiveness to the distress of her child. Rousseau distinguished natural compassion from moral virtues, which require the use of reason. I agree with Adshead that having this affective capacity is likely to be critical to acquiring the capacity to have other-regarding moral beliefs.Radden’s incisive commentary poses the problem of how to show that the psychopath lacks the capacity to form other-regarding moral beliefs, since this does not follow from the fact that he fails to form them. In the light of Adshead’s commentary, I should like to try a different approach to this problem. At least one type of situation in which we say that something, x, cannot do a certain sort of thing, d, is one where a causally necessary condition for x doing d is absent. For example, we should say of a car, not simply that it does not run, but that, as it is presently constituted, it cannot run, if we found that the carburetor of its... (shrink)

I must begin by apologizing for taking a somewhat well-worn subject for my theme. My reason is that I have not yet found a recent treatment of it which is altogether to my satisfaction. Most of them seem to me too often to approach the subject from a point of view which, in a way, expects too much from the study of Plato or any other ancient author, and consequently either makes exaggerated claims for it or fails to do (...) justice to what we really can learn. (shrink)

In this volume we situate the future directions of feminist phenomenology in the here and now. We contend that in this moment feminist phenomenology is well positioned to take a leading role, not simply in terms of consolidating existing feminist methodologies but also in engaging the difficult task of thinking through the actual in the fullness of its relational, agential, ontological, experiential, and fleshly being, thereby opening up future possibilities. We also think there is some urgency to this claim. For (...) many, faith in the rational human subject has been shattered by the events of twentieth and twenty-first centuries’ worldwide conflicts and increasing sectarianism. The concept of the subject as such is either obsolete or needs to be dynamically rethought. The current options appear to include resuscitating the rational liberal subject or agent, acknowledging limited agency in the performativity of language and gesture, or recognizing the agency of matter. We want to argue instead for a feminist phenomenological approach that begins with multiple, meaningful points of view on relational being. (shrink)

A novel approach to the scientific understanding of phenomenal awareness is presented that accepts consciousness as ontologically fundamental and is based on the hypothesis that the whole range of phenomenal nuances is inherent in the frequency spectrum of a ubiquitous field of consciousness. Pursuing this idea, it is postulated that the brain employs a universal interaction mechanism through which it taps into this field, thereby acquiring phenomenal qualities. I argue that the edifice of modern physics can not only (...) offer a promising candidate for the field of consciousness, consisting in the zero-point field (ZPF), but also an appropriate interaction mechanism. What is more, the empirical body of evidence supports the conclusion that conscious processes make use of exactly this mechanism. More specifically, the neural correlates of consciousness suggest that in the stimulus-oriented operating mode the brain produces streams of consciousness by periodically writing information states into the ZPF, while in the stimulus-independent operating mode the brain is receptive to previously generated ZPF information states that constitute the repository of conscious experiences, implying that self-referential conscious states are retrieved by periodically reading information states from the ZPF. Beyond its explanatory power the presented approach opens up new horizons for the future research strategy. (shrink)

Given a simple non-trivial finite-dimensional Lie algebra L, fields $K_i$ and Chevalley groups $L(K_i)$ , we first prove that $\Pi_{\mathcal{U}} L(K_i)$ is isomorphic to $L(\Pi_{\mathcal{U}}K_i)$ . Then we consider the case of Chevalley groups of twisted type ${}^n\!L$ . We obtain a result analogous to the previous one. Given perfect fields $K_i$ having the property that any element is either a square or the opposite of a square and Chevalley groups ${}^n\!L(K_i)$ , then $\pu{}^n\!L(K_i)$ is isomorphic to ${}^n\!L(\pu K_i)$ . (...) We apply our results to prove the decidability of the set of sentences true in almost all finite groups of the form L(K) where K is a finite field and L a fixed untwisted Chevalley type. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Guibert of Tournai's Letter to Lady Isabelle:An Introduction and English TranslationLarry F. Field, Jacques Dalarun, Sean L. Field, and Guibert of TournaiIntroductionGuibert, from the noble family of As-Piès, was born near Tournai around 1200. From his hometown he traveled to Paris for his art degree, and completed the curriculum in theology there before entering the Franciscan Order around 1240. He may have participated in Louis IX's crusade (...) of 1248, but, if so, was surely back in Paris by 1254 at the latest, since he preached a cycle of sermons de dominicis et de sanctis to the university community before summer 1255.1 His regency as Franciscan master of theology at Paris was probably around 1259–1261,2 about the time he [End Page 31] completed his Eruditio regum et principum for Louis IX,3 and began his most substantial work, the Erudimentum doctrinae.4 Other significant treatises include his De pace et animi tranquillitate (ca. 1275)5 written for Marie de Dampierre, and the Collectio de scandalis ecclesiae, prepared for the Second Council of Lyon.6 Guibert died in Tournai on 7 October 1284.7Sometime around 1254, Guibert wrote a long letter of spiritual advice to Isabelle (1225–70), the sister of King Louis IX.8 Isabelle was herself a remarkable figure. She had rejected several proposals of marriage, including that with Conrad, the heir to Emperor Frederick II, in 1243, in spite of pressure from her family and Pope Innocent IV. But following a bout of serious illness at about that time,9 her family accepted her [End Page 32] decision to remain unwed. There is no evidence, however, that Isabelle ever pronounced a formal vow of virginity. Through the 1250s she simply remained at the Capetian court as a virgin princess with an increasing reputation for piety and indeed holiness, praised in lavish terms by Innocent IV in 1253 and Alexander IV in 1256.10 This piety took a distinctly Franciscan turn by 1254, when Pope Innocent IV granted her request for Franciscan confessors,11 which would ultimately result in her foundation of Longchamp, a house of Sorores minores just west of Paris, by 1260.12 Guibert's letter shows no awareness of such a project, indicating that it must have been written before spring 1255, by which time the land for Longchamp was being purchased on Isabelle's behalf.13 Guibert thus wrote at the moment when Isabelle was forming her first ties to the Franciscans, but well before her move to Longchamp, where she lived out the 1260s as resident lay patron (but never a nun).Guibert's Letter is really a short treatise of spiritual and moral advice, tailored to a celibate princess. It is organized around Psalm 44:14–15, All the glory of the king's daughter is within in golden fringes, clothed around with varieties. In a five-part structure, the king's daughter stands for a heavenly inheritance; glory within represents internal purity; gold indicates virginity; the fringes are a sign of humility; and clothed around with varieties points to honest comportment. The resulting "royal garment," however, is rather unequally woven together, with section one on the "heavenly inheritance" and the intertwined sections three and four on virginity and humility receiving by far the most space. In fact, section one forms a sort of treatise-within-a-treatise, organized as a ten-step ascent to the heavenly inheritance awaiting the daughter of the king. [End Page 33]The Letter to Lady Isabelle was first edited by Alphonse de Poorter in 1931, from a manuscript which contained only part of the text.14 The full text was brought into print by Sean Field in 2003,15 and translated into French by Jacques Dalarun in 2014.16 Yet in spite of these advances, the Letter has remained little noticed by scholars. Anne-Hélène Allirot offered several perceptive pages in 2010, stressing the way Guibert's treatment of hereditas implies that female members of the royal family might be particularly able to embody Capetian claims to holiness.17 That same year, in the only recent article dedicated specifically to this Letter, Rina Lahav... (shrink)

We consider first-order theories of topological fields admitting a model-completion and their expansion to differential fields . We give a criterion under which the expansion still admits a model-completion which we axiomatize. It generalizes previous results due to M. Singer for ordered differential fields and of C. Michaux for valued differential fields. As a corollary, we show a transfer result for the NIP property. We also give a geometrical axiomatization of that model-completion. Then, for certain differential valued fields, we extend (...) the positive answer of Hilbert’s seventeenth problem and we prove an Ax–Kochen–Ershov theorem. Similarly, we consider first-order theories of topological fields admitting a model-companion and their expansion to differential fields, and under a similar criterion as before, we show that the expansion still admits a model-companion. This last result can be compared with those of M. Tressl: on one hand we are only dealing with a single derivation whereas he is dealing with several, on the other hand we are not restricting ourselves to definable expansions of the ring language, taking advantage of our topological context. We apply our results to fields endowed with several valuations. (shrink)

As we know, Merleau-Ponty was struggling with a dynamic shift in his thinking at the premature end of his life. In those last notes he raises the question of how to elaborate a phenomenology of “’the other world’, as the limit of a phenomenology of the imaginary and the ‘hidden’”—a phenomenology that would open onto an invisible life, community, other and culture (VI, Jan. 1960). In her essay on “Eye and Mind”, “To Paint the Invisible”, Luce Irigaray shows why Merleau-Ponty (...) was not yet ready to address this question, why he was not yet ready to engage the limits of his vision posed by the presence of an other. Against Merleau-Ponty’s assertion that the artist has no other task than to bring to appearance the world in the way he corporeally encounters it employing no “other technique than what his eyes and hands discover in seeing and painting”, Irigaray argues that the painter as phenomenologist then appropriates what is other to his vision without reflecting upon a limit to vision, as well as the limit provided by the invisible of an other, an other world. This is not to say that there are no intertwinings with this other, for there are other metabolisms with which we engage the world. Moreover, the sharing of vision with an other can alter the ways I see, challenging cultural complicity, rather than providing evidence that we share the same world. Irigaray is of course not the first to challenge a phenomenological approach to art and to vision—and here I turn specifically to Gilles Deleuze—who is critical of the phenomenological tendency to take on a world given to us by others. His artist, Francis Bacon, focuses on the sensation, which remains unmediated by narration or the feelings of others. Finally, the artworks of abstract expressionist artist Joan Mitchell are considered in the ways that they open up a different time-space; they suggest an other world with which we intertwine without appropriation. Her works, I argue, defy reduction to essences, but also do not rely merely on sensation—for this reason they point in the direction of how to think phenomenology anew. For I do think Merleau-Ponty would be open to these conversations, to these other worlds and other visions. (shrink)

As we know, Merleau-Ponty was struggling with a dynamic shift in his thinking at the premature end of his life. In those last notes he raises the question of how to elaborate a phenomenology of “’the other world’, as the limit of a phenomenology of the imaginary and the ‘hidden’”—a phenomenology that would open onto an invisible life, community, other and culture. In her essay on “Eye and Mind”, “To Paint the Invisible”, Luce Irigaray argues that Merleau-Ponty was not yet (...) ready to address this question, of the limits posed to his vision by the presence of an other. The artworks of abstract expressionist artist Joan Mitchell are considered in the ways that they open up a different time-space suggesting an other world with which we intertwine without appropriation. Her works, I argue, defy reduction to essences, but also do not rely merely on sensation—for this reason they point in the direction of how to think phenomenology anew. For I do think Merleau-Ponty would be open to these conversations, to these other worlds and other visions. (shrink)

In thePeristephanon, a collection of hymns in praise of the Christian martyrs, the Spanish poet Aurelius Prudentius Clemens refers back to a time more than a hundred years before he was writing, when Christianity was not the predominant influence in the Roman world but the religion of a beleaguered minority. In the course of Prudentius' lifetime, the trials that were suffered by that minority under emperors such as Decius and Diocletian became an important point of reference for increasing numbers (...) of Roman converts seeking to identify with Christianity and its sectarian past. At the time, however, those trials were recorded in only meagre written accounts. Prudentius, whose successful administrative career might have culminated in elevation to a senior position in the imperialscrinia, displays particular interest in the extent of the official archival material in thePeristephanon. In a number of passages in this work, he comments on the fragility of historical documents, which are easily destroyed by acts of malice or the effects of time. The following discussion will examine the ways in which he reflects on the permanence, or otherwise, of his own written texts. Analysis of his imitation of elegiac verse inscriptions will demonstrate how he draws attention to the inadequacy of even the most monumental types of human writing. But I will argue that, by identifying his poems with the martyrs' perishable bodies, Prudentius claims that they too can be a medium for a divine presence not confined to any perishable physical form. (shrink)

In this essay, which is preceded by an interview with the translator, Luce Irigaray revisits her earlier critique of Maurice Merleau-Ponty’s privileging of the visible, but also takes further her own thinking by drawing specifically on the issues raised within the context of painting and the creation of artworks. The focal point of her discussion is Merleau-Ponty’s essay on art, “Eye and Mind.”.

This paper attempts a comprehensive account of the comparative merits of paracomplete and dialetheic approaches to the semantic paradoxes. It argues that aside from issues about conditionals, there can be no strong case for paracomplete approaches over dialetheic, or dialetheic over paracomplete, and indeed that in absence of conditionals, the two approaches are plausibly seen as notational variants. Graham Priest disagrees: many of his arguments favoring dialetheic solutions over paracomplete do not turn on issues about conditionals. The paper discusses his (...) arguments on these points in some detail. On the matter of conditionals, it argues that extant paracomplete approaches are far better than extant dialetheic approaches, a fact that traces in part to dialetheists having focused too heavily on “relevant logics”. It holds out hope for better dialetheic treatments of conditionals, but it also suggests that this is the one area where paracomplete approaches are inevitably better. (shrink)

Fix an algebraically closed field of characteristic zero and let G be its geometry of transcendence degree one extensions. Let X be a set of points of G. We show that X extends to a projective subgeometry of G exactly if the partial derivatives of the polynomials inducing dependence on its elements satisfy certain separability conditions. This analysis produces a concrete representation of the coordinatizing fields of maximal projective subgeometries of G.

The reception of Dewey's work has suffered, in terms of his political philosophy, from a certain mistrust. First, in the field of education, Dewey's refusal to grant "ultimate" or "high" status to certain values, even those of the French Republic, has made him a mistrusted figure.1 Apart from the pedagogues of Education Nouvelle, which defied the then dominant "Cartesian tradition of the dualistic philosophy of reason" in France, Dewey was little studied before the 1960s. In 2013, Kambouchner perceived an (...) opposition between Dewey and Durkheim;2 however, the French reception of The Public and Its Problems in 1927 also suffered from suspicion and skepticism.3 To begin, there was suspicion with regard to this... (shrink)

We construct a fibered dimension function in some topological differential fields.

In Dellunde et al. 997–1015), we determined the complete theory Te of modules of separably closed fields of characteristic p and imperfection degree e, eω{∞}. Here, for 0≠eω, we describe the closed set of the Ziegler spectrum corresponding to Te. Further, we establish a correspondence between certain submodules and n-types and we investigate several notions of dimensions and their relationships with the Lascar rank. Finally, we show that Te has uniform p.p. elimination of imaginaries and deduce uniform weak elimination of (...) imaginaries. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 40.1 (2002) 134-135 [Access article in PDF] Book Review Merleau-Ponty's Last Vision: A Proposal for the Completion of 'The Visible and the Invisible Douglas Low. Merleau-Ponty's Last Vision: A Proposal for the Completion of 'The Visible and the Invisible.' Evanston, IL: Northwestern University Press, 2000. Pp. xv + 124. Cloth, $75.00. Paper, $19.95. Low sets himself an impossible task, that of completing the (...) uncompleted work of a philosopher whose untimely decease prevented him from doing so himself. What he does succeed in providing is a systematic commentary and a rich integration of Merleau-Ponty's later philosophy. This task itself is important since it is believed by many that Merleau-Ponty's premature death prevented the completion of a book that would have altered the philosophical scene of Paris in the 1960s, and that, moreover, even in its incomplete form, speaks to pressing contemporary philosophical debates on such issues as mind/body dualism, and our relation to nature.The main focus of Low's reading is Merleau-Ponty's philosophy of language, which Low appropriately situates as a mediation between a modernist philosophy of presence and a postmodern Derridean approach to language as the constant deferral of meaning. Language is not the repository for ideal essences, nor do existents have an immediate [End Page 134] coincidence or fusion with things or the world. Indeed, the strength of Merleau-Ponty's philosophy is that he begins with an understanding of human action as meaningfully orientated; to move in the world is to interpretatively encounter it. As Low points out, "an ontological priority [is] granted to the body and the world upon which it opens, for together in lived experience they sustain a field of stable meanings, meanings that are then sublimated in the bodily gesture called speech" (22). Low differs from most Merleau-Ponty scholars in his assumption that there is no significant break between the earlier Phenomenology of Perception, where Merleau-Ponty carefully worked out his descriptions of embodied perception, and the later work that lays out the ontology. Indeed, one accomplishment of Low's book is to show how they fit together, explaining how the insights of the first work are necessary for grounding the ontology Merleau-Ponty began to work out in the later one.Low's book is divided into two sections. The first section, "The Visible and Nature," focuses on how we encounter the world, concluding with a helpful summary and assessment of Merleau-Ponty's ontology. Drawing upon the late essay "Eye and Mind," Low lays out Merleau-Ponty's ontology through his intuition that modern art, unlike the representational focus of Renaissance art, reveals our contact with the world as a "system of exchanges between the sensing and the sensible" (56). Perceiving the artwork is not an intellectual computation of a second-order representation of the world; rather, we see according to the work. It is a bodily process that reveals a reversibility between the viewer and the world. The second section, "The Invisible and Logos," focuses on how these encounters are sublimated or taken up in language. Language is, for Merleau-Ponty, first speech since it relies upon a speaker to take it up, "to sustain and modify it." Signs, gestures, and meaning are folded into one another. As embodied beings, we literally grasp meaning (89).This book would be of enormous benefit to scholars embarking on a reading of Merleau-Ponty's works, and it is one I highly recommend for that purpose. Although it is not original in its interpretations, its value lies in its gathering and integration of complex themes that provide an important introduction to Merleau-Ponty's late philosophy. The book maps out, moreover, a chronology of these themes and the specifics of where to find them; it also shows how the fragments fit together, indicating directions in which they might lead. His writing style is accessible without being simplistic. By interweaving his interpretations with long quotes from... (shrink)

Most of these eight essays on contemporary figures were given as lectures or speeches between 1990 and 1996. A piece on Ernst Cassirer’s humanistic legacy gives the collection its title, but the other subjects treated are far-ranging: Karl Jaspers on the clash of religious cultures, Georg Henrik von Wright’s noncognitive ethics, Gershom Scholem’s magisterial biography of the kabbalist Sabbatai Sevi, Karl-Otto Apel’s hermeneutics, Johann Baptist Metz on the Jewish element in Christianity, Michael Theunissen on the relation of negative theology to (...) social theory, and a review of the work of script writer and film director Alexander Kluge. Habermas unifies this panoply by his fascination with the transformation of the modern West’s key symbols through their confrontation with other cultures. Prime among these symbols are language and religious doctrines, especially Christian and Jewish. When he examines this general theme in particular cases, Habermas first presents an exposé of a thinker, then raises critical questions, and finally points out insights of enduring significance. One decided advantage of his method is its attention to clarity and organization. Probably because these essays were originally delivered orally, they never leave the reader in doubt as to what topics they will handle and when each is being taken up. (shrink)

In computational mathematics, it is a matter of deep concern to recognize which of the given iteration schemes converges quickly with lesser error to the desired solution. Fixed point iterative schemes are constructed to be used for solving equations emerging in many fields of science and engineering. These schemes reformulate a nonlinear equation f s = 0 into a fixed point equation of the form s = g s ; such application determines the solution of the original equation (...) via the support of fixed point iterative method and is subject to existence and uniqueness. In this manuscript, we introduce a new modified family of fixed point iterative schemes for solving nonlinear equations which generalize further recursive methods as particular cases. We also prove the convergence of our suggested schemes. We also consider some of the mathematical models which are categorically nonlinear in essence to authenticate the performance and effectiveness of these schemes which can be seen as an expansion and rationalization of some existing techniques. (shrink)

At the centre of Powers' (2019) China and England is an extraordinary forgotten episode in the history of political ideas. There was a time when English radicals critiqued the corruption and injustice of the English political system by contrasting it with the superior example of China. There was a time when they advocated adopting a Chinese conceptual framework for thinking about politics. So dominant and prevalent was the English radicals' use of this framework, that their opponents took to dismissing their (...) points as 'the argument from the Chinese'. In my review of Powers' book, I welcome the profound reconfiguration of our political understandings that knowledge of this historical episode brings. However, I question Powers' framing presumption that the generic problems of any complex society lead to convergence on a single master political value of 'social justice'. Surely there are deep and enduring differences amongst thinkers of political value, even within a single society, let alone across different societies. Taking this point seriously would challenge the simple linear directionality of Powers' story of moral and political progress. (shrink)