Open peer commentary on the target article “How and Why the Brain Lays the Foundations for a Conscious Self” by Martin V. Butz. Excerpt: In this commentary to Martin V. Butz’s target article I am especially concerned with his remarks about language (§33, §§71–79, §91) and modularity (§32, §41, §48, §81, §§94–98). In that context, I would like to bring into discussion my own work on computational models of self-monitoring (cf. Neumann 1998, 2004). In this work I explore the (...) idea of an anticipatory drive as a substantial control device for modelling high-level complex language processes such as selfmonitoring and adaptive language use. My work is grounded in computational linguistics and, as such, uses a mathematical and computational methodology. Nevertheless, it might provide some interesting aspects and perspectives for constructivism in general, and the model proposed in Butz’s article, in particular. (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)

Erscheint anlasslich des 15. Weltkongresses der Internationalen Vereinigung fur Rechts- und Sozialphilosophie (IVR) vom 18. bis 24. August 1991 in Gottingen und enthalt eine Selbstdarstellung der deutschen Sektion der IVR. Die Autoren berichten uber ihre eigene theoretische Position oder uber neuere Diskussionszusammenhange, die ihnen wichtig erscheinen. Aus dem Inhalt: K. Adomeit: Menschenrechte und Rechtsphilosophie u H. Albert: Erkenntnis, Recht und soziale Ordnung u R. Alexy: Idee und Struktur eines vernunftigen Rechtssystems u O. Ballweg: Analytische Rhetorik als juristische Grundlagenforschung u R. (...) Dreier: Zur gegenwartigen Diskussion des Verhaltnisses von Recht und Moral u W. Eichhorn: Wege und Irrwege einer Transformation u M. Frommel: Mannliche Gerechtigkeitsmathematik versus weiblicher Kontextualismus? u H. Garrn: Zur rechtspraktischen Bedeutung einer Theorie der juristischen Rhetorik u G. Haney: Das Widerspruchsvolle des Rechtsbegriffs u W. Hassemer: Rechtsphilosophie, Rechtswissenschaft, Rechtspolitik - am Beispiel des Strafrechts u A. Kaufmann: 45 Jahre erlebte Jahre Rechtsphilosophie u H. Klenner: Die ontologische und gnoseologische Dimension der Sein/Sollen-Problematik u U. Klug: Multidimensionale Rechtsphilosophie u H.-J. Koch/H. Russmann: Juristische Methodenlehre und analytische Philosophie u M. Kriele: Die demokratische Weltrevolution u K. Kuhl: Rehabilitierung und Aktualisierung des kantischen Vernunftrechts u E.-J. Lampe: Moderne Rechtsanthropologie u K.A. Mollnau: Vom Beginn der Niedergangsjurisprudenz in der DDR u U. Neumann: Sprachphilosophische Ansatze in der neueren Rechtsphilosophie u u.a. (Franz Steiner 1991). (shrink)

Human articulated motion can be readily recognized robustly even from impoverished so-called point-light displays. Such sequence information is processed by separate visual processing channels recruiting different stages at low and intermediate levels of the cortical visual processing hierarchy. The different contributions that motion and form information make to form articulated, or biological, motion perception are still under investigation. Here we investigate experimentally whether and how specific spatio-temporal features, such as extrema in the motion energy or maximum limb expansion, indicated by (...) the lateral and longitudinal extension, constrain the formation of the representations of articulated body motion. In order to isolate the relevant stimulus properties we suggest a novel masking technique, which allows to selectively impair the ankle information of the body configuration while keeping the motion of the point-light locations intact. Our results provide evidence that maxima in feature channel representations, e.g., the lateral or longitudinal extension, define elemental features to specify key poses of biological motion patterns. These findings provide support for models which aim at automatically building visual representations for the cortical processing of articulated motion by identifying temporally localized events in a continuous input stream. (shrink)

The connection of the structure of statistical selection procedures with measure theory is investigated. The methods of measure theory are applied in order to analyze a mathematical description of preparation and registration of physical systems that is used by G. Ludwig for a foundation of quantum mechanics.

Zgodnie z klasycznym podejściem kultura jest przeciwieństwem natury, a człowiek jako istota przekształcająca świat jest motorem rozwoju cywilizacji. Pisma C. G. Junga zawierają nieklasyczną koncepcję kultury, zgodnie z którą nieświadomość zbiorowa determinuje sposób interpretacji i rozumienia rzeczywistości, a tym samym rozwój kultury. Psychiatra uważał człowieka za istotę tworzącą symbole. Pisał o „popędzie symbolu”, który sprawia, że powstają one spontanicznie. Istnieje związek między działaniem instynktów, które mają podłoże biologiczne, a archetypowym źródłem symboli. W nieświadomości tkwią siły natury – w szczególności popęd (...) libido i instynkty. Kultura powstaje pomiędzy nieświadomością a świadomością, a przy tym proces jej rozwoju ma aspekt gatunkowy. (shrink)

Implicit and explicit filling-in phenomena should be distinguished. Blind spot phenomena and mechanisms of boundary completion can be accounted for by implicit filling-in. Surface regions are “painted” with perceptual quantities, such as brightness, by explicit filling-in. “Filling-in” and “finding-out” relate to different computational tasks. Mechanisms of purposive computation (e.g., for navigation) evaluate local measurements, thus “finding out”; whereas mechanisms for grasping might require passive reconstruction, thus “filling in.”.

Auf der Grundlage der Lehre von C.G. Jung, den Erfahrungen des Zweiten Weltkrieges und der atomaren Bedrohung Ende des 20. Jahrhunderts entwirft der Autor eine neue Ethik der Tiefenpsychologie, die der psychologischen Situation des modernen Menschen gerecht werden soll.

Das Verhaltnis von Regel und Fall ist ein Grundthema der Rechtsphilosophie und der juristischen Methodenlehre. Im Zentrum stehen dabei meist Probleme der Regelanwendung. Die nachstehend aufgefuehrten Beitrage zur Tagung der Deutschen Sektion der IVR stellen demgegenueber Fragen der Regelbildung in den Vordergrund. Das Generalthema wird unter Gesichtspunkten der Moralphilosophie, der Rechtsdogmatik, der juristischen Methodenlehre, der Rechtsinformatik und der gerichtlichen Praxis behandelt. Aus dem Inhalt: Einfuehrungsreferat zum Generalthema (A. Kaufmann) u Regel und Fall in der juristischen Methodenlehre (L. Kuhlen/K. Luederssen) u (...) Zur Regelbildung in der Dogmatik des Zivilrechts (J. Schmidt/K. Wietholter) u Das Universalisierbarkeitsproblem in der Moralphilosophie (G. Meggle) u Normbegruendung und Normanwendung in Recht und Ethik (K. Guenther) u Probleme der Regelbildung in der richterlichen Entscheidungspraxis (G. Ellscheid/J. Berkemann) u Stile der Reprasentation juristischen Wissens unter besonderer Beruecksichtigung von Individualisierung und Generalisierung (U. Moncke). (shrink)

Celebrated and castigated as the “Hobbes of the twentieth century” and even a modern Machiavelli. Carl Schmitt (1888–1984) is undoubtedly the most controversial legal and political theorist of the twentieth century. He greatly influenced the thinking of such political scientists and political philosophers as Hans J. Morgenthau, Franz Neumann, Otto Kirchheimer, Leo Strauss, and Julien Freund. But Schmitt always spoke and wrote as a jurist. He grounded his thinking in jurisprudence and was the teacher in the wider sense of (...) such jurists as Ernst‐Wolfgang Böckenförde and Ernst‐Rudolf Huber. (shrink)

A connection between two fundamental concepts of information and symmetry breaking (SB) is established. A concept called transform information (TI) is introduced. The known information measures (Hartley, von Neumann-Shannon-Wiener, Fisher informations, Renyi entropies) can be derived as (or mathematically expressed by) the particular forms of TI for certain transforms of a physical systems (when they are described by the probability measures). As TI is zero when the system is invariant under respective transform, it can be considered, when nonzero, as (...) a quantitative SB measure in the system under study. The classical information measures that are derived from TI also can be perceived as SB measures. This fact is a base for assigning a sense to information. The concept of TI is extended to the cases when systems are described without the use of probability concept. (shrink)

We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the (...) situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system. (shrink)

“Who are you? Tu quis es?” The interrogator was the German philosopher and pedagogue Eduard Spranger. The subject was Carl Schmitt. The place: Berlin. The time: summer of 1945. The question was “precipitous,” as Schmitt acknowledged in Ex Captivitate Salus, the book he completed following his release from Nuremberg in 1947. “Who are you?” Who, but one of the most highly acclaimed and esteemed jurists and political thinkers of the Weimar Republic, whose writings captured the attention of Georg Lukács, Karl (...) Korsch, Felix Gilbert, Leo Strauss, Ferdinand Toennies, and whose concepts significantly influenced Walter Benjamin, Herbert Marcuse, Otto Kirchheimer, Franz Neumann, Karl Mannheim and many other intellectuals and writers on the Left and the Right? (shrink)

In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics. The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim (...) was the introduction of a classical level in the context of QM, treating formally a set of basic quantities, to be considered as beables in the sense of Bell, as continuously taken under observation. However the effect of such assumption was a permanent modification of the Liouville-von Neumann equation for the statistical operator by the introduction of a dissipative term which is in conflict with basic conservation rules in all reasonable models we had considered. Difficulties were even encountered for a relativistic extension of the formalism. In this paper I propose a modified version of the original formalism which seems to overcome both difficulties. First I study the simple models of an harmonic oscillator and a free scalar field in which a coarse grain position and a coarse grained field respectively are treated as beables. Then I consider the more realistic case of spinor electrodynamics in which only certain coarse grained electric and magnetic fields are introduced as classical variables and no matter related quantities. (shrink)

In the popular imagination, the relevance of Turing's theoretical ideas to people producing actual machines was significant and appreciated by everybody involved in computing from the moment he published his 1936 paper ‘On Computable Numbers’. Careful historians are aware that this popular conception is deeply misleading. We know from previous work by Campbell-Kelly, Aspray, Akera, Olley, Priestley, Daylight, Mounier-Kuhn, Haigh, and others that several computing pioneers, including Aiken, Eckert, Mauchly, and Zuse, did not depend on Turing's 1936 universal-machine concept. Furthermore, (...) it is not clear whether any substance in von Neumann's celebrated 1945 ‘First Draft Report on the EDVAC’ is influenced in any identifiable way by Turing's work. This raises the questions: When does Turing enter the field? Why did the Association for Computing Machinery honor Turing by associating his name to ACM's most prestigious award, the Turing Award? Previous authors have.. (shrink)

The approach used by physics is based on the identification and study of ideal objects, which is also the basis of biophysics, in combination with von Neumann heuristic modeling and functional fractionation according to R.Rosen is discussed as a tool for studying the properties of consciousness. The object of the study is a kind of line of analog systems: the human brain, the vertebrate brain, the invertebrate brain and artificial neural networks capable of reflection, which is a key property (...) characteristic of consciousness. Reflection in the broad sense of the word, understood as an internal representation of the external world, is characteristic of a wide range of animals, and some of them (bumblebees, fish) even demonstrate reflection in the narrow sense of the word, understood as an inner self-representation. This complex behavior is realized by miniature brains of ~1 million neurons. The use of simple recurrent neural networks (RNNs) to obtain answers to general questions is illustrated. For example, it has been shown a small RNS is able to pass delayed matching to sample (DMTS) test, forming an individual dynamic representation of the received stimulus, allowing decoding by a special external neural detector.. It has been demonstrated in the reflexive game “even-odd”, the RNS has a huge advantage over a multi-layered neural network, with the same and a larger number of neurons – reflection defeats regression. It was found that the asymmetry of outcomes in the odd-even game, which was explained by various causes, including psychological ones – “it’s easier to catch up than to run away”, is reproduced in the game of two RNNs. Obviously, there are no psychological causes here and the advantage of the player playing for “even” is explained by the more complex strategy of the “odd” player – he needs to predict the opponent’s move and choose the opposite one. (shrink)

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany (...) and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture. (shrink)

The wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results—hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value (...) problem of differential equations; solutions defined on mutiply connected spaces. Section 3: geometrical theory of diffraction; identificiation of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a μ-sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function. (shrink)

Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann (...) proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the ‘beables’ of the theory, to use Bell’s term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm’s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system. (shrink)

The idea of quantum logic first appears explicitly in the short Section 5 of Chapter III. in von Neumann’s 1932 book on the mathematical foundations of quantum mechanics [31]; however, the real birthplace of quantum logic is commonly identified with the 1936 seminal paper co-authored by G. Birkhoff and J. von Neumann [5]. The aim of this review is to recall the main idea of the Birkhoff-von Neumann concept1 of quantum logic as this was put forward in (...) the 1936 paper. The review is motivated partly by two facts related to quantum logic: one, peculiar, is that the 1936 von Neumann concept is an almost totally neglected2 topic in the enormous quantum logic literature [17]; the other, not very well-known, is that von Neumann was never completely satisfied with how he had worked out quantum logic. (shrink)

Erich Neumann (1905-1960) was a student, close collaborator, and life-long friend of C. G. Jung's. He moved from Berlin to Palestine in 1934 where he endured WW11 with much distress. This provoked intense and depthful research into topics such as evil, consciousness, and creativity that would occupy his attention for the rest of his life- as well as challenge his friend's (Jung) thinking in many ways. His writings are still valuable and ever so pertinent for our understanding of human (...) nature and the changing developments that have resulted in "the eruption of the shadow and psychic chaos in today's world." (Jerome Bernstein) Eternal Echoes offers the reader an overview of Neumann's opus, which is large and multifaceted. Beginning with an introduction of Erich Neumann including a series of his active imagination watercolors, we see an intimate view into his internal process. The Jung-Neumann Correspondence examines evil as witnessed during WW11. The work Neumann focused on during this period resulted in his exploration of his own Roots of Jewish Consciousness, both Revelation and Apocalypse, and Hasidism. From there we move into an exploration of his exceptional and iconic books, The Origins and History of Consciousness, and The Great Mother, and two papers "Mass Man and the Phenomena of Recollectivation" and "Narcissism". Neumann continued his study of mythology and archetypes in Amor and Psyche: The Development of the Feminine. Later in Neumann's life, he wrote a number of books on creativity exploring its nature and source which began with his important early paper on "Mystical Man": Creative Man, Art and the Creative Unconscious, The Place of Creation. Neumann's works lead us back to our ground of being, where we live with opposites that are fiercely alive, impacting our lives and cultures. His writings are comprehensive, clear and steeped in deeply felt experiences that help to place us on firm ground. Since many of his themes and concepts are universal-beginning with archetypes, myths, and images-this book is not only pertinent to Jungian psychotherapists but anyone interested in understanding the profundity of human nature and its development. (shrink)

In this article the school of C.G. Jung is presented as a movement that, following the Swiss psychologist, tries to coimply inconscious and conscious in a symbolic language of senses. As a representative of the Jung School the psycology of Erich Neumann is offered, belonging to the Eranos Circ..

This confrontation of analytical psychology with ethics is intended as a philosophical examination of the justification of Jung's and Erich Neumann's claim to have offered in their so-called individuation process the new ethics demanded by the discovery of the psychic reality of the collective unconscious. As a standard of evaluation the author first tries to establish the idea of self-realization as a moral imperative. Aware of the difficulty of finding agreement in matters of ethics, he turns to self-awareness as (...) the source of his ethical principle. Beginning with a discussion of Kant's understanding of moral life, the author recognizes the categorical imperative as an expression of an absolute and universal law of practical reason to be an unsatisfactory representation of subjective morality, and rediscovers in the awareness of the individual law of G. Simmel the evidence of the immediate givenness of our self as a strict moral obligation. The awareness of the self as a moral ideal pre supposes freedom, which, following Sartre's existentialistic [[sic]] understanding, is identified with human reality as such and is found not to allow any kind of determination of human existence; consciousness of impulses implies "original choice," and unconsciousness means abdicated freedom. Compared with the ideal reality of the self and with the conditions of its realization as experienced in immediate awareness, the psychic reality of the individuation process as described in complex psychology lacks every moral qualification. Jung's individuation process does not represent a realization or even a recognition of the self, as the second part of the book attempts to show. A natural process enforced by an archetype of the self, demanding as moral obligations only a conscious awareness of alleged unconscious contents of a collective and personal unconscious in a confrontation of archetypes of the process, and an integration or combination of opposing conscious and unconscious psychic elements, is essentially different from a free and responsible realization of one's individual law in active confrontation with one's own historical situation and reality, and with the moral demands of the physical and social world. Confusing subjective interpretations with objective psychic facts in its doctrine of the archetypes, and morality with mental health in its understanding of the individuation process, analytic psychology is rightly found to ignore decisive aspects of human existence and especially to disregard moral reality as an essential phenomenon of human life.--M. S. (shrink)

In 1936, G. Birkhoff and J. v. Neumann published an article with the title The logic of quantum mechanics'. In this paper, the authors demonstrated that in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important proper ties of which are given by an orthocomplemented and quasimodular lattice Lq. Furthermore, this lattice of quantum mechanical proposi tions has, from a formal point of view, many similarities (...) with a Boolean lattice L8 which is known to be the lattice of classical propositional logic. Therefore, one could conjecture that due to the algebraic structure of quantum mechanical observables a logical calculus Q of quantum mechanical propositions is established, which is slightly different from the calculus L of classical propositional logic but which is applicable to all quantum mechanical propositions. This calculus has sometimes been called 'quan tum logic'. However, the statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are based on the empirically well-established quantum theory, is exposed to two serious objec tions: Logic is a theory which deals with those relationships between various propositions that are valid independent of the content of the respective propositions. Thus, the validity of logical relationships is not restricted to a special type of proposition, e. g. to propositions about classical physical systems. (shrink)

A permutation group G on a set A is ${\kappa }$ -homogeneous iff for all $X,Y\in \bigl [ {A} \bigr ]^ {\kappa } $ with $|A\setminus X|=|A\setminus Y|=|A|$ there is a $g\in G$ with $g[X]=Y$. G is ${\kappa }$ -transitive iff for any injective function f with $\operatorname {dom}(f)\cup \operatorname {ran}(f)\in \bigl [ {A} \bigr ]^ {\le {\kappa }} $ and $|A\setminus \operatorname {dom}(f)|=|A\setminus \operatorname {ran}(f)|=|A|$ there is a $g\in G$ with $f\subset g$.Giving a partial answer to a question of (...) P. M. Neumann [6] we show that there is an ${\omega }$ -homogeneous but not ${\omega }$ -transitive permutation group on a cardinal ${\lambda }$ provided (i) ${\lambda } {\omega }$ we give a method to construct large ${\kappa }$ -homogeneous, but not ${\kappa }$ -transitive permutation groups. Using this method we show that there exist ${\kappa }^+$ -homogeneous, but not ${\kappa }^+$ -transitive permutation groups on ${\kappa }^{+n}$ for each infinite cardinal ${\kappa }$ and natural number $n\ge 1$ provided $V=L$. (shrink)

The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper [1936]. Since that time there has been much argument about whether, or in what sense, quantum 'logic' can be actually considered a true logic (see, e.g. Bell and Hallett [1982], Dummett [1976], Gardner [1971]) and, if so, how it is to be distinguished from classical logic. In this paper I put forward a simple and natural semantical (...) framework for quantum logic which reveals its difference from classical logic in a strikingly intuitive way, viz. through the fact that quantum logic admits (suitably formulated versions of) the characteristic quantum-mechanical notions of superposition and incompatibility of attributes. That is, precisely the features that distinguish quantum from classical physics also serve, within this framework, to distinguish quantum from classical logic. Some light is shed on the question of whether quantum logic is a genuine logical system by introducing a natural entailment relation for quantum-logical formulas with the implication symbol. The novelty is that, although implication behaves as it should (i.e. the 'deduction theorem' holds), the order of introduction of premises is significant. The fact that a reasonable entailment relation can be formulated for quantum logic supports the view that it is a genuine logical system and not merely an algebraic formalism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:366 HISTORY OF PHILOSOPHY In harmony with Glaucon or Kant, but unlike Thrasymachus, Ballard is unconvinced by Socrates' virtual identification of virtue with art (T~xpv)or expert knowledge (cf. 24f., 50-79). For the "tragic" intellectualism embraced by both Socrates and Thrasymachus precludes the "existential loyalty" prized by Ballard's Plato and Plato's Glaucon. Against "existential loyalty," Socrates' philosopher-kings, if left to themselves, would commit crimes of omission perhaps more heinous than (...) the crimes of commission perpetrated by Thrasymachus' paragon of wisdom, the perfect tyrant. Although aware that only their leadership can prevent the greatest evils in states, philosophers nevertheless refuse to rule, even in the ideal state, unless compelled (cf. Republic, 519B7-520A4). Thus neither Thrasymachus' tyrant nor Socrates' philosopher would willingly sacrifice their own pleasure and happiness for the common good. Their "epicurean" taste contrasts sharply with Ballard's more Kantian or Biblical call for "existential loyalty." No compulsion would be necessary to obtain the return of Ballard's philosophers to the political responsibilities of the "cave." For his subordination of reason to myth precludes escape from the "cave" either in the satanic direction of Thrasymachus or the divine direction of Socrates (cf. 120). However one may evaluate Ballard's solution to the central problem of Platonism, his book surely encourages the dialectic which, in spite of his intentions, may lead to the knowledge cherished by the Republic's Thrasymachus and Socrates. Against their "tragic" intellectualism, neither Ballard nor anyone else can prove more than what the Republic's Socrates admitted: The fact of infallible knowledge is incontestable only for those experiencing it within themselves, while the claim to possess it necessarily seems mere pretense or, at worst, tragic hubris to men whose introspection reveals no rational instrument (~p~,~ov) capable of apprehending the absolute good (Republic, 527D5--528A1; cf. Protagoras, 352A8-353B3; Aristotle, Nicomachean Ethics, l177B27-11791A3; Metaphysics, 982B28-98385). The following minor errors were noted: Page 6, note 1: read "Bury" for "Bary"; page 24 (line 7 from bottom): read "Prot. 358C for "Prot. 385C" ; page 28, line 4: read "Nicias" for "Nisias" ; page 66 (line 8 from bottom): read "Republic IX" for "Republic IV." HARRY NEUMANN Scripps College Plato on Immortality. By Robert Leet Patterson. (University Park, Pa.: The Pennsylvania State University Press, 1965. Pp. 141. $5.00.) In this sympathetic account of Plato's arguments for the immortality of the soul (as presented in the Phaedo and the Phaedrus) Professor Patterson has attempted to argue that Plato believed that his arguments were complete 'demonstrations' of the immortality of the soul. The author is concerned to indicate the intention, the background, and the structure of the various arguments which Socrates presents in defense of the view that the soul is immortal. In the course of his discussions Patterson seems to involve himself in a number of large issues (e.g, the problem of psycho-physical dualism, the concept of substance, the critique of materialism and epiphenomenalism, and the meaning of Plato's doctrine of Forms) which are not dealt with comprehensively and which transcend the primary concern of his book. The digressions which lead Patterson into exceedingly difficult philosophical problems and, in some cases, into the realm of exotic analogies (e.g., he at one point compares Plato's dualism to the views of Jainism, Hinayana, Samkhya, Nyaya-Vaiseshik, and Mimamsa metaphysics I) detract from the value of the book and tend to divert him from his basic intention. His defences of Plato's arguments are, on the other hand, interesting, if debatable. The basic teaching of the Phaedo is, it is said, that the soul in essence does not belong to the realm of becoming, but is a sempiternal entity. The first argument which Socrates prepublic : Utopia or Dystopia? " (The Modern Schoolman, May, 1967). On the relation of sophistry to the problem of the xwp~qp~,see Diotim~ts Concept of Love," American Journal of Philology, 86 (1965), 47-50. BOOK REVIEWS 367 sents is said to have a "Heraclitean" structure (p. 22) presumably because it appeals to a conception of "opposites." On this basis, the argument could just as well be described as Pythagorean. At any rate, the argument assumes... (shrink)

What value should we put on our chances of obtaining a good? This paper argues that, contrary to the widely accepted theory of von Neumann and Morgenstern, the value of a chance of some good G may be a nonlinear function of the value of G. In particular, chances may have diminishing marginal utility, a property that is termed chance uncertainty aversion. The hypothesis that agents are averse to uncertainy about chances explains a pattern of preferences often observed in (...) the Ellsberg paradox. While these preferences have typically been taken to refute Bayesian decision theory, it is shown that chance risk aversion is perfectly compatible with it. (shrink)

I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of (...) all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals. (shrink)

This volume presents, for the first time, an assemblage of contributions on the philosophical dimensions of the impersonal, the multiplicity of its linguistic, social, scientific, religious and artistic perspectives, as well as initial approaches to its unified definition. Linguistic and logical impersonality The “It" in K. Kraus “Impersonality” in the subject and in events The impersonal ontology of H. Rombach Levinas on the “Il y a” Organisation in non-egological consciousness The witness of consciousness in the Vedānta traditions Anonymous self-consciousness G. (...) Deleuzes figures of the impersonal The impersonal in G. Agamben's Philosophy Formal and collective thought in Spinoza Cusanus and the person as stake in the game of life Impersonal subjectivity and the comedy of solipsism Dimensions of the impersonal in T. Nagel, E. Husserl and H. Plessner On the figure of the impersonal in the Anthropocene Language and mask in F. Nietzsche Theodoros Terzopoulos on impersonality and theatre With contributions by Michael Astroh, Eric Ebner, Eric Eggert, Rolf Elberfeld, Katrin Felgenhauer, Ralf Gisinger, Annika Hand, Stefan Lang, Robert Lehmann, Enrico Müller, Daniel Neumann, Frank Raddatz, Christian Rößner, Thomas Schmaus, Fabian Strobel and Theodoros Terzopoulos. (shrink)

The First International Congress for Analytical Psychology was held in Zurich from 7 to 12 August 1958. On this occasion a small group of Israeli psychologists, represented by Erich Neumann, was accepted as a charter group member of the International Association for Analytical Psychology, which marked the foundation of the Israel Association of Analytical Psychology. The history leading up to this official birth date is mainly associated with the efforts of Erich Neumann – and rightly so; however, a (...) number of other therapists, scholars and patients have been forgotten or deleted from this historical narrative, to their detriment. While I was working on the edition of the correspondence between C. G. Jung and Erich Neumann I came across their names, which were often only casually mentioned re some episode, and I have since tried to find out their stories and what happened to them. In this article I discuss the contributions to the development of analytical psychology in British Mandate Palestine, later Israel, of two such figures, Max M. Stern and Margarete Braband-Isaac. Both had been in personal contact with C. G. Jung and built a bridge between the isolated Jewish therapists in British Mandate Palestine and the Zurich circles. In Tel Aviv they collaborated for a while with Neumann, with whom for different reasons both fell out. The article shows the cause of these controversies with Neumann and tries to find out why those two characters were historically marginalized. (shrink)

Au cours de l'année 1934, une jeune philosophie et mathématicienne allemande, Grete Hermann, se rend à Leipzig pour participer au séminaire organisé par l'un des plus célèbres pionniers de la physique quantique, W. Heisenberg. C.F. von Wizsäcker y est présent, entre autres éminents scientifiques. Fervente adepte de la philosophie kantienne réinterprétée par J.F. Fries et L. Nelson, G. Hermann arrive avec un objectif précis : démontrer la compatibilité entre physique quantique et philosophie kantienne. En particulier, concilier la catégorie de causalité, (...) forme a priori de la pensée selon Kant, avec les prédictions statistiques de la nouvelle physique. Après une année de débats avec ses interlocuteurs, G. Hermann publie le présent opuscule, traduit ici pour la première fois. Elle y développe une interprétation tout à fait originale de la mécanique quantique, et réfute, trente ans avant J. Bell, la démonstration de J. von Neumann contre les variables cachées. -- 4ème de couverture. (shrink)

As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of Quantum Mechanics (...) are depending on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame. (shrink)