L S Penrose’s Limit Theorem – which is implicit in Penrose [7, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely and the relative quota is pegged, then – under certain conditions – the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover [4] prove some special cases of Penrose’s Limit Theorem. (...) They give a simple counter-example showing that the theorem does not hold in general even under the conditions assumed by Penrose; but they conjecture, in effect, that under rather general conditions it holds ‘almost always’ – that is with probability 1 – for large classes of weighted voting games, for various values of the quota, and with respect to several measures of voting power. We use simulation to test this conjecture. It is corroborated with respect to the Penrose–Banzhaf index for a quota of 50% but not for other values; with respect to the Shapley–Shubik index the conjecture is corroborated for all values of the quota. (shrink)

LS Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf index’). His limit theorem – which is implicit in Penrose (1952) and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while the quota is pegged at half the total weight, then – under certain conditions – the ratio between the voting powers (as (...) measured by him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined weighted voting games, other values of the quota, and other measures of voting power. We provide proofs for some special cases. (shrink)

Grush and Churchland (1995) attempt to address aspects of the proposal that we have been making concerning a possible physical mechanism underlying the phenomenon of consciousness. Unfortunately, they employ arguments that are highly misleading and, in some important respects, factually incorrect. Their article ‘Gaps in Penrose’s Toilings’ is addressed specifically at the writings of one of us (Penrose), but since the particular model they attack is one put forward by both of us (Hameroff and Penrose, 1995; 1996), (...) it is appropriate that we both reply; but since our individual remarks refer to different aspects of their criticism we are commenting on their article separately. The logical arguments discussed by Grush and Churchland, and the related physics are answered in Part l by Penrose, largely by pointing out precisely where these arguments have already been treated in detail in Shadows of the Mind (Penrose, 1994). In Part 2, Hameroff replies to various points on the biological side, showing for example how they have seriously misunderstood what they refer to as ‘physiological evidence’ regarding to effects of the drug colchicine. The reply serves also to discuss aspects of our model ‘orchestrated objective reduction in brain microtubules – Orch OR’ which attempts to deal with the serious problems of consciousness more directly and completely than any previous theory. (shrink)

Lanczos, C. Einstein's path from special to general relativity.--Balazs, N. L. The acceptability of physical theories: Poincaré versus Einstein.--Ellis, G. F. R. Global and non-global problems in cosmology, by G. F. R. Ellis and D. W. Sciama.--Ehlers, J. The geometry of free fall and light propagation, by J. Ehlers, F. A. E. Pirani and A. Schild.--Trautman, A. Invariance of Lagrangian systems.--Penrose, R. The geometry of impulsive gravitational waves.--Exact solutions of the Einstein-Maxwell equations for an accelerated charge.--Taub, A. H. Plane-symmetric (...) similarity solutions for self-gravitating fluids.--Robinson, I. Equations of motion in the linear approximation, by I. Robinson and J. R. Robinson.--Florides, P. W. Rotating bodies in general relativity.--Chandrasekhar, S. A limiting case of relativistic equilibrium.--Israel, W. The relativistic Boltzmann equation.--Thompson, W. B. The self-consistent test-particle approach to relativistic kinetic theory. (shrink)

We argue that the set of humanly known mathematical truths (at any given moment in human history) is finite and so recursive. But if so, then given various fundamental results in mathematical logic and the theory of computation (such as Craig’s in J Symb Log 18(1): 30–32(1953) theorem), the set of humanly known mathematical truths is axiomatizable. Furthermore, given Godel’s (Monash Math Phys 38: 173–198, 1931) First Incompleteness Theorem, then (at any given moment in human history) humanly known mathematics must (...) be either inconsistent or incomplete. Moreover, since humanly known mathematics is axiomatizable, it can be the output of a Turing machine. We then argue that any given mathematical claim that we could possibly know could be the output of a Turing machine, at least in principle. So the Lucas-Penrose (Lucas in Philosophy 36:112–127, 1961; Penrose, in The Emperor’s new mind. Oxford University Press, Oxford (1994)) argument cannot be sound. (shrink)

Until recently, Albert Einstein's complaints in his later years about the intelligibility of Quantum Mechanics often led philosophers and physicists to dismiss him as, essentially, an old fool in his dotage. Happily, this kind of thing is now coming to an end as philosophers and mathematicians of the caliber of Karl Popper and Roger Penrose conspicuously point out the continuing conceptual difficulties of quantum theory [cf. Penrose's searching discussion in The Emperor's New Mind, chapter 6, "Quantum magic and (...) quantum mystery," Oxford 1990]. The Paradox of Schrödinger's Cat is sometimes now even presented, not as a wonderful exciting implication of the theory, but for what it originally was: a reductio ad absurdum argument against the "new" quantum mechanics of Heisenberg and Bohr. Schrödinger shared the misgivings of Einstein and others. (shrink)

Whether it was John Searle’s Chinese Room argument (Searle, 1980) or Roger Penrose’s argument of the non-computable nature of a mathematician’s insight – an argument that was based on Gödel’s Incompleteness theorem (Penrose, 1989), we have always had skeptics that questioned the possibility of realizing strong Artificial Intelligence (AI), or what has become known by Artificial General Intelligence (AGI). But this new book by Landgrebe and Smith (henceforth, L&S) is perhaps the strongest argument ever made against strong AI. (...) It is a very extensive review of what building a mind essentially amounts to drawing on insights and results from biology, physics, linguistics, computability, philosophy, and mathematics. (shrink)

In The Large, the Small and the Human Mind, Sir Roger Penrose, the Rouse Ball Professor of Mathematics at Oxford, unfolds his theory of the evolution of the Cosmos on the reasonable assumptions that Nature is functionally one and that natural systems are consequently historically and energetically related through their common substrate. His argument unfolds in three main stages, as the title of the book suggests. The main argument has already been presented to the educated public in two important (...) books: first in The Emperor’s New Mind, published in 1989, and later in Shadows of the Mind, published in 1994 partly to refute the counter-arguments leveled against his thesis about the human mind, a thesis which irked a large number of people whose assumptions were being challenged. (shrink)

To construct their first lexicon, infants must determine the relationship between native phonological variation and the meanings of words. This process is arguably more complex for bilingual learners who are often confronted with phonological conflict: phonological variation that is lexically relevant in one language may be lexically irrelevant in the other. In a series of four experiments, the present study investigated English–Mandarin bilingual infants’ abilities to negotiate phonological conflict introduced by learning both a tone and a non-tone language. In a (...) novel word learning task, bilingual children were tested on their sensitivity to tone variation in English and Mandarin contexts. Their abilities to interpret tone variation in a language-dependent manner were compared to those of monolingual Mandarin learning infants. Results demonstrated that at 12–13 months, bilingual infants demonstrated the ability to bind tone to word meanings in Mandarin, but to disregard tone variation when learning new words in English. In contrast, monolingual learners of Mandarin did not show evidence of integrating tones into word meanings in Mandarin at the same age even though they were learning a tone language. However, a tone discrimination paradigm confirmed that monolingual Mandarin learning infants were able to tell these tones apart at 12–13 months under a different set of conditions. Later, at 17–18 months, monolingual Mandarin learners were able to bind tone variation to word meanings when learning new words. Our findings are discussed in terms of cognitive adaptations associated with bilingualism that may ease the negotiation of phonological conflict and facilitate precocious uptake of certain properties of each language. (shrink)

Il dibattito sul ruolo e le implicazioni del teorema di Gödel per l'intelligenza artificiale ha recentemente ricevuto nuovo impeto grazie a due importanti volumi pubblicati da Roger Penrose, The Emperor's New Mind [1989] e Shadows of the Mind [1994]. Naturalmente, Penrose non è il primo né l'ultimo a usare il teorema di Gödel allo scopo di trarne conseguenze per i fondamenti dell'intelligenza artificiale. Tuttavia il recente dibattito suscitato dai due libri di Penrose è significativo sia per ampiezza (...) sia per profondità. In queste pagine si vuole dare una rassegna di tale dibattito, cominciando dai suoi precursori negli anni '60 (fra cui Lucas, Putnam, e Chihara), per passare poi alle complesse argomentazioni proposte da Penrose e le reazioni di una serie di commentatori (ad esempio Dennett, Feferman, McDermott, Davis). (shrink)

Purpose. The dynamics and pace of social and economic transformations that are characteristic of modern society, lead to an increase in tension and the destruction of habitual stereotypes – ideals, values, norms, patterns of behaviour that unite people. These moments encourage us to rethink the understanding of "security" essence, in particular, psychological, which emphasizes the urgency of its study in the philosophical and sociocultural coordinates. Theoretical basis of the research is based on the philosophical methodology of K. Jaspers, E. Fromm (...) and the A. Maslow’s psychological approach to understanding of a person. Originality. Psychological security is considered at different levels: first and foremost, society is a characteristic of social security, that is an analysis of how today’s social technologies, social changes affect the quality of life of the country’s population; secondly, the social environment – the family, the immediate environment, reference groups, training teams; thirdly, a person is an experience of his own security-insecurity, when it is possible to talk about the manifestations of psychological violence, when certain behavioral acts contribute to the violation of the security of the other or to self-destruction. It is found out that the knowledge of psychological security is closely connected with the socio-historical conditions of being, with the level of development of material and spiritual culture, with the interests and values prevailing in society, which determines its ontological, epistemological and axiological features. The presented issue is considered in the correlation of psychological security with types of scientific rationality – classical, nonclassical and post-nonclassical approaches, within the framework of which various perspectives, aspects, forms and types of psychological security are studied. Conclusions. The concept of security requires a systematic description of its manifestations, types, levels, concepts: security as the absence of dangers ; security as a certain activity to ensure or to prevent any threats or dangers ; security as a conscious necessity, the value of the individual. The study systematizes various ideas about psychological security in accordance with the logic of scientific knowledge: in the mainstream of classical, non-classical and post-nonclassical approaches. (shrink)

In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptation, difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new (...) research avenue in program refinement, (conceptual) tools are needed to reason about them. In this line, the paper’s main contribution is a study of the correspondence between logical interpretations and morphisms of a particular kind of coalgebras. This opens way to the use of coalgebraic constructions, such as simulation and bisimulation, in the study of interpretations between (abstract) logics. (shrink)

This provocative study revives a classical idea about rationality by developing analogies between the structure of personality and the structure of society in the context of contemporary work in the philosophy of mind, ehtics, decision theory, and social choice theory.

I argue that Davidson's anti-skeptical thesis can survive objections made against it by treating skepticism as logically possible, but not epistemically possible. That is, the skeptical hypothesis of massive error conflicts with what we must take ourselves to know if we are to have coherent thought and speech.

Background: The intentions of clinicians are widely considered to be relevant to the ethical assessment of their actions. A better understanding of the psychological factors that influence the ascription of intentions in clinical practice is important for improving the self-understanding of clinical decision-making and, ultimately, the ethics of clinical care. Drawing on empirical research on intentionality that has been done in other contexts, this is the first study to test whether the “asymmetric effect” of intention ascription is exhibited by respondents (...) when presented with clinical decision-making scenarios. Objective: To assess how individuals attribute intentions to clinical actors in clinical decision-making scenarios. Methods: A total of 149 first and second year medical students was randomly assigned to two groups. Subjects in each group read two scenarios and submitted anonymous responses to questions regarding each scenario. Results: The asymmetric effect was strongly exhibited by the responses given to scenario 2, but it was not exhibited by the responses given to scenario 1. Conclusion: The present study provided evidence for the view that people’s ascription of intentions to others is influenced by their previous evaluative judgement of the conduct in question. (shrink)

My purpose in what follows is not so much to defend the basic principle of utilitarianism as to indicate the form of it which seems most promising as a basic moral and political position. I shall take the principle of utility as offering a criterion for two different sorts of evaluation: first, the merits of acts of government, social policies, and social institutions, and secondly, the ultimate moral evaluation of the actions of individuals. I do not take it as implying (...) that the individual should live his life on the basis of constant evaluations of this sort. For there are different levels of decision making each with its appropriate criteria. For example, we each inevitably make many of our decisions from the point of view of our own personal self-fulfilment and this cannot regularly take a directly utilitarian form, nor should the utilitarian want it to do so. His claim is at most that we should sometimes review our life from the point of view of a kind of impersonal moral truth of a universalistic utilitarian character. (shrink)

The increasing demand for horticultural products for nutritional and economic purposes by lesser developed countries (LDC's) is well-documented. Technological demands of the LDC's producing horticultural products is also increasing. Pesticide use is an integral component of most agricultural production, yet chemicals are often supplied without supplemental information vital for their safe and efficient implementation. Illiteracy rates in developing countries are high, making pesticide education even more challenging. For women, who perform a significant share of agricultural tasks, illiteracy rates are even (...) higher than for men. The dilemma exists of how a developing country can improve its nutritional and economic situation without giving consideration to social and environmental consequences. (shrink)

. This paper examines the association between long-term compensation and corporate social responsibility for 90 publicly traded Canadian firms. Social responsibility is considered to include concerns for social factors and the environment, 564-578; Kane, E. J., 341-359). Long-term compensation attempts to focus executives efforts on optimizing the longer term, which should direct their attention to factors traditionally associated with socially responsible executives. As hypothesized, we found a significant relationship between the long-term compensation and total CSR weakness as well as the (...) product/environmental weakness dimension of CSR. In addition, we found a marginally significant relationship between long-term compensation and total corporate responsibility. Our findings are that executives long-term compensation is associated with a firms environmental actions, and that firms that utilize long-term compensation are more likely to mitigate product/environment weaknesses than those that do not. Implications for practice and research are discussed. (shrink)

The period of the mid-1920s to the mid-1980s was a portentous period for Soviet psychology. As this period recedes into the past, the figure of L. S. Vygotskii rises more and more before us. Vygotskii died of tuberculosis when not quite 37 years old. He was a psychologist for only 10 years, and it was only in the last 6 of these that he did the work we now associate with his name. During those brief years Vygotskii wrote over 120 (...) works, including more than 10 large books. His was a short life — filled with inspired, indefatigable, and heroic work. A significant part of his written work has remained unpublished and indeed much of it remained unfinished. A seven-volume collection of Vygotskii's work is currently underway, and even this will not contain everything he wrote. The final volume of this collection will include his articles "The Sense of the Psychological Crisis" and "Spinoza's Theory of the Passions.". (shrink)