A critical discussion is provided of three central assumptions underlying Nunez's approach to modeling cortical activity. A plea is made for neurophysiologically realistic models involving nonlinearities, multiple time scales, and stochasticity.

A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This yields that the realization (...) of hypercomputing devices is implausible, and that Thesis P is not essentially different from the standard Church-Turing Thesis. (shrink)

The physicist's conception of space-time underwent two major upheavals thanks to the general theory of relativity and quantum mechanics. Both theories play a fundamental role in describing the same natural world, although at different scales. However, the inconsistency between them emerged clearly as the limitation of twentieth-century physics, so a more complete description of nature must encompass general relativity and quantum mechanics as well. The problem is a theorists' problem par excellence. Experiment provide little guide, and the inconsistency mentioned above (...) is an important problem which clearly illustrates the intermingling of philosophical, mathematical, and physical thought. In fact, in order to unify general relativity with quantum field theory, it seems necessary to invent a new mathematical framework which will generalise Riemannian geometry and therefore our present conception of space and space-time. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new kind of geometry may enter physics, and space-time itself can be reinterpreted as an approximate, derived concept. The main purpose of this article is to show the great significance of space-time geometry in predetermining the laws which are supposed to govern the behaviour of matter, and further to support the thesis that matter itself can be built from geometry, in the sense that particles of matter as well as the other forces of nature emerges in the same way that gravity emerges from geometry. Scientific research is not a process of steady accumulation of absolute truths, which has culminated in present theories, but rather a much more dynamic kind of process in which there are no final theoretical concepts valid in unlimited domains. (David Bohm). (shrink)

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and (...) Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems. (shrink)

Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism. There are now many forms of structural realism and an extensive literature about them. There are interesting connections with debates in metaphysics, philosophy of physics and philosophy of mathematics. This entry is intended to be a comprehensive survey of the field.

When a group of processes achieves such closure that a set of states of affairs recurs continually, then the effect of that coherence on the world differs from what would occur in the absence of that closure. Such altered effectiveness is an attribute of the system as a whole, and would have consequences. This indicates that the network of processes, as a unit, has ontological significance. Whenever a network of processes generates continual return to a limited set of states of (...) affairs, the system may function as a “whole”— with respect to appropriate interaction partners. The balance achieved by the processes provides the form of definiteness of a unified agent. The causal powers of such coherent aggregates are indeed just the powers of the “constituents acting in concert”. However, the components act in concert in the specific way they do only because of their inclusion in the closed set of interactions that defines the coherence. This renders the causal powers of the coherence defined by that closure non-redundant, and hence the coherence, as a unit, is ontologically significant. The form of definiteness that provides internal coherence also grounds external efficacy of the societal aggregation. The closure is a structural feature of the coherence — possibly, but not necessarily, apparent in spatial structuring. This approach can provide a unified account that includes quantum microphysics, systems biology, and the philosophy of organism ─ without reducing any of these to another. (shrink)

According to David Chalmers, the hard problem of consciousness consists of explaining how and why qualitative experience arises from physical states. Moreover, Chalmers argues that materialist and reductive explanations of mentality are incapable of addressing the hard problem. In this chapter, I suggest that Chalmers’ hard problem can be usefully distinguished into a ‘how question’ and ‘why question,’ and I argue that evolutionary biology has the resources to address the question of why qualitative experience arises from brain states. From this (...) perspective, I discuss the different kinds of evolutionary explanations (e.g., adaptationist, exaptationist, spandrel) that can explain the origins of the qualitative aspects of various conscious states. This argument is intended to clarify which parts of Chalmers’ hard problem are amenable to scientific analysis. (shrink)

The question about divine action remains contested in the discussion between theology and science. This issue is further exacerbated with the entry of pentecostals and charismatics into the conversation, especially with their emphases on divine intervention and miracles. I explore what happens at the intersection of these discourses, identifying first how the concept of "laws of nature" has developed in theology and science and then probing what pentecostal-charismatic insights might add into the mix. Drawing from the triadic and evolutionary metaphysics (...) of Charles Sanders Peirce, I propose a reconsideration of the "laws of nature" as habitual, dynamic, and general but nevertheless real tendencies through which the Holy Spirit invites the world to inhabit the coming kingdom of God. This proposal contributes to the articulation of an authentic Pentecostal-charismatic witness at the theology-and-science table while also enabling a more plausible and coherent account of divine action for pentecostal-charismatic piety and Christian practice in the twenty-first century. (shrink)

Recent years have witnessed rapidly increasing interests in developing quantum theoretical models of human cognition. Quantum mechanisms have been taken seriously to describe how the mind reasons and decides. Papers in this special issue report the newest results in the field. Here we discuss why the two levels of commitment, treating the human brain as a quantum computer and merely adopting abstract quantum probability principles to model human cognition, should be integrated. We speculate that quantum cognition models gain greater modeling (...) power due to a richer representation scheme. (shrink)

Abstract Die moderne Physik besteht nicht nur aus neuen Entdeckungen und Erfindungen durch die Relativitätstheorie und durch die Quantenphysik. Sie besteht auch aus völlig neuen Sichtweisen und flexiblen Denkweisen von Zusammenhängen und Verschränkungen zwischen den Dingen. Die moderne Physik hat sich von dem Klischee des Schwarz-Weiß-Denkens verabschiedet, für das es nur getrennte Dinge, ohne fließende Übergänge gibt. Solche unbeweglichen, dogmatischen schwarzweißen Denkweisen können wir zurückverfolgen bis zu dem griechischen Philosophen Aristoteles. In der Zeit der Klassischen Mechanik hatten sie einen überwältigenden (...) Erfolg. Galilei behauptete, das Buch der Natur sei in der Sprache der Mathematik geschrieben. Das war die sehr kurzgefasste Formulierung der Klassischen Mechanik. Die moderne Physik hat sich keineswegs von der Mathematik verabschiedet, ganz und gar nicht. Doch der heilige Ernst und der starre und absolute Dogmatismus hat nachgelassen. Moderne Denkweisen in der Physik können mit den Begriffen von fließenden Übergängen, von Zwischenstufen, von Zusammenhängen zwischen den Dingen und von Schwingungen gekennzeichnet werden. Seit Faraday und Maxwell hat sich eine Verschiebung der Untersuchungsobjekte ergeben: Seit der Mitte des 19. Jahrhunderts, seit ca 1850, drehen sich die Denkmodelle der modernen Physik nicht mehr um getrennte, isolierten Körper, die im Nichts schwimmen, sondern um die Zwischenräume zwischen den Körpern und um die flexiblen Beziehungsgeflechte zwischen den Dingen und um die Netzwerke, die die Dinge umgeben. Das sind ganz neue physikalische Denkweisen, die durchaus Dunkelzonen und Zweifel und Ungewissheiten kennen, die den Bereich der Exaktheit überschatten. Neue Beiträge der physikalischen Denkweisen sind auch durch eine Flexibilität bei der Bildung von Begriffen gekennzeichnet. Sie lassen sich nicht auf einige wenige Begriffe oder auf eine starre und exakte Festlegung der Wortwahl festnageln. -/- „Jede Philosophie bezieht ihre Farbe von der geheimen Lichtquelle eines Vorstellungshintergrunds, der niemals ausdrücklich in ihrenGedankenketten auftaucht“ (Whitehead) (1) . (shrink)

The main goal of this paper is to argue against Karl Rogers's attacks on realism in physics. Rogers argues that electrons do not exist independently of the relevant socio-technological process, but I show that such an assumption would make our best scientific theories incomprehensible. While the paper supports Rogers's attempts to refute positivism, it demonstrates that his own position is positivistic, and it corrects his overemphasis on the roles of technology and the experimenter. Rogers assumes that the founders of modern (...) science were simply mechanists, but I show how they were actually Platonic realists. Contrary to Rogers, realist faith in the fundamental unifying power of the laws of physics is shown to be reasonable, and any denial of this belief would imply that science is impossible. (shrink)

This essay interprets the meaning of one of the cards in aTarot deck, "The Magician," in the context of process philosophy in the tradition of Alfred North Whitehead. It brings into the conversation the philosophical legacy of American semiotician Charles Sanders Peirce as well as French poststructuralist Gilles Deleuze. Some of their conceptualizations are explored herein for the purpose of explaining the symbolic function of the Magician in the world. From the perspective of the logic of explanation, the sign of (...) the Magician is an index of nonmechanistic, mutualist or circular, causality that enables self-organization embedded in coordination dynamics. Its action is such as to establish an unorthodox connection crossing over the dualistic gap between mind and matter, science and magic, process and structure, the world without and the world within, subject and object, and human experience and the natural world, thereby overcoming what Whitehead called the paradox of the connectedness of things. The Magician represents a certain quality that acts as a catalytic agent capable of eliciting transmutations, that is, the emergence of novelty. I present a model for process∼structure that uses mathematics on the complex plane and the rules of projective geometry. The corollary is such that the presence of the Magician in the world enables a particular organization of thought that makes pre-cognition possible. (shrink)

The overriding question in contemporary philosophy is as follows: We now have a reasonably well-established conception of the basic structure of the universe. But it is not at all easy to reconcile the basic facts we have come to know with a certain conception we have of ourselves, derived in part from our cultural inheritance but mostly from our own experience. Various aspects of this question are examined, concerning consciousness, intentionality, language, rationality, free will, society and institutions, politics, and ethics.

In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of a reducing theory (...) T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (shrink)

The aim of this paper is to refute the hypothesis that the observer’s consciousness is necessary in the quantum mechanics measurement process. In order to achieve our target, we propose and investigate a variation of the Schrödinger’s cat thought experiment called “DAP”, short for “Dead-Alive Physicist”, in which a human being replaces the cat. This strategy enables us to logically disprove the consistency of the above hypothesis, and to oblige its supporters either to be trapped in solipsism or to rely (...) on an alternative interpretation of quantum mechanics in which the conscious observer plays the sole role of acknowledging the experimental results. Our analysis hence provides support to clarify the relationship between the observer and the objects of her/his experimental observation; this and a few other implications are discussed in the fourth section and in the conclusions. (shrink)

Discussions about the achievements and limitations of the various approaches to the development of intelligent systems can have an essential impact on empirically based research, and with that also on the future development of computer technologies. However, such discussions are often based on vague concepts and assumptions. In this context, we claim that the proposed `three-world ontology'' offers the most appropriate conceptual framework in which the basic problems concerned with cognition and computation can be suitably expressed and discussed, although the (...) solutions of some of these problems seem to lie beyond the horizon of our current understanding. We stress the necessity to differentiate between authentic and functional cognitive abilities; although computation is not a plausible way towards authentic intelligence, we claim that computational systems do offer virtually unlimited possibilities to replicate and surpass human cognitive abilities on the functional level. (shrink)

A famous essay by Wigner is reexamined in view of more recent developments around its topic, together with some remarks on the metaphysical character of its main question about mathematics and natural sciences.

¿Cómo se nos presenta, fenomenológicamente la realidad humana? Es la que vemos diariamente en nuestra vida personal y social. Estamos hechos de materia, formamos parte del universo evolutivo. Además, está formada en nosotros una vida psíquica: la sensación, un sistema de percepciones, una conciencia integrada, una condición de sujeto psicológico; producimos conocimiento, emociones, motivaciones; pero, sobre todo, tenemos una mente que discurre racionalmente y nos instala en un mundo de emociones humanas; esta razón emocional está en la base de la (...) búsqueda de la verdad del universo, del sentido de la vida y de la responsabilidad moral, en la vida personal y social. Nuestra realidad humana es, pues, una realidad personal. Somos personas. Ahora bien, ¿cómo explica hoy la ciencia, la neurología, el hecho de que nuestra realidad humana posea estas propiedades que nos hacen personas? Esto debería poder explicarse desde el mundo físico-biológico. Ahora bien, en concreto, ¿cómo la ciencia hace posible explicar que la evolución nos haya producido a nosotros en nuestra condición de personas? Es decir, ¿cuál es el soporte físico que hace inteligible la ontología psico-bio-física que produce evolutivamente nuestra experiencia personal fenomenológica? Esta es, en último término, todavía hoy la cuestión fundamental de las ciencias humanas. Lo que la ciencia, a saber, la neurología, debe explicar es obvio: el hecho de que haya emergido la sensibilidad-conciencia, nuestra condición de sujetos psíquicos, el conocimiento y la razón emocional; de tal manera que, una vez emergida la razón emocional, lleve por sí misma a constituir la actividad racional y las emociones propias de la persona humana encaminada a construir el sentido de su vida. Estas son las cuestiones que abordamos en este artículo. (shrink)

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief (...) that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed. (shrink)

We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require (...) quantum computation or similar mechanisms. (shrink)

Joule’s Energy Conservation Law was the first “meta-law”: a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles—such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable—but simplified—analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that (...) not only Joule’s principle remains true—it is actually strengthened: it is no longer a principle that all physical theories should satisfy—it is a principle that all physical theories do satisfy. (shrink)

The alleged proof of the non-mechanical, or non-computational, character of the human mind based on Gödel’s incompleteness theorem is revisited. Its history is reviewed. The proof, also known as the Lucas argument and the Penrose argument, is refuted. It is claimed, following Gödel himself and other leading logicians, that antimechanism is not implied by Gödel’s theorems alone. The present paper sets out this refutation in its strongest form, demonstrating general theorems implying the inconsistency of Lucas’s arithmetic and the semantic inadequacy (...) of Penrose’s arithmetic. On the other hand, the limitations to our capacity for mechanizing or programming the mind are also indicated, together with two other corollaries of Gödel’s theorems: that we cannot prove that we are consistent, and that we cannot fully describe our notion of a natural number. (shrink)

Rudyard Kipling, the famous english author of « The Jungle Book », born in India, wrote one day these words: « Oh, East is East and West is West, and never the twain shall meet ». In my paper I show that Kipling was not completely right. I try to show the common ground between buddhist philosophy and quantum physics. There is a surprising parallelism between the philosophical concept of reality articulated by Nagarjuna and the physical concept of reality implied (...) by quantum physics. For neither is there a fundamental core to reality, rather reality consists of systems of interacting objects. Such concepts of reality cannot be reconciled with the substantial, subjective, holistic or instrumentalistic concepts of reality which underlie modern modes of thought. (shrink)

Benjamin Libet compared the perceived time of direct brain stimulation to the perceived time of skin stimulation. His results are among the most controversial experiments at the interface between psychology and philosophy. The new element that I bring to this discussion is a reanalysis of Libet's raw data. Libet's original data were difficult to interpret because of the manner in which they were presented in tables. Plotting the data as psychometric functions shows that the observers have great uncertainty about the (...) relative timing of events, as seen the shallow psychometric slopes. A second indication of uncertainty comes from Libet's use of three response categories, A first; B first; and A and B simultaneous. The large number of “perceptually simultaneous” responses provides a further measure of the difficulty of the judgment. There are thus a very broad range of stimulus delays in which the subject is unable to make an accurate ordering response. These points provide evidence that there is no compelling reason to invent exotic or ad hoc mechanisms to account for Libet's data since the uncertainty window is large enough to allow simple mechanism such as memory shifts. Libet argued that his data provide evidence for a backward referral in time. I argue that even though Libet's own data are weak, there are good arguments for a backward referral mechanism to help the subject make sense out of the tangled chaos of asynchronous information associated with experienced events. (shrink)

Quantum cognition is an emerging field making uses of quantum theory to model cognitive phenomena which cannot be explained by classical theories. Usually, in cognitive tests, subjects are asked to give a response to a question, but, in this paper, we just observed the subjects’ behaviour and the question and answer method was not applied in order to prevent any mental background on participants’ minds. Finally, we examined the experimental data on Hardy’s non-locality argument, and we noticed the violation of (...) HNA in human behaviour. (shrink)

This paper presents an analysis and critique of Roger Penrose’s epistemological, methodological, and ontological positions. The analysis is relevant not only because Penrose is an influential scientist, but also because of the particular traits of his thought. These traits are directly connected with his background and approach to science: ontological and epistemological realism, mathematical Platonism, emphasis on the continuities of science, epistemological inclusiveness and essential openness of science, the role of common sense, emphasis on the connection between science, ethics, and (...) philosophy. The paper articulates Penrose’s position and criticizes some of its possible shortcomings. It contributes to the perception of science as an open activity, as illustrated in Penrose’s particular approach, and provides an interesting case-study that can contribute to understanding how epistemological and ontological positions are connected with particular scientific practices. (shrink)

Under certain conditions private information can be a source of trade. Arbitrage for instance can occur as a result of the existence of private information. In this paper we want to explicitly model information. To do so we define an ‘information function’. This information function is a mathematical object, also known as a so called ‘wave function’. We use the definition of wave function as it is used in quantum mechanics and we attempt to show the usefulness of this wave (...) function in an economic context. We attempt to answer the following questions. How does the information function relate to private information? How can we use the information function to define the ‘quantity’ of information? How can we use the information function in arbitrage-based option pricing? How can the information function be used in the formulation of a so called Universal Brownian motion? (shrink)

We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources. The final world model treated here contains only gravonons and a scalar matter field. The gravonons (...) are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: There is a chooser mechanism for the selection of the localization site. The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation. (shrink)

Physical processes manifest an objective order that science manages to discover. Commonly, it is considered that these processes obey the “laws of nature.” Bergson disputes this idea which ultimately constitutes a kind of Platonism. In contrast, he develops the idea that physical processes are a particular case of automatic behaviors. In this sense, they imply a motor memory immanent to matter, whose actions are triggered by some perceptions. This approach is obviously panpsychist. It gives matter a certain consciousness, even if (...) the latter is different in nature from our consciousness. In some respects, this approach is similar to contemporary panpsychism because it claims that the psychic is a fundamental characteristic of nature, causally active. But it is also original because it does not constitute a theory of the origin of mind in nature. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

Scientific exploration and thus our knowledge about the outside world is subject to the conditions of our experience.These conditions are condensed here into an interface model which,besides being physical,has an additional interface structure not reducible to physics. We suggest that this structure can dynamically be characterized by separate modes.Their selection and operation presupposes free will and a rudimentary concept of time and space. Based on some analogies with quantum networks it is argued that the 'observed' gets 'dressed'as a consequence of (...) the observing. Interface dynamics and system dynamics supplement each other without over- determination. (shrink)

Quantum mechanical theories of consciousness are contrasted to classical ones. A key difference is that the quantum laws are fundamentally psychophysical and provide an explanation of the causal effect of conscious effort on neural processes, while the laws of classical physics, being purely physical, cannot. The quantum approach provides causal explanations, deduced from the laws of physics, of correlations found in psychology and in neuropsychology.

The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen (...) in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well. -/- In addition to exhibiting sensitive dependence, chaotic systems possess two other properties: they are deterministic and nonlinear (Smith 2007). This entry discusses systems exhibiting these three properties and what their philosophical implications might be for theories and theoretical understanding, confirmation, explanation, realism, determinism, free will and consciousness, and human and divine action. (shrink)

Nagarjuna and Quantum physics. Eastern and Western Modes of Thought. Summary. The key terms. 1. Key term: ‘Emptiness’. The Indian philosopher Nagarjuna is known in the history of Buddhism mainly by his keyword ‘sunyata’. This word is translated into English by the word ‘emptiness’. The translation and the traditional interpretations create the impression that Nagarjuna declares the objects as empty or illusionary or not real or not existing. What is the assertion and concrete statement made by this interpretation? That nothing (...) can be found, that there is nothing, that nothing exists? Was Nagarjuna denying the external world? Did he wish to refute that which evidently is? Did he want to call into question the world in which we live? Did he wish to deny the presence of things that somehow arise? My first point is the refutation of this traditional translation and interpretation. 2. Key terms: ‘Dependence’ or ‘relational view’. My second point consists in a transcription of the keyword of ‘sunyata’ by the word ‘dependence’. This is something that Nagarjuna himself has done. Now Nagarjuna’s central view can be named ‘dependence of things’. Nagarjuna is not looking for a material or immaterial object which can be declared as a fundamental reality of this world. His fundamental reality is not an object. It is a relation between objects. This is a relational view of reality. Reality is without foundation. Or: Reality has the wide open space as foundation. 3. Key terms: ‘Arm in arm’. But Nagarjuna did not stop there. He was not content to repeat this discovery of relational reality. He went on one step further indicating that what is happening between two things. He gave indications to the space between two things. He realised that not the behaviour of bodies, but the behaviour of something between them may be essential for understanding the reality. This open space is not at all empty. It is full of energy. The open space is the middle between things. Things are going arm in arm. The middle might be considered as a force that bounds men to the world and it might be seen as well as a force of liberation. It might be seen as a bondage to the infinite space. 4. Key term: Philosophy. Nagarjuna, we are told, was a Buddhist philosopher. This statement is not wrong when we take the notion ‘philosophy’ in a deep sense as a love to wisdom, not as wisdom itself. Philosophy is a way to wisdom. Where this way has an end wisdom begins and philosophy is no more necessary. A.N. Whitehead gives philosophy the commission of descriptive generalisation. We do not need necessarily a philosophical building of universal dimensions. Some steps of descriptive generalisation might be enough in order to see and understand reality. There is another criterion of Nagarjuna’s philosophy. Not his keywords ‘sunyata’ and ‘pratityasamutpada’ but his 25 philosophical examples are the heart of his philosophy. His examples are images. They do not speak to rational and conceptual understanding. They speak to our eyes. Images, metaphors, allegories or symbolic examples have a freshness which rational ideas do not possess. Buddhist dharma and philosophy is a philosophy of allegories. This kind of philosophy is not completely new and unknown to European philosophy. Since Plato’s allegory of the cave it is already a little known. The German philosopher Hans Blumenberg has underlined the importance of metaphors in European philosophy. -/-. (shrink)

Philosophical work on free will, contemporary as well as historical, is inevitably framed by the problem of free will and determinism. One of my goals in what follows is to give a feel for the main lines of that debate in philosophy today. I will also be outlining a particular perspective on free will. Many working philosophers consider themselves Compatibilists; the perspective outlined, building on a number of arguments in the recent literature, is a contemporary form of such a view. (...) It cannot, however, claim to be the contemporary philosophical perspective. There is no such thing. Against a background of the perennial problem of free will and determinism, through ongoing argument and debate, philosophers continue to try to work toward an understanding of precisely what it means for an action to be free. (shrink)

This paper is informed by Charles Sanders Peirce’s philosophy as semiotics or the doctrine of signs. The paper’s purpose is to explore Peirce’s category of abduction as not being limited to the inference to the best explanation. In the context of the logic of discovery, abduction is posited as a necessary although not sufficient condition for the production of meanings. The structure of a genuine sign is triadic and represents a synthesis between precognitive ideas and conceptual representations. The novel model (...) of reasoning is offered, based on the mathematical formalism borrowed from Gauss’ interpretation of the complex number. It is suggested that this model in a form of a diagram not only represents a semiotic process-structure but also overcomes the long-standing paradox of new knowledge. For Peirce, it is a diagram as a visual representation that may yield solutions to the otherwise unsolvable logical problems. What appears to us as a paradox is the very presence of abductive, or hypothetical, inference, as Peircean generic category of Firstness within the Thirdness of the total thought-process. Firstness , Secondness , and Thirdness together constitute a dynamic structure of experience. (shrink)

The conclusion of physics, within both a historical and more recent context, that an objectively progressive time and present moment are derivative notions without actual physical foundation in nature, illustrate that these perceived chronological features originate from subjective conscious experience and the neurobiological processes underlying it. Using this conclusion as a stepping stone, it is posited that the phenomena of an in-built subjective conception of a progressive present moment in time and that of conscious awareness are actually one and the (...) same thing, and as such, are also the outcome of the same neurobiological processes. A possible explanation as to how this might be achieved by the brain through employing the neuronal induced nonconscious cognitive manipulation of a small interval of time is proposed. The CIP phenomenon, elucidated within the context of this study is also then discussed. (shrink)

There are many ontologies of the world or of specific phenomena such as time, matter, space, and quantum mechanics1. However, ontologies of information are rather rare. One of the reasons behind this is that information is most frequently associated with communication and computing, and not with ‘the furniture of the world’. But what would be the nature of an ontology of information? For it to be of significant import it should be amenable to formalization in a logico-grammatical formalism. A candidate (...) ontology satisfying such a requirement can be found in some of the ideas of K. Turek, presented in this paper. Turek outlines the ontology of information conceived of as a part of nature, and provides the ‘missing link’ to the Z axiomatic set theory, offering a proposal for developing a formal ontology of information both in its philosophical and logicogrammatical representations. (shrink)

The aim of the presented article is to provide an in-depth analysis of the adequacy of designating Penrose as a complex Pythagorean in view of his much more common designation as a Platonist. Firstly, the original doctrine of the Pythagoreans will be briefly surveyed with the special emphasis on the relation between the doctrine of this school and the teachings of the late Platonic School as well as its further modifications. These modifications serve as the prototype of the contemporary claims (...) of the mathematicity of the Universe. Secondly, two lines of Penrose’s arguments in support of his unique position on the ontology of the mathematical structures will be presented: their existence independent of the physical world in the atemporal Platonic realm of pure mathematics and the mathematical structures as the patterns governing the workings of the physical Universe. In the third step, a separate line of arguments will be surveyed that Penrose advances in support of the thesis that the complex numbers seem to suit these patterns with exceptional adequacy. Finally, the appropriateness of designation Penrose as a complex Pythagorean will be assessed with the special emphasis on the suddle threshold between his unique position and that of the adherents of the mathematicity of the Universe. (shrink)