The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that (...) has no meet-prime element or join-prime element. This lattice L has |L| = |LC| = 2ℵ0 where Lc is the set of compact elements of L. (shrink)

The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \ \cong^{d} {{\rm S}_{p}}}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices (...) satisfy the Jónsson–Kiefer property. (shrink)

Bridging the gap between the world of science and the realm of the spiritual, B. Alan Wallace introduces a natural theory of human consciousness that has its roots in contemporary physics and Buddhism. Wallace's "special theory of ontological relativity" suggests that mental phenomena are _conditioned_ by the brain, but do not _emerge_ from it. Rather, the entire natural world of mind and matter, subjects and objects, arises from a unitary dimension of reality that is more fundamental than these dualities, as (...) proposed by Wolfgang Pauli and Carl Jung. To test his hypothesis, Wallace employs the Buddhist meditative practice of _samatha_, refining one's attention and metacognition, to create a kind of telescope to examine the space of the mind. Drawing on the work of the physicist John Wheeler, he then proposes a more general theory in which the participatory nature of reality is envisioned as a self-excited circuit. In comparing these ideas to the Buddhist theory known as the Middle Way philosophy, Wallace explores further aspects of his "general theory of ontological relativity," which can be investigated by means of _vipasyana_, or insight, meditation. Wallace then focuses on the theme of symmetry in reference to quantum cosmology and the "problem of frozen time," relating these issues to the theory and practices of the Great Perfection school of Tibetan Buddhism. He concludes with a discussion of the general theme of complementarity as it relates to science and religion. The theories of relativity and quantum mechanics were major achievements in the physical sciences, and the theory of evolution has had an equally deep impact on the life sciences. However, rigorous scientific methods do not yet exist to observe mental phenomena, and naturalism has its limits for shedding light on the workings of the mind. A pioneer of modern consciousness research, Wallace offers a practical and revolutionary method for exploring the mind that combines the keenest insights of contemporary physicists and philosophers with the time-honored meditative traditions of Buddhism. (shrink)

Bridging the gap between the world of science and the realm of the spiritual, B. Alan Wallace introduces a natural theory of human consciousness that has its roots in contemporary physics and Buddhism. Wallace's "special theory of ontological relativity" suggests that mental phenomena are _conditioned_ by the brain, but do not _emerge_ from it. Rather, the entire natural world of mind and matter, subjects and objects, arises from a unitary dimension of reality that is more fundamental than these dualities, as (...) proposed by Wolfgang Pauli and Carl Jung. To test his hypothesis, Wallace employs the Buddhist meditative practice of _samatha_, refining one's attention and metacognition, to create a kind of telescope to examine the space of the mind. Drawing on the work of the physicist John Wheeler, he then proposes a more general theory in which the participatory nature of reality is envisioned as a self-excited circuit. In comparing these ideas to the Buddhist theory known as the Middle Way philosophy, Wallace explores further aspects of his "general theory of ontological relativity," which can be investigated by means of _vipasyana_, or insight, meditation. Wallace then focuses on the theme of symmetry in reference to quantum cosmology and the "problem of frozen time," relating these issues to the theory and practices of the Great Perfection school of Tibetan Buddhism. He concludes with a discussion of the general theme of complementarity as it relates to science and religion. The theories of relativity and quantum mechanics were major achievements in the physical sciences, and the theory of evolution has had an equally deep impact on the life sciences. However, rigorous scientific methods do not yet exist to observe mental phenomena, and naturalism has its limits for shedding light on the workings of the mind. A pioneer of modern consciousness research, Wallace offers a practical and revolutionary method for exploring the mind that combines the keenest insights of contemporary physicists and philosophers with the time-honored meditative traditions of Buddhism. (shrink)

This paper serves two purposes: first, the proposition of an ethical fiduciary theory that substantiates the often-cited assertion that the patient–physician relationship is fiduciary in nature; and second, the application of this theory to the case of informed consent. Patients’ decision-making preferences vary significantly. While some seek fully autonomous decision-making, others prefer to delegate parts of their decision. Therefore, we propose an ethical fiduciary theory that allows physician and patient to jointly determine the physician’s role on a spectrum from fiduciary (...) as advisor to fiduciary as agent. Drawing on legal concepts of the fiduciary relationship and on phenomenological accounts of obligation by Lévinas and Løgstrup, our theory relies on the key attributes of trust, vulnerability and otherness. Finally, practical implications of this theory for the informed consent process are developed: we propose a preassessment of patients’ risk and value profiles as well as a restructuring of the oral consent interview and the written consent materials. (shrink)

In this paper, we consider how certain longstanding philosophical questions about mental representation may be answered on the assumption that cognitive and perceptual systems implement hierarchical generative models, such as those discussed within the prediction error minimization framework. We build on existing treatments of representation via structural resemblance, such as those in Gładziejewski :559–582, 2016) and Gładziejewski and Miłkowski, to argue for a representationalist interpretation of the PEM framework. We further motivate the proposed approach to content by arguing that it (...) is consistent with approaches implicit in theories of unsupervised learning in neural networks. In the course of this discussion, we argue that the structural representation proposal, properly understood, has more in common with functional-role than with causal/informational or teleosemantic theories. In the remainder of the paper, we describe the PEM framework for approximate Bayesian inference in some detail, and discuss how structural representations might arise within the proposed Bayesian hierarchies. After explicating the notion of variational inference, we define a subjectively accessible measure of misrepresentation for hierarchical Bayesian networks by appeal to the Kullbach–Leibler divergence between posterior generative and approximate recognition densities, and discuss a related measure of objective misrepresentation in terms of correspondence with the facts. (shrink)

The late Jacob Klein’s important book is, remarkably, a lucid presentation of esoteric argument. Dealing with the famed Platonic triad, Theaetetus, Sophist, and Statesman, Klein settles the dispute about the missing dialogue, "The Philosopher," by first denying that it is missing and second showing that it is unnecessary. He argues, in short, that the triad is a dyad. That argument is reinforced by the distinction Klein strongly implies between the Socratic Theaetetus and the Eleatic Sophist and Statesman. "We can now (...) understand why the conversations of the ‘trilogy’ occur in two, not three, days and why the Sophist, the Statesman, and the Philosopher are dealt with in two, not three, dialogues". (shrink)

Prominent philosophers have argued that contradictions contain either too much or too little information to be useful. We dispute this with what we call the “Paradox of the Two Firefighters.” Suppose you are awakened in your hotel room by a fire alarm. You open the door. You see three possible ways out: left, right, straight ahead. You see two firefighters. One says there is exactly one safe route and it is to your left. The other says there is exactly one (...) safe route and it is to your right. While the two firemen are giving you contradictory information, they are also both giving you the perhaps useful information that there is a safe way out and it is not straight ahead. We give two analyses. The first uses the “Opinion Tetrahedron,” introduced by Dunn as a generalization of Audun Jøsang’s “Opinion Triangle.” The Opinion Tetrahedron in effect embeds the values of the “Belnap-Dunn 4-valued Logic” into a context of subjective probability generalized to allow for degrees of belief, disbelief, and two kinds of uncertainty—that in which the reasoner has too little information and that in which the reasoner has too much information. Jøsang had only a single value for uncertainty. We also present an alternative solution, again based on subjective probability but of a more standard type. This solution builds upon “linear opinion pooling.” Kiefer had already developed apparatus for assessing risk using expert opinion, and this influences the second solution. Finally, we discuss how these solutions might apply to “Big Data” and the World Wide Web. (shrink)

In this paper, I argue that theories of perception that appeal to Helmholtz’s idea of unconscious inference (“Helmholtzian” theories) should be taken literally, i.e. that the inferences appealed to in such theories are inferences in the full sense of the term, as employed elsewhere in philosophy and in ordinary discourse. -/- In the course of the argument, I consider constraints on inference based on the idea that inference is a deliberate acton, and on the idea that inferences depend on the (...) syntactic structure of representations. I argue that inference is a personal-level but sometimes unconscious process that cannot in general be distinguished from association on the basis of the structures of the representations over which it’s defined. I also critique arguments against representationalist interpretations of Helmholtzian theories, and argue against the view that perceptual inference is encapsulated in a module. (shrink)

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that (...) a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantisation of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantisation, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantisation of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science. (shrink)

Vom 30. Mai bis 1. Juni 1963 fand an der Cornell-Universität eine kleine Tagung zur Natur der Zeit statt, ausgerichtet von den aus Wien stammenden Astrophysikern Hermann Bondi und Thomas Gold. Kurt Gödel war nicht anwesend. Dabei hatte der berühmte Mathematiker etwa 15 Jahre zuvor Arbeiten veröffentlicht, die ganz wesentlich und weitreichend mit dem Begriff der Zeit zu tun hatten.

From 30 May to 1 June Cornell University hosted a small conference on the nature of time, organised by the originally Viennese astro-physicists Hermann Bondi and Thomas Gold. Kurt Gödel did not attend, although roughly 15 years earlier the famous mathematician had made a significant contribution to this field.

The _Platform Sutra_ records the teachings of Hui-neng, the Sixth Patriarch, who is revered as one of the two great figures in the founding of Ch'an (Zen) Buddhism. This translation is the definitive English version of the eighth-century Ch'an classic. Phillip B. Yampolsky has based his translation on the Tun-huang manuscript, the earliest extant version of the work. A critical edition of the Chinese text is given at the end of the volume. Dr. Yampolsky also furnishes a lengthy and detailed (...) historical introduction which contains much information hitherto unavailable even to scholars, and provides the context essential to an understanding of Hui-neng's work. He gives an account of the history and legends of Ch'an Buddhism, with particular attention to the traditions associated with Hui-neng, quoting or summarizing the most important narratives. He then discusses the various texts of the _Platform Sutra_, and analyzes its contents. (shrink)

An approach to implementing variational Bayesian inference in biological systems is considered, under which the thermodynamic free energy of a system directly encodes its variational free energy. In the case of the brain, this assumption places constraints on the neuronal encoding of generative and recognition densities, in particular requiring a stochastic population code. The resulting relationship between thermodynamic and variational free energies is prefigured in mind–brain identity theses in philosophy and in the Gestalt hypothesis of psychophysical isomorphism.

This study analyzes the symbols present in the sacred image of Our Lady of Guadalupe, contextualizing their meanings in the context of catholic christian symbology and nahuatl symbology, and seeks to relate this symbolic identification of the Virgin with the process of christianization of the indigenous peoples of Mexico, mediated by the theoretical and critical assumptions of interreligious dialogue. The methodology adopted consisted of a bibliographical revision of primary and secondary sources, in order to understand how the socio-cultural construction of (...) devotion was carried out during the first two centuries of its existence and its relation with the conversion of indigenous peoples to catholic faith. The main reference consulted was Nican Mopohua, the first document to bring the account of the apparitions of Our Lady to the indian Juan Diego in 1531, published in 1649 as part of the Huei tlamahuiçoltica, in nahuatl language. The motivation of the work was to understand how Guadalupe devotion, represented symbolically with elements of the nahuatl culture, contributed to the christianization of the indigenous peoples of Mexico, using theoretical presuppositions of interreligious dialogue, such as inculturation and syncretism. From the double interpretation of symbols, it was possible to understand the dimension of the process of inculturation of the Christian faith in Mexico and the use of Marian devotion to influence the Christianization of the Aztec nation, as well as to identify whether or not there was a dialogue among religions in this sense. Along the way, we can see the importance of the Virgin of Guadalupe cult not only for the colonization process, but also for the legitimacy of the culture and nationalism of the Mexican people. (shrink)

Este artigo faz uma análise substancial acerca da concepção do direito em Gustav Radbruch, procurando destacar, dentre outros aspectos, a “injustiça extrema”. É peremptório afirmar que para o grande jurista alemão, a questão da obediência à lei não se resolve pela força, como afirma a tradição. A pergunta essencial não é por que obedecer à “lei injusta”, mas porque se apoia na “lei injusta”, obedecendo-a. Ora, tudo isto significa a rigor, que a positividade no direito se contenta com a validade (...) formal das normas jurídicas, quando todo o problema se situa numa esfera mais profunda, correspondente ao valor ético do direito. Inclusive, a ausência de justiça não aflige apenas o sistema jurídico, mas outros sistemas sociais apresentam injustiças gritantes. (shrink)

This chapter focuses on what’s novel in the perspective that the prediction error minimization (PEM) framework affords on the cognitive-scientific project of explaining intelligence by appeal to internal representations. It shows how truth-conditional and resemblance-based approaches to representation in generative models may be integrated. The PEM framework in cognitive science is an approach to cognition and perception centered on a simple idea: organisms represent the world by constantly predicting their own internal states. PEM theories often stress the hierarchical structure of (...) the generative models they posit. The novel explanatory power of the PEM account derives largely from the way in which pairs of generative and recognition models interact. “Predictive coding” refers to an encoding strategy in which predicted portions of an input signal are subtracted from the actual signal received, so that only the difference between the two is passed as output to the next stage of information processing. (shrink)

This volume offers the reader a singular overview of current thinking on indirect reports. The contributors are eminent researchers from the fields of philosophy of language, theoretical linguistics and communication theory, who answer questions on this important issue. This exciting area of controversy has until now mostly been treated from the viewpoint of philosophy. This volume adds the views from semantics, conversation analysis and sociolinguistics. Authors address matters such as the issue of semantic minimalism vs. radical contextualism, the attribution of (...) responsibility for the modes of presentation associated with Noun Phrases and how to distinguish the indirect reporter’s responsibility from the original speaker’s responsibility. They also explore the connection between indirect reporting and direct quoting. Clearly indirect reporting has some bearing on the semantics/pragmatics debate, however, there is much controversy on “what is said”, whether this is a minimal semantic logical form or a much richer and fully contextualized logical form. This issue will be discussed from several angles. Many of the authors are contextualists and the discussion brings out the need to take context into account when one deals with indirect reports, both the context of the original utterance and the context of the report. It is interesting to see how rich cues and clues can radically transform the reported message, assigning illocutionary force and how they can be mobilized to distinguish several voices in the utterance. Decoupling the voice of the reporting speaker from that of the reported speaker on the basis of rich contextual clues is an important issue that pragmatic theory has to tackle. Articles on the issue of slurs will bring new light to the issue of decoupling responsibility in indirect reporting, while others are theoretically oriented and deal with deep problems in philosophy and epistemology. (shrink)

This volume offers the reader a singular overview of current thinking on indirect reports. The contributors are eminent researchers from the fields of philosophy of language, theoretical linguistics, and communication theory, who answer questions on this important issue. This exciting area of controversy has until now mostly been treated from the viewpoint of philosophy. This volume adds the views from semantics, conversation analysis and sociolinguistics. Authors address matters such as the issue of semantic minimalism vs. radical contextualism, the attribution of (...) responsibility for the modes of presentation associated with Noun Phrases, and how to distinguish the indirect reporter's responsibility from the original speaker's responsibility. They also explore the connection between indirect reporting and direct quoting. Clearly indirect reporting has some bearing on the semantics/pragmatics debate, however, there is much controversy on "what is said", whether this is a minimal semantic logical form (enriched by saturating pronominals) or a much richer and fully contextualized logical form. This issue will be discussed from several angles. Many of the authors are contextualists and the discussion brings out the need to take context into account when one deals with indirect reports, both the context of the original utterance and the context of the report. It is interesting to see how rich cues and clues can radically transform the reported message, assigning illocutionary force, and how they can be mobilized to distinguish several voices in the utterance. Decoupling the voice of the reporting speaker from that of the reported speaker on the basis of rich contextual clues is an important issue that pragmatic theory has to tackle. Articles on the issue of slurs will bring new light to the issue of decoupling responsibility in indirect reporting, while others are theoretically oriented and deal with deep problems in philosophy and epistemology. (shrink)

The compact and, with \ M\, very massive object located at the center of the Milky Way is currently the very best candidate for a supermassive black hole in our immediate vicinity. The strongest evidence for this is provided by measurements of stellar orbits, variable X-ray emission, and strongly variable polarized near-infrared emission from the location of the radio source Sagittarius A* in the middle of the central stellar cluster. Simultaneous near-infrared and X-ray observations of SgrA* have revealed insights into (...) the emission mechanisms responsible for the powerful near-infrared and X-ray flares from within a few tens to one hundred Schwarzschild radii of such a putative SMBH. If SgrA* is indeed a SMBH it will, in projection onto the sky, have the largest event horizon and will certainly be the first and most important target for very long baseline interferometry observations currently being prepared by the event horizon telescope. These observations in combination with the infrared interferometry experiment GRAVITY at the very large telescope interferometer and other experiments across the electromagnetic spectrum might yield proof for the presence of a black hole at the center of the Milky Way. The large body of evidence continues to discriminate the identification of SgrA* as a SMBH from alternative possibilities. It is, however, unclear when the ever mounting evidence for SgrA* being associated with a SMBH will suffice as a convincing proof. Additional compelling evidence may come from future gravitational wave observatories. This manuscript reviews the observational facts, theoretical grounds and conceptual aspects for the case of SgrA* being a black hole. We treat theory and observations in the framework of the philosophical discussions about “realism and underdetermination”, as this line of arguments allows us to describe the situation in observational astrophysics with respect to supermassive black holes. Questions concerning the existence of supermassive black holes and in particular SgrA* are discussed using causation as an indispensable element. We show that the results of our investigation are convincingly mapped out by this combination of concepts. (shrink)