"What is mathematics?" is a question that has been debated since antiquity. This book presents a groundbreaking and surprising answer to the question-showing through the concept of the physicalization of metamathematics how both mathematics and physics as experienced by humans can be seen to emerge from the unique underlying computational structure of the recently formulated ruliad. Written with Stephen Wolfram's characteristic expositional flair and richly illustrated with remarkable algorithmic diagrams, the book takes the reader on a unprecedented intellectual (...) journey to the center of some of the deepest questions about mathematics and its nature-and points the way to a new understanding of the foundations and future of mathematics, taking a major step beyond ideas from Plato, Kant, Hilbert, Gödel and others. (shrink)

This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation (...) that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation. (shrink)

The most elementary way to think about Mathctrtati ca is as an enhance calculator — a calculator that does not only numerical computation but also algebraic computation and graphics. Matltcmatica can function much like a standard calt".1a- tor. you type in a question, you get back an answer. But Mat/tctttadca ga's turthcr I ue an ordinary calculator. You can type in questions that require answers that arc longer than a calculator can handle. For example, Matltcmatictt can giv; you thc numerical (...) value of tr to a hundred decimal places, or the exact result for a numerical calculation as complicated as the result of 3)tI0, (m Fig. 1). (shrink)

Sir Roger Penrose, retired professor of mathematics at the University of Oxford and collaborator with Stephen Hawking on black hole theory, has written 'a complete guide to the laws of the universe' called The Road to Reality. His publisher calls it the most important and ambitious work of science for a generation. Penrose caused a furore in the world of consciousness studies with his 1989 book The Emperor's New Mind, which conjectured a new mechanism for consciousness and kept a (...) faithful band of researchers busy for a decade with models based on microtubules and the like. Sadly, the idea fizzled out. The title of the 2002 Tucson 'Toward a Science of Consciousness' conference poetry slam winner was: Microtubules - my ass! (shrink)

Stephen Wolfram has recently outlined an unorthodox, multicomputational approach to fundamental theory, encompassing not only physics but also mathematics in a structure he calls The Ruliad, understood to be the entangled limit of all possible computations. In this framework, physical laws arise from the the sampling of the Ruliad by observers (including us). This naturally leads to several conceptual issues, such as what kind of object is the Ruliad? What is the nature of the observers carrying out the (...) sampling, and how do they relate to the Ruliad itself? What is the precise nature of the sampling? This paper provides a philosophical examination of these questions, and other related foundational issues, including the identification of a limitation that must face any attempt to describe or model reality in such a way that the modeller-observers are included. (shrink)

What should philosophical theology look like after the critique of Onto-theology, after Phenomenology, and in the age of Speculative Realism? What does Kabbalah have to say to Philosophy? Since Kant and especially since Husserl, philosophy has only permitted itself to speak about how one relates to God in terms of the intentionality of consciousness and not of how God is in himself. This meant that one could only ever speak to God as an addressed and yearned-for holy Thou, but not (...) to God as infinite creator of all. In this book-length essay, the author argues that reality itself is made up of the Holy Name of God. Drawing upon the set-theoretical ontology of Alain Badiou, the computational theory of Stephen Wolfram, the physics of Frank Tipler, the psychoanalytical theory of Jacques Lacan, and the genius of Georg Cantor, the author works to demonstrate that the universe is a computer processing the divine Name and that all existence is made of information (the bit). As a result of this ontic pan-computationalism, it is shown that the future resurrection of the dead can take place and how it may in fact occur. Along the way, the book also offers compelling critiques of several significant theories of reality, including the phenomenological theologies of Emmanuel Levinas and Jean-Luc Marion, Process Theology, and Object-Oriented Ontology. Reality in the Name of God explores how the concepts of Jewish mysticism can be articulated and deployed as philosophical theses within current metaphysical debates. It provides a new and dynamic Structural Realist ontology of information. Ultimately, the book aims to deal a death blow to the restriction of philosophy and theology in relation to elaborations of a how a believer relates to a God outside the mind and to return thought to a direct encounter with the divine nature of reality itself and its creator"--Website of the publisher, October 19, 2020. (shrink)

"Featuring seventeen original essays on the ethics of Artificial Intelligence by some of the most prominent AI scientists and academic philosophers today, this volume represents the state-of-the-art thinking in this fast-growing field and highlights some of the central themes in AI and morality such as how to build ethics into AI, how to address mass unemployment as a result of automation, how to avoiding designing AI systems that perpetuate existing biases, and how to determine whether an AI is conscious. As (...) AI technologies progress, questions about the ethics of AI, in both the near-future and the long-term, become more pressing than ever. Should a self-driving car prioritize the lives of the passengers over the lives of pedestrians? Should we as a society develop autonomous weapon systems that are capable of identifying and attacking a target without human intervention? What happens when AIs become smarter and more capable than us? Could they have greater than human moral status? Can we prevent superintelligent AIs from harming us or causing our extinction? At a critical time in this fast-moving debate, thirty leading academics and researchers at the forefront of AI technology development come together to explore these existential questions, including Aaron James, Allan Dafoe, Andrea Loreggia, Andrew Critch, Azim Shariff, Carrick Flynn, Cathy O'Neil, Eliezer Yudkowsky, Eric Schwitzgebel, Frances Kamm, Francesca Rossi, Hanna Gunn, Iyad Rahwan, Jessica Taylor, JF Bonnefon, K. Brent Venable, Kate Devlin, Mara Garza, Nicholas Mattei, Nick Bostrom, Patrick LaVictoire, Peter Asaro, Peter Railton, S. Matthew Liao, Shannon Vallor, Stephen Wolfram, Steve Petersen, Stuart Russell, Susan Schneider, Wendell Wallach "--. (shrink)

Prominent views about representation share a premise: that mathematical communication theory is blind to representational content. Here I challenge that premise by rejecting two common misconceptions: that Claude Shannon said that the meanings of signals are irrelevant for communication theory (he didn't and they aren't), and that since correlational measures can't distinguish representations from natural signs, communication theory can't distinguish them either (the premise is true but the conclusion is false; no valid argument can link them).

The rise of cognitive neuroscience is the most important scientific and intellectual development of the last thirty years. Findings pour forth, and major initiatives for brain research continue. The social sciences have responded to this development slowly--for good reasons. The implications of particular controversial findings, such as the discovery of mirror neurons, have been ambiguous, controversial within neuroscience itself, and difficult to integrate with conventional social science. Yet many of these findings, such as those of experimental neuro-economics, pose very direct (...) challenges to standard social science. At the same time, however, the known facts of social science, for example about linguistic and moral diversity, pose a significant challenge to standard neuroscience approaches, which tend to focus on "universal" aspects of human and animal cognition. A serious encounter between cognitive neuroscience and social science is likely to be challenging, and transformative, for both parties. Although a literature has developed on proposals to integrate neuroscience and social science, these proposals go in divergent directions. None of them has a developed conception of social life. This book surveys these issues, introduces the basic alternative conceptions both of the mental world and the social world, and show how, with sufficient modification, they can be fit together in plausible ways. The book is not a "new theory " of anything, but rather an exploration of the critical issues that relate to the social aspects of cognition which expands the topic from the social neuroscience of immediate interpersonal interaction to the whole range of places where social variation interacts with the cognitive. The focus is on the conceptual problems produced by any attempt to take these issues seriously, and also on the new resources and considerations relevant to doing so. But it is also on the need for a revision of social theoretical concepts in order to utilize these resources. The book points to some conclusions, especially about how the process of what was known as socialization needs to be understood in cognitive science friendly terms. But there is no attempt to resolve the underlying issues within cognitive science, which will doubtless persist. (shrink)

Reviewed Works:Gaisi Takeuti, Proof Theory.Georg Kreisel, Proof Theory: Some Personal Recollections.Wolfram Pohlers, Contributions of the Schutte School in Munich to Proof Theory.Stephen G. Simpson, Subsystems of $\mathbf{Z}_2$ and Reverse Mathematics.Solomon Feferman, Proof Theory: A Personal Report.

This interdisciplinary book considers the relationship between language and thought from a philosophical perspective, drawing both on the philosophical study of language and the purely formal study of grammar, and arguing that the two should align. The claim is that grammar provides homo sapiens with the ability to think in certain grammatical ways and that this in turn explains the vast cognitive powers of human beings. Evidence is considered from biology, the evolution of language, language disorders, and linguistic phenomena.

Harry Collins is a science studies scholar no other description fits without qualification who has contributed enormously to the discussion of tacit knowledge. Collins says that he is providing an account for the ontologically bashful, meaning, presumably, that it does not carry the burdens of Durkheim's notion of the collective consciousness. Polanyi says that 'a wholly explicit knowledge is unthinkable'. Collins wants to translate this into 'strings must be interpreted before they are meaningful'. Somatic limits are the source of the (...) mystery element of tacit knowledge. In fact, machines can be programmed to do the things it involves, although they will do it in a different way. In Social Cartesianism, the individual is not the unit of analysis: the individual merely shares the collectivity's knowledge. Collins point in these contexts is that functional substitutability implies nothing about similarity in underlying causal structure. (shrink)

After summarizing the content of my book, Kant and Mysticism, I warn against four preliminary misconceptions. The book never argues that Kant viewed himself as a mystic, fully acknowledges Kant’s negative view of mysticism, offers no comprehensive overview of mystical traditions, and aims to initiate a dialogue, not to have the final word. I then respond to the foregoing essays by the five critics.

The prelims comprise: Half‐Title Page Title Page Copyright Page Dedication Page Table of Contents Preface Acknowledgments Abbreviations.

Palmquist’s Commentary provides the first definitive clarification on Kant’s Philosophy of Religion in English; it includes the full text of Pluhar’s translation, interspersed with explanations, providing both a detailed overview and an original interpretation of Kant’s work. Offers definitive, sentence-level commentary on Kant’s Religion within the Bounds of Bare Reason Presents a thoroughly revised version of Pluhar’s translation of the full text of Kant’s Religion, including detailed notes comparing the translation with the others still in use today Identifies most of (...) the several hundred changes Kant made to the second (1794) edition and unearths evidence that many major changes were responses to criticisms of the first edition Provides both a detailed overview and original interpretation of Kant’s work on the philosophy of religion Demonstrates that Kant’s arguments in Religion are not only cogent, but have clear and profound practical applications to the way religion is actually practiced in the world today Includes a glossary aimed at justifying new translations of key technical terms in Religion, many of which have previously neglected religious and theological implications. (shrink)

Journal of Chinese Philosophy, EarlyView.

In his second book, Tierney argues that the purpose of education must move to the heart of the educational debate. Purpose will significantly influence what schools and the education system as a whole will do next.

This article was written before the British general election in which the Labour party had a landslide victory. It is an interesting indication of the philosophy of Christians within the new Labour government.

This book symposium on Jason Holt’s Kinetic Beauty: The Philosophical Aesthetics of Sport includes commentaries from Stephen Mumford, John E. MacKinnon and Andrew Edgar with replies from Holt.

Dorothy Emmet, in two books, one of which was based on extensive personal contact with Robert Merton and Columbia sociology, provides the closest thing we have to an authorized philosophical defense of Merton. It features a deflationary account of functionalism which dispenses with the idea of general teleological ends. What it replaces it with is an account of “structures” that have various consequences and that are maintained because, on Emmet’s account, of the mutual reinforcement of motives produced by the structure.

A revised version of this paper became chapter I of Kant's Critical Religion.

This essay is a systematic exposition and partial defense of Kant's philosophy of prayer. "Does Kant even HAVE a philosophy of prayer?" you may ask. Read on...and you'll see.

This comment discusses the suggestions made in Mahoney’s “Constructivist Set-Theoretic Analysis: An Alternative to Essentialist Social Science” (2023). Mahoney presents an approach to cases of intersectionality or confounding which produce causal results unlike those that result from traditional net effects causal modeling. He presents it as an alternative to “essentialism,” which he describes as a cognitive error. These alternatives have the same problems as those he attributes to net effects analysis, with one exception: the method does allow for the identification (...) of subpopulations with different causal mechanisms producing different outcomes for this subpopulation. (shrink)

This chapter shows that science and quasi-science are already largely subject to various forms of "governance," including forms of self-governance. In science, as with other debating societies, governance characteristically begins with the problem of membership and the problem of regulating participation in discussion. The standard solutions to the problem of governance in the external sense recognize the inability of public discussion of the sort "demanded" by Beck to deal effectively with science. The history of particular forms of expertise, such as (...) the expertise of agricultural science, shows quite clearly that establishing credibility is difficult. When Leibig first introduced commercial chemical fertilizers with the backing of "science," the fertilizers had various unexpected and unintended side effects that harmed farmers—this was among the first of the science-made environmental disasters. The interesting thing about this process is the incredible difficulty and fragility of expertise. (shrink)

This chapter focuses on a question about one role: the explanatory role of normativism or normativity in relation to ordinary 'scientific', meaning social scientific, explanations of actions and beliefs, especially the empirical, observable, or empirically relevant aspects of human conduct. Call this the epistemic form of the naturalistic moment problem. It call this a 'naturalistic moment', a place where normativism makes factual assertions about real processes in the natural world. This pseudo argument boils down to a series of equivocations. The (...) normativist must claim that there is some super-added normative element that cannot be accounted for naturalistically or by social science. Transcendental arguments to the effect that they have to have such and such mental content are likely to fail the mosquito test. The default position of rationalistic normativists, well encapsulated by Korsgaard, who rejects it, is that normativity in particular, rightness is an objective property grasped by reason. (shrink)

The common saying, “it is better to give than to receive”, is so widespread that its truth is often merely assumed. But can this ethical maxim withstand a careful philosophical analysis? The relevant concepts (“giving”, “receiving”, and “better”)can be interpreted in too many ways to discuss thoroughly in a single essay. Instead, this essay classifies the various ways of interpreting the distinction between giving and receiving, then explores in depth one of the options, based on a pivotal distinction between active (...) and passive types of both giving and receiving. I defend the controversial claim that there is at least one important sense (arguably the most important, for ethical purposes) in which it is not better to give than receive, but that in this sense precisely the opposite holds true. Indeed, the survival of the human race may depend on our willingness to receive. (shrink)

At what is arguably the most significant turning point in the Critique of Pure Reason, where Immanuel Kant has just completed his exploration of the safe ground of possible experience and is about to embark on the Transcendental Dialectic’s exploration of the stormy sea of metaphysics, he introduces one of the greatest curiosities in the Kantian corpus: a “table … of the concept of nothing” (A290/B346-A292/B349). The brief passage, which is tacked on to the end of a “Remark” that supplements (...) an Appendix to a weighty chapter exploring “the Ground of the Distinction of all Objects [Gegenstände] in General into Phenomena and Noumena” (A235/B294), appears as an afterthought to an afterthought to an afterthought and is thus easily overlooked by interpreters. Indeed, the passage may seem to be little more than an amusing distraction, perhaps intended as light entertainment before Kant undertakes the real work of demolishing traditional metaphysics; or at best, it might be one of those annoying sections whose only reason for existing is to fill a perceived (but artificial) gap in the completeness of Kant’s systematic conception of reason’s architectonic unity. This chapter takes the argument seriously, notwithstanding its widespread neglect, by unpacking the specific purpose served by each perspective on “nothing” that appears in Kant’s table. Closer analysis shows how the table clarifies Kant’s notion of “something in general” by contrasting it with four distinct opposites. The passage thereby orients us to appreciate how the Critique secures the status of metaphysics as queen of the sciences. (shrink)

Paul of Venice joined the Austin Friars at an early age and was sent by them from Padua to study at Oxford in 1390. When he returned, full of ideas and laden with books, he began his prodigious writing career with several books on logic, including the Logica Magna, which runs to some half a million words. The current volume contains the final treatise, on insolubles - that is, logical paradoxes. After surveying fifteen previous solutions, Paul develops his own, based (...) on the idea that such propositions falsify themselves. Besides a critical edition of the Latin text, the volume also contains an English translation, a detailed commentary, excerpts from two other logical works of Paul, and a substantial introduction. The introduction describes the fourteenth-century background to Paul's treatise; it also gives a detailed rebuttal of a recent claim that the Logica Magna is not by Paul because its content clashes with genuine works of his. All in all, the volume greatly enhances our understanding of the development of logic, in particular of the semantics of propositions, during a crucial century in its history. (shrink)

The term Human Sciences is primarily a French usage, but it refers back to a much deeper tradition in the literature claiming that works of the spirit and human experience cannot be reduced to the realm of causal science, and require different methods. Following Kant, much of this discussion has focused on the problem of the conceptual formation of human experience. Methodologically, discussion has shifted back and forth between an emphasis on concepts, on experience, and external facts. Foucault and Bourdieu (...) extended the critical possibilities of the notion of misrecognition to ally the human sciences with critique. (shrink)