The scope of Platonism is extended by introducing the concept of a “Platonic computer” which is incorporated in metacomputics. The theoretical framework of metacomputics postulates that a Platonic computer exists in the realm of Forms and is made by, of, with, and from metaconsciousness. Metaconsciousness is defined as the “power to conceive, to perceive, and to be self-aware” and is the formless, con-tentless infinite potentiality. Metacomputics models how metaconsciousness generates the perceived actualities including abstract entities and physical and nonphysical realities. (...) It is postulated that this is achieved via digital computation using the Platonic computer. The introduction of a Platonic computer into the realm of Forms thus bridges the “inverse explanatory gap” and therefore solves the “inverse hard problem of consciousness” in the philosophy of mind. (shrink)

Plato's theory of forms is developed and compared to the modern theory of recursion. I show how Plato's theory, as it applies to mathematical objects, is essentially a primitve version of modern recursion theory, which has all the essential elements of the ancient theory. However, Plato himself thought there was more than mathematics to his forms. He believed that form had a noncomposite, unanalyzable component. So, while recursion theory provides an adequate formalization of Plato's theory, it cannot be considered identical (...) to it. I argue--drawing from material in the "Meno," "Phaedo," and "Republic"--that Plato's arguments for noncomposite form are largely fallacious. Plato would, I believe, have taken the computational version developed here seriously, since mathematics was his primary source for clear examples of forms (one could argue that it was his only source short of dipping into mysticism). In fact, there is a long-standing oral tradition that Plato developed a more formal version of his theory in lecture notes for courses he taught at the Academy (the university he founded in Athens). Any such notes, if they existed at all, have been lost. But if such a formal version did exist, it is tantalizing to wonder to what extent Plato may have anticipated modern theoretical computer science and metamathematics. (shrink)

We first discuss Michael Dummett’s philosophy of mathematics and Robert Brandom’s philosophy of language to demonstrate that inferentialism entails the falsity of Church’s Thesis and, as a consequence, the Computational Theory of Mind. This amounts to an entirely novel critique of mechanism in the philosophy of mind, one we show to have tremendous advantages over the traditional Lucas-Penrose argument.

Atheistic Platonism is an alternative to both theism and nihilistic atheism. It shows how any jobs allegedly done by God are better done by impersonal Platonic objects. Without Platonic objects, atheism degenerates into an illogical nihilism. Atheistic Platonism instead provides reality with foundations that are eternal, necessary, rational, beautiful, and utterly mindless. It argues for a plenitude of mathematical objects, and an infinite plurality of possible universes. It provides mindless rational grounds for objective values, and for objective moral laws for (...) the persons who evolve in universes. It defines a meaningful way of life, which facilitates self-improvement. Atheistic Platonists argue for computational theories of life after death. Atheistic Platonism includes a rich system of spiritual symbols. It values transformational practices and ecstatic experiences. Where atheisms based on materialism fail, atheisms based on Platonism succeed. (shrink)

The scope of Platonism is extended by introducing the concept of a “Platonic computer” which is incorporated in metacomputics. The theoretical framework of metacomputics postulates that a Platonic computer exists in the realm of Forms and is made by, of, with, and from metaconsciousness. Metaconsciousness is defined as the “power to conceive, to perceive, and to be self-aware” and is the formless, con-tentless infinite potentiality. Metacomputics models how metaconsciousness generates the perceived actualities including abstract entities and physical and nonphysical realities. (...) It is postulated that this is achieved via digital computation using the Platonic computer. The introduction of a Platonic computer into the realm of Forms thus bridges the “inverse explanatory gap” and therefore solves the “inverse hard problem of consciousness” in the philosophy of mind. (shrink)

Hartry Field's formulation of an epistemological argument against platonism is only valid if knowledge is constrained by a causal clause. Contrary to recent claims (e.g. in Liggins (2006), Liggins (2010)), Field's argument therefore fails the very same criterion usually taken to discredit Benacerraf's earlier version.

Olszewski claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. The key step of his argument employs an example of a supposedly effectively computable but not Turing-computable function. I argue that the process he describes is not an effective computation, and that the argument relies on the illegitimate conflation of effective computability with there being a way to find out . ‘Ah, but,’ you say, ‘what’s the use of its being right twice (...) a day, if I can’t tell when the time comes?’ Why, suppose the clock points to eight o’clock, don’t you see that the clock is right at eight o’clock? Consequently, when eight o’clock comes round your clock is right. Lewis Carroll. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:After Gödel: Platonism and Rationalism in Mathematics and LogicMark C. R. SmithRichard Tieszen. After Gödel: Platonism and Rationalism in Mathematics and Logic. Oxford-New York: Oxford University Press, 2011. Pp. xi + 245. Cloth, $75.00.Tieszen’s new book offers a synthesis and extension of his longstanding project of bringing the method of Husserl’s phenomenology to bear on fundamental questions—both epistemological and ontological—in the philosophy of mathematics. Gödel held Husserl’s philosophy (...) in high regard, and thought that it offered the most promising avenue for an adequate understanding of the foundations of mathematical thought and practice, but Gödel himself did not give a full systematic statement of how phenomenology might carry out that project. Tieszen takes up the task in this book, which is structured around two main guiding themes. The first is to locate the sources of Gödel’s philosophical views—principally [End Page 303] in Plato, Leibniz, and of course Husserl, along with Kant as a sort of backcloth—and the second is to argue that from these materials, a promising rationalism in mathematics and logic can be consistently articulated. Along the way we also encounter a good many of Gödel’s arguments against an array of reductive positions, Hilbert’s formalism and Carnap’s “logical syntax” project among them, as well as arguments against the prospects of a mechanical or purely computational understanding of the human mind. Many of the arguments (both negative and positive) stem from a reflection on the consequences of Gödel’s landmark incompleteness results of 1931.The core of Tieszen’s positive proposals comes in chapters 4, 5, and 6: here is where we meet with “constituted Platonism,” Tieszen’s name for the rationalist, realist synthesis of Husserl’s method and Gödel’s mathematical insights. Methodologically, the starting point is the actual practice of mathematics as a human undertaking, and its conditions of possibility. At the most general level, it is characteristic of thought to be intentional, that is, to be (or try to be) about something, to have a target, to be a bearer of meaning. So it goes for thought about items in sensory awareness, about fictional objects, or about mathematical subject-matter. Concerning the latter, what we encounter in mathematical experience are frequently “phenomena that resist our will, so that we are ‘forced’ in certain directions” (170); what accounts for this resistance to our will are invariants, which have the further characteristics of repeatability—both for a single subject, and among many subjects—and availability for convergence (221), which, I take it, means availability as structures or concepts upon which many independent rational investigators will come to rest. Thinking mathematical thoughts is quite unlike thinking thoughts about fictional items, because fictions are indefinitely plastic in the face of human will. It is also unlike thought about sensory items, in that the intentional objects at issue are not available to outer sense; but from another angle it is more like thought about real material items than imaginary beings, because our mathematical thoughts are exposed to the possibility of error or misrepresentation in various ways. (An elementary example: most people think that 1 is distinct from 0.9999... repeating: this is a misrepresentation, because they are in fact identical.)The phenomenology of mathematical practice is such that we assay various conjectures and proposals about invariants already given to consciousness by previous practice, and discover what further invariant structures or concepts are revealed as necessary constraints upon the various possibilities that we can experimentally float for ourselves. Sometimes our conjectures or intentions are fulfilled, sometimes they are frustrated; but it is the very fact of fulfillment and frustration which points us to a Platonic reality. It is not the noumenal realm of the “naive” Platonist, in Tieszen’s phrase, but nevertheless an objective reality marked off “on the basis of what stabilizes or becomes invariant in our experience, on the basis of what has a history and a sedimentation that permits of further elaboration, development, constraints, surprises, and so on” (101). In something like this way, human reason and consciousness “constitute the meaning of being” of mathematical objects... (shrink)

This article is devoted to examining the ontological foundations of computer-generated music scores. Specifically, we focus on the categorial question, i.e., the inquiry that aims to determine the kind of ontological category that musical works belong to. This task involves considerations concerning the existence and persistence conditions for musical works, and it has consequences for the determination of what it is to compose a musical work. Our contention is that not all the possible answers to the categorial question in the (...) ontology of music are equally compatible with the hypothesis that creative music systems compose musical works. The thesis defended here is that musical Platonism is the proposal that best accommodates this hypothesis. We claim that musical Platonism is the answer to the categorial question that offers the most straightforward explanation for the possibility of considering creative music systems as genuinely composing musical works. Moreover, we uphold that the notion of creative-evaluative discovery as the characterization of what it is to compose a musical work entailed by Platonism is the simplest explanation of the process developed by a computer in producing musical works. For this purpose, we will take as empirical data the features of the Iamus computer, a system that produces musical works autonomously using evolutionary algorithms and following an evo-devo strategy. The works generated by this computer have been recorded by the London Symphony Orchestra and other renowned international soloists, and its impact has been notable in the literature (Ball, 2012; Coghlan, 2012; Berger, 2013). (shrink)

"The Emperor's New Mind" by Roger Penrose has received a great deal of both praise and criticism. This review discusses philosophical aspects of the book that form an attack on the "strong" AI thesis. Eight different versions of this thesis are distinguished, and sources of ambiguity diagnosed, including different requirements for relationships between program and behaviour. Excessively strong versions attacked by Penrose (and Searle) are not worth defending or attacking, whereas weaker versions remain problematic. Penrose (like Searle) regards the notion (...) of an algorithm as central to AI, whereas it is argued here that for the purpose of explaining mental capabilities the architecture of an intelligent system is more important than the concept of an algorithm, using the premise that what makes something intelligent is not what it does but how it does it. What needs to be explained is also unclear: Penrose thinks we all know what consciousness is and claims that the ability to judge Go "del's formula to be true depends on it. He also suggests that quantum phenomena underly consciousness. This is rebutted by arguing that our existing concept of "consciousness" is too vague and muddled to be of use in science. This and related concepts will gradually be replaced by a more powerful theory-based taxonomy of types of mental states and processes. The central argument offered by Penrose against the strong AI thesis depends on a tempting but unjustified interpretation of Goedel's incompleteness theorem. Some critics are shown to have missed the point of his argument. A stronger criticism is mounted, and the relevance of mathematical Platonism analysed. Architectural requirements for intelligence are discussed and differences between serial and parallel implementations analysed. (shrink)

One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. J. (...) Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. We show that every recursively enumerable random real dominates all other recursively enumerable reals. We conclude that the recursively enumerable random reals are exactly the Ω-numbers [G. J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. Second, we show that the sets in a universal Martin-Lof test for randomness have random measure, and every recursively enumerable random number is the sum of the measures represented in a universal Martin-Lof test. (shrink)

Since its conception nearly 20 years ago, Logic Programming - the idea of using logic as a programming language - has been developed to the point where it now plays an important role in areas such as database theory, artificial intelligence and software engineering. However, there are still many challenging research issues to be addressed and the UK branch of the Association for Logic Programming was set up to provide a forum where the flourishing research community could discuss important issues (...) of Logic Programming which were often by-passed at the large international conferences. This volume contains the twelve papers which were presented at the ALPUK's 3rd conference which was held in Edinburgh, 10-12 April 1991. The aim of the conference was to give a broad but detailed technical insight into the work currently being done in this field, both in the UK and by researchers as far afield as Canada and Bulgaria. The breadth of interest in this area of Computer Science is reflected in the range of the papers which cover - amongst other areas - massively parallel implementation, constraint logic programming, circuit modelling, algebraic proof of program properties, deductive databases, specialised editors and standardisation. The resulting volume gives a good overview of the current progress being made in the field and will be of interest to researchers and students of any aspects of logic programming, parallel computing or database techniques and management. (shrink)

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents the state (...) of the art in the area. (shrink)

As an atheist, Dawkins strives to develop a scientific alternative to theism, and while he declares that science is not a religion, he also proclaims it to be a spiritual enterprise. His books are filled with fragmentary sketches of this "spiritual atheism", resembling a great unfinished cathedral. This book systematizes and completes Dawkins' arguments, and reveals their deep roots in Stoicism and Platonism. Expanding on Dawkins' ideas, Steinhart shows how atheists can develop powerful ethical principles, compelling systems of symbols and (...) images, and meaningful personal and social practices. Believing in Dawkins is a rigorous and potent entreaty for the use of science and reason to support spiritually rich and optimistic ways of thinking and living. (shrink)

This article explores some of the ways in which the conceptual apparatus of A Thousand Plateaus, and especially its machinic metaphysics, can be connected to recent developments in computer modelling and social simulation, which provide new tools for thinking that are becoming increasingly popular among philosophers and social scientists. Conversely, the successful deployment of these tools provides warrant for the flat ontology articulated in A Thousand Plateaus and therefore contributes to the ‘reversal of Platonism’ for which Deleuze had called in (...) his earlier works, such as Logic of Sense. The first major section offers a brief exposition of some key concepts in A Thousand Plateaus in order to set the stage for the second and third major sections, which argue that the fabrication of a metaphysics of immanence can be accelerated by connecting its conceptual apparatus more explicitly to insights derived from philosophical analyses of computational modelling and simulation and the social scientific use of ‘assemblage theory’. The article concludes with a summary of the argument and a brief consideration of some of the potential ethical and political implications of this interdisciplinary engagement. (shrink)

The project of this Précis de philosophie de la logique et des mathématiques (vol. 1 under the direction of F. Poggiolesi and P. Wagner, vol. 2 under the direction of A. Arana and M. Panza) aims to offer a rich, systematic and clear introduction to the main contemporary debates in the philosophy of mathematics and logic. The two volumes bring together the contributions of thirty researchers (twelve for the philosophy of logic and eighteen for the philosophy of mathematics), specialists in (...) the history or philosophy of logic or mathematics. Each volume consists of ten chapters; each chapter is about forty pages, is independent from the others and deals with a particular philosophical question about logic or mathematics. The objective is to offer to the French-speaking reader a reference book. On many of the issues addressed, this Précis offers the first clear and thorough synthesis that is available in French. -/- This book is intended for third year / master's students, but also for teachers of philosophy in secondary or higher education, for logicians and mathematicians willing to take a philosophical look at the fundamental concepts of their discipline, and for any reader interested in the basic issues discussed in the philosophy of logic and mathematics. Each chapter is self-contained, although some basic training in logic (or in mathematics, as the case may be) is required. The book should be looked at as a comprehensive framework for contemporary discussions in the philosophy of logic and mathematics, while also giving some guidance on the disciplinary content required by these discussions. -/- The first three chapters of the present volume (on the philosophy of mathematics) are devoted to the history of the philosophy of mathematics: from antiquity to the modern era, and from this period to the foundational crisis of the nineteenth century, to the twentieth century. Next, four chapters deal with the crucial questions for the philosophy of mathematics of the twentieth century: the opposition and/or comparison of set theory and category theory as foundational frameworks for mathematics; mathematical constructivism; the analysis of calculability; and Benaceraff's problem. The two following chapters are focused on the philosophy of mathematical practice, by treating the notion of ideals of proof, in particular explanation and purity, and the notion of informal proof and the use of visual artifacts in mathematical argumentation. Finally the last chapter deals with the applicability of mathematics, including the role of probability. -/- In Chapter 1, Sébastien Maronne and David Rabouin present the history of the philosophy of mathematics from antiquity to the modern era. The goal is to show that the philosophy of mathematics has a history as ancient as mathematics and philosophy itself, a history largely continuous with the latter, often by staying out of sync with respect to the former. In Chapter 2, Sébastien Gandon discusses the question of the foundations of mathematics from Kant to the end of the nineteenth century. By tying this question to Kant, he is able to show that the discussion of the foundations of mathematics that occupied a large part of these two centuries has much older roots. Accent is placed on the differences between the framework proposed by Kant for making sense of classical mathematics and the use made by Frege and then Russell of logical tools for giving a different reading of arithmetic and real analysis. The link between between these different conceptions and the evolution of mathematics itself is also underlined. -/- Chapter 3, written by Hourya Benis-Sinaceur and Mirna Džamonja, deals with the evolution of mathematics in the twentieth century, notably the structuralist turn of Dedekind, E. Noether, and Bourbaki, and certain more recent developments. They devote themselves, among other things, to explaining how these developments can be understood as responses to and extensions of questions posed during the foundational debate of the immediately preceding era. -/- In Chapter 4, Jean-Pierre Marquis and Jean-Jacques Szczeciniarz discuss the different foundational options coming from set theory and category theory. They discuss, among other things, Lawvere's program to replace ZF with an axiomatization of the category of sets, the latter judged better adapted to the needs of contemporary mathematics. Different reactions, as much philosophical as technical, raised by this program are also taken into account. -/- Constructive mathematics are the object of Chapter 5, in which Gerhard Heinzmann and Mark van Atten examine in a critical and comparative manner a variety of constructivisms, including intuitionism, constructive type theory, predicativism, and finitism. -/- In Chapter 6, Guido Gherardi and Maël Pegny present computability theory, stressing its philosophical consequences. They discuss the basic concepts of this theory, for the computability of both the natural numbers and the real numbers. They then tackle the theory of computational complexity. -/- In Chapter 7, Andrea Sereni and Fabrice Pataut present Benacerraf's problem, opposing every possible account of mathematical knowledge to the availability of a theory of truth founded on an abstract ontology of mathematical objects. They give an overview of the original problem and its reformulation by Hartry Field, and reconstruct the debate that this problem has raised, by meeting at once the major opposing positions today of the analytic affiliation of the philosophy of mathematics, as much those on the platonist side as on that of nominalism. -/- In Chapter 8, Valeria Giardino and Yacin Hamami treat certain crucial aspects of the philosophy of mathematical practice. They deal in particular with the notion of an informal proof and on the role of artifacts in mathematical reasoning. They consider how such proofs, making use of these means, can contribute to the understanding of theorems and mathematical theories, thanks also to the role of visualisation and the aid of computer tools. -/- Why do mathematics often give several proofs of the same theorem? This is the question that Andrew Arana raises in Chapter 9, introducing the notion of an epistemic ideal and discuss two such ideals, the explanatoriness and purity of proof. -/- Chapter 10 is devoted to the applicability of mathematics in the study of empirical phenomena. After summarizing the history of this question, going back to Plato and Aristotle and passing by Mill and Kant, Daniele Molinini and Marco Panza reconstruct the contemporary debate, in relation, among other things, to questions raised in the philosophy of science. -/- Two appendices complete the volume. In the first Frédéric Patras treats the French tradition in philosophy of mathematics of the 20th century. In the second, Maria Carla Galavotti discusses the notion of probability and its use in science. (shrink)

In their Minds and Machines essay How would you know if you synthesized a Thinking Thing? (Kary & Mahner, Minds and Machines, 12(1), 61–86, 2002), Kary and Mahner have chosen to occupy a high ground of materialism and empiricism from which to attack the philosophical and methodological positions of believers in artificial intelligence (AI) and artificial life (AL). In this review I discuss some of their main arguments as well as their philosophical foundations. Their central argument: ‘AI is Platonism’, which (...) is based on a particular interpretation of the notion of ‘definition’ and used as a critique against AI, can be counter criticized from two directions: first, Anti-Platonism is not a necessary precondition for criticizing AI, because outspoken Platonist criticism against AI is already known (Penrose, The emperor’s new mind (with a foreword by M. Gardner), 1989). Second, even in case that AI would essentially be ‘Platonism’ this would not be a sufficient argument for proving AI wrong. In my counter criticism I assume a more or less Popperian position by emphasizing the openness of the future: Not by quasi-Scholastic arguments (like Kary and Mahner’s), but only after being confronted with a novel ‘thinking thing’ by future AI engineers we can start to analyze its particular properties (Let me use a history analogon to illustrate my position: In the 19th century, mechanized aviation was widely regarded impossible—only natural organisms (such as birds or bees) could fly, and any science of aerodynamics or aviation did not exist. Only after some non-scientific technicians had confronted their astonished fellows with the first (obviously) flying machine the science of ‘Artificial Aviation’ came into existence, motivated by the need for understanding and mastering that challenging and puzzling new phenomenon). (shrink)

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?" "This clear and engaging book takes a unique approach, encompassing nonstandard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such (...) as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis."--BOOK JACKET. (shrink)

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and (...) set theory--that give rise again and again to philosophical considerations. (shrink)

_Philosophy of Mathematics_ is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

We describe in some detail how to build an infinite computing machine within a continuous Newtonian universe. The relevance of our construction to the Church-Turing thesis and the Platonist-Intuitionist debate about the nature of mathematics is also discussed.

The finite age of the universe and the existence of cosmological horizons provides a strong argument that the observable universe represents a finite causal region with finite material and informational resources. A similar conclusion follows from the holographic principle. In this paper I address the question of whether the cosmological information bound has implications for fundamental physics. Orthodox physics is based on Platonism: the laws are treated as infinitely precise, perfect, immutable mathematical relationships that transcend the physical universe and remain (...) totally unchanged by physical processes, however extreme. If instead the laws of physics are regarded as akin to computer software, with the physical universe as the corresponding hardware, then the finite computational capacity of the universe imposes a fundamental limit on the precision of the laws and the specifiability of physical states. That limit depends on the age of the universe. I examine how the imprecision of the laws impacts on the evolution of highly entangled states and on the problem of dark energy. (shrink)

Much of The Reason’s Proper Study is devoted to defending the claim that simply by stipulating an abstraction principle for the “number-of” functor, we can simultaneously fix a meaning for this functor and acquire epistemic entitlement to the stipulated principle. In this paper, I argue that the semantic and epistemological principles Hale and Wright offer in defense of this claim may be too strong for their purposes. For if these principles are correct, it is hard to see why they do (...) not justify platonist strategies that are not in any way “neo-Fregean,” e.g. strategies that treat “the number of Fs” as a Russellian definite description rather than a singular term, or employ axioms that do not have the form of abstraction principles. (shrink)

We informally discuss some recent results on the incompleteness of formal systems. These theorems, which are of great importance to contemporary mathematical epistemology, are proved using a variety of conceptual tools provably stronger than those of finitary axiomatisations. Those tools require no mathematical ontology, but rather constitute particularly concrete human constructions and acts of comprehending infinity and space rooted in different forms of knowledge. We shall also discuss, albeit very briefly, the mathematical intelligence both of God and of computers. We (...) hope in this manner to help the reader overcome formalist reductionism, while avoiding naive Platonist ontologies, typical symptoms of Godelitis which affected many in the last seventy years. (shrink)

These essays by some of the most prominent figures in linguistics, artificial intelligence, and psychology explore the problems involved in creating a general cognitive science that will treat language, thought, and behavior in an integrated fashion. They address the fundamental questions of the relations between linguistic structures and cognitive processes, between cognitive processes and language behavior, and between language behavior and linguistic structure. Contents: Introduction, Thomas G. Bever (Columbia University), John M. Carroll and Lance A. Miller (IBM Thomas J. Watson (...) Research Center). "Philosophy and "Linguistics: An Outline of Platonist Grammar, Jerrold J. Katz (CUNY). Sense and Reference in a Psychologically Based Semantics, Ray Jackendoff (Brandeis University). Some Thoughts on the Boundaries and Components of Linguistics, Charles J. Fillmore (University of California, Berkeley). Psychology: Approaches to the Study of the Psychology of Language, Walter Kintsch (University of Colorado). Toward An Abstract Performance Grammar, Charles E. Osgood (University of Illinois). Upgrading a Mind, David Premack (University of Pennsylvania). Computational "Models: "Memory, Meaning, and Syntax, Roger Schank (Yale University) and Lawrence Birnbaum (Yale University). Some Inadequate Theories of Human Language Processing, Mitchell P. Marcus (AT&T Bell Laboratories). (shrink)

This paper offers an introduction to poststructuralist interpretivist research in information systems, through a poststructuralist theoretical reading of the phenomenon and experience of social networking websites, such as Facebook. This is undertaken through an exploration of how loyally a social networking profile can represent the essence of an individual, and whether Platonic notions of essence, and loyalty of copy, are disturbed by the nature of a social networking profile, in ways described by poststructuralist thinker Deleuze’s notions of the reversal of (...) Platonism. In bringing a poststructuralist critique to such hugely successful and popular social information systems, the paper attempts to further open up the black box of the computer ‘user’, extend interpretive approaches to information systems research to embrace poststructuralism, and explore how notions of the Self might be reflected through engagement with information system (IS), and how an IS appreciation of the phenomenon of global social networking may benefit from embracing such a poststructuralist approach. (shrink)

We argue about a conceptual approach to quantum formalism. Starting from philosophical conjectures (Platonism, Idealism and Realism) as basic ontic elements (namely: math world, data world, and state of matter), we will analyze the quantum superposition principle. This analysis bring us to demonstrate that the basic assumptions affect in different ways:(a) the general problem of the information and computability about a system, (b) the nature of the math tool utilized and (c) the correspondent physical reality.

In lieu of an abstract, here is a brief excerpt of the content:Welcome To The Pharmacy: Addiction, Transcendence, and Virtual RealityAnn Weinstone (bio)1. The Question of Addiction and TranscendenceIt has become a truism to say that virtual reality (VR) is addictive. Case, the protagonist of William Gibson’s Neuromancer, dreams of connection to the net like a junkie jonesing for a fix. In Jeff Noon’s novel Vurt, you get to cyberspace by tickling the back of your throat with addictive, government-produced feathers. (...) Verity of Kathleen Ann Goonan’s Queen City Jazz sports nanotechnology implants that compel her to enter virtual worlds into which she sinks with feelings of deep bliss. As in Vurt, in Pat Cadigan’s Synners, everything’s an addiction: cyberspace, people, rock and roll.But let’s move away from fiction. Graphic cyberartist Nicole Stenger, a self-professed neo-Platonist, writes, “[a]nd what if the passage to a new level of humanity actually meant abolishing indeed the natural one, or at least some part of it?... Will it not require immense effort to recover from this enhancement of the senses, from this habit of perfection? [Stenger 57]. Michael Benedikt, editor of Cyberspace: First Steps, deems VR “a new and irresistible development in the elaboration of human culture and business under the sign of technology” [1; my emphasis]. Ad copy for “Origin,” a VR game, reads, “You must die to learn how to live.... Death is not an option. It’s an addiction.” And an article in the New York Times titled “The Lure and Addiction of Life on Line” displays a graphic of a bespectacled male, tapping away at a computer located inside of a panopticon-sized rendering of a globe to which the avid user is happily chained [see Asciu]. From advertisements to scholarly texts, it is difficult to find any writing about VR that does not engage in and, as I will argue, rely upon the rhetorics of addiction. William Gibson dubbed cyberspace a “consensual hallucination.” That was 1984. In 1996, critic Robert Markley rechristened VR “a consensual cliché” [56]. Surely, the “addictiveness” of cyberspace contributes to the sense of tired familiarity. My question is this: Why does cyberspace have to be addictive? What work is addiction doing in discourses of virtual reality?In this essay, I’m concerned with the production of what might be called hyper-real transcendence. Jean Baudrillard, in his influential schema “three orders of simulacra,” identifies a first, “natural” order in which “a transcendent world, a radically different universe, is portrayed... in contrast to the continent of the real” [309]. I propose that a third-order, hyper-real, transcendence has survived the collapse of the distance between the model and the original. This transcendence relies on rhetorics of disembodiment, [End Page 77] immortality, and extra-human reproductive and generative powers within virtual spaces. Such spaces include scholarly and technical essays about VR or cyberspace, science fiction, advertisements for VR games, VR game narratives, and other advertising copy that borrows from current discourses of virtuality. My discussion takes place in a field crowded with talk of the death of logocentrism and the end of phonocentric culture. 1 Derrida has written that “scientific language [e.g. computer code] challenges intrinsically and with increasing profundity the ideal of phonetic writing” [Grammatology 10], the logocentric relation of voice to mental experiences. Baudrillard writes mournfully that the “third-order” world of simulated simulacra, of hyper-reality, leaves “no room for any kind of transcendentalism” [310]. Baudrillard and Derrida write with differing affects of the same effect—the waning or death of the foundation of Western notions of transcendence. In this tradition, transcendence commences with the penetration of the self by a supra-enlivened Other, whether that other be a king, a god, nature, the voice of logos, the Law, or an abstracted version of vitality itself. Particularly, I question the persistent coupling of rhetorics of transcendence with rhetorics of addiction. My initial point will be that following the established Western logocentric tradition, rhetorical relationships of addiction between VR users and VR narratives are the “software” with which hyper-real transcendence is produced and sustained. In other words, VR demands, as the price of transcendence, that the user become of the medium... (shrink)

While developing his theory of world 3, Popper rejects two claims made by Plato: first, that the inhabitants of world 3, ideas, are a source of ultimate explanation, a divine revelation of truth, and second, that these ideas are unchanging. I will rehabilitate the second claim. Man does not construct world 3 by creating his theories, nor is it a source of ultimate truth. Instead, world 3 is discovered by man, and it destroys some of his theories: destructive Platonism. I (...) discuss the impact of the modified position on the Grundlagenstreit in mathematics, taking into account Gillies’s constructive Aristotelianism. I then turn to the philosophy of computers and discuss how destructive Platonism relates to computers and the Internet. In particular, I criticize Popper’s claim that computers are nothing but elaborate pens as too pessimistic and incautious, and the fashionable “singularity” theory as too optimistic and at the same time too fatalistic. In my closing remarks, as an antidote against both views, I provide a more modest and reasonable speculation about the ultimate goal and meaning of life. (shrink)

Wright is correct in surmising that Wittgenstein's refusal to be drawn into the metaphysical and epistemological questions that his own discussion of rules allegedly raises results from his rejection of the assumptions that pit the Platonist against the communitarian. This paper shows why the entire idea (which continues to dazzle philosophers)—that in speaking a language or in engaging in other normative practices we are operating a calculus according to strict rules—has to be rejected. It results, in part, from the conflation (...) of different understandings of 'knowing the rules': one in which rules can be 'read off' from the practice by a theorist and those in which expressions of rules are consulted within the course of the practice. (shrink)

The research programme of the philosophy of information (PI) proposed in 2002 made it an independent area or discipline in philosophical research. The scientific concept of ‘information’ is formally accepted in philosophical inquiry. Hence a new and tool-driven philosophical discipline of PI with its interdisciplinary nature has been established. Philosophy of information is an ‘orientative’ rather than ‘cognitive’ philosophy. When PI is under consideration in the history of Western philosophy, it can be regarded as a shift of large tradition. There (...) are three large traditions at large, known as Platonic, Kantian and Leibniz-Russellian. In the discussion of the position of the possible worlds, we have modal Platonism and modal realism, but both of the theories are made in the framework of Western philosophy. In this essay, it is argued that possible worlds could be seen as worlds in information, which is then an interpretation of modal information theory (MIT). Our interpretation is made on the basis of Leibniz’s lifelong connection with China, a fact often overlooked by the Western philosophers. Possible world theory was influenced by the Neo-Confucianism flourishing since the Song Dynasty of China, the foundation of which is Yijing. It could be argued that Leibniz’s possible world theory was formulated in respect to the impact of the thoughts reflected in Yijing, in that one of the prominent features is the model-theoretic construction of theories. There are two approaches to theory construction, i.e., axiom-theoretic and model-theoretic. The origin of the former is from ancient Greece and the latter from ancient China. And they determined the different features of theoretic structures between the oriental and occidental traditions of science and technology. The tendency of the future development of science and technology is changing from the axiom-theoretic to the model-theoretic orientation, at least the two approaches being complementary each other. To some extent, this means the retrospective of tradition in the turning point of history, and some of the China’s cultural traditions might become the starting points in formulating the future Chinese philosophy of science and technology. (shrink)

Robert Hanna (Rationality and logic. MIT Press, Cambridge, 2006) articulates and defends the thesis of logical cognitivism, the claim that human logical competence is grounded in a cognitive faculty (in Chomsky’s sense) that is not naturalistically explicable. This position is intended to steer us between the Scylla of logical Platonism and the Charybdis of logical naturalism (/psychologism). The paper argues that Hanna’s interpretation of Chomsky is mistaken. Read aright, Chomsky’s position offers a defensible version of naturalism, one Hanna may accept (...) as far as his version of naturalism goes, although not one that supports the claim that cognitive science offers a place for logic that is somehow outside the natural, contingent order. (shrink)

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...) for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct. (shrink)

This paper connects information with computation and cognition via concept of agents that appear at variety of levels of organization of physical/chemical/cognitive systems – from elementary particles to atoms, molecules, life-like chemical systems, to cognitive systems starting with living cells, up to organisms and ecologies. In order to obtain this generalized framework, concepts of information, computation and cognition are generalized. In this framework, nature can be seen as informational structure with computational dynamics, where an (info-computational) agent is needed for the (...) potential information of the world to actualize. Starting from the definition of information as the difference in one physical system that makes a difference in another physical system – which combines Bateson and Hewitt’s definitions, the argument is advanced for natural computation as a computational model of the dynamics of the physical world, where information processing is constantly going on, on a variety of levels of organization. This setting helps us to elucidate the relationships between computation, information, agency and cognition, within the common conceptual framework, with special relevance for biology and robotics. (shrink)

'Middle' Platonism has some claim to be the single most influential philosophical movement of the last two thousand years, as the common background to 'Neoplatonism' and the early development of Christian theology. This book breaks with the tradition of considering it primarily in terms of its sources, instead putting its contemporary philosophical engagements front and centre to reconstruct its philosophical motivations and activity across the full range of its interests. The volume explores the ideas at the heart of Platonist philosophy (...) in this period and includes a comprehensive selection of primary sources, a significant number of which appear in English translation for the first time, along with dedicated guides to the questions that have been, and might be, asked about the movement. The result is a tool intended to help bring the study of Middle Platonism into mainstream discussions of ancient philosophy. (shrink)

A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical (...) objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist. (shrink)

This paper presents a theoretical study of the binary oppositions underlying the mechanisms of natural computation understood as dynamical processes on natural information morphologies. Of special interest are the oppositions of discrete vs. continuous, structure vs. process, and differentiation vs. integration. The framework used is that of computing nature, where all natural processes at different levels of organisation are computations over informational structures. The interactions at different levels of granularity/organisation in nature, and the character of the phenomena that unfold through (...) those interactions, are modeled from the perspective of an observing agent. This brings us to the movement from binary oppositions to dynamic networks built upon mutually related binary oppositions, where each node has several properties. (shrink)

Platonism has played a central role in Christianity and is essential to a deep understanding of the Christian theological tradition. At times, Platonism has constituted an essential philosophical and theological resource, furnishing Christianity with an intellectual framework that has played a key role in its early development, and in subsequent periods of renewal. Alternatively, it has been considered a compromising influence, conflicting with the faith's revelatory foundations and distorting its inherent message. In both cases the fundamental importance of Platonism, as (...) a force which Christianity defined itself by and against, is clear. Written by an international team of scholars, this landmark volume examines the history of Christian Platonism from antiquity to the present day, covers key concepts, and engages issues such as the environment, natural science and materialism. (shrink)