Ikujiro Nonaka, whose formative experience is Japanese, is an established scholar who has written about large business organizations. He sees knowledge at the heart of the organization and its products and aims to develop Michael Polanyi’s conception of tacit knowledge in a practical direction to enhance organizational “knowledge creation.” For Nonaka, what matters is the practice, the doing, the embodiment of knowledge. An organization can amplify and crystallize individuals’ tacit knowledge in a process that allows them to experience deeper understanding. (...) Nonaka holds that it is iimportant to explore the potential that knowledge holds. His spiral process describes disciplined practices that make tacit knowledge independent and available to restructure the organizational knowledge context. (shrink)

I present a new interpretation of Wittgenstein's later philosophy of logic and mathematics. This interpretation, like others, emphasizes Wittgenstein's attempt to reconcile platonistic and constructivistic approaches. But, unlike other interpretations, mine explains that attempt in terms of Wittgenstein's position about the relations between our concepts of necessity and provability. If what I say here is correct, then we can rescue Wittgenstein from the charge of naive relativism. For his relativism extends only to provability, and not to necessity.

A substantial guide providing an overview of both physicalism and metaphysical naturalism, reviewing both questions of formulation and justification for both doctrines. Includes a diagnostic strategy for understanding talk of naturalism as a metaphysical thesis.

This paper explores different interpretations of the word ‘deep’ as it is used by mathematicians, with a large number of examples illustrating various criteria for depth. Most of the examples are theorems with ‘historical depth’, in the sense that many generations of mathematicians contributed to their proof. Some also have ‘foundational depth’, in the sense that they support large mathematical theories. Finally, concepts from mathematical logic suggest that it may be possible to order certain theorems or problems according to ‘logical (...) depth’. (shrink)

Inside What Would Plato Do?, you'll find the basics of philosophy, written in an easy, digestible way we can all understand, along with questions to help you apply these important theories to your own life. So, after you've learned about a philosophical concept, you'll then be challenged to test yourself and see how the results can impact your daily life. For instance, after learning about Kant's theory of morality and the importance of intention you're challenged with questions like: Can good (...) people do bad things? Was there a time when you intended to do something helpful that ended up being hurtful? Does that make you a good person (because you intended to do good) or a bad person (because the results were bad)? What Would Plato Do? will not only help you better understand some of the greatest thinkers ever but will also help you think of the world around you in a whole new way! (shrink)

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a (...) large extent, the story of philosophy of mathematics. (shrink)

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse (...) Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics. (shrink)

Ne vers 1180 a Aurillac, mort le 30 mars 1249, Guillaume d'Auvergne est nomme eveque de Paris des 1228. Son oeuvre est contemporaine de la querelle de l'aristotelisme qui gagne la faculte de theologie, et du bouleversement de l'histoire theorique qui l'accompagne. Quelle est la cause efficiente de la pensee? D'ou vient l'intelligible necessairement present dans l'ame qui pense? C'est a cela que repondent les neuf premieres parties du chapitre sept du De anima, ecrit vers 1240. La noetique de Guillaume (...) d'Auvergne, complexe, s'y deploie et sensiblement se demarque de l' augustinisme avicennisant qui traditionnellement la caracterise. L'ame, dans son rapport au sensible, est principium agens, lectrice, en tant qu'elle pense, d'un livre dont elle-meme est l'auteur, et dont la verite se passe en partie de l'illumination divine. (shrink)

We are immersed within an odorous sea of chemical currents that we parse into individual odors with complex structures. Odors have been posited as determined by the structural relation between the molecules that compose the chemical compounds and their interactions with the receptor site. But, naturally occurring smells are parsed from gaseous odor plumes. To give a comprehensive account of the nature of odors the chemosciences must account for these large distributed entities as well. We offer a focused review of (...) what is known about the perception of odor plumes for olfactory navigation and tracking, which we then connect to what is known about the role odorants play as properties of the plume in determining odor identity with respect to odor quality. We end by motivating our central claim that more research needs to be conducted on the role that odorants play within the odor plume in determining odor identity. (shrink)

The following three related contributions jointly serve to lift up elements of the thought of the anthropolo­gist Gregory Bateson that can be fruitfully compared with elements of Michael Polanyi’s thought. In a brief introduction, William Stillwell reviews Bateson’s life and developing interests. Stillwell also provides, in a creative dialog form akin to Bateson’s own dialogs, a short review article on Noel Charlton’s Understanding Gregory Bateson: Mind, Beauty and the Sacred Earth. The third piece is Jere Moorman’s short 1991 (...) essay (now out of print) discussing Polanyi’s ideas about tacit knowing and their connection with Bateson’s ideas about the double bind. (shrink)

Hilbert took to using ideal elements in the 1890's, in both algebraic number theory and geometry. His Zahlbericht of 1897 popularized the concept of the ideal introduced by Dedekind in 1871 (which in turn formalized the concept of "ideal number" introduced by Kummer in the 1840's). His geometric work likewise followed a long history of ideal elements, some that originated in geometry and others that originated elsewhere and were applied to geometry. Important examples were:Piero della Francesca's Ideal City.Points at infinity (...) in projective geometry, originating in the 1430s from the "vanishing points" in perspective drawing.Imaginary points in algebraic geometry, originating from the imaginary numbers used by .. (shrink)

We perceive smells as perduring complex entities within a distal array that might be conceived of as smellscapes. However, the philosophical orthodoxy of Odor Theories has been to deny that smells are perceived as having a distal location. Recent challenges have been mounted to Odor Theories’ veracity in handling the timescale of olfactory perception, how it individuates odors as a distal entities, and their claim that olfactory perception is not spatial. The paper does not aim to dispute these criticisms. Rather, (...) what will be shown is that Molecular Structure Theory, a refinement of Odor Theory, can be further developed to handle these challenges. The theory is further refined by focusing on distal perception that requires considering the perceptual object as mereologically complex persisting odor against a background scene conceived of as a smellscape. What will be offered is an expansion of Molecular Structure Theory to account for distal smell perception within natural environments. (shrink)

How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence (...) on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as "infinitesimal algebra," and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field's power and progress. (shrink)

This is a book grounded in the real ethical challenges of modern business practice, with a world-religious perspective so necessary in an era of globalization.

When it originated in the late 19th century, psychometrics was a field with both a scientific and a social mission: psychometrics provided new methods for research into individual differences, and at the same time, these psychometric instruments were considered a means to create a new social order. In contrast, contemporary psychometrics - due to its highly technical nature and its limited involvement in substantive psychological research - has created the impression of being a value-free discipline. In this article, we develop (...) a contrasting characterization of contemporary psychometrics as a value-laden discipline. We expose four such values: that individual differences are quantitative (rather than qualitative), that measurement should be objective in a specific sense, that test items should be fair, and that utility of a model is more important than its truth. Our goal is not to criticize psychometrics for employing these values, but rather to bring them into the open and to show that these values are not inevitable and are in need of systematic evaluation. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

First collected in Italy in 1985, _Art's Claim to Truth_ is considered by many philosophers to be one of Gianni Vattimo's most important works. Newly revised for English readers, the book begins with a challenge to Plato, Aristotle, Kant, and Hegel, who viewed art as a metaphysical aspect of reality rather than a futuristic anticipation of it. Following Martin Heidegger's interpretation of the history of philosophy, Vattimo outlines the existential ontological conditions of aesthetics, paying particular attention to the works of (...) Kandinsky, which reaffirm the ontological implications of art. Vattimo then builds on Hans-Georg Gadamer's theory of aesthetics and provides an alternative to a rationalistic-positivistic criticism of art. This is the heart of Vattimo's argument, and with it he demonstrates how hermeneutical philosophy reaffirms art's ontological status and makes clear the importance of hermeneutics for aesthetic studies. In the book's final section, Vattimo articulates the consequences of reclaiming the ontological status of aesthetics without its metaphysical implications, holding Aristotle's concept of beauty responsible for the dissolution of metaphysics itself. In its direct engagement with the works of Gadamer, Heidegger, and Luigi Pareyson, _Art's Claim to Truth_ offers a better understanding of the work of Vattimo and a deeper knowledge of ontology, hermeneutics, and the philosophical examination of truth. (shrink)

Father Williams explains how the conscience is formed through our training and experiences and informed by the Holy Spirit, making it an essential tool for daily living. He uses familiar and surprising characters to illustrate the positive choices conscience can direct--and the disaster that results when a conscience is undeveloped or ignored. Questions he tackles include "Is it more important to be smart or good?""Is there a morally right thing to do in every situation?" and "Is the Christian moral life (...) an exciting adventure, or a necessary burden?" Rich, provocative, and practical for everyday decision making, KNOWING RIGHT FROM WRONG is a must-read for all who hunger for personal holiness. (shrink)

Man (Islam); Islamic philosophy; Islamic ethics.

In Nicomachean Ethics X.7–8, Aristotle defends a striking view about the good for human beings. According to Aristotle, the single happiest way of life is organized around philosophical contemplation. According to the narrowness worry, however, Aristotle's contemplative ideal is unduly Procrustean, restrictive, inflexible, and oblivious of human diversity. In this paper, I argue that Aristotle has resources for responding to the narrowness worry, and that his contemplative ideal can take due account of human diversity.