Husserl’s first work formulated what proved to be an algorithmically complete arithmetic, lending mathematical clarity to Kronecker’s reduction of analysis to finite calculations with integers. Husserl’s critique of his nominalism led him to seek a philosophical justification of successful applications of symbolic arithmetic to nature, providing insight into the “wonderful affinity” between our mathematical thoughts and things without invoking a pre-established harmony. For this, Husserl develops a purely descriptive phenomenology for which he found inspiration in Mach’s proposal of a “universal (...) physical phenomenology.” To account for applications to any domain, Husserl envisages a theory of all possible deductive systems, which he develops extensively in his Göttingen lectures wherein he engages with Hilbert’s work on deductive systems for geometry, real arithmetic, and physics. This leads Husserl to formulate claims of decidability and proofs of completeness for various arithmetics that result from his analysis of Kronecker’s general arithmetic. Careful attention to these proofs seem to show that Husserl was not oblivious to problems that underlie our incompleteness theorems, namely that of showing that some inversions of his algorithmic arithmetic are undefined. His growing preoccupation with the issue of a pre-established harmony between mathematical thought and reality motivate his pursuit of a “supramathematics” of all possible complete theory forms to demystify such harmony, by having such a form on hand for describing any empirical domain. He soon decides that a transcendental idealism of nature will reveal the wonderful affinity of thoughts and things comprising such harmony, to be a wonderful “parallelism of objective unities and constituted manifolds of consciousness.” But the paradoxes of logic and set theory cloud the clarity of mathematics, which Weyl would restore with Brouwer’s intuitionism and Hilbert with his metamathematics. Husserl informed Weyl that his student Becker had formulated a phenomenological foundation not only for Weyl’s generalization of relativity theory but also for the Brouwer-Weyl continuum. But Weyl eventually rejected much of Becker’s work, especially when it became clear that his phenomenological intuitionism could not account for the success of Hilbert’s transfinite mathematics in quantum physics. Becker responded to this “crisis of phenomenological method” with his mantic phenomenology celebrating the magic of mathematical mysticism, which Husserl finally rejects in favor of a pluralistic phenomenology of mathematics and nature. (shrink)

This book grew out of a graduate student paper [261] in which I set down some criticisms of J. R. Lucas' attempt to refute mechanism by means of G6del's theorem. I had made several such abortive attempts myself and had become familiar with their pitfalls, and especially with the double edged nature of incompleteness arguments. My original idea was to model the refutation of mechanism on the almost universally accepted G6delian refutation of Hilbert's formalism, but I kept getting stuck on (...) questions of mathematical philosophy which I found myself having to beg. A thorough study of the foundational works of Hilbert and Bernays finally convinced me that I had all too naively and uncritically bought this refutation of formalism. I did indeed discover points of surprisingly close contact between formalism and mechanism, but also that it was possible to under mine certain strong arguments against these positions precisely by invok ing G6del's and related work. I also began to realize that the Church Turing thesis itself is the principal bastion protecting mechanism, and that G6del's work was perhaps the best thing that ever happened to both mechanism and formalism. I pushed these lines of argument in my dis sertation with the patient help of my readers, Raymond Nelson and Howard Stein. I would especially like to thank the latter for many valuable criticisms of my dissertation as well as some helpful suggestions for reor ganizing it in the direction of the present book. (shrink)

Husserl’s lifelong interest in Kant eventually becomes a preoccupation in his later years when he finds his phenomenology in competition with Neokantianism for the title of transcendental philosophy. Some issues that Husserl is concerned with in Kant are bound up with the works of Lambert. Kant believed that the role played by principles of sensibility in metaphysics should be determined by a “general phenomenology” on which Lambert had written. Kant initially believed that man is capable only of symbolic cognition, not (...) intellectual intuition. Lambert saw an increasing need in mathematics for symbolic cognition as exemplified in his proofs of the irrationality of π and e. Kant takes from Leibniz and Lambert an unrestricted notion of construction, allowing him to view mathematics as constructing its concepts in intuition, while Lambert’s proofs convince him that all mathematical problems are eventually solvable. Husserl criticizes Kant’s intuitionism for its inadequate accommodation of meaning to intuition, which he redresses with his theory of categorial intuition. This may improve on Kant’s intuition of the axiom of parallels but not so clearly on his spatial intuition. Husserl opposes Kant’s view of space as the form of outer intuition with his own view of it as the form of things. Husserl’s exploration of the geometry of visual space, which involves his earliest uses of epoché and reduction, converges however with Hilbert’s logical analysis of Kantian spatial intuition in leading to Euclidean spatial judgments. Hilbert’s analysis leads him to affirm the solvability of all well posed mathematical problems, a thesis complicated by the outbreak of logical paradoxes. Untroubled by such paradoxes, Husserl develops a supramathematics of all possible deductive systems whose completeness implicitly would also provide solutions of all such problems. Husserl’s full transcendental turn coincides with his realization that in effecting his Copernican turn, Kant was really the first to detect the “secret longing” of modern philosophy for a phenomenological clarification of being. Husserl now finds that Kant’s transcendental deductions presuppose a pure ego not adequately analyzed by Kant that survives the phenomenological reduction. Husserl’s idealism leads him to develop his own intuitionism, which adds to Kant’s, a “method of clarification” of mathematical concepts intended to clarify difficult impossibility proofs, but neither Husserl nor Kant base arithmetic on time. Husserl’s critique of the room left in Kant’s idealism, for things in themselves, leads to his own monadological solution of the problem of intersubjectivity. Husserl’s final judgment on Kant is that his form of transcendental idealism did not enable him to achieve absolute subjectivity through a genuine transcendental reduction. (shrink)

Ethics in Early China: An Anthology is a major contribution to the philosophical study of early Chinese ethics and comparative ethics by a collection of some of the most distinguished scholars in these fields. This anthology honors Professor Chad Hansen's many and important contributions to the study of Chinese philosophy, but the work is not a festschrift per se. Instead of discussing the honoree's oeuvre in a collection of essays, these new, innovative, and outstanding writings engage, bear upon, develop, and (...) contend with important themes in Hansen's work, including, for example, Hansen's provocative interpretations of the meanings of dao 道 and de 德 in early Chinese sources, his analysis of the action-guiding .. (shrink)

This article examines different ways agrarian thought has been interpreted and employed by ancient Chinese and early modern Japanese philosophers to criticize and attempt to limit the state’s power, and, in at least one case, to try to strengthen it. It analyzes the manner in which arguably the most fundamental human activities of farming, weaving, and governing have been conceptualized in a normative way, and the extent to which thinkers and statesmen in these East Asian historical contexts debated their correct (...) interrelation. The state’s critics were deeply concerned about the tragic occurrence of death by starvation during their ages, and by the conditions that allowed it to happen. They identified and advocated certain ethical values and political measures they believed would mitigate and help prevent this avoidable circumstance. Conversely, the state’s supporters appropriated agrarian thinking to demonstrate how the sovereign’s control of the realm and its subjects could be significantly enhanced by strategically apportioning the land in a particular way. Lastly, both groups of thinkers sought unity, ethically or geopolitically, but they conceived of this ideal in contrasting ways. (shrink)

American men experience worse outcomes on a wide range of health and well-being variables compared to women, including disease, educational problems, violence, addiction, suicide, unemployment, and life expectancy. Because of this, organizations have created programs that focus on helping men both psychologically and spiritually; however, it is important to assess the effectiveness of these programs. The Crucible Project, founded in 2002, attempts to facilitate the development of integrity, courage, and grace in men using a weekend retreat format. The purpose of (...) this pilot study was to explore the effect of the weekend retreat on participants’ authenticity, assertiveness, and willingness to forgive. Participants completed measures before the weekend retreat, immediately after the weekend retreat, and at a 1-month follow-up. Results indicate that weekend retreat participants demonstrated a significant increase in scores on measures of authenticity and willingness to forgive and a trend toward increased scores on the measure of assertiveness over time. We conclude by discussing limitations of the study, areas for future research, and implications for spiritual and character development. (shrink)

Strict constructivist philosophers conclude that no truth claims can be verified on the basis of mystical exploration due to the thoroughly conditioned character of such experiences. In response, Bede Griffiths’s life of dialogue between Christianity and Hinduism suggests that mystical knowing incorporates both conditioned and unconditioned elements. In the cross-culturally identifiable experience of self-transcendence in meditation, the relationship between the conditioned subject and the unconditioned sacred “object” is transformed, resulting in an intuitive knowledge for which different criteria of verifiability are (...) both needed and available. Griffiths’s multireligious experience thus supports the identification of common ground for various religions in mystical knowing. (shrink)

The metamathematical theorems of Gödel and Church are frequently applied to the philosophy of mind, typically as rational evidence against mechanism. Using methods of Post and Smullyan, these results are presented as purely mathematical theorems and various such applications are discussed critically. In particular, J. Lucas's use of Gödel's theorem to distinguish between conscious and unconscious beings is refuted, while more generally, attempts to extract philosophy from metamathematics are shown to involve only dramatizations of the constructivity problem in foundations. More (...) specifically, philosophical extrapolations from metamathematics are shown to involve premature extensions of Church's thesis. (shrink)

Both local and global issues are typically dealt with in the Social Studies curriculum, or in curriculum areas with other names but similar intents. In the literature about Social Studies the imagination has played little role, and consequently it hardly appears in texts designed to help teachers plan and implement Social Studies lessons. What is true of Social Studies is also largely reflected in general texts concerning planning teaching. Clearly many theorists and practitioners are concerned to engage students' imaginations in (...) learning, even though they use terms other than 'imagination' in doing so. This article suggests that a more explicit attention to imagination can make our efforts to engage students in learning more effective. We provide, first, a working definition of imagination, then show how students' imaginations can be characterized in terms of the 'cognitive toolkits' they bring to learning. We look at such 'cognitive tools' as stories, images, humor, binary oppositions, a sense of mystery and how these can be used to engage students' imaginations in learning Social Studies and other content from kindergarten to about grade four. We then consider 'cognitive tools' commonly deployed by students from about grade four to grade nine, including a sense of reality, the extremes of experience and limits of reality, and associating with the heroic. We also provide examples of how using such tools could influence planning and teaching Social Studies topics. (shrink)

Aristotle's Physics is a work of extraordinary intellectual power which has had a profound influence on scientists and philosophers throughout the ages, and on the development of physics itself. This collection of major, previously unpublished, essays by leading Aristotelian scholars examines a wide range of major issues in the Physics and other related works. They offer fresh approaches to Aristotle's work and important new interpretations of his thought.

This presentation was delivered at the Self, Motivation & Virtue Project's 2015 Interdisciplinary Moral Forum, held at Marquette University in Milwaukee, Wisconsin.

On the basis of what Aristotle says in the Posterior Analytics about how sciences are differentiated and about the impermissibility of ‘kind-crossing’, many commentators suppose that when it comes to his scientific practice, Aristotle treats the boundaries of the sciences as impermeable, so that if subject-matter X is the business of one science, it simply cannot be the business of another. I call this the impermeable boundary theory of the sciences: knowledge is divided into watertight compartments, determined by their distinct (...) genera, and what goes on in one compartment cannot turn up in another. I argue that, even if this is a correct account of Aristotle’s position in the Analytics, the view that he accepts the impermeable boundary theory when it comes to his scientific and philosophical work outside the Analytics is simply untenable. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

Lambda, the twelfth book of Aristotle's Metaphysics, is an outline for a much more extended work in metaphysics or, more accurately, in what Aristotle calls 'first philosophy', the inquiry into 'the principles and causes of all things'. Lindsay Judson provides a rigorous translation of this important book and a detailed philosophical commentary.

I argue that Metaphysicsλ‎ is a unified work, and one which is not a continuation of the central books ΖΗΘ‎. It outlines an extensive project in First Philosophy, which has close connections with ΑΒΓΕ‎, but which proceeds on a different trajectory from ΖΗ‎. The principal problem in understanding λ‎ as a whole is how to reconcile Aristotle's explicit presentation of the book as a highly unified study with the disparate character of its two halves – the first a general‐metaphysical enquiry (...) into the features which changeable substances have as being substances of that kind, the second a detailed investigation of the specific character and activity of immaterial substances. My paper aims to show how this reconciliation is possible, and what we can learn about Aristotle's conception of first philosophy as a result. (shrink)