We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the (...) Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

A surprisingly large number of scholars believe that (a) we are blameworthy, and therefore punishable, only for what we have control over; (b) we have control only over our actions and intentions, not the consequences of our actions; and therefore (c) if two agents perform the very same action (e.g., attempting to kill) with the very same intentions, then they are equally blameworthy and deserving of equal punishment – even if only one of them succeeds in killing. This paper argues (...) against these “equivalence theorists” that harmful consequences do make a moral difference, that the harm produced by the killer’s attempt retroactively makes her action more blameworthy, and therefore deserving of more punishment, than the failed attempter’s attempt. The primary argument for this “non-equivalence theory” is an analogy with gambling. Just as a gambler makes a deal with the casino to allow metaphysical luck to retroactively determine the “profit status” of her bet, so too the attempted killer makes a deal with “the casino of morality” to allow metaphysical luck to retroactively determine the moral status of her attempt. She makes the “moral deal” that if her attempt succeeds, her attempt was more blameworthy than if her attempt does not succeed. And it is the greater blameworthiness of the killer’s attempt that justifies our intuition that the killer should be punished more harshly than the failed attempter. (shrink)

The problem of evil can be captured by the following four statements which taken together are inconsistent: 1) God made the world 2) God is a perfect being 3) A perfect being would not create a world containing evil 4) The world contains evil Traditional attempts to grapple with this problem typically center on rejecting (3). Thus Descartes, following Augustine, rejects (3), arguing that evil is the result of man’s exercise of his free will. However, given Descartes plausible claim that (...) God could have created man in such a way that through exercising his free will man comes to only virtuous actions, it is not clear how the problem is solved. Descartes also repeats the Augustinian orthodoxy that though the world contains evil it does not contain it as a positive existence; evil has no real being but is simply the reflection of the inherent lack of full-being in merely finite individuals. Again, that this is a solution is open to serious doubt. (shrink)

Shambhala: We wanted to talk with you about Boomeritis, which will be released in a few months--especially about some of the real-life models for the people in it, how you came to write it, and the extraordinary buzz that's building around it. But before that, word has it that you just finished writing volume 3 of the Kosmos Trilogy.

To what extent can individuals make a claim on their community to provide for upkeep and healing of their bodies? Can the philosophy of natural rights that animates the American political tradition be applied usefully to the health care debate? With Michael Boylan, Helen John, and Patrick Sullivan.

What are the moral stakes involved when we will have the same power to engineer our bodies as we do our automobiles? Which specific bioethics problems will put the most pressure on our ethical traditions? What should we do now to prepare for this brave new world? With Greg Loeben, Ronald Munson, and Wade Robison.

What are the moral stakes involved when we will have the same power to engineer our bodies as we do our automobiles? Which specific bioethics problems will put the most pressure on our ethical traditions? What should we do now to prepare for this brave new world? With Greg Loeben, Ronald Munson, and Wade Robison.

Why is thinking about time so confusing, yet time itself seems to be... well, right now? And then? Can we get a better handle on time than did the good bishop of Hippo, who was clear about time - until he thought about it? With Verna Gehring and Farzad Mahootian.

What are the philosophical implications of the theory of evolution? What beliefs about man can we rule out in light of scientific knowledge of the theory of natural selection? Are there different ways to interpret the Darwinian revolution? How should we regard the evolutionary musings of thinkers such as Henri Bergson or Teilhard de Chardin? With H. James Birx, John Loughney, and Drew Arrowood.

Who gets to use force and when? How are we supposed to justify the use of violence in achieving political goals and establishing and maintaining political communities and structures? With Anthony Ellis , David Garren , and Scott Hibbard.

We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.

Ken Elkins retired as chief photographer of the Anniston Star in 2000, and this selection of his work demonstrates his brilliant eye for finding and capturing images of rural southern lives and landscapes in all their difficulty, candor, and humor. These are unadorned images of a timeless landscape and proud resourceful people, who know well their neighbors, honor their past, and face the tests of daily life with wit and a stoic sense of endurance.

v. 1. The spectrum of consciousness ; No boundary ; Selected essays -- v. 2. The Atman Project ; Up from Eden -- v. 3. A sociable god ; Eye to eye -- v. 4. Integral psychology ; Transformations of consciousness ; Selected essays -- v. 5. Grace and grit : spirituality and healing in the life and death of Treya Killam Wilber. 2nd ed. -- v. 6. Sex, ecology, spirituality : the spirit of evolution. 2nd, rev. ed. -- v. (...) 7. A brief history of everything ; The eye of spirit -- v. 8. The marriage of sense and soul ; One taste. (shrink)

In this essay I present the philosophy of Nishida Kitarō, the father of the Kyoto School tradition, as an alternative version of transcendental philosophy. While following the steps of Kant and Husserl in important ways, Nishida attempts to take the transcendental approach even further, finally leaving us with a different view of reality that is neither realist nor idealist, but, rather, radically realist. I call this radical transcendental position, “awakened realism”. Due to word limitations, I can only set the stage (...) for further discussion on what kind of implication this may have for transcendental philosophy. But if I succeed in making my presentation clear enough, it should naturally ignite discussion on how far we can radicalize transcendental philosophy without making it into something else. (shrink)

Ever since the publication of his first book, The Spectrum of Consciousness, written when he was twenty-three, Ken Wilber has been identified as the most comprehensive philosophical thinker of our times. This introductory sampler, designed to acquaint newcomers with his work, contains brief passages from his most popular books, ranging over a variety of topics, including levels of consciousness, mystical experience, meditation practice, death, the perennial philosophy, and Wilber's integral approach to reality, integrating matter, body, mind, soul, and spirit. Here (...) is Wilber's writing at its most reader-friendly, discussing essential ideas of the world's great psychological, philosophical, and spiritual traditions in language that is lucid, engaging, and inspirational. (shrink)

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements "every mapping is sequentially nondiscontinuous", "every sequentially nondiscontinuous mapping is sequentially continuous", and "every sequentially continuous mapping is continuous". As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism.

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian (...) decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making. (shrink)

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We show that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that "every mapping is strongly extensional", "every sequentially nondiscontinuous mapping is sequentially continuous", and a weak version of Markov's principle are equivalent. Also, assuming a consequence of Church's thesis, we prove a version of the Kreisel-Lacombe-Shoenfield-Tsĕitin theorem.

Classically, weak König's lemma and Brouwer's fan theorem for detachable bars are equivalent. We give a direct constructive proof that the former implies the latter.

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

Constructive mathematics – mathematics in which ‘there exists’ always means ‘we can construct’ – is enjoying a renaissance. Fifty years on from Bishop’s groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject’s myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, (...) constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches. (shrink)

Ken Binmore's previous game theory textbook, Fun and Games, carved out a significant niche in the advanced undergraduate market; it was intellectually serious and more up-to-date than its competitors, but also accessibly written. Its central thesis was that game theory allows us to understand many kinds of interactions between people, a point that Binmore amply demonstrated through a rich range of examples and applications. This replacement for the now out-of-date 1991 textbook retains the entertaining examples, but changes the organization to (...) match how game theory courses are actually taught, making Playing for Real a more versatile text that almost all possible course designs will find easier to use, with less jumping about than before. In addition, the problem sections, already used as a reference by many teachers, have become even more clever and varied, without becoming too technical. Playing for Real will sell into advanced undergraduate courses in game theory, primarily those in economics, but also courses in the social sciences, and serve as a reference for economists. (shrink)

Consistency with the formal Church’s thesis, for short CT, and the axiom of choice, for short AC, was one of the requirements asked to be satisfied by the intensional level of a two-level foundation for constructive mathematics as proposed by Maietti and Sambin From sets and types to topology and analysis: practicable foundations for constructive mathematics, Oxford University Press, Oxford, 2005). Here we show that this is the case for the intensional level of the two-level Minimalist Foundation, for short MF, (...) completed in 2009 by the second author. The intensional level of MF consists of an intensional type theory à la Martin-Löf, called mTT. The consistency of mTT with CT and AC is obtained by showing the consistency with the formal Church’s thesis of a fragment of intensional Martin-Löf’s type theory, called \, where mTT can be easily interpreted. Then to show the consistency of \ with CT we interpret it within Feferman’s predicative theory of non-iterative fixpoints \ by extending the well known Kleene’s realizability semantics of intuitionistic arithmetics so that CT is trivially validated. More in detail the fragment \ we interpret consists of first order intensional Martin-Löf’s type theory with one universe and with explicit substitution rules in place of usual equality rules preserving type constructors -rule which is not valid in our realizability semantics). A key difficulty encountered in our interpretation was to use the right interpretation of lambda abstraction in the applicative structure of natural numbers in order to model all the equality rules of \ correctly. In particular the universe of \ is modelled by means of \-fixpoints following a technique due first to Aczel and used by Feferman and Beeson. (shrink)

Natural Justice is a bold attempt to lay the foundations for a genuine science of morals using the theory of games. Since human morality is no less a product of evolution than any other human characteristic, the book takes the view that we need to explore its origins in the food-sharing social contracts of our prehuman ancestors. It is argued that the deep structure of our current fairness norms continues to reflect the logic of these primeval social contracts, but the (...) particular fairness norm a society operates is largely a product of cultural evolution. In pursuing this point, the book proposes a naturalistic reinterpretation of John Rawls' original position that reconciles his egalitarian theory of justice with John Harsanyi's utilitarian theory by identifying the environment appropriate to each. (shrink)

Binmore argues that game theory provides a systematic tool for investigating ethical matters.

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian (...) decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making. (shrink)

In this paper, I argue that later Nishida's analysis of self-awareness (jikaku) provides a new perspective on the nature of self-awareness as understood in the philosophical literature today. I argue that the contemporary literature deals with two kinds of self-awareness; the higher-order theory understands self-awareness to be an objectified awareness and the phenomenological tradition generally understands self-awareness to be, at least primarily, a non-objectified awareness. In light of this, I first give an account of Nishida's ?acting-intuition? with reference to the (...) ?historical body.? Then I argue that later Nishida's analysis of self-awareness depicts the inadequacy of the two kinds of self-awareness as both being stuck in the subject-object dichotomy which, according to Nishida, is but one mode of experience, namely the mode of difference. Nishida provides an account that ultimately foregrounds the experiential mode of unity that negates any sense of differentiation between the subject and object. (shrink)

[Ken Gemes] In some texts Nietzsche vehemently denies the possibility of free will; in others he seems to positively countenance its existence. This paper distinguishes two different notions of free will. Agency free will is intrinsically tied to the question of agency, what constitutes an action as opposed to a mere doing. Deserts free will is intrinsically tied to the question of desert, of who does and does not merit punishment and reward. It is shown that we can render Nietzsche's (...) prima facie conflicting assertions regarding free will compatible by interpreting him as rejecting deserts free will while accepting the possibility of agency free will. It is argued that Nietzsche's advances an original form of compatibilism which takes agency free will to be a rare achievement rather than a natural endowment. /// [Christopher Janaway] This paper aims to distinguish a conception of 'free will' that Nietzsche opposes (that of the pure agent unaffected by contingencies of character and circumstance) and one that he supports. In Human, All Too Human Nietzsche propounds the 'total unfreedom' of the will. But by the time of Beyond Good and Evil and the Genealogy he is more concerned (a) to trace the affective psychological states underlying beliefs in both free will and 'unfree will', (b) to suggest that the will might become free in certain individuals, a matter of having a consistent strong character, self-knowledge, and ability to create values. The paper explores the kind of autonomy required in agents who would 'revalue' existing values. (shrink)