This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties (...) (Q 3 ) of the variety Q 3. (shrink)

This paper is devoted to the study of some subvarieties of the variety Q of Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q subscript 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q subscript 3 and we construct (...) the lattice of subvarieties lambda (Q subscript 3) of the variety Q subscript 3. (shrink)

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This (...) historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic. (shrink)

Human conflict and its resolution is obviously a subject of great practical importance. Equally obviously, it is a vast subject, ranging from total war at one end of the spectrum to negotiated settlement at its other end. The literature on the subject is correspondingly vast and, in recent times, technical, thanks to the valuable contributions made to it by game theorists, economists, and writers on industrial and international relations. In this essay, however, I shall discuss only one familiar form of (...) conflict-resolution. There is room for such a discussion, because philosophers have lately neglected compromise, despite the interest shown in it by the aforementioned experts, and despite the classic treatments of it by Halifax, Burke and Morley. Truly, ‘…compromise is not so widely discussed by philosophers as one might expect’, and ‘…the idea of compromise has been largely neglected by Anglo-American jurisprudence’. (shrink)

After describing Heidegger's critique of metaphysics as ontotheology, I unpack the metaphysical assumptions of several transhumanist philosophers. I claim that they deploy an ontology of power and that they also deploy a kind of theology, as Heidegger meant it. I also describe the way in which this metaphysics begets its own politics and ethics. In order to transcend the human condition, they must transgress the human.

Humanity does not gradually progress from combat to combat until it arrives at universal reciprocity, where the rule of law finally replaces warfare; humanity installs each of its violences in a system of rules and thus proceeds from domination to domination. (Foucault, 1984, 85)In this essay, I take a note from Michel Foucault regarding the notion of biopolitics. For Foucault, biopolitics has both repressive and constitutive properties. Foucault's claim is that with the rise of modern government, the state became exceedingly (...) concerned about the body politic, the bodies that make up the polis, including the health of those bodies. However, Giorgio Agamben claims that Foucault and all western political philosophy misses the relationship between power and Sovereignty, with disastrous results and totalizing tendencies. I explore the case of Terri Schiavo claiming that the social conservatives have attempted to politicize bare life in its legal maneuverings, but I also show how the social liberals open an uncontrollable space between life and death. Both the left and the right miss the aporia at the heart of western political philosophy, and bioethics is complicit in the totalizing effects of contemporary medicine. (shrink)

This essay places Foucault's work into a philosophical context, recognizing that Foucault is difficult to place and demonstrates that Foucault remains in the Kantian tradition of philosophy, even if he sits at the margins of that tradition. For Kant, the forms of intuition—space and time—are the a priori conditions of the possibility of human experience and knowledge. For Foucault, the a priori conditions are political space and historical time. Foucault sees political space as central to understanding both the subject and (...) objects of medicine, psychiatry, and the social sciences. Through this analysis one can see that medicine's metaphysics is a metaphysics of efficient causation, where medicine's objects are subjected to mechanisms of efficient control. (shrink)

In the mid-1970s, the biomedical model of medicine gave way to the biopsychosocial model of medicine; it was billed as a more comprehensive and compassionate model of medicine. After more than a century of disentangling medicine from religion, the medicine and spirituality movement is attempting to bring religion and spirituality back into medicine. It is doing so under a biopsychosociospiritual model. I unpack one model for allowing religion back into medicine called the RCOPE. RCOPE is an instrument designed to categorize (...) religion and spirituality as psychological coping mechanisms. I explore how such instruments are related to the history of statistical measurement and demonstrate the political impetus that governs such enterprises. The biopsychosociospiritual medicine is billed as a more holistic and comprehensive model. This new model of medicine offers total care. However, I demonstrate how this total care becomes totalizing, indeed totalitarian, admitting religion and spirituality back into the fold of medicine under a new secularized medical control. (shrink)

Some affirm, but others deny, that works of fine art, or at any rate certain sorts of them, should be true or probable. This is the question which I investigate in the present essay. It has been debated by philosophers from Plato on, and much can still be learnt from earlier writers, particularly Aristotle. But I have found some recent discussions especially helpful; namely, what Strawson and Hart say about and in connexion with presupposition; Hospers' and Harris' remarks about truth-to (...) and plausibility respectively; and Beardsley's treatment of these matters in his admirable survey of the problems of aesthetics. (shrink)

Doctors are regularly confronted with requests for sterilisation of mentally handicapped people who cannot give consent for themselves. They ought to act in a medical vacuum because there doesn't exist a consensus about a model for decision making on this matter. In this article a model for decision making is proposed, based on a review of the literature and our own research data. We have attempted to select and classify certain factors which could enable us to arrive at an ethically (...) justifiable method of making a medical decision. In doing so we distinguish two major criteria: heredity and parenting competence, and six minor criteria: conception risk, IQ, age, personality, medical aspects and prognosis and finally support and guidance for the mentally handicapped person. The major criteria give rise to a "situation of necessity". In this situation the physician is confronted with a conflict of values and interests. The minor criteria are of an entirely different ethical order. They can only be considered once the major criteria have created a "situation of necessity". Ultimately it comes down to deciding whether the benefits of sterilisation outweigh the drawbacks and whether the means are appropriate to the end, where efficient contraception is the end and irreversible sterilisation is the means. (shrink)

We isolate two abstract determinacy theorems for games of length $\omega_1$ from work of Neeman and use them to conclude, from large-cardinal assumptions and an iterability hypothesis in the region of measurable Woodin cardinals thatif the Continuum Hypothesis holds, then all games of length $\omega_1$ which are provably $\Delta_1$ -definable from a universally Baire parameter are determined;all games of length $\omega_1$ with payoff constructible relative to the play are determined; andif the Continuum Hypothesis holds, then there is a model of (...) ${\mathsf{ZFC}}$ containing all reals in which all games of length $\omega_1$ definable from real and ordinal parameters are determined. (shrink)

Takeuti introduced an infinitary proof system for determinate logic and showed that for transitive models of Zermelo-Fraenkel set theory with the Axiom of Dependent Choice that contain all reals, the cut-elimination theorem is equivalent to the Axiom of Determinacy, and in particular contradicts the Axiom of Choice. We consider variants of Takeuti's theorem without assuming the failure of the Axiom of Choice. For instance, we show that if one removes atomic formulae of infinite arity from the language of Takeuti's proof (...) system, then cut elimination is equivalent to a determinacy hypothesis provable, e.g., in ZFC + “there are infinitely many Woodin cardinals.” A slight extension of the proof system admits cut elimination for countable sequents under the same assumptions. A simple modification of the proof system yields analogs of the results above for the Axiom of Real Determinacy and uncountably many Woodin cardinals. (shrink)