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.

We deal with a restricted form WC-N' of the weak continuity principle, a version BT' of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N'. BT' + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

In this paper, we deal with compact operators on a Hilbert space, within the framework of Bishop's constructive mathematics. We characterize the compactness of a bounded linear mapping of a Hilbert space into C n , and prove the theorems: Let A and B be compact operators on a Hilbert space H , let C be an operator on H and let α ϵ C . Then α A is compact, A + B is compact, A ∗ is compact, CA (...) is compact and if C ∗ exists, then AC is compact; An operator on a Hilbert space has an adjoint if and only if it is weakly compact. (shrink)

We introduce Kripke models for propositional substructural logics with strong negation, and show the completeness theorems for these logics using an extended Ishihara's canonical model construction method. The framework presented can deal with a broad range of substructural logics with strong negation, including a modified version of Nelson's logic N$^-$, Wansing's logic COSPL, and extended versions of Visser's basic propositional logic, positive relevant logics, Corsi's logics and M\'endez's logics.

Ishiharaʼs boundedness principleBD-N was introduced in Ishihara [5] and has turned out to be most useful for constructive analysis, see e.g. Ishihara [6]. It is equivalent to the statement that every sequentially continuous function from NN to N is continuous w.r.t. the usual metric topology on NN. We construct models for higher order arithmetic and intuitionistic set theory in which both every function from NN to N is sequentially continuous and in which the axiom of choice from NN (...) to N holds. Since the latter is known to be inconsistent with the statement that all functions from NN to N are continuous these models refute BD-N. (shrink)

The article analyzes literature addressing the problem of reality in modern anti-realist theories. The purpose of the review is to expand the circle of researchers, including not only representatives of analytical philosophy, but also those of the phenomenological tradition, since the principle of phenomenological reduction corresponds to the general conceptual attitude of anti-realists, and in methodological terms, phenomenology more consistently implements the program of anti-realism. The principle of anti-realist philosophy is shown as exemplified in solutions of the “difficult problem of (...) consciousness” within analytical philosophy and also in the development of a phenomenological attitude. Such a combination of two, by far the most respectable, philosophical schools makes it possible to more accurately determine the contribution of theorists of both directions to the theory of reality, to identify problematic nodes, internal disagreements and points of intersection of the ideas of phenomenologists and representatives of analytical philosophy in understanding the nature of reality. The works of modern researchers of the problems of reality R. Berghofer, V. Vasyukov, Ya. Ishihara, V. Ladov, L. Makeeva, R. Pils, A. Fursov, D. Chalmers and many others, as well as the works of E. Husserl, W. Quine, H. Putnam’s works, which have become philosophical classics, allow us to clarify the ideas about reality that have developed in the anti-realist discourse from different sides. New studies of the principle of phenomenological reduction by Yu. Himanka and the origins of the formation of phenomenological philosophy by N.V. Motroshilova make it possible to clarify the contribution of phenomenologists to the anti-realist tradition. (shrink)

In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N.

The notions of permutable and weak-permutable convergence of a series|$\sum _{n=1}^{\infty }a_{n}$|of real numbers are introduced. Classically, these two notions are equivalent, and, by Riemann’s two main theorems on the convergence of series, a convergent series is permutably convergent if and only if it is absolutely convergent. Working within Bishop-style constructive mathematics, we prove that Ishihara’s principle BD-|$\mathbb {N}$|implies that every permutably convergent series is absolutely convergent. Since there are models of constructive mathematics in which the Riemann permutation theorem (...) for series holds but BD-|$\mathbb{N}$|does not, the best we can hope for as a partial converse to our first theorem is that the absolute convergence of series with a permutability property classically equivalent to that of Riemann implies BD-|$\mathbb {N}$|. We show that this is the case when the property is weak-permutable convergence. (shrink)

This is a new edition, revised and expanded, of a seminal work in the logic and philosophy of time, originally published in 1968. Arthur N. Prior was the founding father of temporal logic. His work has attracted increased attention in the decades since his death: its influence stretches beyond philosophy and logic to computer science and formal linguistics. Prior's fundamental ideas about the logic of time are presented here along with his investigations into the formal properties of time and tense. (...) Already in 1969 Prior had been planning a new edition of Papers on Time and Tense, to incorporate his more recent work. Because of his untimely death this plan was never followed through--till now. Seven important papers have been added to the original selection, as well as a comprehensive bibliography of his work and an illuminating interview with his widow, Mary Prior, about his life and work. In addition, the Polish logic which made the original book difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book. (shrink)

This is the compelling story of one of the most fascinating thinkers of the twentieth century- a richly toned portrait of a modern-day Thoreau.

Comprehensive work on history and philosophy of Nātha sect in India.

On Yoga; based on various texts on yoga philosophy.

Censurado durante la última década, sale finalmente a la luz Biografía de las ideas, de Isaiah Berlin. El libro pone de relieve el modo en que el sector liberal-conservador más poderoso, con sede en Oxford, ha construido la ficción en torno a la figura de Isaiah Berlin. Sir Isaiah Berlin es conocido como una lumbrera del pensamiento político del siglo XX, uno de los máximos exponentes intelectuales del liberalismo democrático, un pensador moralmente comprometido con la causa de la libertad y (...) la lucha contra el totalitarismo. El lector podrá comprobar que la imagen que se atribuye a Isaiah Berlin es una mitificación, una ficción forjada con el propósito de defender una serie de intereses académicos (y reforzar así la marca Oxford), políticos (en torno al sector liberal-conservador anglosajón) y nacionales (al objeto de cantar la leyenda de una Corona británica comprometida –así dicen– por la defensa de la democracia Occidental). Como Research Fellow en la Universidad de Oxford, el autor ha tenido oportunidad de examinar esta realidad y ver con sus propios ojos cómo los liberal-conservadores fabrican sus mitos. Las conclusiones de este estudio no dejarán indiferentes ni a académicos –principalmente, del área de Historia de las Ideas, y Teoría Política y Moral–, ni a escritores y políticos como el Premio Nobel Mario Vargas Llosa o la marquesa Cayetana Álvarez de Toledo, auto-denominados liberal-conservadores, porque derrumba un pilar de su religión. (shrink)

This article discusses the 2005 OUP biography of Michael Polanyi by William T. Scott and Martin X. Moleski S.J., Michael Polanyi, Scientist and Philosopher . The discussants are N. E. Wetherick, Brian G Gowenlock, and John Puddefoot; Martin X. Moleski, S. J. briefly responds, providing a previously unpulished letter from Polanyi to Reverend Dr. Knox, a Presbyterian mininster.