The article details the biography and teachings of Śāntarakṣita, a famous Buddhist scholar and enlightener, a leading figure in the spread of Buddhism in Tibet and his closest student Kamalaśīla. Śāntarakṣita is the author of several treatises, including Compendium of Entities - Tattvasaṃgraha, a monumental work that can rightfully be called the Buddhist Philosophical Encyclopedia, consisting of 26 sections, in which all key philosophical schools of India, namely: Mīmāṃsa, Vedānta, Sāṃkhya, Yoga, Nyāya, Vaiśeṣika, Lokāyata, Jainism and Buddhism of other sects) (...) are analyzed and subsequently refuted. Kamalaśīla is a direct student of Śāntarakṣita, the author of a word-to-word commentary on the teacher's Tattvasaṃgraha. The article also dwells on the history of the discovery and study of the Tattvasaṃgraha. The novelty of the study lies in a full-length encyclopedic presentation of the philosophy of Śāntarakṣita and his immediate student Kamalaśīla. A special contribution of the author to the study of the topic is the demonstration that Śāntarakṣita, as a representative of the Yogācāra-Madhyamaka school, worked in the genre of synthesis of the teachings of Yogācāra and Madhyamaka, and in the field of epistemology he continued the theories of Dignāga and Dharmakīrti. (shrink)

Introduction A good example of emergentism - interpreted by M. Siderits [1] as - Buddhist reductionism) is an excerpt from the dialogue between King Milinda[4] and the monk Nāgasena[5] about the self, which is part of the text close to the Abhidhamma tradition entitled "Milindapaha". The text was published by V. Trenckner in 1880 in [2] and translated into English by T.W. Rhys Davids [3] in the series "Sacred Books of the East". Furthermore, there is an English translation by I. (...) B. Horner [4] and Bhikkhu Pesala [5] and into Russian by A.V. Paribok [6]. There are also German [7] and French translations [8; 9]. Yet the classical translation by Rhys Davids is currently largely obsolete. Paribok's translation into Russian is not convenient for practical use as it would need to be further translated into English, and this double translation, which is not very good from the point of view of the philological approach to the text. We have therefore decided to make our own, new translation of the passage from "Milindapaha", in which the dialogue about the self is being held. (shrink)

ʻAl ḥinukh ha-yeladim -- ʻAl ḥinukh le-midot ṭovot.

The article examines the controversy between the “orthodox” Indian philosophical school Vaiśeṣika and one of the greatest Buddhist philosophers - Vasubandhu on the existence of subject as a reality. The discussion is investigated on the example of the text “Pudgalaviniścaya”. PV of Vasubandhu - literally “Study on the Self”, or “pudgala” - is traditionally considered the 9th chapter of “Abhidharmakośabhaṣya” of the same author and is one of the most important polemical treatises on the self, or ātman, in Buddhist philosophy. (...) Among the issues discussed are the famous “epistemological argument”, the ability of recall and perception, how a difference between moments of consciousness is possible, whether the substrate for consciousness is necessary. One of the strategies of Vasubandhu is that he tries to find internal contradictions in the arguments of opponents. We can say that the main argument of Vasubandhu is aimed at justifying the mechanism of the cause-and-effect occurrence of all phenomena. If the Vaiśeṣikas proceed from their logic about the need for a substance for qualities, then Vasubandhu tries to persuade them to his side and offer a fundamentally new explanatory model, according to which there are only sequence-like moments-phenomena that flow from each other according to the law of cause and effect. (shrink)

Śiḥot maran ha-Mashgiaḥ Mohari Leṿinshṭain, zatsal -- Ḥidushe torato ʻa. Mas. B.ḳ. ṿe-liḳuṭim -- Leḳeṭ mi-maʼamraṿ mi-moreshet Daṿid Heber ṿe-ʻinyene ha-shaʻah.

We suggest an algebraic approach to proof-theoretic analysis based on the notion of graded provability algebra, that is, Lindenbaum boolean algebra of a theory enriched by additional operators which allow for the structure to capture proof-theoretic information. We use this method to analyze Peano arithmetic and show how an ordinal notation system up to 0 can be recovered from the corresponding algebra in a canonical way. This method also establishes links between proof-theoretic ordinal analysis and the work which has been (...) done in the last two decades on provability logic and reflection principles. Because of its abstract algebraic nature, we hope that it will also be of interest for non-prooftheorists. (shrink)

The first volume in the new critical edition of Lev Shestov's work in English, which I have been asked to coordinate. The volume includes my preface and annotations.

Progressions of iterated reflection principles can be used as a tool for the ordinal analysis of formal systems. We discuss various notions of proof-theoretic ordinals and compare the information obtained by means of the reflection principles with the results obtained by the more usual proof-theoretic techniques. In some cases we obtain sharper results, e.g., we define proof-theoretic ordinals relevant to logical complexity Π1 0 and, similarly, for any class Π n 0 . We provide a more general version of the (...) fine structure relationships for iterated reflection principles (due to U. Schmerl [25]). This allows us, in a uniform manner, to analyze main fragments of arithmetic axiomatized by restricted forms of induction, including IΣ n , IΣ n − , IΠ n − and their combinations. We also obtain new conservation results relating the hierarchies of uniform and local reflection principles. In particular, we show that (for a sufficiently broad class of theories T) the uniform Σ1-reflection principle for T is Σ2-conservative over the corresponding local reflection principle. This bears some corollaries on the hierarchies of restricted induction schemata in arithmetic and provides a key tool for our generalization of Schmerl's theorem. (shrink)

By a result of Paris and Friedman, the collection axiom schema for $\Sigma_{n+1}$ formulas, $B\Sigma_{n+1}$ , is $\Pi_{n+2}$ conservative over $I\Sigma_n$ . We give a new proof-theoretic proof of this theorem, which is based on a reduction of $B\Sigma_n$ to a version of collection rule and a subsequent analysis of this rule via Herbrand's theorem. A generalization of this method allows us to improve known results on reflection principles for $B\Sigma_n$ and to answer some technical questions left open by Sieg (...) [23] and Hájek [9]. We also give a new proof of independence of $B\Sigma_{n+1}$ over $I\Sigma_n$ by a direct recursion-theoretic argument and answer an open problem formulated by Gaifman and Dimitracopoulos [8]. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In this paper, I attempt to describe Mark Burgin’s results in non-Diophantine mathematics, which are important for the foundation of mathematics and its application in quantum field theory. In particular, the elimination of divergences in quantum electrodynamics is described.

From the institutional inauguration of the discipline in 1972, philosophy of sport tends to expand, spreading itself around the world from one country to another, and including new philosophical in...

At IAPS Ljubljana conference (September 2007) Dag Vidar Hanstad and Sigmund Loland presented a paper on elite-level athletes' duty to provide information on their whereabouts, to decide between two opposing positions: is this WADA demand justifiable anti-doping work or an indefensible surveillance regime? They concluded that on moral grounds this regime is conditionally acceptable, the condition being the acceptability of a general framework and objectives embodied in anti-doping global legislative foundations (the World Anti-Doping Code). But, as they said, principled objections (...) against the system have more universal relevance, which has to be taken seriously . To take this ambiguous and intriguing conclusion a step further, I propose a legal rather than ethical approach, from the aspect of constitutional and international human rights law, and the possible clash of two legally acknowledged values - the concept of elite sport without doping, and the concept of individual human rights. This conflict between ideological or moral values and the legality of individual rights is not a novelty. This paper presents three instances of this conflict: Bernard de Mandeville's differentiation between public and private values; Eug ne Sue's parallel legal and civil morals; and the contemporary moralisation of law which conflates legality into morality. The subordination of legality to morality has potentially dangerous consequences: here, Agamben's 'state of exception' comes to mind, with his analysis of potestas and auctoritas. However, in the case of sport and the war against doping, the origin of power is not in the nation state; it originates in civil society's non-governmental national and international bodies recognised as autonomous sources of legal order. (shrink)

It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no ``probability'' for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: a). A ``sleeping pill'' gedanken experiment which makes correspondence between an illegitimate question: ``What is the probability of an outcome of a quantum measurement?'' with a legitimate question: ``What is the probability that ``I'' am in the world corresponding to that (...) outcome?''; b). A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and c). Relativistic causality, which together with explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and ``caring measure'' replacing probability measure are discussed. (shrink)