Foundations of Science recently published a rebuttal to a portion of our essay it published 2 years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his 2005 book, Conflicts between generalization, rigor, and intuition. He further argues that our attempt to show that Cauchy is part of a long infinitesimalist tradition confuses text with context and thereby misunderstands the significance of Cauchy’s use of infinitesimals. Here we defend our original analysis of various misconceptions and misinterpretations concerning (...) the history of infinitesimals and, in particular, the role of infinitesimals in Cauchy’s mathematics. We show that Schubring misinterprets Proclus, Leibniz, and Klein on non-Archimedean issues, ignores the Jesuit context of Moigno’s flawed critique of infinitesimals, and misrepresents, to the point of caricature, the pioneering Cauchy scholarship of D. Laugwitz. (shrink)

Russian Orthodoxy during the twentieth century presented a rich and varied body of thought about the nature of humanity and the human condition. This article surveys the major thinkers within this tradition, beginning with its background in the Slavophile movement and culminating in the work of more recent Orthodox thinkers such as Sergei Bulgakov, Georges Florovsky, Vladimir Lossky, and Alexander Schmemann.

This book constitutes the refereed proceedings of the 20th International Conference on Logic Programming, ICLP 2004, held in Saint-Malo, France in September 2004. The 28 revised full papers and 16 poster papers presented together with 2 invited papers were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on program analysis, constraints, alternative programming paradigms, answer set programming, and implementation.

[From an Evolutionary Point of View: The Concept of Evolution in Contemporary Philosophy].

David Miller v pracích Critical Rationalism a Out of Error se jako jeden z mála Popperových žáků snaží nejen o vysvětlení a obhájení Popperova kritického racionalismu, ale zároveň i o jeho další rozvinutí. Millerovo znovunastolení kritického racionalismu ovšem předpokládá, že k racionálnímu jednání není třeba žádných „dobrých důvodů“, ale jen argumentů. Uvedená stať se zaměřuje právě na tuto otázku existence tzv. „dobrých důvodů“ ve spojení s racionalitou a racionálním rozhodováním a ukazuje, že Millerův požadavek neexistence „dobrých důvodů“ je nejen příliš (...) radikální, ale i nepřijatelný z hlediska Popperova nebo Musgravova pojetí kritického racionalismu. (shrink)

Stať se zabývá diskusemi o epistemologicko-metodologické roli simulací v soudobé vědě. Soustředí se nejprve na aktuálnost těchto diskusí v současné metodologii vědy a následně na její návaznost na určitou myšlenkovou tradici z osmdesátých let 20. století, kdy diskuse kolem modelování vyvolaly řadu otázek zpochybňujících tradiční pojmové distinkce, především mezi experimentem a teorií. Stať se přiklání v rámci těchto diskusí k názorům, které řadí simulace k novým a specifickým nástrojům vědy, jež také vyžadují novou a specifickou metodologii a epistemologické postavení. Pro (...) podporu této názorové pozice jsou uvedeny některé aktuální analýzy konkrétních příkladů simulací a jejich specifického postavení v moderní vědě. (shrink)

Physicalism as a metaphysical or ontological concept has maintained a dominant position since the second half of the last century to the present day. The claim that everything is physically constituted often accompanies microphysical reductionism, which assumes the existence of fundamental laws to which everything is reducible. In this context, a question regarding the status and possible autonomy of the laws of special sciences arises. The article focuses on the basic philosophical discussions between the strong, weak, and non-reductive physicalism that (...) treat the laws of special sciences in different ways, but none of which can be considered sufficiently convincing and successful. The article seeks to prove the existence of a universal mechanism that leads to the emergence of new and complex entities and regulations of their behaviour, thus justifying the autonomous status of special sciences and laws. (shrink)

A definable pair of disjoint non-OD sets of reals exists in the Sacks and ????0-large generic extensions of the constructible universe L. More specifically, if a∈2ω is eith...

The keynote idea of the theses is contained in the author’s assumption that modern philosophy doesn’t meet its claiming pretensions: to be universal form of knowledge. First of all philosophy is connected not with knowledge but with ideas and secondly being authentic it “exists only in everyday life”.1 In orderthat philosophy could realize its innate essence corresponding conditions of social being should exist but they are still absent and therefore philosophy is absent as well. Its place is occupied by metaphysics (...) which is free movement of thinking that has no definiteness as the condition of being of any form of thought. That iswhy we watch crisis state of “philosophy” which becomes apparent in vagueness of its subject: “philosophy is not only one, there are many of them”. The author supposes that philosophy as the highest relation of mankind to objective reality is the only one. Philosophy lowered down from the heaven (Platon, Ciceron) in the field of human being must raise people not only to purity of thought, but mainly to purity of their activity both with each other and with nature. Then real interaction of men and nature will take place. This will be the beginning of spiritualization of the Universe. It may exist only under the conditions of social uniformity as historical form of Weltanschauung (world outlook) that removes religious form. Realization of its being supposes fundamental change of social life. It is necessary that private property should be replaced with social property in the sphere of social production. Only under these conditions philosophy may appear and exist as historical form of Weltanschauung. (shrink)

This volume offers a wide range of both reconstructions of Nikolai Vasiliev’s original logical ideas and their implementations in the modern logic and philosophy. A collection of works put together through the international workshop "Nikolai Vasiliev’s Logical Legacy and the Modern Logic," this book also covers foundations of logic in the light of Vasiliev’s contradictory ontology. Chapters range from a look at the Heuristic and Conceptual Background of Vasiliev's Imaginary Logic to Generalized Vasiliev-style Propositions. It includes works which cover Imaginary (...) and Non-Aristotelian Logics, Inconsistent Set Theory and the Expansion of Mathematical Thinking, Plurivalent Logic, and the Impact of Vasiliev's Imaginary Logic on Epistemic Logic. The Russian logician, Vasiliev, was widely recognized as one of the forerunners of modern non-classical logic. His "imaginary logic" developed in some of his work at the beginning of 20th century is often considered to be one of the first systems of paraconsistent and multi-valued logic. The novelty of his logical project has opened up prospects for modern logic as well as for non-classical science in general. This volume contains a selection of papers written by modern specialists in the field and deals with various aspects of Vasiliev's logical ideas. The logical legacy of Nikolai Vasiliev can serve as a promising source for developing an impressive range of philosophical interpretations, as it marries promising technical innovations with challenging philosophical insights. (shrink)

El presente trabajo se propone rescatar la resistencia y la crítica al poder imperial romano del libro del Apocalipsis como una fuente fundamental para la teología moral cristiana, que lo convirtieron en un foco de luz que ilumina el camino de la conducta humana hacia un mundo mejor. Al mismo tiempo, ofrece pautas para la defensa de la vida en un entorno donde los totalitarismos políticos, económicos y religiosos atentan contra ella. Además, quiere destacar dicha resistencia y crítica como uno (...) de los factores generadores, y por tanto centrales, de la teología del Apocalipsis. Para ello se utilizarán los principios metodológicos de la lectura contextual que parten de la convicción según la cual el texto es una expresión de las vivencias comunitarias del hagiógrafo y de su actitud ante las circunstancias sociales que lo provocaron. El libro busca afectar el entorno, pero este también configura el contenido de la obra escrita. En un segundo momento, con el método se indaga qué de ese momento histórico puede iluminar el presente del lector. En el caso del Apocalipsis, se elegirán los textos en los que el autor presente los temas y actores principales de la trama, a saber: el ser supremo sentado en el trono, el cordero y el mal —simbolizado específicamente en el tercer jinete—, ya que en ellos se juega el mensaje del libro, la soberanía divina que humaniza o la soberanía diabólica deshumanizante. (shrink)

The travelling salesman problem (TSP) belongs to the class of NP-hard problems, in which an optimal solution to the problem cannot be obtained within a reasonable computational time for large-sized problems. To address TSP, we propose a hybrid algorithm, called GA-TCTIA-LBSA, in which a genetic algorithm (GA), tour construction and tour improvement algorithms (TCTIAs) and a list-based simulated annealing (LBSA) algorithm are used. The TCTIAs are introduced to generate a first population, and after that, a search is continued with the (...) GA. The problem of premature convergence of the GA to local optimum is tackled by a method called social disaster technique. Afterwards, the LBSA is applied to generate a new population based on one of two proposed operators called packing and judgement day. The proposed algorithm is implemented in the MATLAB environment, and its two variants, called GA-TCTIA-LBSA packing and GA-TCTIA-LBSA judgement day, are tested on symmetric and asymmetric instances from TSPLIB. The overall results demonstrate that the proposed GA-TCTIA-LBSAs offer promising results, particularly for small-sized instances. (shrink)

The article considers the basic arguments of some “critics of epistemology”, according to which the philosophical analysis of the problems associated with the processes of cognition (including science) should be eventually replaced by the study of these problems by means of special cognitive sciences. It is shown that these arguments are in part incorrect and in part can be seen as an indication of the real difficulties in the modern philosophy of cognition. A future philosophical epistemology is associated with the (...) reform of its conceptual apparatus, the methodological arsenal and problem field. An interaction between epistemology and the sciences dealing with cognition is the only and necessary way of development for philosophical epistemology. There are two ways of such interaction. Firstly, there is an analysis of scientific discussions, on the basis of which one identifies new opportunities to overcome the well-known philosophical controversies (between rationalism and empiricism, realism and constructivism, fundamentalism and relativism, etc.). On this way, epistemology moves into a position of horizontal moderation of interdisciplinary discourse and creates a trading (Harry Collins). Secondly, epistemology provides a rational criticism of the foundations of special sciences, and selects semantic levels in the content of its own categories (truth, rationality, agent, object, etc.) referring to different cognitive practices. These practices are evaluated normatively in terms of a value perspective of modern culture. Both ways are complementary to each other. (shrink)

We consider games over a finite alphabet with Gurevich-Harrington's winning conditions and restraints as in Yakhnis-Yakhnis . The game tree, the Gurevich-Harrington's kernels of the winning condition and the restraints are defined by finite automata. We give an effective criterion to determine the winning player and an effective presentation of a class of finite automata defined winning strategies.Our approach yields an alternative solution to the games considered by Büchi and Landweber . The BL algorithm is an important tool for solving (...) effectively presented games. The differences between the BL and our algorithms are as follows. Our algorithm is uniformly applicable to winning sets that correspond to boolean combinations of BL winning conditions, while the BL algorithm requires a transformation of such boolean combinations into a single BL condition. Our algorithm directly applies to a larger class of game trees for a given game alphabet than does the BL one. We describe Büchi-Landweber's class of winning conditions in a more transparent way by using finite automata and Gurevich-Harrington's form of winning conditions. Our algorithms that determine the winner of the game and find a winning strategy, are based on a translation of the events in the game in terms of the transition table of the automaton representing the game. This automaton differs from the ones that represent BL winning conditions. Both algorithms need further investigation.The algorithm determining the winner in the game, can be used as a verifier of concurrent programs. This is because programs can be viewed as strategies in Gurevich-Harrington's games and program specifications could be regarded as winning conditions for such games. The algorithm which finds a winning strategy could be used as a basis for automated concurrent program design.The present paper is a sequel to Annals of Pure and Applied Logic 48 277–297. (shrink)

Qu'est-ce que l'ironie? Quelles en sont les formes? Quels en sont les pièges aussi? Autant de délicates questions auxquelles l'auteur répond, non sans ironie lui-même, avec l'aide d'une infinité d'exemples qui montrent son immense culture, musicale aussi bien que philosophique. Sommairement, qu'est-ce que l'ironie, sinon la conscience, mais une bonne conscience joyeuse, ce en quoi elle se distingue de l'hypocrisie? Pas d'humour sans amour, ni d'ironie sans joie. L'ironie, en somme, sauve ce qui peut être sauvé. Elle est mortelle aux (...) illusions ; partout elle tisse les toiles d'araignée où se prendront les pédants, les vaniteux et les grotesques. " Ironie, vraie liberté! ", s'écrie Proudhon au fond de sa cellule de Sainte-Pélagie. L'ironie remet tout en question ; par ses interrogations indiscrètes elle ruine toute définition, dérange à tout moment la pontifiante pédanterie prête à s'installer dans une déduction satisfaite. Grâce à l'ironie, la pensée respire plus légèrement quand elle s'est reconnue, dansante et grinçante, dans le miroir de la réflexion. (shrink)

This note is about the “calculational style” of presenting proofs introduced by Dijkstra and Scholten and adopted in some books on theoretical computer science. We define the concept of a calculation, which is a formal counterpart of the idea of a calculational proof. The definition is in terms of a new formalization DS of predicate logic. Any proof tree in the system DS can be represented as a sequence of calculations. This fact shows that any logically valid predicate formula has (...) a calculational proof. (shrink)

This article discusses the connection between the ideas of Fyodor M. Dostoevsky and Vladimir S. Solovyov on the need for cultural and moral transformation of those who would claim to participate in...

Philosopher Vladimir Jankélévitch has only recently begun to receive his due from the English-speaking world, thanks in part to discussions of his thought by Jacques Derrida, Emmanuel Lévinas, and Paul Ricoeur. His international readers have long valued his unique, interdisciplinary approach to philosophy’s greatest questions and his highly readable writing style. Originally published in 1967, Le Pardon, or Forgiveness, is one of Jankélévitch’s most influential works. In it, he characterizes the ultimate ethical act of forgiving as behaving toward the (...) perpetrator as if he or she had never committed the action, rather than merely forgetting or rationalizing it—a controversial notion when considering events as heinous as the Holocaust. Like so many of Jankélévitch’s works, Forgiveness transcends standard treatments of moral problems, not simply generating a treatise on one subject but incorporating discussions of topics such as free will, giving, creativity, and temporality. Translator Andrew Kelley masterfully captures Jankélévitch’s melodic prose and, in a substantive introduction, reviews his life and intellectual contributions. Forgiveness is an essential part of that legacy, and this indispensable English translation provides key tools for understanding one of the great Western philosophers of the twentieth century. (shrink)

My dear Aleksandr!I have finally found some quiet time for a slow and attentive read of your article “The Beginning of the Black Notebooks.”1 I very much liked the article, especially for your trul...

Le merite de cette etude est son refus de reduire la theologie d'Eckhart au developpement systematique d'une seule notion fondamentale. Mais cette theologie n'y est pas non plus concue comme une sorte d'eclectisme ou chacune de ces notions aurait sa place et trouverait successivement son tour. S'il y a chez Eckhart une notion fondamentale, c'est celle de Dieu, ou, plutot, c'est celle de l'ineffabilite de Dieu. Dieu est l'etre, assurement, mais n'est-il pas plutot l'Un? Ou l'Intellect? Comprendre qu'il est chacune (...) de ces perfections, absolument, purement, donc en apparence a l'exclusion des autres, c'est justement en quoi consiste l'ignorance transcendante qui eleve Dieu au-dela de toutes les affirmations. Vladimir Lossky a ainsi voulu mettre en lumiere le refus qu'oppose Eckhart a toute tentative d'inclure la divinite dans une notion qui se tiendrait pour suffisante a la definir. (shrink)

This report of the roundtable that took place on 25 November 2021 at The Peoples’ Friendship University of Russia attempts to explain the obvious growth of interest in Neo-Kantian philosophy in general and the philosophy of the head of the Marburg School of Neo-Kantianism, Hermann Cohen, in particular. In their contributions, the participants in the discussion demonstrated that the current interest in Neo-Kantianism does not solely or even largely have to do with the history of philosophy but rather with the (...) relevance of many of the ideas of Marburg Neo-Kantianism for the modern theory of cognition, the philosophy of culture, ethics and the philosophy of religion. The course of the discussion highlighted the relevance of Cohen’s theory of cognition based on logic and rationality. The main outcome of the discussion was the conviction that the potential of many of Cohen’s ideas has yet to be fully tapped and there are grounds for considering them to be heralds of a new philosophy which, in many of its features, is only maturing. (shrink)

Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledge-intensive applications. ASP programs consist of rules that look like Prolog rules, but the computational mechanisms used in ASP are different: they are based on the ideas that have led to the creation of fast satisfiability solvers for propositional logic.

Recently, psychologists have explored moral concepts including obligation, blame, and ability. While little empirical work has studied the relationships among these concepts, philosophers have widely assumed such a relationship in the principle that “ought” implies “can,” which states that if someone ought to do something, then they must be able to do it. The cognitive underpinnings of these concepts are tested in the three experiments reported here. In Experiment 1, most participants judge that an agent ought to keep a promise (...) that he is unable to keep, but only when he is to blame for the inability. Experiment 2 shows that such “ought” judgments correlate with judgments of blame, rather than with judgments of the agent’s ability. Experiment 3 replicates these findings for moral “ought” judgments and finds that they do not hold for nonmoral “ought” judgments, such as what someone ought to do to fulfill their desires. These results together show that folk moral judgments do not conform to a widely assumed philosophical principle that “ought” implies “can.” Instead, judgments of blame play a modulatory role in some judgments of obligation. (shrink)

[The theory of relativity and the relativity of theory].

Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...) S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics have fmp w.r.t. admissibility. (shrink)