Set theory -- Logic -- Proofs -- Functions -- Group theory -- Linear algebra.

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing "the laws of (...) thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language. (shrink)

This article seeks to clarify the concept of progress in philosophy. It treats progress as a kind of development. But not every development is a progress. When we talk about progress, what really matters is the direction of development. In some cases it is relatively easy to reach agreement about this direction. But not in the case of philosophy, if we abstract it from the obvious and the trivial, like the number of books on philosophy. As a result, the article (...) concludes that there cannot be progress in philosophy. Instead we see a continual multiplication of interpretations. (shrink)

Logic is usually presented as a tool of rational inquiry; however, many logicians in fact treat logic so that it does not serve us, but rather governs us – as rational beings we are subordinated to the logical laws we aspire to disclose. We denote the view that logic primarily serves us as logica serviens, while denoting the thesis that it primarily governs our reasoning as logica dominans. We argue that treating logic as logica dominans is misguided, for it leads (...) to the idea of a “genuine” logic within a “genuine” language. Instead of this, we offer a naturalistic picture, according to which the only languages that exist are the natural languages and the artificial languages logicians have built. There is, we argue, no language beyond these, especially none that would be a wholesome vehicle of reasoning like the natural languages and yet be transparently rigorous like the artificial ones. Logic is a matter of using the artificial languages as idealized models of the natural ones, whereby we pinpoint the laws of logic by means of zooming in on a reflective equilibrium. (shrink)

We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability (...) of formulas with coefficients also works via verification of admissibility. (shrink)

ABSTRACT Two models of the Aristotelian syllogistic in arithmetic of natural numbers are built as realizations of an old Leibniz idea. In the interpretation, called Scholastic, terms are replaced by integers greater than 1, and s.Ap is translated as “s is a divisor of p”, sIp as “g.c.d. > 1”. In the interpretation, called Leibnizian, terms are replaced by proper divisors of a special “Universe number” u < 1, and sAp is translated as “s is divisible by p”, sIp as (...) ‘l.c.m. < u”. Both interpretations are proved to be adequate to the Aristotelian syllogistic. They are extended to syllogistic including term negation and term conjunction as well. (shrink)

The purpose of the study is to establish a causal relationship of job satisfaction depending on the average number of employees, the level of wages, the number of applications and the time factor. The article deals with the problem of modeling socio-economic satisfaction with the work of employees in the provision of public services. Based on the correlation analysis, linear and nonlinear models of the interrelationships of factors related to this problem are formed. Econometric models have been developed to effectively (...) assess the level of satisfaction of employees in the provision of public services. The scientific novelty lies in the study of new models that are statistically superior to domestic developments in this field of activity. As a result, the most significant factors affecting the level of job satisfaction were identified. (shrink)

The Cell Cycle Ontology (CCO) has the aim to provide a ‘one stop shop’ for scientists interested in the biology of the cell cycle that would like to ask questions from a molecular and/or systems pe...

. We demonstrate that a comprehensive nonstandard set theory can be developed in the standard $\displaystyle{\in}$ -language. As an illustration, a nonstandard ${\sf Law of Large Numbers}$ is obtained.

We study the problem of finding a basis for all rules admissible in the intuitionistic propositional logic IPC. The main result is Theorem 3.1 which gives a basis consisting of all rules in semi-reduced form satisfying certain specific additional requirements. Using developed technique we also find a basis for rules admissible in the logic of excluded middle law KC.

This article seeks to show how several rhetorical tools were used and, in fact, played a central role in the argumentation advanced by Niles Eldredge and Stephen Jay Gould in their 1972 seminal article on the theory of Punctuated Equilibria. It is analyzed how Eldredge and Gould proceeded through three steps that, sequentially integrated, made their argument compelling. It is shown how they made use of analogies, metaphors and other rhetorical tools. It is sustained that they began by priming the (...) reader to distrust the current interpretation of the fossil record offered by most paleontologists and then, in a second step, they used specific visual representations in order to suggest that the competitor theory was committed to the idea of an even and slow evolution at a constant rate, an image utilized by them as straw man. Finally, it is analyzed how, in their third step, Eldredge and Gould made use of several rhetorical arguments to present their theory as new for paleontology while, at the same time, placing it well inside the frame of the modern synthesis, and how they also managed to present their theory as more promising and capable of making predictions for future researches than the competitor theory. (shrink)

- Vibrations of light, a sound, a smell, taste, heat and volume transfer energy information (sense) of physical object to consciousness of the person. - Change of physical parameters of object is perceived by the person in time as event. - Event is the information on current of "invisible" process of transfer of energy between cooperating objects. - Process this ordered movement of energy from one object to other object, changing their physical parameters. - Phases of a condition of processes (...) on the Earth describe laws of dialectics. - The-certain alternation of phases of development of process shows the order of movement of energy incooperating objects (paper pic. N3) - Laws of dialectics it is laws of harmony of succession of events. - Harmony of development of process (movement of energy) is financially(material) perceived by the person as development of event. - A sign on great limit (taiczi) philosophy Dao are graphic expression of laws of dialectics. - Energy of the Sun gives rise to all processes on the Earth. - The INFORMATION is a part of energy reflected or rediated by object written down in memory of the person, a material, space. (shrink)

Este artigo visa a contribuir para a reflexão ética a partir da filosofia de Cassirer. Trata-se de analisar se a denominada "ampliação" que Cassirer realizou da epistemologia kantiana pode ser estendida à esfera moral. Ou seja, se há um paralelo entre o problema epistemológico e a moral em Kant, e se Cassirer explora o problema epistemológico por outra perspectiva e que consequências isso acarreta para o âmbito moral. Embora Cassirer, em sua produção intelectual, não tenha explorado sistematicamente a questão ética, (...) os problemas com os quais se preocupou, no decorrer de sua produção filosófica, fornecem subsídios importantes para uma reflexão nesse sentido. Para Cassirer, o ser humano é um animal symbolicum, um ser que cria signos e símbolos e, dessa forma, constrói a realidade. Tal fato implica, para ele, a coexistência de diferentes formas de compreensão do mundo igualmente válidas, diferentes formas simbólicas, como ele denomina, por exemplo, o mito, a religião, a ciência. Pensar a ética na perspectiva da Filosofia das formas simbólicas implica considerar a coexistência de tais construções simbólicas, bem como a tolerância ante a consequente diversidade epistemológica e axiológica, destacando-se o fundamental papel da filosofia nesse processo. (shrink)

The author examines Herzen's political outlook as reflected in his journal Kolokol and discusses his relationships with other revolutionary and reformist Russian thinkers of his time.

In trying to control various aspects concerning utterance production in multi-party human–computer dialogue, argumentative considerations play an important part, particularly in choosing appropriate lexical units so that we fine-tune the degree of persuasion that each utterance has. A preliminary step in this endeavor is the ability to place an ordering relation between semantic forms (that are due to be realized as utterances, by the machine), concerning their persuasion strength, with respect to certain (explicit or implicit) conclusions. Thus, in this article, (...) we propose a mechanism for assessing utterances, in terms of their argumentative force. The framework designed conflates insights from Asher and Lascarides’ SDRT (“Segmented Discourse Representation Theory”), and from Anscombre and Ducrot’s AT (“Argumentation Theory”). These mechanisms are included in a language generation component of a multi-party dialogue system for book reservation applications (i.e., a “virtual librarian”), and thus evaluated via typical human–machine conversations. (shrink)

Философия науки возникла в итоге неспособности теории познания ответить на важные вопросы, вставшие перед научным сообществом в конце XIX века. И в дальнейшем философия науки и теория познания шли каждая свом путем, оказывая друг на друга немалое влияние, но ставя и решаявесьма разные задачи. Главным различием между ними является то, что эпистемология является теоретическим видом знания, тогда как философия науки – посттеоретическая дисциплина. Эпистемология – это теория, включающая в себя объяснительную схему, это философский проект познания, это дисциплина, содержащая набор запретов (...) и предписаний. Философия науки представляет собой изучение научногопоиска как состоявшегося реального события, а также экспертную оценку результатов. Философия науки предполагает критическое и рефлексивное сравнение проекта и результата, тогда как теория познания совершенствует нормативы и регулятивы познавательной активности. Там, где теория познания создает метод и сама опирается на метод, философия науки обходится историко‐критической рефлексией, логико-грамматическим анализом, поиском культурных или социальных детерминант. (shrink)

Este livro é o resultado do II Encontro Nacional de Pesquisadores em Filosofia e Psicanálise, realizado em 2006 na Universidade de São Paulo, e reúne vários pesquisadores em torno de três temas - a filosofia após Freud, os problemas ...

Trata-se de abordar o problema da teoria hegeliana da linguagem a partir do ponto onde pragmática e ontologia se articulam. Isto exige uma reflexão sobre a maneira com que Hegel organiza as dinâmicas da pragmática da linguagem levando em conta os modos de manifestação de uma negação ontológica no interior do campo de experiências lingüísticas da consciência.

Explaining his love of philosophy, Slavoj Žižek notes that he ‘secretly thinks reality exists so that we can speculate about it’. This article takes the view that links between mathematics and continental philosophy are part of reality, the reality of philosophy and its history, and hence require speculation. Examples from the work of Jacques Derrida and Henri Poincaré are discussed.

For a better understanding of the present situation in Romania it is necessary to go beyond the limited political approach, i.e., to seek the germs of contemporary conflicts in the history of that country — especially in the history of the Romanian Communist Party. We have to mink about the origins of Romanian communism in 1921, when the Socialist Left split into a strong and active radical minority and a “reformist” traditional Social-Democratic wing. The situation of the Left in Romania (...) was further complicated by an ethnic syncretism. Because of the incorporation of Transylvania, Bessarabia, and North Bukovinaand the subsequent national, social, economic, and cultural claims of the Hungarian, German, Jewish, Ukrainian, and Russian minorities, the ethnic problem became an obsession during the inter-war period. (shrink)

Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – (...) for restricted cases, to show the problems arising in the course of study. (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 personification of wisdom with golden hair and a radiant aura echoes both the eternal feminine and the world soul. Rooted in Christian and Jewish mysticism, Eastern Orthodox iconography, Greek philosophy, and European romanticism, the Sophiology that suffuses Solovyov's philosophical and artistic works is both intellectually sophisticated and profoundly inspiring. Judith Deutsch Kornblatt brings together key texts from Solovyov's writings about Sophia: poetry, fiction, drama, and philosophy, all extensively annotated and some available in English for the first time (with assistance (...) from the translators Boris Jakim and Laury Magnus)."--Amazon website. (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...

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...

Less known in the anglophone world than Berdyaev (who was a pupil of his), or Martin Buber, Vladimir Solovyov (1853-1900), philosopher, mystic, poet, has nevertheless a contribution of the first importance to offer to Western scholarship. He came from a rich and not yet fully understood tradition; his erudition was stupendous. Like his predecessors he was extremely sensitive to such problems as the religious meaning of history, of creativity, of culture. It is important to emphasize a general link between (...) Solovyov and preceding currents of Russian thought, for his Christian philosophy in a sense embraces them all. Dostoyevsky and Leo Tolstoy sat at his feet. Godmanhood is the problem of restoring all mankind; it is a concept of salvation as a process of becoming divine. The differences between the Orthodox, Roman, and Anglo-Catholic and many of the Protestant Churches are not found in relation to the great dogmas or articles of the creed. Solovyov has a vital and unique message to Christians of all denominations; he offers a basis for reunion rarely suggested in Western Christianity. (shrink)

ABSTRACTThe concept of Methodenstreits is used to analyse the relationship between behavioral and mainstream economics. A Methodenstreit is understood by the authors as a dispute between the more a...

PurposeThe purpose of this paper is to present implications of the seller's ability to bid in the four classical auction forms, with independent private values: English, Dutch, first‐ and second‐price auctions.Design/methodology/approachUnder each auction form, the identity of the winning bidder and the expected winning bid are compared between the case when the seller may bid and when he cannot, using equilibrium bidder strategies. The seller's incentive to bid is evaluated.FindingsThe strategies and the welfare results differ with auction type and underlying (...) information assumptions – bidders are either aware or unaware of the seller's ability to bid. In the Dutch and the first‐price auctions, seller‐bidding does not affect any classical results. In the English and the second‐price auctions, it leads to no lower expected prices than without it and higher prices with positive probability. In the English and the second‐price auctions, the seller bids above his reservation value and may unintentionally win the auction. These auctions result in inefficiency with positive probability.Practical implicationsThe English and the second‐price auctions are the most common real‐world auctions. In these auctions, the seller's ability to bid – secretly or publicly – redistributes welfare among participants and introduces a possibility of inefficiency. Making this ability publicly known does not solve the latter problem. Auctioneers must prevent the seller from bidding, or must select a different auction form when seller‐bidding is anticipated.Originality/valueThe paper clarifies to regulators, auction designers, bidders, and other readers which auction forms are susceptible to subversion by seller‐bidding and what the potential damages are. (shrink)