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)

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...) calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. (shrink)

The first beginnings of modern logic in Croatia are recognizable as early as in the middle of the 19th century in Vatroslav Bertić. At the turn of the 20th century, Albin Nagy, who was teaching in Italy, made contributions to algebraic logic and to the philosophy of logic. At that time, a distinctive author Mate Meršić stood out, also working on algebraic logic. In the Croatian academic philosophy, until the publication of Gajo Petrović's textbook (1964) and the contributions by Heda (...) Festini, a critical or indifferent attitude toward modern logic prevailed. The first comprehensive modern logic textbook in Croatian was written by mathematician Vladimir Devidé (1964), known, for example, for his axiomatizations of natural numbers and classical propositional logic. In the Croatian philosophy of the 1980s and 1990s, influential logicians are Goran Švob and mathematician Zvonimir Šikić. At the turn of the 21st century, logical investigations are being intensified and extended to various branches of the contemporary logic. (shrink)

The Lazy Argument, as it is preserved in historical testimonies, is not logically conclusive. In this form, it appears to have been proposed in favor of part-time fatalism (including past time fatalism). The argument assumes that free will assumption is unacceptable from the standpoint of the logical fatalist but plausible for some of the nonuniversal or part-time fatalists. There are indications that the layout of argument is not genuine, but taken over from a Megarian source and later transformed. The genuine (...) form of the argument seems to be given in different form and far closer to Megarian logical fatalism and its purpose is not to defend laziness. If the historical argument has to lead to a logically satisfactory solution, some additional assumptions and additional tuning is needed. (shrink)

The essay presents the main ideas of the philosophical system «OntoTopoLogia», developed and promoted since 1990 at the I-IV, VIII Russian Philosophical Congresses, the XX World Philosophical Congress (Boston, 1998), Conference «Problems of Consciousness in Philosophy and Science» (Institute of Philosophy RAS, 1996), Conference «Philosophy of Physics: Current Problems» (MSU, 2010), seven International contests The Foundational Questions Institute (USA, FQXi Essay 2012-2020), International scientific conference «Modern Ontology» (St. Petersburg , 2013, 2017, 2019, 2023), Third All-Russian Scientific Conference «Philosophy of Mathematics: (...) Current Problems» (MSU, 2013), International Congress «Fundamental Problems of Natural Science» (St. Petersburg, 2013, 2016, 2022), Conference «Foundations of Fundamental Physics and Mathematics» (RUDN University, 2023). The ideas of the «OntoTopoLogia» system are aimed at overcoming the conceptual-paradigmatic crisis in the metaphysical/ontological basis of fundamental science (mathematics, physics, cosmology) on the basis of a holistic paradigm («paradigm of understanding»), a comprehensive conceptual-figurative synthesis, a method of dialectical-ontological construction, MetaCategory, MetaAxiom, SuperPrinciple and Metasymbol, a new holistic understanding of matter, its ontological unification across all levels of existence of the Universe as eternal holistic process of generating more and more new meanings, forms and structures. A model of the Primordial (absolute) generating structure is being built - a single ontological basis of knowledge: ontological frameworc, carcass, foundation as an all-encompassing Ideality, a single basis for the «sciences of nature» and «sciences of the spirit». (shrink)

In the current philosophical literature, determinism is rarely defined explicitly. This paper attempts to show that there are in fact many forms of determinism, most of which are familiar, and that these can be differentiated according to their particular components. Recognizing the composite character of determinism is thus central to demarcating its various forms.

The work tends to point out the deficiency of some opinions claiming simplified presentation of the promise as the act that directly rise obligation for the promisor. Promises, either in the moral or legal sphere, are based on communication and so form an order of dependent steps that indicates their procedural nature. These characteristics may differ to a lesser extent, depending on the legal systems, moral norms of the society and its technical level and its needs. In all these cases, (...) however, the procedural characteristics of promises, especially in conditional promises, as well as the promises in contractual relations, persists. In our analysis we wish to show that the consistent conception of promise has to take into account a step of acceptance. The outcome of this approach relativizes a strong distinction between promise and offer. (shrink)

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

The paper deals with the possible readings of The Reaper Argument premisses. Some conjectures related to the Stoics’ alleged proof of the argument are discussed.

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 ...

The short exposition of the triplet model of concepts and some definitions connected with it are given. In this model any concept may be depicted as having three characteristics: a base, a representing part and the linkage between them. The paper introduces the fuzzification of concepts in terms of the triplet model.

Cílem studie je zodpovědět otázku, co znamená v interpretujících humanitních či sociálních vědách zkoumat narativně. Interpretace je pojata jako explikace utváření významu. V návaznosti na toto pojetí je identifikována řada interpretačních dilemat. V tomto kontextu je uveden narativní přístup jako řešení těchto dilemat. Je pojednáno o povaze narativní perspektivy, o vztahu narativity a zkušenosti a o povaze narativních dat. Narativní výzkum je chápán jako rekonstrukce způsobů, jakými je utvářen význam narativními prostředky. Narativní interpretace umožňuje pohybovat se pružně a efektivně: 1) (...) mezi explicitními daty a exemplifikačními schématy, 2) mezi jedincem a kulturou, 3) mezi hermeneutikou podezření a hermeneutikou důvěry, 4) mezi částmi a celkem, 5) mezi obsahem a formou, 6) mezi strukturou a funkcí. (shrink)

The article deals with the question of correct reconstruction of and solutions to the ancient paradoxes. Analyzing one contemporary example of a reconstruction of the so-called Crocodile Paradox, taken from Sorensen’s A Brief History of Paradox, the author shows how the original pattern of paradox could have been incorrectly transformed in its meaning by overlooking its adequate historical background. Sorensen’s quoting of Aphthonius, as the author of a certain solution to the paradox, seems to be a systematic failure since the (...) time of Politiano’s erroneous attributing it to Aphthonius. In the conclusion, the author claims that neglecting the historical background of the ancient paradoxes into account, we are neither able to evaluate their modern interpretations as adequate nor their solutions as successful. (shrink)

The article deals with some current pioneering formal reconstructions and interpretations of the problem well known in antiquity as The Master Argument. This problem is concerning with enrichment of formal logical systems with modal and temporal notions. The opening topic is devoted to reconstruction of Arthur Prior. while the other here included approach to the problem arc mostly reactions. revisions or additions to this one.

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

Determinism is usually understood as a commonly clear and obvious thesis. In the most of the actual literature a character of determinism is rarely enough explicitly underlined and we believe that it is the reason why common uses of the term often leads to inconsistencies and present a source of misunderstandings of different sorts. Here we will try to show that that there are many forms of determinism; that the concept of determinism has a composite character; and that conceptions of (...) determinism can be mutually discriminated and organized according to particular elements they are consisting of by applying the procedure of classification. (shrink)

This article aims to show that it is impossible to put Cicero’s testimonies regarding The Fabius Argument in a consistent inferential order. Either we must suppose that additional premises are tacitly assumed in the text or we must com-pare it with other sources, which leads to inconsistencies in the proof’s reconstruction. Cicero’s reconstruction of the progression of the argument has formal shortcomings, and the paper draws attention to some of these deficiencies. He interpreted sources in a revised and intentionally simplified (...) way, with the aim of undermining the views of his opponents, casting them as inconsistent and similar to views held by Diodorus. Rather than being a consistently interpreted argument faithfully transcribed from the Stoic sources, Cicero’s Fabius Argument is ultimately anti-Stoic. (shrink)

One of the main and currently dominating attempt in theories of philosophical psychology is the way of describing psychological facts as cognitive state of affairs or mental events which could be individuated by the same means as it were natural species. This idea resulted from incapability of the " folk" psychology to give complete and satisfactory scientific explanation by the intentionality approach. The author claims that many certain advantages of the cognitive theories could be disputable if we try to consistently (...) analyze the ways of describing and individuation of entities in such "deeper" theories. And, especially if we can recognize them as spatiotemporally restricted (i .e. historical) entities. This alternative case could be, as it seems, theoretically more appropriate to their subjects: particular thoughts, believes, desires, representations and other mental events would be individuated as genealogically reconstructed subjects which forms potentially stronger explanatory power than in the case of explanations given by covering laws and in accordance with the presupposition of nomological necessity. (shrink)

The article discusses some aspects of the narrative explanation, and its nature and role in explaining the historical entities. The author defends possibility of formulating status of narrative explanation as scientific and adequate for all historical sciences, here defined as sciences concerned with the spatio-temporally restricted entities. lie suggests that uniqueness and particularity of historical objects are not in contradiction with the claims based on the classical model of explanation in the way of logical inferring. Results of discussion are that (...) undeveloped explanations, like explanation sketches, could be adopt, not just in accordance with pragmatic reasons, but also as the step toward full-fledged or complete explanation trough mediation of developing the scientific research programs on which they are based. (shrink)

The article deals with some items of Gödelian time travel problem well-known as an illustration of a specific kind of causality paradox. Its first part presents “the travel into the past” according to several recent physical hypotheses, which, from theoretical standpoint, seem to make such an idea possible. The familiar concept of backward causation is also discussed; we need to accept and develop it, if we wish to escape this type of time-travel paradoxes. The second part of the contribution is (...) devoted to philosophical interpretations of the precedence in order of cause and effect, and of the relation between temporal and causal order. The author claims, that if we wish to save coherent picture of nature, it is necessary to revise the concept of causality to make it compatible with the concept of backward causation. (shrink)

In the opening lines of this article it is claimed that history is a discipline taking role as part of unique body of science. The concept of scientific rationality is presented as the criterion of demarcation between science and pseudoscience. From this statement as a starting point, it follows that the methodological grounds for scientific predictions are common for all scientific disciplines. Different aspects of scientific predicting are critically examined: thesis of symmetry, determinism and predictability, indeterminism and predictability, reflexivity of (...) predictions, prediction of novelty and progress, predictions in relation to the time of their uttering, the prediction sketch, truthfulness and regularity in implying prediction, and predictability of human actions. In the concluding section, the author admits of the possibility of constructing the theory of history, opposed to eschatological philosophy of history, as a predictive theory with a scientific basis and a theory whose specifications limit its misuse in practice. (shrink)

Physical theories are complex and necessary tools for gaining new knowledge about their areas of application. A distinction is made between abstract and practical theories. The last are constantly being improved in the cognitive activity of professional physicists and studied by future physicists. A variant of the philosophy of physics based on a modified structural-nominative reconstruction of practical theories is proposed. Readers should decide whether this option is useful for their understanding of the philosophy of physics, as well as other (...) philosophies of particular sciences. (shrink)

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)

The paper has two objectives: to introduce the fundamentals of a triplet model of a concept, and to show that the main concept models may be structurally treated as its partial cases. The triplet model considers a concept as a mental representation and characterizes it from three interrelated perspectives. The first deals with objects (and their attributes of various orders) subsumed under a concept. The second focuses on representing structures that depict objects and their attributes in some intelligent system. The (...) third concentrates on the ways of establishing correspondences between objects with their attributes and appropriate representing structures. (shrink)

Philosophy of Science; Ukraine; Polysytemic nature of theories; Practical theories; Subsystems of a theory.

We analyzed remarkable stories linked to the famous Anatoly Vlasov equations in plasma physics. Their creation, modification, and application are interesting from a scientific viewpoint. We also show the relations between those equations dealing with electromagnetism and analogous Jeans equations describing, in particular, gravitational instability in astrophysics. The second half of the essay is devoted to the controversies and political struggle in Soviet (before 1991) and Russian (after 1991) physical communities related to Vlasov’s personality, career, and posthumous recognition. The never-ending (...) destructive influence of Russian totalitarianism on science is demonstrated. (shrink)

The scheme for classifications of concepts is introduced. It has founded on the triplet model of concepts. In this model a concept is depicted by means of three kinds of knowledge: a concept base, a concept representing part and the linkage between them. The idea of triplet classifications of concepts is connected with a usage of various specifications of these knowledge kinds as classification criteria.

Cicero's De fato: On Hellenistic Conditionals and Free Will. The Serbo-Croatian translation of Cicero's De fato, with comments and detailed analysis of some arguments and problems of the text. -/- (s/h): Tekst Ciceronovog spisa "de fato", prevod, komentari i u dodacima, detaljnija analiza pojedinih argumenata i problema sadržanih u tekstu.

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

The paper has three objectives: to expound a set-theoretical triplet model of concepts; to introduce some triplet relations (symbolic, logical, and mathematical formalization; equivalence, intersection, disjointness) between object concepts, and to instantiate them by relations between certain physical object concepts.

Článek reflektuje Hayekovy výklady o povaze pravidel. Ukazuje, že jeho pojetí pravidel je extrémně široké a vazba mezi pravidly a pravidelnostmi je nepřijatelně úzká. Následně je nastíněno alternativní - užší - vymezení pojmu pravidla. Nakonec je podrobeno kritice Hayekovo příliš úzké chápání pojmu normativních pravidel a je navrženo jeho širší vymezení.

The present crisis of foundations in Fundamental Science is manifested as a comprehensive conceptual crisis, crisis of understanding, crisis of interpretation and representation, crisis of methodology, loss of certainty. Fundamental Science "rested" on the understanding of matter, space, nature of the "laws of nature", fundamental constants, number, time, information, consciousness. The question "What is fundametal?" pushes the mind to other questions → Is Fundamental Science fundamental? → What is the most fundamental in the Universum?.. Physics, do not be afraid of (...) Metaphysics! Levels of fundamentality. The problem №1 of Fundamental Science is the ontological justification (basification) of mathematics. To understand is to "grasp" Structure ("La Structure mère"). Key ontological ideas for emerging from the crisis of understanding: total unification of matter across all levels of the Universum, one ontological superaxiom, one ontological superprinciple. The ontological construction method of the knowledge basis (framework, carcass, foundation). The triune (absolute, ontological) space of eternal generation of new structures and meanings. Super concept of the scientific world picture of the Information era - Ontological (structural, cosmic) memory as "soul of matter", measure of the Universum being as the holistic generating process. The result of the ontological construction of the knowledge basis: primordial (absolute) generating structure is the most fundamental in the Universum. (shrink)

There are no universally adopted answers to the natural questions about scientific concepts: What are they? What is their structure? What are their functions? How many kinds of them are there? Do they change? Ironically, most if not all scientific monographs or articles mention concepts, but the scientific studies of scientific concepts are rare in occurrence. It is well known that the necessary stage of any scientific study is constructing the model of objects in question. Many years logical modeling was (...) dominant in the concept studies. Last decades, concepts came to be regarded as the subject of mathematical modeling. However, different authors take different features of concepts as independent variables of their models. Our objective is to characterize informally the spectra of relevant variables for the modeling of scientific concepts. (shrink)

The changes of concepts are described in the frame of concept triplet model. -/- .

The triplet model treats a concept as complex structure that expresses three kinds of information. The first is about entities subsumed under a concept,their properties and relations. The second is about means and ways of representing the first information in intelligent systems. The third is about linkage between the first and second ones and methods of its constructing. The application of triplet models to generalization and development of concept models in philosophy, logic, cognitive psychology, cognitive science, linguistics, artificial intelligence has (...) been demonstrated. The componential structure of the triplet model and extended concept classification have been given. Theoretical considerations are combined with historical case-studies of concept history. For scientists and students with an interest in problems of knowledge structure and representation. Abstract and Extended Summary in English. (shrink)

An application of diagrams for separating modes of theory development.

Recientemente entre los defensores de la responsabilidad moral colectiva ha surgido una línea que defiende que los colectivos no sólo son moralmente responsables, sino que además pueden serlo aun si ninguno de los individuos que compone el colectivo es moralmente responsable. A esta posición se la puede denominar la tesis de la autonomía moral colectiva o TAMC. Creo que esta tesis no sólo es errada, sino que además es bastante peligrosa. El objetivo de este texto será mostrar que no hay (...) argumentos fuertes para sostener la verdad de la TAMC, más aún, que la TAMC requiere de una condición contradictoria para poder ser verdadera. Para ello comenzaré por mostrar, en la primera sección, una diferencia importante acerca de las acciones colectivas y por qué para algunos es plausible pensar que los colectivos son moralmente responsables. En las tres secciones siguientes reconstruiré brevemente las teorías de Peter French, Margaret Gilbert y David Copp, todos ellos defensores de la TAMC. En la sección cinco ofreceré las características básicas de la responsabilidad moral. En la sección seis presentaré un requisito que considero indispensable para el funcionamiento de la TAMC, pero mostraré que es imposible de obtener, para, en la última sección, mostrar cómo French, Gilbert y Copp, así como cualquier otra defensa de la TAMC, caen inevitablemente en el error de solicitar algo imposible. (shrink)

Development of ideas on UN reform presented in the essay "United Humanity: from "UN 2.0" to "UN 3.0" The conceptual model of the United Nations for the XXI century" (2017).

Este capítulo trata la división, o brecha, que hay entre las ciencias sociales y humanas, por un lado, y las ciencias naturales, por el otro. Analiza el pasado de esta brecha, rastreando algunos de sus orígenes, y muestra lo dañina que esta división ha llegado a ser (sin desconocer la importancia de respetar los límites disciplinares). Termina por ofrecer algunas recomendaciones de cara al futuro para ir cerrando los aspectos más perjudiciales de esta brecha.

Organisms that share the capability of storing information about experiences in the past have an actively generated background resource on which they can compare and evaluate more recent experiences in order to quickly or even better react than in previous situations. This is an essential competence for all reaction and adaptation purposes of living organisms. Such memory/learning skills can be found from akaryotes up to unicellular eukaryotes, fungi, animals and plants, although until recently, it had been mentioned only as a (...) capability of higher animals. With the rise of epigenetics, the context-dependent marking of experiences at both the phenotype and the genotype level is an essential perspective to understand memory and learning in all organisms. Both memory and learning depend on a variety of successful communication processes within the whole organism. (shrink)

It is proposed to analyze fuzzy concepts and relations between them in the frame of triplet concept modeling. Fuzzy concepts are introduced by means of the so-called fuzzification of dichotomous concepts. The cognitive and psychological aspects of concept possession are separated and studied.

Comparative philosophical studies can seek to fit some Eastern patterns of thought into the general philosophical framework, or, on the contrary, to improve understanding of Western ones through the view "from abroad". I try to hit both marks by means of establishing, firstly, the parallels between Indian versions of theodicy and the Hellenic and Christian ones, then by defining to which of five types of Western theodicy the Advaita-Vedanta and Nyaya versions belong and, thirdly, by considering the meaning of the (...) fact that some varieties of Western theodicy, like the explanation of evil by free will and divine dispensation aiming at the improvement of man, have Indian counterparts while others lack them. Some considerations concerning the remainders of primordial monotheisms ("an argument from theodicy") under the thick layers of other religious world-outlooks are also offered to the reader at the end of the article. (shrink)

It is proposed to analyze the unity of scientific knowledge in terms of its structure-nominative reconstruction. -/- .