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 text is a classic of Lenin - his essay explores materialism and its relation to capitalism and how Communism can get over this psychological wish for material and empirical ownership.

Several attempts have recently been made to point to ‘the proper place’ for hydrogen in the Periodic Table of the elements. There are altogether five different types of arguments that lead to the following conclusions: hydrogen should be placed in group 1, above lithium; hydrogen should be placed in group 17, above fluorine; hydrogen is to be placed in group 14, above carbon; hydrogen should be positioned above both lithium and fluorine and hydrogen should be treated as a stand-alone element, (...) in the center of the Periodic Table. Although all proposals are based on arguments, not all of them sound equally convincing. An attempt is made, after critical reexamination of the arguments offered, to hopefully point to the best possible choice for the position of hydrogen. A few words are also mentioned on the structure of the Periodic Table and the attempts to reorganize it. (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.

In this paper we prove the following theorem: Any one-dimensional definably connected group G over an o-minimal structure is, as an abstract group, isomorphic to either pPp∞δ or δ.

“Toy worlds” involving actions, such as the blocks world and the Missionaries and Cannibals puzzle, are often used by researchers in the areas of commonsense reasoning and planning to illustrate and test their ideas. We would like to create a database of generalpurpose knowledge about actions that encodes common features of many action domains of this kind, in the same way as abstract algebra and topology represent common features of specific number systems. This paper is a report on the first (...) stage of this project—the design of an action description language in which this database will be written. The new language is an extension of the action language C+. Its main distinctive feature is the possibility of referring to other action descriptions in the definition of a new action domain. (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)

In this paper1 we study admissible consecutions in multi-modal logics with the universal modality. We consider extensions of multi-modal logic S4n augmented with the universal modality. Admissible consecutions form the largest class of rules, under which a logic is closed. We propose an approach based on the context effective finite model property. Theorem 7, the main result of the paper, gives sufficient conditions for decidability of admissible consecutions in our logics. This theorem also provides an explicit algorithm for recognizing such (...) consecutions. Some applications to particular logics with the universal modality are given. (shrink)

The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, (...) are completely virtual and yet clearly organized. This organization can be recognized in the creation of axioms or in the arrival at new theorems and definitions. It results either from a formalization of an intuitive idea or from a combinatorics that has not been guided by intuition. In all four possible cases—therefore, also in the two in which there is no intuitive “lead”, we can plausibly talk about a discovery of mathematical facts and thus support the Platonist view. (shrink)

Key premises of the target article by Juslin & Vll (J&V) are challenged. It is also shown that most of the six proposed by the authors as underlying the induction of emotion by music involve nonmusical proximal causes. As a replacement for the state of being-moved is proposed.

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)

El siguiente artículo aborda la crítica que manifiesta que John Stuart Mill incurrió en la falacia naturalista y en la falacia de composición. Esta temática se puede abordar de dos formas: una consistiría en analizar si Mill realmente desconoce la distinción entre lo deseado y lo deseable; otra sobre si su concepción de hedonismo, felicidad, conlleva la comisión de las falacias mencionadas. Esta última forma es el tema principal que se aborda; en otras palabras, se mencionará brevemente lo relativo a (...) si Mill confunde deseado/deseable, es/debe, y se puntualiza en cómo el hedonismo y la idea de felicidad millianos no llevan a caer en la falacia naturalista ni en la falacia de composición. En todo esto la educación jugará un papel valioso. (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)

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)

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)

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.

Tato stať se zabývá implicitním vztahem pojmu nutnosti a náhodnosti (bytí jsoucího) a pojmu zákona (bytí jsoucího) v Marxově filosofii spjaté (svázané) s explicitním vztahem pojmu nutnosti a náhodnosti (bytí lidsky jsoucího v ekonomicko-společenské bytné sféře) a pojmu zákona (bytí lidsky jsoucího v ekonomicko-společenské bytné sféře) v Marxově politické ekonomii a ukazuje její ontologicko-nomologické přednosti, poukazujíc však na její antropologicko-ontologické nedostatky, spjaté zvláště s jejím historicismem (s "bídou historicismu").

The aim of this paper is to offer an overview of the long-lasting friendship between Georges Florovsky and St. Justin Popović, as well as their common project to build an Orthodox theological synthesis on the basis of the patristic tradition. The paper focuses on three periods from Florovsky’s and Popović’s lives, from late 1910 to early 1920, from the late 1920s to late 1930s, and finally into the 1940s. I argue that in the first period both authors developed their theological (...) visions relying on Solovyov and Florensky, on the one hand, and in opposition to the ecclesial nationalism of the Slavophiles and conservative Orthodox hierarchs, on the other hand. Further, I investigate how during the late 1920s and 1930s both authors searched for an Orthodox synthesis mostly in dialogue with their Orthodox predecessors, especially Solovyov, Florensky, and Bulgakov, as well as the modern western philosophical tradition. The focus will shift then to the 1940s, which was characterized by frequent meetings between Florovsky and Popović in Belgrade, Yugoslavia. I argue that in this period the Church Fathers became for both authors the golden standard for Orthodox theology, and the idea of the Neopatristic synthesis developed in full scale. (shrink)

What do we learn when we find out that an argument is logically incorrect? If logically incorrect means the same as not logically correct, which in turn means not having a valid logical form, it seems that we do not learn anything too useful—an argument which is logically incorrect can still be conclusive. Thus, it seems that it makes sense to fix a stronger interpretation of the term under which a logically incorrect argument is guaranteed to be wrong. In this (...) paper, we show that pinpointing this stronger sense is much trickier than one would expect; but eventually we reach an explication of the notion of logical incorrectness which we find non-trivial and viable. (shrink)

Understanding has usually been seen as a method of hermeneutics. Until recently, philosophers of science paid little attention to the topic of scientific understanding because they came to the conclusion that understanding can be nothing more than a psychological by-product of scientific activity. However, many scientists believed that understanding was an important aim of science. The article states that understanding is a universal cognitive phenomenon applicable to the knowledge of not only cultural and historical phenomena, but also natural objects and (...) processes. Understanding does not oppose explanation; some types of the latter produce scientific understanding. In the course of criticism of the standard model of scientific explanation, the first concepts of “scientific understanding” arose – unifying and causal-mechanistic. A pragmatic approach to scientific understanding is also considered, linking it to the cognitive skills of a scientist or a group of scientists. (shrink)

The paper discusses various aspects of the concept of “cultural memory” coined by Jan Assmann and related both to the problem of determining the categories of culture that became the first objects of philosophical reflection in the era of the Axial Age and to the issues of the modern crisis of the ideology of globalism and multiculturalism. Using the example of some categories of an archaic myth that have not lost their cultural and social relevance at present, the variability of (...) the genesis of philosophy in various civilizations of the epoch of the “Axial Age” is demonstrated - both those in which it arises as an independent form of worldview and those where this process stops at the stage of a highly speculative myth. Special attention is paid to the cultural and social aspects of memory and recollection of the past as forms of spiritual “resistance” to external cultural influences and the preservation of religious and ethnic identity, which is equally relevant both during the genesis of philosophy and in modern post-industrial society during the crisis of globalist ideology and the philosophy of multiculturalism. (shrink)

Článek ukazuje, jaká je role tradiční role logické analýzy v rámci filosofického bádání. Naznačuje rovněž, že současné logické metody začínají otevírat cestu k modelování procesů, které filosofie tradičně zkoumá.

Tato stať ("K pojmu "přirozeného zákona" - bytí lidsky jsoucího - v Lockově filosofii") je dodatkem k mé studii "K pojmu "přirozeného zákona" (bytí lidsky jsoucího) v Hobbesově filosofii". Určuji v ní blíže momenty totožnosti pojmu "přirozeného zákona" (bytí lidsky jsoucího) v Lockově filosofii a pojmu "přirozeného zákona" (bytí lidsky jsoucího) ve filosofii Hobbesově, tj. bytný zdroj, (obsažnou) bytnost a (bytostnou) formu "přirozeného zákona" (bytí lidsky jsoucího) a bytný zdroj, (obsažnou) bytnost a (bytostnou) formu (státo-právně) společenského zákona (bytí lidsky jsoucího). (...) A určuji v ní též blíže momenty rozdílnosti pojmu "přirozeného zákona" (bytí lidsky jsoucího) v Lockově filosofii a pojmu "přirozeného zákona" (bytí lidsky jsoucího) ve filosofii Hobbesově, tj. platnost (závaznost) "přirozeného zákona" (bytí lidsky jsoucího), platnost (závaznost) (státo-právně) společenského zákona (bytí lidsky jsoucího) a vztah "přirozeného zákona" (bytí lidsky jsoucího) a (státo-právně) společenského zákona (bytí lidsky jsoucího). Tato stať ("K pojmu "přirozeného zákona" - bytí lidsky jsoucího - v Lockově filosofii"), jsouc dodatkem k mé studii "K pojmu "přirozeného zákona" (bytí lidsky jsoucího) v Hobbesově filosofii", ukazuje, že pojem "přirozeného zákona" (bytí lidsky jsoucího) v Lockově filosofii je antropologicko-ontologicko-nomologicky širší a hlubší než pojem "přirozeného zákona" (bytí lidsky jsoucího) ve filosofii Hobbesově; a ukazuje též, že pojem "přirozeného zákona" (bytí lidsky jsoucího) v Lockově filosofii, ač antropologicko-ontologicko-nomologicky širší a hlubší než pojem "přirozeného zákona" (bytí lidsky jsoucího) v Hobbesově filosofii, není pojmem mravního zákona (bytí lidsky jsoucího) a nepředbíhá ani nepředjímá ani Kantův pojem mravního zákona (bytí lidsky jsoucího). (shrink)

Reproductive biotechnologies, also known as assisted reproductive technologies (ART), have undergone significant development over time, reaching a remarkable level of evolution in the 20th century. Currently, several biotechnologies stand out, among which Artificial Insemination (AI), widely spread globally, Embryo Production (EP) both in vivo and in vitro for embryo transfer, Intracytoplasmic Sperm Injection (ICSI), sexing, among other innovations. In Vitro Production (IVP) of embryos has emerged as the biotechnology that has experienced the greatest development and evolution in recent decades, covering (...) various fields such as research in assisted human reproduction, obtaining transgenic animals for biomedicine, preservation of endangered species and conservation of animals of high genetic value. This research aims to analyze the relevance of IVP, as well as the fundamental elements that make up this complex process. IVP of embryos involves several stages, from oocyte procurement, oocyte selection and in vitro maturation, sperm preparation, in vitro fertilization, to the culture of the resulting zygotes to blastocysts. These blastocysts, once transferable to recipients, culminate in the birth of a new being. However, this process has both advantages and disadvantages, which motivates continuous innovation in the field. (shrink)

Tato stať - recenze - "Od polovzdělanosti k nevzdělanosti" - se zabývá knihou K. P. Liessmanna "Teorie nevzdělanosti"; v jejích stopách promýšlí a domýšlí tyto otázky: 1. Jaký je dřívější zakládající a zacilující vztah k ideji vzdělanosti? 2. Jaký je nynější vztah k ideji vzdělanosti, zakládající se mimo ni a zacilující se proti ní? 3. Jaká je zakládající a zacilující antiidea dnešního "vzdělávání"? 4. Jaká je zakládající a zacilující antiidea "vzdělávání" v dnešních "vzdělávacích institucích", zvláště pak ve školách jako "vzdělávacích (...) institucích"? 5. Jaký je bytný základ zakládající a zacilující antiideje dnešního "vzdělávání" (tj. i jaký je bytný základ zakládající a zacilující antiideje "vzdělávání" v dnešních "vzdělávacích institucích", tj. i ve školách jako "vzdělávacích institucích")? - Tato recenzní stať - "Od polovzdělanosti k nevzdělanosti", zabývajíc se knihou K. P. Liessmanna "Teorie nevzdělanosti" a v jejích stopách promýšlejíc a domýšlejíc ony otázky, dodává dodatek o struktuře dnešního školství, dle nějž struktura dnešního školství tkví v rozdělení na vyšší školy - továrny a nižší školy - stoky i v propojení vyšších škol - továren a nižších škol - stok posuvnou hranicí, tj. hranicí posuvnou pouze směrem nahoru, nikoli ovšem směrem dolů. (shrink)

In some systems of Legniewskian Ontology were introduced as a toolkit for Husserl's and Meinong's theory of objects. Here such consi- deration is extended to Brentano-Husserl's theory of time. So-called antidiodo- rean logics are used as the foundations of the approach undertaken.

In [12] it was shown that the factor semantics based on the notion ofT-F-sequences is a correct model of the ukasiewicz's infinite-valued logics. But we could not consider some important aspects of the structure of this model because of the short size of paper. In this paper we give a more complete study of this problem: A new proof of the completeness of the factor semantic for ukasiewicz's logic using Wajsberg algebras [3] (and not MV-algebras in [1]) and Symmetrical Heyting (...) monoids [7] is proposed. Some consequences of such an approach are investigated. (shrink)

Benevolenski and Kortunov discuss the array of moral, ethnic, and nationalistic questions emerging after the disintegration of the Soviet Union. They suggest that the cause for the collapse was not poor economic performance, but a moral bankruptcy the people could no longer endure.

The paper aims to analyze the early ecumenical views of Amfilohije Radović with reference to the influence exerted on him by his spiritual father Justin Popović. This investigation is important because Radović’s ecumenical engagement is often a matter of controversy, which results in conflicting views. Sources for studying Radović’s early ecumenical views are: his correspondence with Justin Popović on ecumenism, his engagement in editing and publishing Popović’s book _Orthodox Church and Ecumenism_, and finally, his article written as a report from (...) an inter-Orthodox conference held in September 1972 in Thessalonica. In addition to Radović’s similarity with Popović's views, the paper also aims to show their differences, i.e. their different interpretations of the same phenomena. (shrink)

The ancient mythology could serve as an effective medium for metaphorically conveying complex concepts and principles to a broad spectrum of people. In this paper we show how the fuzzy logic approach can be used to translate the metaphoric language of ancient myths and legends into a 'soft' scientific paradigm which helps us to understand better the social complexity of our time.

In this paper, we study the genesis and evolution of geometric ideas and techniques in investigations of movable singularities of algebraic ordinary differential equations. This leads us to the work of Mihailo Petrović on algebraic differential equations and in particular the geometric ideas expressed in his polygon method from the final years of the nineteenth century, which have been left completely unnoticed by the experts. This concept, also developed independently and in a somewhat different direction by Henry Fine, generalizes the (...) famous Newton–Puiseux polygonal method and applies to algebraic ODEs rather than algebraic equations. Although remarkable, the Petrović legacy has been practically neglected in the modern literature, although the situation is less severe in the case of results of Fine. Therefore, we study the development of the ideas of Petrović and Fine and their places in contemporary mathematics. (shrink)

Alan Baker argues that mathematical objects play an indispensable explanatory role in science. There are several examples cited in the literature as solid candidates for such a role. We discuss two such examples and show that they are very different in their strength and (im)perfection, although both are recognized by the scientific community as examples of the best scientific explanations of particular phenomena. More specifically, it will be shown that the explanation of the cicada case has serious shortcomings compared with (...) the explanation of the case of Königsberg’s bridges. We will argue that the latter is a perfectly reliable scientific explanation that employs mathematical reasoning whereas the former is not. (shrink)