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)

It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension, that every countable ordinal-definable set of reals belongs to the ground universe. It is true in the Solovay collapse model that every non-empty OD countable set of sets of reals consists of \ elements.

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)

An application of diagrams for separating modes of theory development.

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.

Le tome 2 du Traité des vertus, intitulé Les Vertus et l'Amour, est consacré à la description des " vertus ", depuis celle du commencement jusqu'à celle de la terminaison, en passant par celles de la continuation et de la conservation. Il distingue en outre deux plans tout à fait hétérogènes : celui des vertus de l'intervalle, que l'homme peut " posséder " et " garder ", mais qui, à peine acquises, tournent en mécanique vertueuse, radotage, complaisance pharisienne et hypocrisie (...) ; et les vertus de pointe que l'homme ne possède jamais, qu'il effleure seulement, d'une tangence impondérable, le temps d'une étincelle et d'une " apparition disparaissante ". Vaut-il mieux être au premier sens, un rentier de la vertu et un vertueux gredin, ou, au sens métempirique, le saint ou le héros d'un instant? L'amour résout peut-être, dans une certaine mesure, cette alternative, qui est aussi celle du bonheur et de la joie. (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 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)

Mindfulness-based interventions have proved effective in reducing various clinical symptoms and in improving general mental health and well-being. The investigation of the mechanisms of therapeutic change needs methods for assessment of mindfulness. Existing self-report measures have, however, been strongly criticized on various grounds, including distortion of the original concept, response bias, and other. We propose a psychophysiological method for the assessment of the mindfulness learned through time-limited mindfulness-based therapy by people who undergo meditation training for the first time. We use (...) the individual pre-post-therapy changes (dERPi) in the event-related brain potentials (ERPs) recorded in a passive meditation task as a measure of increased mindfulness. dERPi is computed through multivariate assessment of individual participant's ERPs. We tested the proposed method in a group of about 70 recurrently depressed participants, randomly assigned in 1.7:1 ratio to mindfulness-based cognitive therapy (MBCT) or cognitive therapy (CT). The therapy outcome was measured by the long-term change (dDS) relative to baseline in the depression symptoms (DS) assessed weekly, for 60 weeks, by an online self-report questionnaire. We found a strong, highly significant, negative correlation (r = -0.55) between dERPi (mean = 0.4) and dDS (mean = -0.7) in the MBCT group. Compared to this result, the relationship between dDS and the other (self-report) measures of mindfulness we used was substantially weaker and not significant. So was also the relationship between dERPi and dDS in the CT group. The interpretation of dERPi as a measure of increased mindfulness was further supported by positive correlations between dERPi and the other measures of mindfulness. In this study, we also replicated a previous result, namely, the increase (dLCNV) of the late contingent negative variation (LCNV) of the ERP in the MBCT group, but not in the control group (in this case, CT). We interpreted dLCNV as a measure of increased meditative concentration. The relationship between dLCNV and dDS was, however, very week, which suggests that concentration might be relatively unimportant for the therapeutic effect of mindfulness. The proposed psychophysiological method could become an important component of a "mindfulness test battery" together with self-report questionnaires and other newly developed instruments. (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)

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.

This commentary discusses dozens of ecologically powerful social-psychological experiments from the1960s and 1970s, which are highly relevant especially for predicting the consequences of revenge. McCullough et al. omitted this work catharsisni's anger-aggression bidirectional-causation (AABC) model and can be usefully incorporated in an adaptationist view of revenge.

There are many methodological considerations that adversely affect external validity as much as, or even more than, unrepresentative sampling does. Among suspect applications, especially worrisome is the incorporation of WEIRD-based findings regarding moral reasoning and retribution into normative expectations, such as might be held by international criminal tribunals in war-torn areas.