People are remarkably smart: They use language, possess complex motor skills, make nontrivial inferences, develop and use scientific theories, make laws, and adapt to complex dynamic environments. Much of this knowledge requires concepts and this study focuses on how people acquire concepts. It is argued that conceptual development progresses from simple perceptual grouping to highly abstract scientific concepts. This proposal of conceptual development has four parts. First, it is argued that categories in the world have different structure. Second, there might (...) be different learning systems that evolved to learn categories of differing structures. Third, these systems exhibit differential maturational course, which affects how categories of different structures are learned in the course of development. And finally, an interaction of these components may result in the developmental transition from perceptual groupings to more abstract concepts. This study reviews a large body of empirical evidence supporting this proposal. (shrink)

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)

Although it is well documented that language plays an important role in cognitive development, there are different views concerning the mechanisms underlying these effects. Some argue that even early in development, effects of words stem from top‐down knowledge, whereas others argue that these effects stem from auditory input affecting attention allocated to visual input. Previous research (e.g., Robinson & Sloutsky, 2004a) demonstrated that non‐speech sounds attenuate processing of corresponding visual input at 8, 12, and 16 months of age, whereas the (...) current study demonstrates that words attenuate visual processing at 10 months but not at 16 months (Experiment 1). Furthermore, prefamiliarization with non‐speech sounds (Experiment 2) resulted in able processing of visual input by 16‐month‐olds. These findings suggest that some effects of labels found early in development may stem from familiarity with human speech. The possibility of general‐auditory factors underlying the effects of words on cognitive development is discussed. (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.

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.

The small, the tiny, and the infinitesimal have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that written by Errett Bishop about Keisler’s book Elementary Calculus: an Infinitesimal Approach. In this skit we investigate both the argument itself, and some of its roots in Bishop George Berkeley’s criticism of Leibnizian and Newtonian Calculus. We also explore some of the consequences to students for whom the infinitesimal approach is congenial. The (...) casual mathematical reader may be satisfied to read the text of the five act play, whereas the others may wish to delve into the 130 footnotes, some of which contain elucidation of the mathematics or comments on the history. (shrink)

We prove that if I is a partially ordered set in a countable transitive model M of ZFC then M can be extended by a generic sequence of reals a i , i ∈ I, such that ℵ M 1 is preserved and every a i is Sacks generic over $\mathfrak{M}[\langle \mathbf{a}_j: j . The structure of the degrees of M-constructibility of reals in the extension is investigated. As applications of the methods involved, we define a cardinal invariant to distinguish (...) product and iterated Sacks extensions, and give a short proof of a theorem (by Budinas) that in ω 2 -iterated Sacks extension of L the Burgess selection principle for analytic equivalence relations holds. (shrink)

The Petrine-Pushkinian era lasted no more than two hundred years. It originated at the Battle of Poltava, where Russian troops first showed themselves not just equal to the Swedes, who were otherwi...

L’article aborde le sujet souvent débattu du rapport entre le détermi­nisme stoïcien et la morale pour rouvrir la question de la notion d’assentiment. Dans ce but, il réexamine les sources pour montrer deux choses : que les inter­prétations dites compatibilistes ont raison dans leur effort général pour montrer que les stoïciens restent déterministes quand ils présentent leur psychologie de l’action et défendent l’idée de responsabilité, mais qu’en même temps elles vont trop loin quand elles affirment – dans un effort de (...) systématisation de la stratégie stoïcienne – que l’assentiment est le simple effet de la rencontre du caractère particulier de l’agent et de l’impression sensorielle. En essayant de restituer l’ac­cent que les stoïciens ont mis sur l’assentiment, l’article indique que c’est égale­ment là que réside l’ambigüité de leur psychologie de l’action, qui a contribué au paradoxe dans l’interprétation du stoïcisme : ce dernier a été dès l’origine, d’un côté, une inspiration pour ceux qui ont voulu argumenter en faveur de la liberté de l’action humaine, et de l’autre, le sujet de la critique pour la réfutation de la liberté de l’action. Dans son ensemble l’interprétation proposée est négative dans le sens où elle veut montrer comment ne pas comprendre l’assentiment, pour ouvrir la possibilité de l’examiner de nouveau, ce qui pourrait montrer enfin que l’ambigüité mentionnée est par conséquent l’expression du plus grand potentiel philosophique de la conception stoïcienne de la raison. (shrink)

The book is a contribution on the early Stoics’ views of action, responsibility and freedom. The central claim, which sets the framework of its three chapters, is that an influential interpretation according to which the Stoics’ concept of responsibility is entirely separate from their concept of freedom (S. Bobzien) is mistaken. The present interpretation does conserve a compatibilist reading but the claim is made that if a person is responsible for an action it is so on the basis of features (...) which make his or her action also (potentially) virtuous and free. Moreover, if responsibility is thought and presented as a kind of paradox, it is the same paradox which is recognizable as a foundaon of virtue and freedom. It is important for this interpretation to see responsibility as based on assent (and not merely on one’s – determined – nature/character) and to see the corresponding compatibilism as a result of a two-sided mental act which is then also to be found in the exercise of virtue. By defending these views, the book offers a unified Stoic theory of action in which psychology (assent) and ethics (virtue and freedom) presuppose similar reflective turns in the soul though on different levels of the soul’s activity. (shrink)

The Stoics’ way of presenting principles – the active and the passive – is ambiguous because they say that principles are two while also suggesting that they are inseparable and thus interdependent. This ambiguity cannot be resolved in favour of one or the other side of the dilemma, as is shown by analysis of two possible models of the relations among principles – a causal and a categories-based model. This ambiguity is rather a necessary consequence of the Stoic view of (...) principles and should be compared to the ambiguity of Plato’s concept of “principles” in the Timaeus. Plato’s Receptacle is in a similar relation to other constitutive elements of his cosmogonical account as are the two Stoic principles, each to the other. In particular, the relation between the Receptacle and qualities in it is to be seen as a systematic parallel to the relation of the Stoic principles (and probably also its historical model). The concluding claim is that Plato and the Stoics advance a similar kind of dualism which should be called such, despite its ambiguity. The ambiguity in both systems is due to the need to see the principles in such a relation as would reveal their dependence, and thus secure the basic unity of the cosmos. (shrink)

The first collective monograph on one of Plato’s most intriguing dialogues with interest for readers of ancient philosophy as well as those who study modern theories of language.

The paper offers an interpretation of Plato’s Necessity in the Timaeus according to which Necessity is an entity which manifests itself in different ways at different stages of the creation of the Universe. The main argument aims to show that Necessity gains at least two different meanings in the course of the creation as described by Plato – that of limiting consequences and that of purposeless motion ; that despite the fact that Necessity is not a self-sustained principle, it has (...) its origin in chōra which is a condition of limiting material spatiality; that the important question what the effects of Necessity in the already created world are should be asked but cannot be easily answered on the basis of what Plato explicitly says. (shrink)

The book by Max Tegmark draws attention to the dangers and benefits that await humanity as a result of the Artificial Intelligence (AI) technologies development. Cosmologist and astrophysicist Tegmark, realizing the impossibility to predict the AI development, offers exciting scenarios of civilization development options for tens, thousands, millions and billions of years. The analysis of the opposite scenarios is aimed at the idea formation that the consequences of creating a general AI, superior to the human level, will be more significant (...) than from all other achievements of civilization. Tegmark is one of the founders and leaders of the “Beneficial AGI” movement, he presents the results of the discussion of the issues he raises with leading experts in the field of AI. Tegmark concludes his book with a call to optimism: “My book urge you to think about what future you would like, and not what future scares you, this way we can find goals for which it’s worth working”. (shrink)

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 author examines the key philosophical problem of theodicy and freedom as it was first formulated by Fyodor Dostoevsky and later developed by Nikolai Berdyaev.

This paper continues the analysis of the advantages and disadvantages of ontic structural realism, which begun in the first part of the paper. Non-eliminative versions of this approach are considered, which try to find a compromise between the ontology of structures and the ontology of objects. It is shown that the semirealism of A. Chakravartti and the constructive structural realism of T. Cao have a number of limitations caused by the authors’ desire to strictly distinguish between the nature of the (...) existence of objects and structures. Then the version of the relationship between structures and entities is presented. Firstly, two concepts are divided according to their content: “object” and “entity”. Second, to solve the problem of causality, I suggest that the nature of entities and structures lie in their ability to act. It is this ability that I propose to use instead of the popular concepts of “causal powers”, “causal properties” or “dispositions”. Third, instead of a rigid alternative to ontological primitives – either essence, or causal relations, or structures – the concept of ontological pluralism and inherited existence is proposed. There each entity is represented as a derivative of another structure and, in turn, creates other entities and structures. Thus, both structures and entities at each level of the complexity hierarchy partially inherit the ability to act and a certain degree of existence from the structures and entities of the previous levels. Finally, I am trying to clarify the modal aspects of the ontic structural realism. Following the popular interpretations of quantum theory, the ability to act, and hence the existence of structures and entities, are considered separately in two worlds – potential and actual ones. The potential world is associated with a set of possible objects and structures of quantum theory, and the actual world is associated with a set of real (observable) objects and structures of classical physical theories. The transition from the potential to the actual world is proposed to be considered as a primitive metaphysical event. The proposed concept partially overcomes the objections to ontic structural realism, thereby strengthening its position in the discussion about the reality of quantum objects. (shrink)

This article is in two parts, with part II to appear in the next issue of JAE (Spring 2013). Part I (with six sections), in this issue, has two related objectives. The first objective is to examine a number of key substantive, methodological, and science-practice issues related to the field designated here as empirical psycho-aesthetics. The second objective is to present an outline of its origin and discuss certain important features of several related fields—experimental philosophy, cognitive-science-and-art, (cognitive) neuroscience of art, (...) and neuroaesthetics. To a certain extent, the comparative goal is approached through the analysis of several recent significant controversies. Throughout the discussion, the .. (shrink)