There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

Neuroeconomics, neuromarketing, neuroaesthetics, and neurotheology are just a few of the novel disciplines that have been inspired by a combination of ancient knowledge along with recent discoveries about how the human brain works.This fascinating and thought provoking new book critically questions our love affair with brain imaging.

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

There is a growing interest in Evald Ilyenkov’s work and its significance for contemporary debates. This interest spans several disciplines. One key thread in Ilyenkov’s ideas concerns a perspective on the relation between biology and psychology. In rejecting crude reductionism and individualism, Ilyenkov put forward a view of mind and personhood as emerging from activity and social practice. In his rejection of brain-bound notions of the mind, Ilyenkov’s ideas bear interesting resonances with current work in 4E cognition. One particularly interesting (...) resonance that has occasionally been noticed are the connections with the enactive approach to life and mind. However, beyond some hints at interesting convergences, there is to date no detailed comparison between the two views. The present article attempts to address this gap, examining both complementarities and possible tensions between the two approaches. Rejecting cognitive views detached from environmental and social processes, the enactive approach, as exemplified by De Jaegher and Di Paolo’s concept of participatory sense-making, emphasises the dynamic constitution of cognition through embodied and situated activities. The article draws parallels between Ilyenkov’s emphasis on historically and culturally situated activity, notably labour, and the enactive understanding of human bodies as dynamically constituted in human activity. The article explores the Ilyenkovian and enactive perspectives on the dialectics of ideality, challenging traditional dualistic views and proposing that the ideal emerges as metastable patterns in the ongoing interactions between world, practices, norms, and bodies. The article concludes by suggesting future research directions for the enactive approach, particularly in areas emphasised by Ilyenkov, such as labour and the mediation of material/cultural artefacts. (shrink)

A growing body of literature documents the important role played by moral outrage or moral anger in stakeholders’ reactions to cases of corporate social irresponsibility. Existing research focuses more on the consequences of moral outrage than a systematic analysis of how appraisals of irresponsible corporate behavior can lead to this emotional experience. In this paper, we develop and test, in two field studies, an extended model of moral outrage that identifies the cognitions that lead to, and are associated with, this (...) emotional experience. This research contributes to the existing literature on reactions to corporate social irresponsibility by explaining how observers’ evaluation of irresponsible corporate behavior leads to reactions of moral anger. The paper also helps clarify the difference between moral outrage and other types of anger and offers useful insights for managers who have to confront public outrage following cases of irresponsible corporate behavior. Finally, the analysis of the causes of stakeholders’ anger at irresponsible corporations opens important avenues for future research that are presented in the paper. (shrink)

We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.

In European culture the sacred and the secular have existed in a dialectical relationship. Prodi sees the fifteenth-century crisis of Christianity as opening up three paths that eroded this dualism and tended towards modernity: civic-republican religion, sacred monarchy, and the territorial churches. Important counter-forces, which sought to maintain dualism, included the Roman-Tridentine Compromise, and those forms of Radical Christianity which rejected confessionalisation outright. During the Eighteenth Century, all these phenomena tended to contribute to one of two tendencies: towards civic religion, (...) or towards political religion. The former preserved a distinction between conscience and law; the latter comprised a state religion which sought to perfect all of human nature. It was civic religion which become embodied in the early USA, alienating God from worldly power, but leaving him as the guarantor of agreements between humans. Back in Europe, Prodi tracks the relationship between the Catholic Church and the new national states. He then turns to the political religions of the Twentieth Century. Prodi concludes by emphasising that this dualism of sacred and secular power lay at the centre of Western modernity, and expresses his fears about the collapse of civic religion into political religion, especially in the USA. (shrink)

Here, I defend the view that fictional narratives are illusionary and that fictional names are to be accounted metalinguistically, a blend of Walton’s and Donnellan’s theories. Besides, I offer a remedial semantic for sentences external to the story which connects those uses back to the text of the story and to the neighborhood of its retellings.

The extreme sexual size dimorphism in spiders has motivated studies for many years. In many species the male can be very small relative to the female. There are several hypotheses trying to explain this fact, most of them emphasizing the role of energy in determining spider size. The aim of this paper is to review the role of energy in sexual size dimorphism of spiders, even for those spiders that do not necessarily live in high foliage, using physical and allometric (...) principles. Here we propose that the cost of transport or equivalently energy expenditure and the speed are traits under selection pressure in male spiders, favoring those of smaller size to reduce travel costs. The morphology of the spiders responds to these selective forces depending upon the lifestyle of the spiders. Climbing and bridging spiders must overcome the force of gravity. If bridging allows faster dispersal, small males would have a selective advantage by enjoying more mating opportunities. In wandering spiders with low population density and as a consequence few male–male interactions, high speed and low energy expenditure or cost of transport should be favored by natural selection. Pendulum mechanics show the advantages of long legs in spiders and their relationship with high speed, even in climbing and bridging spiders. Thus small size, compensated by long legs should be the expected morphology for a fast and mobile male spider. (shrink)

Este artículo compara las secuencias compositivas de la Antígona del escritor Jean Anouilh en relación con la pieza homónima de Sófocles. Se analizan las confluencias y los aspectos divergentes entre los personajes protagónicos y secundarios de ambas creaciones y se menciona la función del coro. Finalmente se exponen las conclusiones, y se subraya el tono fundamentalista que el personaje de Creón adquiere en el final de la obra. This article compares the compositional sequences of the Jean Anouilh's Antigone in relation (...) with the homonym Sophoclean play. Convergences and divergent aspects between the protagonists and secondary characters of both plays are analyzed and also the role of the Chorus is mentioned. Finally conclusions are presented, highlighting the fundamentalist tone which Creon acquires at the end of the play. (shrink)

Este trabajo se propone estudiar las características de los paralogismos de composición y división (Retórica II 24.II, 1401a), de la consecuencia (Retórica II 24.VI, 1401b20-30) y de la causa aparente (Retórica II 24.VII, 1401b30-34), de modo de analizar si Eurípides los utiliza en el agón de Andrómaca de los versos 577 a 746 This paper intends to study the characteristics of paralogisms due to composition and division (Rhetoric II 24.II, 1401a), due to consequent (Rhetoric II 24.VI, 1401b20-30), and due to (...) false cause (Rhetoric II 24.VII, 1401b30-34), in order to analyze if Euripides uses them in the agon in Andromache (577-746). (shrink)

La struttura a livelli modella il tutto e le sue parti con grande generalità. Lo dimostrano le argomentazioni teoriche (4.3), (4.4) e (4.5), e lo comprova la casistica che è stata aggiunta. Una tale struttura non presenta affatto i problemi a), b) e c) che sono tipici della struttura ad albero. Essa corregge inoltre deviazioni concettuali che sono diffuse nel settore informatico. L’immediatezza deviazioni concettuali che sono diffuse nel settore informatico. L’immediatezza visiva, infine, ne facilita la diffusione sul piano professionale (...) e tecnico.Per concludere, ritengo che la struttura a livelli possa fornire un contributo anche alle ricerche di ontologia e in particolare possa favorire i tentativi di unificazione condotti sia sul piano teorico, sia su quello applicativo [Uschold 1996]. Le difficoltà ed i limiti che la teoria degli insiemi oppone ad un formalismo generale (ad esempio quando riduce la casistica della relazione concetto di livello possiede una valenza estremamente ampia e ciò lo predispone per gli auspicati sviluppi ontologici. (shrink)