In this paper we present the problem of a noisy lexical taxonomy and suggest two tasks as potential remedies. The first task is to identify and eliminate incorrect hypernymy links, and the second is to repopulate the taxonomy with new relations. The first task consists of revising the entire taxonomy and returning a Boolean for each assertion of hypernymy between two nouns (e.g. brie is a kind of cheese). The second task consists of recursively producing a chain of hypernyms for (...) a given noun, until the most general node in the taxonomy is reached (e.g. brie → cheese → food → etc.). In order to achieve these goals, we implemented a hybrid hypernym-detection algorithm that incorporates various intuitions, such as syntagmatic, paradigmatic and morphological association measures as well as lexical patterns. We evaluate these algorithms individually and collectively and report findings in Spanish, English and French. (shrink)

O presente texto constitui-se como resenha do livro Dispositivi della Normatività, de Antonio Tucci, professor da Università degli Studi di Salerno, Itália. Ao longo da obra, Tucci joga luzes sobre a questão da norma, da normalização e dos dispositivos de segurança, inserindo temas como o da soberania — referente às questões fronteiriças —, da identidade e da cidadania —, ao abordar questões relacionadas aos processos de subjetivação e à necessária reespacialização do espaço político, em um panorama da governamentalidade biopolítica.

Inhaltsverzeichnis/Table of Contents:IntroductionAntónio ZILHÃO: Folk-Psychology, Rationality and Human ActionJoão BRANQUINHO: The Problem of Cognitive DynamicsJ.P. MONTEIRO: Hume, Induction and Single ExperimentsMarco RUFFINO: The Primacy of Concepts and the Priority of Judgments in Frege's LogicJoão Vergílio Gallerani CUTER: Die unanwendbare Arithmetik des TractatusSílvio PINTO: Wittgenstein's Anti-PlatonismFernando FERREIRA: A Substitutional Framework for Arithmetical ValidityJ.R. CROCA & R.N. MOREIRA: Indeterminism Versus CausalismLuíz MONIZ PEREIRA: The Logical Impingement of Artifical Intelligence.

INCONTINENCE, HONOURING SUNK COSTS AND RATIONALITY According to a basic principle of rationality, the decision to engage in a course of action should be determined solely by the analysis of its consequences. Thus, considerations associated with previous use of resources should have no bearing on an agent’s decision-making process. Frequently, however, agents persist carrying on an activity they themselves judge to be nonoptimal under the circumstances because they have already allocated resources to that activity. When this is the case, agents (...) are said to be honouring sunk costs. Honouring sunk costs is thus typically viewed as irrational economic behaviour. Two striking findings of the psychological literature on the sunk cost effect are that it is, in general, not lessened by having taken previously courses in economics, and that agents who did take such courses and that do honour sunk costs seem to be frequently aware of a cognitive dissonance in their behaviour. Davidson’s account of the possibility conditions of incontinent action renders continent action materially unfeasible. The very idea of incontinent action becomes thus a hollow one. I’ll present an alternative description of these possibility conditions that renders continent action materially feasible, and both, continent and incontinent action, cognitively plausible. In a nutshell, my proposal rests upon the drawing of an essential cognitive contrast between explicit processes of deliberative reasoning and lower level heuristic procedures. I conclude the paper arguing that my redescription of incontinent action accounts for the above mentioned cognitive dissonance effect better than the alternatives and that viewing at least an important subset of behaviours of honouring sunk costs as incontinent actions will enable us to consider them as peculiar manifestations of a more general and meaningful pattern in human behaviour. (shrink)

Leibnizian-Newtonian calculus was a theory that dealt with geometrical objects; the figure continued to play one of the fundamental roles it had played in Greek geometry: it susbstituted a part of reasoning. During the eighteenth century a process of de-geometrization of calculus took place, which consisted in the rejection of the use of diagrams and in considering calculus as an 'intellectual' system where deduction was merely linguistic and mediated. This was achieved by interpreting variables as universal quantities and introducing the (...) notion of function, which replaced the study of curves. However, the emancipation of calculus from its basis in geometry was not comprehensive. In fact, the geometrical properties of curves were attributed de facto to functions and thus eighteenth-century calculus continued implicitly to use principles borrowed from geometry. There was therefore no transition to a purely syntactical theory based on axiomatically introduced terms, a shift which only took place subsequently in modern times. (shrink)

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

Antonio Negri wrote the two essays that comprise Time for Revolution while serving a prison sentence for alleged involvement with radical left-wing groups. Although the essays were written two decades apart, their concerns are the same: is there a place for resistance in a society utterly subsumed by capitalism? In the wake of the global crisis of capitalism heralded by the 2008 crash, the question has never been more relevant and Negri remains an insightful and passionate guide to any (...) attempt to answer it. (shrink)

Central to the legal positivism of the nineteenth and the first half of the twentieth century was the dogma of the Ideal Legislator. Legal materials were to be interpreted as the work of an omniscient, coherent, consistent legislator. We argue that this dogma persists in the different guise of the competent speaker model, on which legal materials are the work of a competent speaker, who follows all the pertinent semantic and pragmatic rules. We will first lay out the Ideal Legislator (...) dogma as applied in legal interpretation, arguing that this dogma does not limit interpretive discretion but rather amplifies it by hiding it under the veil of an inexistent, purely instrumental rationality. We will then turn to the competent speaker model, showing that, despite its apparent neutrality, it proves to be a reincarnation of the Ideal Legislator dogma, for it, too, amplifies interpretive discretion, only it hides it under the veil of an inexistent, purely linguistic rationality. Finally, we will inquire into the different types of rationality and their relations, arguing that there is always a choice and value judgment involved in ascribing rationality to legislators, and that these choices and judgments need to be carefully inspected and normatively justified. (shrink)

Caro leitor! Em busca de sempre mais apresentar reflexões consistentes e relevantes para o pensar teológico, em conexão com o mundo e às urgências da Igreja, a presente edição trás importantes temas que ajudam refletir a realidade humana à luz do mistério de Deus. Por isso, os artigos oferecidos nas mais variadas áreas, a saber: bíblico-teológica, dogmática, moral, pastoral, antropologia teológica, filosofia e eclesiologia, dão suporte científico e metodológico para a reflexão teológica. Antes de conferir as novidades desta edição, gostaria (...) de comunicar que esta Revista Eletrônica conquistou um espaço ainda maior de publicação, ao tornar-se indexada na base de dados do Directory of Open Access Journals (DOAJ). (shrink)

How is the tension between conflict and deliberation resolved in shareholder engagement? We address this question by studying shareholder engagement as a deliberative process with three stages: establishing dialogue, solution development, and solution implementation. We theorize that two interactionist mechanisms, deliberative interaction and the voicing of disagreement, play different roles at different stages of the process. We test our hypotheses with a proprietary database of 169 environmental, social, and governance engagements with US public companies over 2007–12. We find that while (...) deliberative interaction does not help advance the engagement process, it positively moderates the effect of disagreement in the solution development stage. By contrast, in the solution implementation stage, deliberative interaction amplifies the negative effect of disagreement, thus hindering progress in the engagement. Our article contributes to shareholder engagement, deliberation theory, and interactionist organization theory by establishing that engagement effectiveness is an interactional achievement shaped by both deliberation and disagreement. (shrink)

“Nudging” is commonly seen as an appealing form of “Smart legislation” based on the findings of Behavioural sciences and alternative to traditional forms of regulation. However, notwithstanding the ever increasing references and a growing body of literature on its acceptability, a proper definition of the concept seems still lacking, since all the attempts to date have only provided over- or under-inclusive definitions. This chapter purports to offer a more plausible definition. Firstly, the received view and especially Thaler’s and Sunstein’s descriptions (...) of nudging will be examined and subjected to a first critical assessment. Secondly, a few examples will be made of policies enacted all around the world which are usually referred to as cases of nudging. Thirdly, some of the elements which have often been associated to nudging as its definitional features will be tested against the set of examples: such test will show that most of those elements must be done away with. Lastly, a “minimal” definition will be offered. While allowing us to distinguish nudging from other forms of conduct-influencing interventions, the minimal definition will exclude many features as its necessary conditions: among others, those related to specific ends and political ideologies. (shrink)

This work proposes research on a still unexplored psychical world: thoughts, emotions, and real events experienced by racket victims of the three largest criminal organizations of the South of Italy: Mafia, Camorra, and ‘Ndrangheta. The purpose is to understand the multifaceted psycho-anthropological and social issues criminal organizations have settled on, and particularly which psycho-relational dynamics and sociocultural codes come into play in the complex and controversial relationship between victim and criminal system, between victim and support systems. With entrepreneurs and tradesmen (...) victims of organized crime, we have analyzed lived experiences—in particular fear—and psychological problems they had to cope with; events and motivations that allowed them “breaking” the silence and asking for help; the representation of a support network before and after their possible pressing charges; the kind of help offered by support systems. Dignity and self-respect, the fight for one's own freedom and honor,.. (shrink)

This paper proposes a critical analysis of that interpretation of the Nāgārjunian doctrine of the two truths as summarized—by both Mark Siderits and Jay L. Garfield—in the formula: “the ultimate truth is that there is no ultimate truth”. This ‘semantic reading’ of Nāgārjuna’s theory, despite its importance as a criticism of the ‘metaphysical interpretations’, would in itself be defective and improbable. Indeed, firstly, semantic interpretation presents a formal defect: it fails to clearly and explicitly express that which it contains logically; (...) the previously mentioned formula must necessarily be completed by: “the conventional truth is that nothing is conventional truth”. Secondly, after having recognized what Siderits’ and Garfield’s analyses contain implicitly, other logical and philological defects in their position emerge: the existence of the ‘conventional’ would appear—despite the efforts of semantic interpreters to demonstrate quite the contrary—definitively inconceivable without the presupposition of something ‘real’; moreover, the number of verses in Nāgārjuna that are in opposition to the semantic interpretation (even if we grant semantic interpreters that these verses do not justify a metaphysical reconstruction of Nagarjuna’s doctrine) would seem too great and significant to be ignored. (shrink)

This article aims to propose some connections between the conceptions of poetry of the Mexican poet Octavio Paz and the German philosopher Martin Heidegger. Both see in poetry the element of recognition of the original condition of the human being, not as an interpretation, but as a perception and affectation of the existential reality of human beings. So that the event of the "poetic saying" is configured as a call to the possibility of glimpsing the being of each entity, inhabiting (...) oneself and, thus, learning to be with others, establishing the poetic field as the clearing of perception and of existential affectation. Poetic speech goes beyond the limits of language, creating and establishing meanings and representations to the affectations that poetry provides. Thus, through poetry man recognizes himself in his worldliness, in search of his own being and in his relationship with other beings. (shrink)

O trabalho pretende, a partir da publicação das “Confissões da Carne”, analisar o impasse que diz respeito a sua não publicação em vida por Foucault, em especial em função da entrada do sujeito como terceiro componente do triângulo arqueológico-genealógico, impondo uma reviravolta decisiva em sua pesquisa. A força aletúrgica do sujeito implica uma definitiva dessoberanização do dispositivo de poder. Por um lado, se a forma moderna prevê a sua transferência de um poder sobre si próprio aos outros, o complexo de (...) estratégias governamentais, que «orientam» a direção da consciência, não implica a abdicação da liberdade por parte da pessoa a qual foi dirigida; por outro, uma segunda operação surge da diferenciação específica entre o modelo antigo e o modelo cristão, quer dizer, se o antigo modelo de direção funciona com vistas à autonomização do sujeito, aquele exame de consciência cristão estabelece como eixo a dependência e desenvolve uma racionalidade pastoral. Assim Foucault chega a uma estética da existência que é puro exercício de liberdade e perfeita atitude, que se oferece aos outros como prova do seu próprio valor. É com isso que o volume quarto da história da sexualidade é confrontado. O que muda drasticamente na experiência cristã da carne é a relação do sujeito com a verdade. A confissão, mais do que expiação dos pecados, neste quadro intervém como atestado e como testemunho de si próprio. Em conclusão, para Foucault, conotado pela imperfeição que o domina, o sujeito cristão liga-se a uma interminável direção de consciência cujo preço é uma perda de identidade indefinida. Assim, a partir deste recorte, o problema que passa a enfrentar é como encontrar uma forma de fundamentar a hermenêutica de si, não no sacrifício, mas numa “emergência positiva”, teórica e prática, de si, expondo tanto o momento transicional das “Confissões da Carne” quanto a própria razão pela qual renuncia à sua publicação. (shrink)

This article aims at providing a critical review of the main studies about Mafia in a theoretical psychological and socio-anthropological framework, and investigating the perception of the phenomenon in relation to moral disengagement and values orientation in two groups of Sicilian teenagers, living in contexts with different Mafia density. Today Mafia is represented as a socio-psychological phenomenon, which has managed to make culture, community, family, and individuals coincide; it is founded on an individualistic social conception according to which violence is (...) the strongest form of self-achievement. (shrink)

According to a well-established interpretive line, the Benthamic judge would be allowed no room for autonomous calculations of utility and his or her task would only be that of mechanically applying substantive law, which expresses the legislator's will. For Gerald Postema, in contrast, Bentham's judge would be granted ample power to decide cases by directly applying the principle of utility. This article criticizes both views, by showing that a adjudication was for Bentham utterly impossible, although this does not mean that (...) judges should be free to decide according to direct utility calculations. Judges must be the tutors of the citizens’ expectations, which, under a system of statute law, will focus on the code. However, they can avoid suboptimality in cases where applying a general rule would not maximize utility, without preponderant damage for law-induced expectations: Bentham's suggestion is that they do so by proposing amendments of the code to the legislature. (shrink)

This paper proposes an interpretation of Nāgārjuna’s doctrine of the two truths that considers saṃvṛti and paramārtha-satya two visions of reality on which the Buddhas, for soteriological and pedagogical reasons, build teachings of two types: respectively in agreement with (for example, the teaching of the Four Noble Truths) or in contrast to (for example, the teaching of emptiness) the category of svabhāva. The early sections of the article show to what extent the various current interpretations of the Nāgārjunian doctrine of (...) the dve satye—despite their sometimes even macroscopic differences—have a common tendency to consider the notion of śūnyatā as a teaching not based on, but equivalent to supreme truth. This equivalence—philologically questionable—leads to interpretative paths that prove inevitably aporetic: indeed, according to whether the interpretation of śūnyatā is ‘metaphysical’ or ‘anti-metaphysical’, it gives rise to readings of Nāgārjuna’s thought incompatible, respectively, with anti-metaphysical and realistic types of verses traceable in the works of the author of the Mūla-madhyamaka-kārikā (MMK). On the contrary, by giving more emphasis to the expression samupāśritya (“based on”), which recurs in MMK.24.8, and therefore, by epistemologically separating the notion of śūnyatā from the notion of paramārtha-satya (and of some of its conceptual equivalents such as nirvāṇa, tattva and dharmatā), we may obtain an interpretation—at once realistic and anti-metaphysical—of the theory of the two truths compatible with the vast majority (or even totality) of Nāgārjuna’s verses. (shrink)

Este trabalho agencia a obra de Gilles Deleuze e Félix Guattari à educação em ciências ao jogar luzes sobre o deslocamento que permeia a organização deste componente curricular. O uso destes autores para pensarmos a educação em ciências, possibilita a (re)inserção da diferença e da multiplicidade, extirpadas do estrato científico pelo sonho moderno de totalização da realidade – que persiste no pedagógico – por meio da redução conceitual operada pela lógica da identidade. Assim, evidencia as (des)continuidades das práticas entre um (...) estrato e outro, como resultado da força de uma tradição que passa a ser subvertida pelo corte epistemológico deleuzo-guattariano. (shrink)

Columbia University Press's multivolume _Prison Notebooks_ is the only complete critical edition of Antonio Gramsci's seminal writings in English. Based on the authoritative Italian edition of Gramsci's work, _Quaderni del Carcere_, this comprehensive translation presents the intellectual as he ought to be read and understood, with critical notes that clarify Gramsci's history, culture, and sources; an index of names; and a contextualization of the thinker's ideas against his earlier writings and letters. This set includes notebooks 1 through 8 with (...) all attendant notes and materials and is an indispensible resource for scholars in the humanities and social sciences. (shrink)

This paper supports the thesis that nihilistic interpretations of Madhyamaka philosophy derive from generally antirealistic and/or metaphysical approaches to Nāgārjuna’s thought. However, the arguments and many images by way of which the author of the Mūlamadhyamakakārikā and his Indian commentators defend themselves from the charge of nihilism show limits in these approaches, and rather confirm that Nāgārjuna’s philosophy should be read as a theoretical proposal that is at once realistic and antimetaphysical. The epistemology inherent to the soteriological dimension of the (...) Buddha’s teaching, of which Nāgārjuna presents himself as a faithful continuer, assesses on the one hand the accomplishment of a ‘cognitive revolution’ consisting in the achievement of a new vision of reality and on the other the avoidance of any metaphysical description of the same vision. Comprehension of the Madhyamaka philosophical enterprise through a realistic-antimetaphysical lens seems to hinder and prevent the possibility of any nihilistic interpretation of Nāgārjuna. (shrink)

This paper supports the thesis that nihilistic interpretations of Madhyamaka philosophy derive from generally antirealistic and/or metaphysical approaches to Nāgārjuna’s thought. However, the arguments and many images by way of which the author of the Mūlamadhyamakakārikā and his Indian commentators defend themselves from the charge of nihilism show limits in these approaches, and rather confirm that Nāgārjuna’s philosophy should be read as a theoretical proposal that is at once realistic and antimetaphysical. The epistemology inherent to the soteriological dimension of the (...) Buddha’s teaching, of which Nāgārjuna presents himself as a faithful continuer, assesses on the one hand the accomplishment of a ‘cognitive revolution’ consisting in the achievement of a new vision of reality and on the other the avoidance of any metaphysical description of the same vision. Comprehension of the Madhyamaka philosophical enterprise through a realistic-antimetaphysical lens seems to hinder and prevent the possibility of any nihilistic interpretation of Nāgārjuna. (shrink)

Some time ago I advanced on the pages of this journal a critique of the interpretation given by Jay L. Garfield and Mark Siderits (hereafter GS) of Nāgārjuna’s doctrine of the two truths (Ferraro, J Indian Philos 41(2):195–219, 2013.1); to my article the two authors responded with a ‘defense of the semantic interpretation’ of the Madhyamaka doctrine of emptiness (GS, J Indian Philos 41(6):655–664, 2013). Their reply, however, could not consider my personal understanding of Nāgārjuna’s notions of śūnyatā and (...) dve satye. My interpretation of these notions was in fact absent in the paper GS responded, and was only related in a second paper of mine (Ferraro, J Indian Philos 41(5):563–590, 2013.2), still unpublished at the time of GS’s drafting of their ‘defense’. Therefore, in the present rejoinder, I found it appropriate, rather than responding point by point to the passages of GS’s reply, to advance a comparison between the semantic interpretation and my ‘realist antimetaphysical’ understanding of Nāgārjuna’s thought. (shrink)

Book Description (Blurb): Cognitive Design for Artificial Minds explains the crucial role that human cognition research plays in the design and realization of artificial intelligence systems, illustrating the steps necessary for the design of artificial models of cognition. It bridges the gap between the theoretical, experimental and technological issues addressed in the context of AI of cognitive inspiration and computational cognitive science. -/- Beginning with an overview of the historical, methodological and technical issues in the field of Cognitively-Inspired Artificial Intelligence, (...) Lieto illustrates how the cognitive design approach has an important role to play in the development of intelligent AI technologies and plausible computational models of cognition. Introducing a unique perspective that draws upon Cybernetics and early AI principles, Lieto emphasizes the need for an equivalence between cognitive processes and implemented AI procedures, in order to realise biologically and cognitively inspired artificial minds. He also introduces the Minimal Cognitive Grid, a pragmatic method to rank the different degrees of biologically and cognitive accuracy of artificial systems in order project and predict their explanatory power with respect to the natural systems taken as source of inspiration. -/- Providing a comprehensive overview of cognitive design principles in constructing artificial minds, this text will be essential reading for students and researchers of artificial intelligence and cognitive science. (shrink)

Este ensaio aborda a problemática do corpo na educação em ciências. Para tanto, toma como exemplo o corpo utópico utilizado na ciência, colocando-o em uma perspectiva crítica a partir do seu não reconhecimento como modelo corporal. Como contraponto, trabalha com a ideia de corpo heterotópico, como corpo real, singular, que se produz e se traduz como prática de resistência. A partir deste conceito evidencia-se o potencial da educação em ciências para a estetização da ciência, recolocando a discussão do reconhecimento e (...) da autodeterminação do outro como pauta para uma agenda formativa humanística, comprometida com uma ético-estética das alteridades na ciência. (shrink)

In the first part of this paper I critically examine some of the main interpretations of “classical” Yogācāra philosophy of Maitreya, Asaṅga and Vasubandhu. Among these interpretations, based on extant textual and contextual data, I consider philologically unlikely both metaphysical-idealistic readings, which ascribe to these authors the view that ultimate reality is a mental or subjective stuff, and epistemological-idealistic readings which advocate that either Yogācāra suspends judgment on the existence of the extramental or that it maintains that the extramental exists (...) in itself and ultimately. Instead, I consider more likely the thesis that classical Yogācāra upholds an epistemological idealism that, while admitting epistemological priority of the mental over the extramental, rules out the ultimate existence of both the former and the latter. This exclusion, however, does not amount to the exclusion of every metaphysics, but rather to the adoption of a metaphysics of emptiness conceived, in fact, as absence of the mental/extramental dichotomy. In the second part of the paper this reading of classical Yogācāra is compared with the interpretation of Nāgārjuna’s philosophy that I elsewhere called “realistic antimetaphysical”, and I reach the conclusion that, while with respect to epistemology between early Madhyamaka and classical Yogācāra there is continuity, regarding metaphysics these two schools are deeply distinct and discontinuous: while Nāgārjuna conceives of emptiness as an extinction of any metaphysical view, Yogācāra emptiness actually presents itself as a metaphysical point of view. (shrink)

In this paper we identify and characterize an analysis of two problematic aspects affecting the representational level of cognitive architectures (CAs), namely: the limited size and the homogeneous typology of the encoded and processed knowledge. We argue that such aspects may constitute not only a technological problem that, in our opinion, should be addressed in order to build arti cial agents able to exhibit intelligent behaviours in general scenarios, but also an epistemological one, since they limit the plausibility of the (...) comparison of the CAs' knowledge representation and processing mechanisms with those executed by humans in their everyday activities. In the fi nal part of the paper further directions of research will be explored, trying to address current limitations and future challenges. (shrink)

In actuarial parlance, the price of an insurance policy is considered fair if customers bearing the same risk are charged the same price. The estimate of this fair amount hinges on the expected value obtained by weighting the different claims by their probability. We argue that, historically, this concept of actuarial fairness originates in an Aristotelian principle of justice in exchange (equality in risk). We will examine how this principle was formalized in the 16th century and shaped in life insurance (...) during the following two hundred years, in two different interpretations. The Domatian account of actuarial fairness relied on subjective uncertainty: An agreement on risk was fair if both parties were equally ignorant about the chances of an uncertain event. The objectivist version grounded any agreement on an objective risk estimate drawn from a mortality table. We will show how the objectivist approach collapsed in the market for life annuities during the 18th century, leaving open the question of why we still speak of actuarial fairness as if it were an objective expected value. (shrink)

In this article, we will show how Derrida’s deconstruction of modern individualism, exemplified by Robinson Crusoe’s attitude toward nature, addresses the contemporary debate on the Anthropocene. Through Hadot’s genealogy of modern “prometheanism,” we will discuss how a different gaze by human beings on themselves and nature can lead us out of the modern self-conception of the human person, that is resulting in the Anthropocene era, its catastrophic results endangering the very survival of humankind. Through Morton’s conception of hospitality and Haraway’s (...) notion of Chthulucene, we argue that a new individual and collective conversion to nature may result in an era in which human beings can conceive of themselves as ethical parts of nature. Hence, a new view on the reciprocal interdependence between human beings and nature can be affirmed, creating a feeling of hospitality without hostility. We conclude by considering Agamben’s recovery of Franciscanism, as a form-of-life, preceding modernity, in which this ethical, natural civilization was firstly foreseen. (shrink)

In this paper I illustrate the evolution of series theory from Leibniz and Newton to the first decades of the eighteenth century. Although mathematicians used convergent series to solve geometric problems, they manipulated series by a mere extension of the rules valid for finite series, without considering convergence as a preliminary condition. Further, they conceived of a power series as a result of a process of the expansion of a finite analytical expression and thought that the link between series and (...) analytical expression was not restricted to the interval of convergence. This gave rise to formal aspects that became progressively more evident while the complexity of the theory increased. Asymptotic and recurrence series emerged as the result of the natural evolution of theory, without the difference between these infinite processes with respect to ordinary series being highlighted. The various aspects of dealing with series can be viewed today as derived from different definitions of the sum. However, mathematicians of that time always considered them as different approaches to a single theory that was based on a unique notion of the sum (even though, later in the eighteenth century, they disagree about what this notion was). (shrink)

In this paper I illustrate the evolution of series theory from Leibniz and Newton to the first decades of the eighteenth century. Although mathematicians used convergent series to solve geometric problems, they manipulated series by a mere extension of the rules valid for finite series, without considering convergence as a preliminary condition. Further, they conceived of a power series as a result of a process of the expansion of a finite analytical expression and thought that the link between series and (...) analytical expression was not restricted to the interval of convergence. This gave rise to formal aspects that became progressively more evident while the complexity of the theory increased. Asymptotic and recurrence series emerged as the result of the natural evolution of theory, without the difference between these infinite processes with respect to ordinary series being highlighted. The various aspects of dealing with series can be viewed today as derived from different definitions of the sum. However, mathematicians of that time always considered them as different approaches to a single theory that was based on a unique notion of the sum (even though, later in the eighteenth century, they disagree about what this notion was). (shrink)