Two questions should be considered when assessing the Kantian dimensions of Kuhn’s thought. First, was Kuhn himself a Kantian? Second, did Kuhn have an influence on later Kantians and neo-Kantians? Kuhn mentioned Kant as an inspiration, and his focus on explanatory frameworks and on the conditions of knowledge appear Kantian. But Kuhn’s emphasis on learning; on activities of symbolization; on paradigms as practical, not just theoretical; and on the social and community aspects of scientific research as constitutive of scientific reasoning, (...) are all outside the Kantian perspective. Kuhn’s admiration for Kant is tempered by his desire to understand the processes of learning, of initiation into a scientific community, of experimentation using instruments, and of persuasion, drawing on the work of familiar influences, including Piaget, Koyré, and Wittgenstein, and less familiar ones, including Langer, Demos, and Frank. Both Kuhn and Kant were interested in the question: what is the status of science, and what is the role of the scientist in its development and justification? But Kuhn presents science in a much more messy, historically contingent, and socially charged way than Kant does. The paper’s conclusion evaluates Kuhn’s reception among researchers including Richardson and Friedman, assessing the prospects for future work. (shrink)

The author of the present paper argues that while trying to explain the institutional success of the science and its broad social impact, it is worth throwing aside the arguments concerning the universal traits of human nature, changes in the human mentality, or transformation of the culture and civilization, such as the development of capitalism or bureaucratic power. In the 16th century no new man emerged, and no mutants with overgrown brains work in modern laboratories. So one must also reject (...) the Great Divide between the cultures of the scientific and pre-scientific and replace it with multiple, uncertain and unexpected ‘not-so-great divides’, which can be described in meticulous anthropological studies. Although the achievements of science are certainly spectacular, and the gap between scientific practice and other areas of activity is so obvious, this does not mean that one must look for the \"great\" reasons behind this situation. One should rather focus on quite down-to-earth practices and tools used by scientists. A significant part of their activities can be described by referring to the craft of writing, reading and transforming of various types of inscriptions (records), and broadly understood visualization – their combining, performing, interpreting, confronting, comparing, shifting, shuffling etc. The important role of these tools and methods is especially visible in situations of scientific controversy. It is so because scientific controversies are won by the one able to muster on the spot the largest number of well aligned and faithful allies, and the technology of writing, printing and visualizing play a special role in mobilizing them. These are necessary to ensure that certain factors can be mobile – easy to move from place to place, and yet, immutable – not undergoing deformation as a result of the movement. This way, scientists are able to not only diffuse different types of factors relevant to the dispute and the process of constituting science, but also concentrate them in the centers of calculation, where, through accumulation, one can take actions not available elsewhere. (shrink)

Starting with a discussion of what I call Koyré’s paradox of conceptual novelty, I introduce the ideas of Damerow et al. on the establishment of classical mechanics in Galileo’s work. I then argue that although the view of Damerow et al. on the nature of Galileo’s conceptual innovation is convincing, it misses an essential element: Galileo’s use of the experiments described in the first day of the Two New Sciences. I describe these experiments and analyze their function. Central to my (...) analysis is the idea that Galileo’s pendulum experiments serve to secure the reference of his theoretical models in actually occurring cases of free fall. In this way Galileo’s experiments constitute an essential part of the meaning of the new concepts of classical mechanics. (shrink)

: In the concluding pages of his Epistolae duae de motu impresso a motore translato (1642), Pierre Gassendi provides a brief summary of the explanation of the tides found in Galileo's Dialogue over the Two Chief World Systems (1632). A comparison between the two texts reveals, however, that Gassendi surreptitiously modifies Galileo's theory in some crucial points in the vain hope of rendering it more compatible with the observed phenomena. But why did Gassendi not acknowledge his departures from the Galilean (...) model? The present article argues that cautiousness was just one of the reasons that stopped the French priest from turning Galileo's theory into his own theory. He was probably also aware of the fact that Kepler's model of planetary motion, which he endorsed in the Epistolae, could not be reconciled with Galileo's explanation of the tides. In the postumously published Syntagma philosophicum (1658), Gassendi tried to mend this major inconsistency by arguing that Galileo's theory of the tides not only remained valid, but became even more coherent, if one attributed to the Earth an elliptic orbit. But given that in the Syntagma Gassendi officially adhered to the Tychonic system, his effort to reconcile Kepler and Galileo, while already unconvincing by itself, appears completely futile. (shrink)

The project of integrated HPS has occupied philosophers of science in one form or another since at least the 1960s. Yet, despite this substantial interest in bringing together philosophical and historical reflections on the nature of science, history of science and formal philosophy of science remain as divided as ever. In this paper, I will argue that the continuing separation between historical and formal philosophy of science is ill-founded. I will argue for this in both abstract and concrete terms. At (...) the abstract level, I reconstruct two possible arguments for the incompatibility of historical and formal philosophy of science and argue that they are both wanting. At the concrete level, I discuss how historical and formal philosophy of science have been brought together in practice, namely: in the form of a largely forgotten research tradition that I will refer to here as the study of formalized macro-units. After a brief exposition, I argue that this research tradition has been unduly overlooked by historically minded philosophers of science. Bringing together these observations, I argue that the divide between historical and formal philosophy of science is not grounded in any substantive arguments, but can be primarily attributed to disciplinary happenstance. (shrink)

CAMILO, Bruno. Aspectos metafísicos na física de Newton: Deus. In: DUTRA, Luiz Henrique de Araújo; LUZ, Alexandre Meyer (org.). Temas de filosofia do conhecimento. Florianópolis: NEL/UFSC, 2011. p. 186-201. (Coleção rumos da epistemologia; 11). Através da análise do pensamento de Isaac Newton (1642-1727) encontramos os postulados metafísicos que fundamentam a sua mecânica natural. Ao deduzir causa de efeito, ele acreditava chegar a uma causa primeira de todas as coisas. A essa primeira causa de tudo, onde toda a ordem e leis (...) tiveram início, a qual para ele assume um caráter divino, Newton aponta para um Deus sábio e poderoso e responsável pela ordem inteligente e pela a harmonia das leis físicas e universais de tudo o que existe – Deus como criador e preservador da ordem do universo. Há ainda a analogia do conceito de Deus com o espaço e o tempo, na medida em que ambos comunicam infinitude e onipresença. Por fim, nas considerações finais apontarei a importância de Newton para a metafísica moderna e como os seus estudos contribuíram para uma visão posterior do universo e suas leis e do homem enquanto ser pensante. (shrink)

Metascientific criteria used for explaining or constraining physical space dimensionality and their historical relationship to prevailing causal systems are discussed. The important contributions by Aristotle, Kant and Ehrenfest to the dimensionality of space problem are considered and shown to be grounded on different causal explanations: causa materialis for Aristotle, causa efficiens for young Kant and an ingenious combination of causa efficiens and causa formalis for Ehrenfest. The prominent and growing rôle played by causa formalis in modern physical approaches to this (...) problem is emphasized. (shrink)

In 1962, the publication of Thomas Kuhn’s Structure ‘revolutionized’ the way one conducts philosophical and historical studies of science. Through the introduction of both memorable and controversial notions, such as paradigms, scientific revolutions, and incommensurability, Kuhn argued against the traditionally accepted notion of scientific change as a progression towards the truth about nature, and instead substituted the idea that science is a puzzle solving activity, operating under paradigms, which become discarded after it fails to respond accordingly to anomalous challenges and (...) a rival paradigm. Kuhn’s Structure has sold over 1.4 million copies and the Times Literary Supplement named it one of the “Hundred Most Influential Books since the Second World War.” Now, fifty years after this groundbreaking work was published, this volume offers a timely reappraisal of the legacy of Kuhn’s book and an investigation into what Structure offers philosophical, historical, and sociological studies of science in the future. (shrink)

ABSTRACT BEER, P. A. C. The matter of truth in knowledge production about psychic suffering: considerations from Ian Hacking and Jacques Lacan. 2020. 250p. Thesis (PhD) – Instituto de Psicologia, Universidade de São Paulo, São Paulo, 2020. The thesis aims to reaffirm the importance of the debate around the matter of truth in relation to the production of knowledge concerning psychic suffering. Its point of departure is the understanding that the matter of truth contains two main appearances: as employed to (...) legitimize produced knowledge while establishing normative patterns, and as presenting itself in a critical form as a disruptive element to established knowledge. As such, it is a discussion that embraces both an affirmation of knowledge’s necessary character and of its variability. It will be argued in the above sense that the term “truth” must be taken as an inclusive and reciprocal gathering of epistemological, ontological, ethical and political elements. Ian Hacking’s historicized understanding of science enables such a consideration of contingent bases to scientific practice, while still producing necessary knowledge. It thus becomes is possible to establish a field in which normative understandings about scientific praxis might be criticized without it resulting in any kind of refusal or disqualification of the relevant, produced knowledge. Hacking’s proposition of a “historical ontology” and of a “dynamic nominalism” also represents an important contribution to the accumulation of knowledge production about psychic suffering debate, by affirming the ontological effects of knowledge. The way as truth is mobilized within Lacanian psychoanalysis flows from that standpoint, seen as focused on three main elements: truth’s autonomy towards the subject, (truth speaks), the opposing and temporary character of a positivized truth facing established knowledge ,(truth as critique), and the negative dimension of truth which relates to the inexhaustibility of this dialectical process of negations, (truth as radical difference). It is argued that it is possible to sustain a particular reasoning style, (in Hacking’s terms), for psychoanalysis, which is based on radical negativity. It is further argued, that the above rationalities in question work with a historicized understanding of knowledge that does not have any external (nor internal) criteria to warrant its truth. However, psychoanalysis takes negativity — arguably the base of knowledge’s variability and of truth’s disruptive character — beyond Hacking’s philosophy of science, and can thus offer even wider possibilities of thinking about the causality of psychic suffering. Even if with different intensities, both approaches signal the necessity of ethical and political implication in knowledge’s production and employment. Once there is no epistemological warranty to knowledge, its production value reverts to social agreements and ethical positioning. There is, therefore, the necessity of considering power relations. Finally, it is argued that the radical negativity sustained from psychoanalysis locates the political as an actually necessary field, inescapable by the very fact that it is not possible to crystalize any form of truth which is not the affirmation of radical difference. It is maintained then that introducing the matter of truth has as horizon the production of a kind of knowledge about psychic suffering which puts into question, at all time, its epistemological, ontological, ethical and political assumptions. (shrink)

Robert Hooke’s theory of gravitation is a promising case study for probing the fruitfulness of Menachem Fisch’s insistence on the centrality of trading zone mediators for rational change in the history of science and mathematics. In 1679, Hooke proposed an innovative explanation of planetary motions to Newton’s attention. Until the correspondence with Hooke, Newton had embraced planetary models, whereby planets move around the Sun because of the action of an ether filling the interplanetary space. Hooke’s model, instead, consisted in the (...) idea that planets move in the void space under the influence of a gravitational attraction directed toward the sun. There is no doubt that the correspondence with Hooke allowed Newton to conceive a new explanation for planetary motions. This explanation was proposed by Hooke as a hypothesis that needed mathematical development and experimental confirmation. Hooke formulated his new model in a mathematical language which overlapped but not coincided with Newton’s who developed Hooke’s hypothetical model into the theory of universal gravitation as published in the Mathematical Principles of Natural Philosophy (1687). The nature of Hooke’s contributions to mathematized natural philosophy, however, was contested during his own lifetime and gave rise to negative evaluations until the last century. Hooke has been often contrasted to Newton as a practitioner rather than as a “scientist” and unfavorably compared to the eminent Lucasian Professor. Hooke’s correspondence with Newton seems to me an example of the phenomenon, discussed by Fisch in his philosophical works, of the invisibility in official historiography of “trading zone mediators,” namely, of those actors that play a role, crucial but not easily recognized, in promoting rational scientific framework change. (shrink)

In this paper I discuss and develop the risk account of scientific objectivity, which I have recently introduced, contrasting it to some alternatives. I then use the account in order to analyse a practice that is relatively common in anthropology, in the history of science, and in the sociology of scientific knowledge: withholding epistemic judgement. I argue that withholding epistemic judgement on the beliefs one is studying can be a relatively efficient strategy against collective bias in these fields. However, taking (...) into account the criticisms presented against the strategy, I also argue that it is a usable strategy only when the distance between the researchers and their ideas, and the people and ideas being studied, is significant enough. (shrink)

The operational perspective here defended permits a reflexive-transcendental point of view that sharply distinguishes the two concepts, while, at the same time, maintaining the connection between them. On the one hand, simply imagining that the experimental apparatus, counterfactually anticipated in a thought experiment, has really been constructed is sufficient to erase any difference between thought and real experiments. On the other hand, this very ‘imagining’, this capacity of the mind to assume every real entity as a possible entity, underpins the (...) difference in principle – a properly transcendental difference – between thought and real experiments. This difference, however, implies the intimate association between experiment and thought experiment: All thought experiments must be thought of as translatable into real ones, and all real experiments as realisations of thought ones. What thought experiments have over and above real experiments is the mere fact that they exist in a purely hypothetical sphere; what real have over and above thought experiments is the mere fact that they overstep the sphere of the possible, in the experiment’s real execution. (shrink)

Les notions ou catégories de causalité et de déterminisme ont accompagné la formation des sciences modernes, et en premier lieu celle de la physique. L'usage courant de nos jours tend souvent, à tort, à les confondre, dans les remises en cause qui en sont faites en physique même. Nous nous proposons, dans ce travail, de clarifier la première de ces notions, plus exactement la causalité physique, en suivant son élaboration avec les débuts de la dynamique, à travers ses premières mises (...) en œuvre et conceptualisations qui accompagnent la mathématisation de la mécanique, avant d'être étendue à la physique d'une manière générale. Nous verrons comment, tout en s'appuyant sur l'un des aspects philosophiques traditionnels de l'idée de causalité (celui de « cause efficiente »), la causalité physique s'établit en rupture avec le sens métaphysique qui lui était précédemment attaché. Bien plutôt que dans les Principia de Newton, c'est dans la ré-élaboration par d'Alembert, dans son Traité de dynamique, des lois du mouvement formulés comme des principes, et exprimées par le calcul différentiel, que l'idée de causalité physique est expressément considérée indissociablement de son effet, qui est le changement de mouvement. Les pensées respectives de Newton et de d'Alembert sur les notions de cause et de force sont à cet égard en opposition en ce qui concerne la nature proprement physique de ce changement, considéré par d'Alembert comme immanent au mouvement, selon la cause circonscrite par son effet, alors qu'il reste mathématique et métaphysique dans la conception newtonienne de la force externe, comme substitut mathématique des causes, telle qu'elle se proposait avant Lagrange. C'est la conception physique, héritée de d'Alembert, qui devait par la suite prévaloir, à travers la mécanique analytique lagrangienne, qui permettait de réintégrer physiquement et rationnellement le concept de force dans sa transcription eulérienne différentielle. Les avatars ultérieurs de la notion de causalité, qui comprennent la causalité relativiste et les développements sur le déterminisme, font l'objet d'un travail complémentaire. (shrink)

Reagere, reactio does not belong to classical Latin. Reagere appears, as late as the fourth century A.D., in Avienus, but not reactio. Nonetheless, antiquity was not unaware of the concept of reciprocal action, where the “patient” reacts in return on the agent. The Aristotelian doctrine of antiperistasis occupied physicists up until the time of Galileo: “All movers, as long as they move, are at the same time moved.” The Latin authors dispense with reagere and reactio. It is the verb pati, (...) designating the passive state to which the prefix re is added in the aphorism attributed to the Scholastics in the 18th century dictionaries: omnis agens agendo repatitur. (shrink)

: Although Galileo's struggle to mathematize the study of nature is well known and oft discussed, less discussed is the form this struggle takes in relation to Galileo's first new science, the science of the second day of the Discorsi. This essay argues that Galileo's first science ought to be understood as the science of matter—not, as it is usually understood, the science of the strength of materials. This understanding sheds light on the convoluted structure of the Discorsi's first day. (...) It suggests that the day's meandering discussions of the continuum, infinity, the vacuum, and condensation and rarefaction establish that a formal treatment of the "eternal and necessary" properties of matter is possible; i.e., that matter as such can be considered mathematically. This would have been a necessary, and indeed revolutionary, preliminary to the mathematical science of the second day because matter itself was thought in the Aristotelian tradition to be responsible for the departure of natural bodies from the unchanging and thus mathematizable character of abstract objects. In addition, the first day establishes that when considered physically, these properties account for matter's force of cohesion and resistance to fracture. This essay closes by showing that this dual style of reasoning accords with the conceptual structure of mixed mathematics. (shrink)

This paper defends a version of J. H. Randall’s thesis that modern empiricism is rooted in the Scholastic regressus method epitomized by Jacopo Zabarella in De Regressu (1578). Randall’s critics note that the empirical practice of Galileo and his contemporaries does not follow Zabarella. However, Zabarella’s account of the regressus is imprecise, which permitted an interpretation introducing empirical hypothesis testing into the framework. The discourse surrounding Galileo’s lunar observations in Sidereus Nuncius (1610) suggests that both Galileo and his interlocutors amended (...) the regressus method in this way, such that a developmental narrative links Scholastic logic to Galilean science. (shrink)

This paper deals with Ágnes Heller’s suggestion, in A Theory of Modernity (1999), to ascribe to science a central role in the ongoing development of modernity. As we shall argue, this is not merely a historical issue but, rather, a historical-philosophical one that entails the problem of defining modernity, science and technology and their mutual interconnections. As for modernity, according to Heller, it is a free developmental project without any foundations other than freedom itself. In particular, the evolution of science (...) and technology is one of its main developmental tendencies. Science, she argues, has become the dominant world explanation while technological thought is the corresponding dominant (but not unique) imaginary institution. Her attempt to isolate the essential cultural features of science-technology owes much to Habermas’s analyses of the 1960s on the technocratic developments of contemporary societies legitimized through an ideological employment of science. Like Habermas, Heller embraces an instrumental and problem-solving conception of technology and ‘normal’ science which appears questionable, however, in the light of conclusions on the intrinsic creativity of the science-technology interface deriving from historical epistemology and an externalist history of science. Considerations and examples derived from the recent agenda of historical epistemology could integrate Heller’s philosophical and cultural analysis of the role of science in modernity while challenging some of her assumptions. (shrink)

The paper is devoted to an overview of Cassirer’s work both as historian of philosophy and historian of science. Indeed, the “intelletcual cooperation” between history of philosophy and history of science represents an essential feature of Cassirer’s style of philosophizing: while the roots of a wide exploration stretching from Renaissance thought to modern physics go back to the Neo-Kantianism of the Marburg School, the results of a similar cross-fertilization of research fields have deeply contributed to shaping new standards of inquiry. (...) Cassirer’s relationship with the Warburg milieu in Hamburg and late in his life with the American intellectual scenario are surely worthy of closer investigation. Distinguished scholars such as Meyerson, Brunschvicg, Burtt, Koyré, Metzger, Lovejoy, Kristeller, have disussed, appreciated, critizised Cassirer’s still today fascinating studies devoted to Pico della Mirandola, Galileo, Newton, Leibniz, to mention but a few. To explore some of these aspects focusing both on affinities and differences within a cosmpolitian intellectual community can provide a better understanding of philosophy and history of science in the first half of 20th century. Cassirer’s legacy requires, therefore, a new assessment. (shrink)

Conceito oriundo do debate a respeito do movimento, o conatus, entendido como inclinação ou esforço, será um dos temas centrais da física seiscentista. Este artigo pretende explicitar o contexto de elaboração do conceito de conatus no século XVII, ou pelo menos na obra de três de seus principais filósofos: Descartes, Hobbes e Espinosa. Em Descartes, o conceito de conatus ainda se separa do conceito de movimento propriamente dito. Tal separação desaparece em Hobbes, para quem o conatus será apresentado como um (...) movimento ínfimo, com consequências não só para a Física, mas também para a Ética e a Política. Com Espinosa, por sua vez, o conceito ganhará contornos nitidamente ontológicos, tornando-se a chave para entender a essência das coisas singulares. (shrink)

We propose a synthetic description of Merleau-Ponty’s phenomenology with the aim of providing physicists and philosophers with an alternative linguistic and conceptual framework to address the logical and ontological problematics emerged in quantum mechanics. Phenomenology’s cognitive devices such as the dynamical relationship between object and horizon, the presumptive synthesis and the constitution of an ontology based on the indivisibility of object and subject, not only show hermeneutic efficacy when applied to the study of human perception, but may prove to be (...) sufficiently innovative to lead to novel insights towards the understanding of the quantum mechanical theoretical structure: the traditional tenet of quantum physics being in discontinuity with the major characteristics of classical physics is shaken at its fundaments and a new perspective of continuity between the two worlds is opened. (shrink)

The article investigates the role of symbolic means of knowledge representation in concept development using the historical example of medieval diagrams of change employed in early modern work on the motion of fall. The parallel cases of Galileo Galilei, Thomas Harriot, and René Descartes and Isaac Beeckman are discussed. It is argued that the similarities concerning the achievements as well as the shortcomings of their respective work on the motion of fall can to a large extent be attributed to their (...) shared use of means of knowledge representation handed down from antiquity and the Middle Ages. While the interpretation of medieval diagrams was unproblematic in the scholastic context from which they arose, in the early modern context, which was characterized by the confluence of natural philosophy and practical mathematics, it became ambiguous. It was the early modern mathematicians’ work within this contradictory framework that brought about a new conceptualization of motion which, in particular, eventually led to an infinitesimal concept of velocity. In this process, the diagrams themselves remained largely unchanged and thus functioned as a catalyst for concept development. (shrink)

Traditionally, Thomas S. Kuhn’s The Structure of Scientific Revolutions (1962) is largely identified with his analysis of the structure of scientific revolutions. Here, we contribute to a minority tradition in the Kuhn literature by interpreting the history of evolutionary biology through the prism of the entire historical developmental model of sciences that he elaborates in The Structure. This research not only reveals a certain match between this model and the history of evolutionary biology but, more importantly, also sheds new light (...) on several episodes in that history, and particularly on the publication of Charles Darwin’s On the Origin of Species (1859), the construction of the modern evolutionary synthesis, the chronic discontent with it, and the latest expression of that discontent, called the extended evolutionary synthesis. Lastly, we also explain why this kind of analysis hasn’t been done before. (shrink)

En los Discorsi Galileo afirma haber realizado un experimento, cuyo resultado fue negativo, para determinar si la luz tarda tiempo en propagarse. En este trabajo analizo ese experimento como crucial entre las hipótesis rivales según las cuales la luz se propaga con velocidad infinita o con velocidad finita. Procuro determinar las hipótesis auxiliares y la carga teórica que presupone el diseño experimental. Argumento que las hipótesis presupuestas son razonables y que la carga teórica es muy baja. Sostengo que en principio (...) es posible un experimento crucial exitoso, esto es, con resultado positivo, como el concebido por Galileo. Concluyo que la hipótesis de que la luz se propaga con velocidad finita no es refutable mediante un experimento de esta clase, por lo cual cualquier resultado negativo es compatible con ambas hipótesis rivales. Como consecuencia de ello, la hipótesis de que la luz, o cualquier otra interacción física, se propagan con velocidad infinita resulta inverificable. (shrink)

In a 1669 letter to his mentor Thomasius, Leibniz writes that "hardly any of the Cartesians have added anything to the discoveries of their master" insofar as they "have published only paraphrases of their leader."1 The book that is the focus of my remarks here—Roger Ariew's Descartes and the First Cartesians —shows that Leibniz was most certainly incorrect. In particular, Ariew draws attention to the fact that there was a concerted effort to present a new sort of Cartesianism that conforms (...) to the structure of the early modern French scholastic curriculum. Though this effort was inspired by Descartes's own attempt to present his views in this manner, the later "Cartesian scholasticism"... (shrink)

The topic of history-of-science explanation is first briefly introduced as a generally important one for the light it may shed on action theory, on the logic of discovery, and on philosophy''s relations with historiography of science, intellectual history, and the sociology of knowledge. Then some problems and some conclusions are formulated by reference to some recent relevant literature: a critical analysis of Laudan''s views on the role of normative evaluations in rational explanations occasions the result that one must make aconceptual (...) distinction between evaluations and explanations of belief, and that there are at leastthree subclasses of the latter, rational, critical, and theoretical; I then discuss the problem of whether explanations of discoveries are self-evidencing and predictive by focusing on views of Hempel and Nickles, and I attempt a formalization of some aspects of the problem. Finally, a more systematic and concrete analysis is undertaken by using as an example the explanation of Galileo''s rejection of space-proportionality, and it is argued that the historical explanation of scientific beliefs is a type of logical analysis. (shrink)

In On Local Motion in the Two New Sciences, Galileo distinguishes between ‘time’ and ‘quanto time’ to justify why a variation in speed has the same properties as an interval of time. In this essay, I trace the occurrences of the word quanto to define its role and specific meaning. The analysis shows that quanto is essential to Galileo’s mathematical study of infinitesimal quantities and that it is technically defined. In the light of this interpretation of the word quanto, Evangelista (...) Torricelli’s theory of indivisibles can be regarded as a natural development of Galileo’s insights about infinitesimal magnitudes, transformed into a geometrical method for calculating the area of unlimited plane figures. (shrink)