Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)

The ‘model approach’ facilitates a quantitative-oriented study of conceptual changes in large corpora. This paper implements the ‘model approach’ to investigate the erosion of the traditional art-nature distinction in early modern natural philosophy. I argue that a condition for this transformation has to be located in the late scholastic conception of final causation. I design a conceptual model to capture the art-nature distinction and formulate a working hypothesis about its early modern fate. I test my hypothesis on a selected corpus (...) of 25 works published in the Dutch academic milieu between 1607 and 1748. I analyse the corpus through a procedure based on concordancing of keywords associated with the model. I argue that the results obtained constitute a successful pilot study for the implementation of the model approach on larger scale research. (shrink)

The article is devoted to the philosophy of cosmology, its history and contemporary conditions, the tradition of studying and modern trends in teaching this discipline in higher education in Ukraine. There is problem of defining the subject of philosophy of cosmology, there are similar and different motifs with modern astrophysics, cosmology on the one hand, and, with the history of philosophy and modern philosophy on the other hand. The change in the subject of the philosophy of cosmology in the history (...) of philosophy and science has been studied in this article. A modern state of the philosophy of cosmology in modern philosophical education is demonstrated. (shrink)

This article critically considers Castoriadis’ central concept of creation ex nihilo. It does so in two ways. It first draws on recent research to suggest that the historical inauguration of the project of autonomy in ancient Greece - in both its political and philosophical aspects - was more complex and contextually anchored than Castoriadis acknowledges: it did not surge forth out of nothing. Second, it considers the idea of creation from a theoretical perspective. Here the idea of creation as contextual (...) rather than absolute is offered. Within this suggested qualification, two lines of discussion - drawn from the hermeneutical and phenomenological traditions - are broached. (shrink)

This paper argues that the Cambridge Platonists had stronger philosophical links to Scottish moral philosophy than the received history allows. Building on the work of Michael Gill who has demonstrated links between ethical thought of More, Cudworth and Smith and moral sentimentalism, I outline some links between the Cambridge Platonists and Scottish thinkers in both the seventeenth century and the eighteenth century. I then discuss Hume's knowledge of Cudworth, in Enquiry concerning the Principles of Morals, Enquiry concerning Human Understanding, The (...) Natural History of Religion and Dialogues concerning Natural Religion. (shrink)

Against the usual interpretation, which states that Afrofuturism is unreservedly technophilic, I argue that Afrofuturism is a radical critique of white technology. White technology (be it imperial, colonial or capitalist) is an acosmic technology that rejects its belonging to the cosmos. The Space Age and what is now called New Space (both of which have neo-colonial aims) are perfect illustrations of white technology and its anthropocentric enthusiasm. Rejecting this colonial and exploitative technology, Afrofuturism – from the music and poems of (...) Sun Ra to the paintings of Wangechi Mutu to the poems and activism of Alexis Pauline Gumbs – is first and foremost an attempt to use outer space not as a space open to conquest, but as a mediation, a stellar detour thanks to which our terrestrial condition could be politically and anthropologically rethought. At odds with any geoengineering project, Afrofuturism conjures up an “epoch of being” (Heidegger) in which technology would be constantly inhabited by a form of uncanny that would definitively prevent human beings from considering technology as a way of mastering the Earth. (shrink)

Against the usual interpretation, which states that Afrofuturism is unreservedly technophilic, I argue that Afrofuturism is a radical critique of white technology. White technology (be it imperial,...

Leibniz frequently argued that reasons are to be weighed against each other as in a pair of scales, as Professor Marcelo Dascal has shown in his article "The Balance of Reason." In this kind of weighing it is not necessary to reach demonstrative certainty – one need only judge whether the reasons weigh more on behalf of one or the other option However, a different kind of account about rational decision-making can be found in some of Leibniz's writings. In his (...) article "Was Leibniz's Deity an Akrates?" Professor Jaakko Hintikka has argued that Leibniz developed a new vectorial model for rational decisions which is better suited to complicated decisions, where values are complementary to each other. This model, related closely to his work in metaphysics and the philosophy of mind, is a heuristic device which helps in finding rational combinations - and in an ideal case an optimum - between plural inclinations to the good. I shall argue that Leibniz applies more or less implicitly both of these models in his practical rationality. In simple situations he applied the pair of scales model and in more complicated situations he applied the vectorial model. (shrink)

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition (...) is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

The phrase ‘To perish from absolute knowledge’ from Nietzsche’s Beyond Good and Evil runs like a red thread throughout Foucault’s reading of Nietzsche, spanning a period of 20 years in which Foucault continuously turned to Nietzsche as his main philosophical and methodological role model. Beginning with his first lectures on Nietzsche in the early 1950s, Foucault repeatedly alluded to this phrase as the key to Nietzsche’s philosophical critique which anticipated the philosophical shift to ontology in the 20th century. Drawing on (...) a host of unpublished essays from Foucault’s archive, it will be shown that this phrase holds the key to Foucault’s Nietzsche interpretation and explains his reliance on historicity as the transcendental basis for his critical project. The article will rely on Foucault’s dynamic analysis of this phrase to narrate the development of his historical methodology between the 1950s and the mid-1970s, and will argue for the continuity and coherence of Foucault’s critical project. (shrink)

An ancient cosmological debate lies behind the spatial part of the first antinomy in Kant’s Critique of Pure Reason. Against the Aristotelian conception of a finite universe, a thought experiment proposed we imagine ourselves situated on the boundary of the world: what happens if we stretch a hand beyond the boundary? This article first shows that aspects of this debate persist in the cosmological claims of Huygens, Wolff, and Crusius. With his presentation of opposing arguments in the first antinomy, Kant (...) famously rejected both sides of the debate and asserted that we cannot meaningfully inquire into the spatial boundary of the world. I then argue that the critical-period Kant nevertheless does not simply dismiss the issue of an outer boundary of the world: he rather reconceives it as the question of the boundary of the legitimate use of our cognitive faculties. The cosmological question of the boundary of the world is transformed—from Kant’s Inaugural Dissertation through his Reflexionen of the 1770s to the first Critique—into the critical question of the boundary of reason. -/- . (shrink)

The employment by seventeenth-century natural philosophers of stock theological notions like creation, immensity, and eternity in the articulation and justification of emerging physical programs disrupted a delicate but longstanding balance between transcendent and immanent conceptions of God. By playing a prominent (if not always leading) role in many of the major scientific developments of the period, God became more intimately involved with natural processes than at any time since antiquity. In this discussion, I am particularly concerned with the causal and (...) spatio-temporal relations between God and nature in the seventeenth century as recent scholarship has revealed how dramatically traditional conceptions of these relations were transformed by philosophers and scientists like Descartes, Malebranche, More, and Newton. (shrink)

This article examines the connections among heuristics, the epistemological and ontological presuppositions that underlie theorizing, and substantive explanations in sociology. It develops and contrasts three heuristics: “doing as knowing” (DK), “categorizing as knowing” (CK), and “praxis as knowing” (PK). These are each composed of four dimensions: the theory of knowledge, the theory of reality, the theory of the growth of knowledge, and the theory of knowledge producers. The article then shows the importance of heuristics for empirical work by demonstrating how (...) they shape explanations in the sociological subfield of the historical sociology of knowledge. The essay draws two main conclusions: it argues that PK offers a more useful basis for developing explanations in sociology than either of the two alternatives (DK and CK) that currently shape substantive work; furthermore, it claims that the exposition of heuristic assumptions is an important task for sociology. (shrink)

ArgumentThe purpose of this paper is to provide an analysis of Giordano Bruno’s conception of mathematics. Specifically, it intends to highlight two aspects of this conception that have been neglected in previous studies. First, Bruno’s conception of mathematics changed over time and in parallel with another concept that was central to his thought: the concept of infinity. Specifically, Bruno undertook a reform of mathematics in order to accommodate the concept of the infinitely small or “minimum,” which was introduced at a (...) later stage. Second, contrary to what Héléne Védrine claimed, Bruno believed that mathematical objects were mind-dependent. To chart the parallel development of the conceptions of mathematics and infinity, a seven-year time span is considered, from the publication of Bruno’s first Italian dialogue (La cena de le ceneri,1584) to the publication of one of his last Latin works (De minimo, 1591). (shrink)

In this article, I consider Descartes’ enigmatic claim that we must assert that the material world is indefinite rather than infinite. The focus here is on the discussion of this claim in Descartes’ late correspondence with More. One puzzle that emerges from this correspondence is that Descartes insists to More that we are not in a position to deny the indefinite universe has limits, while at the same time indicating that we conceive a contradiction in the notion that the universe (...) has a limit. I reject one attempt to resolve this apparent conflict which appeals to Descartes’ admission to More that divine omnipotence requires that God can create a vacuum in nature, and focus instead on his response to More’s claim that this omnipotence requires the possibility of a completion of the division of matter that results in atoms. Finally, I distinguish Descartes’ indefinite from two other kinds of infinity with which it might well be confused. The first is an essentially incomplete ‘potential infinity’ that Descartes discusses in the Third Meditation, and the second is the sort of quantitative infinity that Leibniz – contrary to Descartes – denies can constitute a completed whole. (shrink)

That science is fundamentally universal has been proclaimed innumerable times. But the precise geographical meaning of this universality has changed historically. This article examines conceptions of scientific internationalism from the Enlightenment to the Cold War, and their varying relations to cosmopolitanism, nationalism, socialism, and ‘the West’. These views are confronted with recent tendencies to cast science as a uniquely European product.

[ES] El presente artículo estudia el influjo de los tratados físicos de Aristóteles sobre la concepción tomista en torno al lugar del infinito en el cosmos creado. Se analiza la posición sostenida por el Aquinate respecto a cuatro aspectos fundamentales de la teoría aristotélica en torno al infinito: existencia de una sustancia infinita, existencia de un cuerpo infinito, existencia de un infinito en acto y la infinitud del tiempo. Asimismo se expone el empleo de la teoría aristotélica del movimiento y (...) los lugares naturales, por parte del Doctor angélico, para la refutación de toda posición que conciba el acto de creación como una mutación temporalmente sucesiva, así como su caracterización de la divinidad como sustancia perfecta cuya infinitud no puede ser comprendida bajo la noción de cantidad. [EN] This article studies the influence of Aristotle’s physical treatises on the Thomist conception on the place of infinity in the created cosmos. It analizes the position held by Aquinas on four fundamental aspects of the Aristotelian theory about infinity: existence of an infinite substance, existence of an infinite body, existence of an infinite in act and the infinity of time. Is also exposed the use of the Aristotelian theory of motion and natural places by the Angelic Doctor for the refutation of every position that presents the act of creation as a temporally successive mutation and his characterization of divinity as a perfect substance whose infinity can not be understood under the notion of quantity. (shrink)

This is the correspondence (1959–1969), on the nature of the evolutionary process, between the biologist Theodosius Dobzhansky and the historian John C. Greene.