Pretende-se apresentar e avaliar o programa inicial de Huet ao publicar a Demonstratio Evangelica (1679), obra de caráter apologético e inclinação cética, frente a seu contexto intelectual, buscando uma melhor compreensão do impacto que tal livro exerceu nas discussões entre grandes intelectuais da República das Letras na Europa do século XVII. Para isso, este artigo contém três momentos: primeiro, procura-se traçar os objetivos da obra e os meios utilizados por Huet para alcançá-los. Posteriormente é exposta uma série de acusações e (...) críticas à Demonstratio Evangelica e, por fim, é feito um balanço a respeito dessas críticas em relação às intenções iniciais de Huet e argumenta-se que esta obra tem certo valor apologético, mas, mais do que isso, exerceu um papel notável no que diz respeito às discussões sobre a história, religião e filosofia no século XVII. (shrink)

Henry More and Nicolas Malebranche, each in his own way, drew a distinction between two kinds of extension, the one indivisible and the other divisible. Spinoza also drew a comparable distinction, explaining that, insofar as extended substance was conceived intellectually, it would be grasped as indivisible, whereas, when it was instead depicted in the imagination, it would be seen as divisible. But, whereas for Spinoza these were just different views on one and the same extended substance, More and Malebranche's two (...) kinds of extension were supposed to be really distinct from one another. Consequently, neither of them could identify Spinoza's substance with both of his own non-identical kinds; and so they faced a choice over which one they would associate it with. The intriguing thing is that here they diverged. More felt that Spinoza's substance was actually divisible, and consequently material. Malebranche felt that it was actually indivisible, and consequently ideal and divine. In each case, they felt that the other kind of extension—whichever that might be—was simply absent from Spinoza's system. This article explores this divergence between More and Malebranche's interpretations of Spinoza's metaphysics, and it seeks an explanation for it in their own respective epistemologies. (shrink)

In this paper I show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that perfect demonstrations (...) are causal demonstrations influenced the reflection on proofs by contradiction. The main protagonist of this part is Wallis. Finally, I analyse some epistemological developments arising from the Cartesian tradition. In particular, I look at Arnauld's programme of providing an epistemologically motivated reformulation of Geometry free of proofs by contradiction. The conclusion explains in which sense these epistemological reflections can be compared with those informing contemporary intuitionism. (shrink)

This paper examines the ethical and religious dimensions of mathematical practice in the early modern era by offering an interpretation of Antoine Arnauld and Pierre Nicole’s Nouveaux éléments de géométrie. According to these important figures of seventeenth-century French philosophy and theology, mathematics could achieve extra-mathematical or non-mathematical goals; that is, mathematics could foster practices of moral self-improvement, deepen the mathematician’s piety and cultivate epistemic virtues. The Nouveaux éléments de géométrie, which I contend offers the most robust account of the virtues (...) cultivated by mathematics in the period, was envisaged by its authors to cultivate moral, Christian and epistemic virtues that could serve in the fulfilment of moral and Christian obligations. In this paper, I set out the goals of mathematical inquiry for the Port-Royalists and describe the specific virtues they believed a revised edition of the Elements of Euclid could foster. I show that Arnauld and Nicole believed that an acquaintance with mathematics could render a student of Euclid more just, truth-loving, attentive and humble, and better able to discern truth from falsity. (shrink)

Incongruent counterparts are pairs of objects which cannot be enclosed in the same spatial limits despite an exact similarity in magnitude, proportion, and relative position of their parts. Kant discerns in such objects, whose most familiar example is left and right hands, a “paradox” demanding “demotion of space and time to mere forms of our sensory intuition.” This paper aims at an adequate understanding of Kant’s enigmatic idealist argument from handed objects, as well as an understanding of its relation to (...) the other key supports of his idealism. The paper’s central finding is that Kant’s idealist argument from incongruent counterparts rests essentially on his theory of freedom. The surprising result sheds new light on deep and overlooked links among the pillars of transcendental idealism, pointing the way to a comprehensive and unified reading of Kant’s system of idealist arguments. (shrink)

Antoine Arnauld is well known as a passionate defender of Jansenism, specifically Jansen’s view on the relation between freedom and grace. Jansen and, early in his career Arnauld, advance compatibilist views of human freedom. The heart of their theories is that salvation depends on both the irresistible grace of God and the free acts of created things. Yet, in Arnauld’s mature writings, his position on freedom seems to undergo a significant shift. And, by 1689, his account of freedom no longer (...) seems Jansenist. In this paper, we offer an interpretation of Arnauld’s mature view on freedom, with a focus on his claim that freedom requires a “power to the opposite.” In order to see what he means by this, we look to several under-examined texts in his corpus for clues about how he understands the related topics of “infallible determination,” habit, and primo-primi motus. We argue that Arnauld’s mature view on freedom should be understood as libertarian. (shrink)