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Proof and eternal truths: Descartes and Leibniz

In Stephen Gaukroger (ed.), Descartes: philosophy, mathematics and physics. Totowa, N.J.: Barnes & Noble. pp. 169--179 (1980)

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  1. Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics.Vasil Penchev - 2023 - Astrophysics, Cosmology and Gravitation Ejournal 2 (52):1-82.
    Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...)
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  • The Ontological Argument as an Exercise in Cartesian Therapy.Lawrence Nolan - 2005 - Canadian Journal of Philosophy 35 (4):521 - 562.
    I argue that Descartes intended the so-called ontological "argument" as a self-validating intuition, rather than as a formal proof. The textual evidence for this view is highly compelling, but the strongest support comes from understanding Descartes's diagnosis for why God's existence is not 'immediately' self-evident to everyone and the method of analysis that he develops for making it self-evident. The larger aim of the paper is to use the ontological argument as a case study of Descartes's nonformalist theory of deduction (...)
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  • Proof-analysis and continuity.Michael Otte - 2004 - Foundations of Science 11 (1-2):121-155.
    During the first phase of Greek mathematics a proof consisted in showing or making visible the truth of a statement. This was the epagogic method. This first phase was followed by an apagogic or deductive phase. During this phase visual evidence was rejected and Greek mathematics became a deductive system. Now epagoge and apagoge, apart from being distinguished, roughly according to the modern distinction between inductive and deductive procedures, were also identified on account of the conception of generality as continuity. (...)
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  • Two Regimes of Logocentrism.Giovanni Menegalle - 2023 - Angelaki 28 (6):50-70.
    This article offers a reconstruction of Derrida’s critique of Leibniz. It suggests that in attempting to fit Leibniz into his conception of the history of metaphysics and the all-embracing notion of logocentrism that underwrites it, Derrida presupposes two regimes of logocentrism: one subjective, the other theological. Subsumed into this second mode, Derrida casts Leibniz as a progenitor of structuralism and the new sciences and technologies of information in order to expose their logocentric foundations. However, in doing so, he ends up (...)
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  • The skeptic's dogmatism: a constructive response to the skeptical problem.Kaplan Levent Hasanoglu - 2011 - Dissertation,
    The problem of philosophical skepticism relates to the difficulty involved in underwriting the claim that we know anything of spatio-temporal reality. It is often claimed, in fact, that proper philosophical scrutiny reveals quite the opposite from what common sense suggests. Knowledge of external reality is thought to be even quite obviously denied to us as a result of the alleged fact that we all fail to know that certain skeptical scenarios do not obtain. A skeptical scenario is one in which (...)
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  • The necessity in deduction: Cartesian inference and its medieval background.Calvin G. Normore - 1993 - Synthese 96 (3):437 - 454.
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  • Deducing false propositions from true ideas: Nieuwentijt on mathematical reasoning.Sylvia Pauw - 2020 - Synthese 197 (11):4927-4945.
    This paper argues that, for Bernard Nieuwentijt, mathematical reasoning on the basis of ideas is not the same as logical reasoning on the basis of propositions. Noting that the two types of reasoning differ helps make sense of a peculiar-sounding claim Nieuwentijt makes, namely that it is possible to mathematically deduce false propositions from true abstracted ideas. I propose to interpret Nieuwentijt’s abstracted ideas as incomplete mental copies of existing objects. I argue that, according to Nieuwentijt, a proposition is mathematically (...)
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  • The Constitutive A Priori.Graciela De Pierris - 1992 - Canadian Journal of Philosophy, Supplementary Volume 18 (sup1):179-214.
    The modem rationalist tradition initiated by Descartes has as one of its central tenets the independence of the human understanding from the senses. Regardless of the different ways in which independence from experience is understood, there is much common ground among the modem views on the a priori. Yet Kant, culminating this tradition, introduces an entirely new conception of the a priori never before articulated in the history of philosophy. This is the notion of elements in knowledge which are independent (...)
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