Cham, Switzerland: Springer Verlag (2018)
AbstractThis book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.
9783319951461 978-3-319-95146-1 978-3-319-95147-8 3030069842 3319951467 3319951483 9783319951478
On the Motivations of Gödel’s Ontological Proof
In recent years there has been a surge of interest in Gödel’s ontological proof of the existence of God. In spite of all this extensive concern, it is not certain whether there is any improvement in understanding the motivations of Gödel’s ontological proof. Why was Gödel so preoccupied with complet... see more
Between Bernays and Carnap
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I attempt to get further insights from Cocchiarella’s history and philosophy of logic in understanding the contrast of Aristotelian and Fregean logic. Recently Cocchiarella proposed a conceptual theory of the referential and predicable concepts used in basic speech and mental acts . This theory is i... see more
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Citations of this work
Mathematics as a Science of Non-Abstract Reality: Aristotelian Realist Philosophies of Mathematics.James Franklin - 2022 - Foundations of Science 27 (2):327-344.
Mathematics as a Science of Non-abstract Reality: Aristotelian Realist Philosophies of Mathematics.James Franklin - 2022 - Foundations of Science 27 (2):327-344.
Review of Woosuk Park, Philosophy’s Loss of Logic to Mathematics: An Inadequately Understood Take-Over. [REVIEW]James Franklin - 2019 - Philosophia Mathematica 27 (3):440-443.
References found in this work
The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics.Crispin Wright & Bob Hale - 2001 - Oxford: Clarendon Press.
Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - Oxford, England and New York, NY, USA: Oxford University Press.
Abductive Cognition: The Epistemological and Eco-Cognitive Dimensions of Hypothetical Reasoning.Lorenzo Magnani - 2009 - Springer Verlag.
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu (ed.) - 1996 - Oxford, England: Oxford University Press.