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De filosofie van de wiskunde is gebaseerd op de grondslagenstudies van de wiskunde en de computerwetenschappen. Dit boek is dan ook bedoeld voor studenten van alle drie de betrokken richtingen én natuurlijk voor een ieder die zich interesseert voor deze grondslagen. Er is niet gekozen voor een statische historische benadering waarbij je je dan zou moeten beperken tot een bespreking van de drie grote scholen: logicisme, intuïtionisme en formalise (en hun fiasco's!). Zoals de auteur zegt: "Het verhaal van de kinderen en kleinkinderen van de grote scholen dient te worden verteld". Recente ontwikkelingen in het grondslagenonderzoek krijgen meer aandacht en verlenen het geheel een optimistische toon. Actuele onderwerpen die aan de orde komen zijn verzamelingentheorie en de continuumhypothese, beslisbaarheid en berekenbaarheid, modeltheorie. Er wordt steeds verwezen naar artikelen en boeken waar onderwerpen uitvoeriger behandeld worden. De schrijver is erin geslaagd om het verband tussen filosofie, wiskunde en computerwetenschappen te gebruiken om analytische bewijsvoering in alle drie de wetenschapsgebieden te verduidelijken.

510.2 --- Academic collection --- 510.1 --- Computerwetenschappen --- Filosofie --- Geschiedenis --- Wiskunde --- Foundations of mathematics --- (zie ook: realistische wiskunde) --- Wiskunde. --- 510.2 Foundations of mathematics --- Mathematics --- Philosophy. --- Philosophy of nature --- Mathematical logic

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Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day.

Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy. --- Reasoning. --- Logic. --- Metaphysics. --- Philosophy --- God --- Ontology --- Philosophy of mind --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Science --- Reasoning --- Thought and thinking --- Ratiocination --- Reason --- Judgment (Logic) --- Logic --- Methodology

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Knowledge, Theory of --- Reasoning --- Evolution --- Ontology --- Théorie de la connaissance --- Argumentation --- Ontologie --- Congresses --- Congrès --- Quine, W. V. --- Congresses. --- Academic collection --- Théorie de la connaissance --- Congrès --- Evolution - Congresses. --- Ontology - Congresses. --- Reasoning - Congresses. --- Knowledge, Theory of - Congresses. --- Quine, Willard Van Orman

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Logic, Symbolic and mathematical. --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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This book contains ten papers that were presented at the symposium about the realism debate, held at the Center for Logic, Philosophy of Science and Philosophy of Language of the Institute of Philosophy at the Katholieke Universiteit Leuven on 10 and 11 March 1995. The first group of papers are directly concerned with the realism/anti-realism debate in the general philosophy of science. This group includes the articles by Ernan McMullin, Diderik Batens/Joke Meheus, Igor Douven and Herman de Regt. The papers of the second group concentrate on specific problems arising from the realism/anti-realism debate. Theo Kuipers' contribution discusses the problem of truth-approximation. Roger Vergauwen's article pertains to the issue of realism in the philosophy of mind and semantics. Jaap van Brakel's article focusses on the relation between everyday concepts and scientific concepts, and on the theory-dependence of observation. Paul Cortois investigates the relation between the question of realism and Kuhn's concept of incommensurability between scientific theories. The final group contains two papers on the realism/anti-realism debate in the special sciences. James Cushing discusses the problem of underdetermination in quantum mechanics and Jean Paul van bendegem addresses the question of the possiblity of an empiricist philosophy of mathematics.

Realism. --- Science --- Philosophy.