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The nature of mathematical knowledge

Oxford: Oxford University Press (1983)

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  1. To Continue With Continuity.Martin Cooke - 2005 - Metaphysica 6 (2):91-109.
    The metaphysical concept of continuity is important, not least because physical continua are not known to be impossible. While it is standard to model them with a mathematical continuum based upon set-theoretical intuitions, this essay considers, as a contribution to the debate about the adequacy of those intuitions, the neglected intuition that dividing the length of a line by the length of an individual point should yield the line’s cardinality. The algebraic properties of that cardinal number are derived pre-theoretically from (...)
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  • Journal of Philosophical Investigations.M. Asgahri - 2015 - Journal of Philosophical Investigations 9 (17):1-227.
    open journal of Philosophical Investigations (PI) is an international journal dedicated to the latest advancements in philosophy. The goal of this journal is to provide a platform for academicians all over the world to promote, share, and discuss various new issues and developments in different areas of philosophy. -/- All manuscripts to be prepared in English or Persian and are subject to a rigorous and fair peer-review process. Generally, accepted papers will appear online. The journal publishes papers including the following (...)
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  • Gödel on Truth and Proof.Dan Nesher - unknown
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  • Kitcher’s modest realism: The reconceptualization of scientific objectivity.Antonio Dieguez - 2010 - Poznan Studies in the Philosophy of the Sciences and the Humanities 101 (1):141-169.
    In Science, Truth, and Democracy (2001a), Kitcher moderates the strongest ontological realist thesis he defended in The Advancement of Science (1993a), with the aim of making compatible the correspondence theory of truth with conceptual relativity. However, it is not clear that both things could be harmonized. If our knowledge of the world is mediated by our categories and concepts; if the selection of these categories and concepts may vary according to our interests, and they are not the consequence of the (...)
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  • Philosophy of mathematics.Jeremy Avigad - manuscript
    The philosophy of mathematics plays an important role in analytic philosophy, both as a subject of inquiry in its own right, and as an important landmark in the broader philosophical landscape. Mathematical knowledge has long been regarded as a paradigm of human knowledge with truths that are both necessary and certain, so giving an account of mathematical knowledge is an important part of epistemology. Mathematical objects like numbers and sets are archetypical examples of abstracta, since we treat such objects in (...)
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  • Argument and explanation in mathematics.Michel Dufour - 2013 - In Dima Mohammed and Marcin Lewiński (ed.), Virtues of Argumentation. Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation (OSSA), 22-26 May 2013. pp. pp. 1-14..
    Are there arguments in mathematics? Are there explanations in mathematics? Are there any connections between argument, proof and explanation? Highly controversial answers and arguments are reviewed. The main point is that in the case of a mathematical proof, the pragmatic criterion used to make a distinction between argument and explanation is likely to be insufficient for you may grant the conclusion of a proof but keep on thinking that the proof is not explanatory.
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  • Wie individuell sind intentionale Einstellungen wirklich?Ralf Stoecker - 2000 - Metaphysica 1:107-119.
    So selbstverständlich es klingt, vom Geist, der Psyche oder auch der Seele eines Menschen zu reden, und so vertraut uns wissenschaftliche Disziplinen sind, die sich philosophisch oder empirisch damit beschäftigen, so schwer fällt es, ein einheitliches Merkmale dafür anzugeben, wann etwas ein psychisches Phänomen ist. Viele der potentiellen Merkmale decken eben nur einen Teil des Spektrums dessen ab, was wir gewöhnlich als psychisch bezeichnen würden, und sind damit bestenfalls hinreichende, aber sicher keine notwendigen Bedingungen des Psychischen. Im Mittelpunkt des folgenden (...)
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  • The dialectical tier of mathematical proof.Andrew Aberdein - 2011 - In Frank Zenker (ed.), Argumentation: Cognition & Community. Proceedings of the 9th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18--21, 2011. OSSA.
    Ralph Johnson argues that mathematical proofs lack a dialectical tier, and thereby do not qualify as arguments. This paper argues that, despite this disavowal, Johnson’s account provides a compelling model of mathematical proof. The illative core of mathematical arguments is held to strict standards of rigour. However, compliance with these standards is itself a matter of argument, and susceptible to challenge. Hence much actual mathematical practice takes place in the dialectical tier.
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