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PASCH’S PHILOSOPHY OF MATHEMATICS
The Review of Symbolic Logic, 2010Moritz Pasch (1843–1930) gave the first rigorous axiomatization of projective geometry in hisVorlesungen über neuere Geometrie(1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Pasch also presented in these lectures the main tenets of his philosophy of mathematics,
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Wittgenstein’s Philosophies of Mathematics
Synthese, 1991Wittgenstein's philosophy of mathematics has long been notorious. Part of the problem is that it has not been recognized that Wittgenstein, in fact, had two chief post-Tractatus conceptions of mathematics. I have labelled these the calculus conception and the language-game conception. The calculus conception forms a distinct middle period.
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1997
The questions concerning the nature and philosophy of mathematics and which are familiar to all acquainted with the history of speculative opinion, form, it is probable, but a small part of those which have at different times occurred to earnest students without perhaps ever passing out of the silent region of thought into the outward world of ...
Ivor Grattan-Guinness, Gérard Bornet
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The questions concerning the nature and philosophy of mathematics and which are familiar to all acquainted with the history of speculative opinion, form, it is probable, but a small part of those which have at different times occurred to earnest students without perhaps ever passing out of the silent region of thought into the outward world of ...
Ivor Grattan-Guinness, Gérard Bornet
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Philosophical Books, 2003
Abstract It is clear that mathematics is involved in our best efforts to gain knowledge of the physical world, through science. Moreover, mathematics itself at least appears to be a knowledge-gathering activity. We speak of what theorems a given person knows and does not know.
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Abstract It is clear that mathematics is involved in our best efforts to gain knowledge of the physical world, through science. Moreover, mathematics itself at least appears to be a knowledge-gathering activity. We speak of what theorems a given person knows and does not know.
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2008
One main interest of philosophy is to become clear about the assumptions, premises and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is achievable or necessary like the articles in the first part of the publication show.
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One main interest of philosophy is to become clear about the assumptions, premises and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is achievable or necessary like the articles in the first part of the publication show.
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Philosophical Books, 1999
Books reviewed:Shapiro, S., Philosophy of MathematicsSteiner, M., The Applicability of Mathematics as a Philosophical ...
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Books reviewed:Shapiro, S., Philosophy of MathematicsSteiner, M., The Applicability of Mathematics as a Philosophical ...
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1984
The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness ...
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The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness ...
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Redrawing Kant's philosophy of mathematics
South African Journal of Philosophy, 2013This essay offers a strategic reinterpretation of Kant’s philosophy of mathematics in Critique of Pure Reason via a broad, empirically based reconception of Kant’s conception of drawing. It begins with a general overview of Kant’s philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the ...
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2000
AbstractThe philosophy of mathematics articulated and defended in this book goes by the name of “structuralism”, and its slogan is that mathematics is the science of structure. The subject matter of arithmetic, for example, is the natural number structure, the pattern common to any countably infinite system of objects with a distinguished initial ...
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AbstractThe philosophy of mathematics articulated and defended in this book goes by the name of “structuralism”, and its slogan is that mathematics is the science of structure. The subject matter of arithmetic, for example, is the natural number structure, the pattern common to any countably infinite system of objects with a distinguished initial ...
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