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Mathematics and Philosophy of Mathematics
Philosophia Mathematica, 1994Nach den Ausführungen des Verf. führt das Studium der Ontologie zu keinen ersten Prinzipien der Mathematik, noch bestimmt die Mathematik die Ontologie. Die Begründung dieser Ansicht stützt sich auf eingehende Studien sowohl von Plato und Proklos sowie der Werke von Gödel, Brouwer, Poincaré, Lebesgue and Bernays.
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Philosophy of Mathematics and Philosophy of History
PARADIGMI, 2011If we suppose that the central activity of mathematicians is analysis, the search for the conditions of solvability of a problem (and more generally, a search for the conditions of intelligibility of the things that mathematics problems concern), then mathematical reasoning must concern narrative as well as argument.
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2010
Philosophy of mathematics is arguably one of the oldest branches of philosophy, and one that bears significant connections with core philosophical areas, particularly metaphysics, epistemology, and (more recently) the philosophy of science. This entry focuses on contemporary developments, which have yielded novel approaches (such as new forms of ...
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Philosophy of mathematics is arguably one of the oldest branches of philosophy, and one that bears significant connections with core philosophical areas, particularly metaphysics, epistemology, and (more recently) the philosophy of science. This entry focuses on contemporary developments, which have yielded novel approaches (such as new forms of ...
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1964
We begin this chapter by recalling in a summary way what we have learnt about the Sun, Line and Cave similes in the preceding chapter. The Sun simile we might set out in an abbreviated form as follows:
R. C. Cross, A. D. Woozley
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We begin this chapter by recalling in a summary way what we have learnt about the Sun, Line and Cave similes in the preceding chapter. The Sun simile we might set out in an abbreviated form as follows:
R. C. Cross, A. D. Woozley
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CONSCIOUSNESS, PHILOSOPHY, AND MATHEMATICS
1975Publisher Summary This chapter describes the importance of consciousness, philosophy, and mathematics. Consciousness in its deepest home seems to oscillate slowly, will-lessly, and reversibly between stillness and sensation. It seems that only the status of sensation allows the initial phenomenon of the said transition.
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Philosophy, 1947
This essay is an attempt to take stock of what has been done by those who have worked on the foundations of mathematics and to suggest, very inadequately in so short a space, what may be a satisfactory approach to this subject for one who is not an expert in it.
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This essay is an attempt to take stock of what has been done by those who have worked on the foundations of mathematics and to suggest, very inadequately in so short a space, what may be a satisfactory approach to this subject for one who is not an expert in it.
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1999
THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world—explicating such facts presents philosophy with some of its subtlest ...
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THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world—explicating such facts presents philosophy with some of its subtlest ...
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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 ...
Gérard Bornet, Ivor Grattan-Guinness
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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 ...
Gérard Bornet, Ivor Grattan-Guinness
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Philosophy and mathematics: interactions.
Physis; rivista internazionale di storia della scienza, 2014From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems ...
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