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Truth and the Philosophy of Mathematics
2012Is truth – qua a primitive notion – fit to play an independent role in the philosophy of mathematics and in the foundational investigations? The problem is handled by surveying axiomatic theories of truth and their implications, with a main concern for ontological and epistemological issues.
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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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Structuralism as a philosophy of mathematical practice
Synthese, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Fictionalism in the philosophy of mathematics
2012Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘∏ is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities,
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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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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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Mathematics in Philosophy, Philosophy in Mathematics: Three Case Studies
2016The interaction between philosophy and mathematics has a long and well articulated history. The purpose of this note is to sketch three historical case studies that highlight and further illustrate some details concerning the relationship between the two: the interplay between mathematical and philosophical methods in ancient Greek thought; vagueness ...
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Mathematical Philosophy and Philosophy of Mathematics
The American Mathematical Monthly, 1920Cassius J. Keyser, Bertrand Russell
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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.
openaire +1 more source