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10. Juni 1998 · Given that the proof of Frege’s Theorem makes no appeal to Basic Law V, some philosophers have argued Frege’s best strategy for producing an epistemologically-justified foundation for arithmetic is to replace the primitive term \(\epsilon F\) with the primitive term \(\#F\), replace Basic Law V with Hume’s Principle, and argue that Hume’s Principle is an analytic principle of logic.
The philosophy of mathematics is also one of the oldest academic fields, more or less coeval with philosophy itself. But contemporary philosophy of mathematics is rather different from its pre-twentieth-century antecedents, largely for three reasons. The first is that since the seventeenth century, mathematics has become integral to science.
30. Sept. 2003 · Philosophy of Arithmetic: Psychological and Logical Investigations with Supplementary Texts from 1887–1901 (Husserliana: Edmund Husserl – Collected Works, 10) [Husserl, Edmund, Willard, Dallas] on Amazon.com. *FREE* shipping on qualifying offers.
- Edmund Husserl
8. Aug. 2015 · The Philosophy of Arithmetic: Exhibiting a Progressive View of the Theory and Practice of Calculation, With Tables for the Multiplication of Numbers As Far As One Thousand: Authors: John Leslie, University Professor Emeritus John Leslie, Sir: Edition: illustrated: Publisher: Creative Media Partners, LLC, 2015: ISBN: 1296561984, 9781296561987 ...
Cambridge Core - Philosophy of Science - Philosophy of Mathematics. 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 ...
Logicism can be either a realist philosophy of mathematics or an anti-realist philosophy of mathematics. Frege was a realist. Frege's logicist believes that mathematical truths are independent of human beings. Frege's version of logicism is epistemologically realist. That is, human beings discover, or fail to discover, mathematical truths. Type.
16. Sept. 2010 · In this paper I present a formalist philosophy mathematics and apply it directly to Arithmetic. I propose that formalists concentrate on presenting compositional truth theories for mathematical languages that ultimately depend on formal methods. I argue that this proposal occupies a lush middle ground between traditional formalism, fictionalism, logicism and realism.
