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foundations of mathematics, the study of the logical and philosophical basis of mathematics, including whether the axioms of a given system ensure its completeness and its consistency. Because mathematics has served as a model for rational inquiry in the West and is used extensively in the sciences, foundational studies have far-reaching ...
5 de abr. de 2020 · Arithmetic. The science of numbers and operations on sets of numbers. Arithmetic is understood to include problems on the origin and development of the concept of a number, methods and means of calculation, the study of operations on numbers of different kinds, as well as analysis of the axiomatic structure of number sets and the properties of ...
Abstract. This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work.
euclidean geometry may be developed without the use of the axiom of continuity; the signifi-cance of Desargues’s theorem, as a condition that a given plane geometry may be regarded as a part of a geometry of space, is made apparent, etc. 5. A variety of algebras of segments are introduced in accordance with the laws of arithmetic.
In Schirn 1976, pp. 215– 28. Kitcher, Philip 1984: The Nature of Mathematical Knowledge. Oxford: Oxford University Press. Klement, Kevin 2002. Frege and the Logic of Sense and Reference. New York and London: Routledge. 23 Kluge, Eike-Henner W. (ed.) 1971: On the Foundations of Geometry and Formal Theories of Arithmetic.
On the Foundations of Geometry and Formal Theories of Arithmetic. F. P. O’Gorman. Philosophical Studies (Dublin) 22:270-272 (1973)
On the foundations of geometry and formal theories of arithmetic | Gottlob Frege, E-.H.W. Kluge | download on Z-Library | Download books for free. Find books Support us in the fight for the freedom of knowledge Sign the petition Hide info
