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19 de mar. de 2018 · The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.
21 de ago. de 2013 · In this research oriented manuscript, foundational aspects of rigid geometry are discussed, putting emphasis on birational side of formal schemes and topological feature of rigid spaces. Besides ...
1 de out. de 1994 · Cantor's set theory has eventually prevailed, and became a formal basis of contemporary mathematics, while Bolzano's approach is generally considered a step in the wrong direction.
11 de nov. de 2013 · Gödel’s two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried ...
On the Foundations of Geometry and Formal Theories of Arithmetic. Howard Jackson. Journal of Symbolic Logic 46 (1):175-179 (1981)
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.
14 de fev. de 2014 · This discussion is significant because it gives a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the philosophy of mathematics. Abstract A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical ...
