수학기초론

노트

위키데이터

• ID : Q833585

말뭉치

1. The questions with which inquiry into the foundations of mathematics starts are philosophical: that is, they are addressed to the nature of the ideas on which other ideas depend.
2. A major advancement of logic, one fated to greatly influence not only foundations of mathematics research but also mathematics and philosophy in general, was achieved by Frege.
3. Different positions concerning the foundations of mathematics have been defended, among them logicism (carrying on Frege's foundational work) and formalism (carrying on Hilbert's).
4. In a sense, foundations of mathematics remain irrelevant to modern science.
5. For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics.
6. Foundations of Mathematics for Virginia is customized to fit the developmental mathematics curriculum created by the Virginia Community College System.
7. The theory of computation arose from concerns about the foundations of mathematics, and was developed in the work of Gödel, Church, Turing, Kleene and others.
8. Gödel has done a great service here in drawing the very precise and formal development of the foundations of mathematics back to the fundamental questions which drove classical epistemology.
9. Edmund Husserl began as a mathematician, moved to psychology to find a solution to the problems raised by the foundations of mathematics, and then to an introspective transcendental system.
10. Knowing the foundations of mathematical thinking is an essential step in mastering the foundations of mathematics.
11. The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems.
12. In their writing of The Foundations of Mathematics, the authors motivate, encourage and teach their readers.
13. The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics.
14. For 2,000 years the foundations of mathematics seemed perfectly solid.
15. 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.
16. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague.
17. The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic.
18. This paper presents Automath encodings (which also are valid in LF/P) of various kinds of foundations of mathematics.
19. , we hope we have given a clear picture of these two different aims in the foundations of mathematics.
20. The thesis that set theory is most suitable for serving as the foundations of mathematics is by no means uncontroversial.

메타데이터

위키데이터

• ID : Q833585

Spacy 패턴 목록

• [{'LOWER': 'foundations'}, {'LOWER': 'of'}, {'LEMMA': 'mathematic'}]