1 Issues in the Foundations of Mathematics
نویسنده
چکیده
I discuss my efforts concerning 3 crucial issues in the foundations of mathematics that are deeply connected with the great work of Kurt Gödel. A. To what extent can set theoretic methods be used in an essential way to further the development of normal mathematics? B. Are there fundamental principles of a general philosophical nature which can be used to give consistency proofs of set theory, including the so called large cardinal axioms? C. To what extent, and in what sense, is the natural hierarchy of logical strengths rep resented by familiar systems ranging from exponential function arithmetic to ZF + j:V AE V robust? Our discussion of A is aimed at mathematicians; B,C at mathematicians & philosophers. This was used as a problem for gifted high school students by Paul Sally at U. Chicago. One student proved n(2) = 11.
منابع مشابه
POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...
متن کاملThe foundations of knowledge in transcendental philosophy
The relation among the three elements of knowledge is considered as an important issue in epistemology. Mollasadra introduced the relation between knowledge and object-known in mental existence and upon his own principals of philosophy believed that the essence of knowledge is the occurring of quiddity and the nature of external object in mind. Knowledge is a kind of existence, which within ...
متن کاملBuckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations
Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...
متن کاملUnity within Diversity: Foundations and Dynamics of National Identity in Iran
The article provides a critical assessment of the more recent literature that relies on theoretical frameworks such as post modernism and globalization to deal with national identity, ethnicity and cultural mobility. Explaining sensitive and complicated issues such as identity requires the extensive use of the native historical, cultural and sociological sources related to the Iranian experienc...
متن کاملJOHN MAYBERRY The Foundations of Mathematics in the Theory of Sets
In The Foundations of Mathematics in the Theory of Sets, John Mayberry attacks the 2000-year-old problem of accounting for the foundations of mathematics. His account comes in three interrelated parts: determining exactly what one should (and should not) expect from a foundation; arguing that set theory can in fact provide such a foundation, and presenting a novel version of set theory (or at l...
متن کاملPrestige and Dominance as Differential Correlates of Moral Foundations and Its Clinical Implications
Objective: The ways people use for social rank (dominance vs prestige) could explain difference attitude toward five moral foundations. The aim of this study was to investigate the differential relationship between prestige, dominance and moral foundations. Methods: This study conducted with 150 participants who respond to the moral foundation questionnaire and dominance-prestige scale. Multip...
متن کامل