TY - BOOK ID - 8558408 TI - Internal logic : foundations of mathematics from Kronecker to Hilbert PY - 2002 SN - 9781402006890 1402006896 9048160529 9401700834 PB - Dordrecht : Kluwer, DB - UniCat KW - Arithmétique KW - Logique mathématique KW - Mathématiques KW - Logique KW - Fondements KW - Philosophie KW - Logic, Symbolic and mathematical. KW - Mathematics KW - Philosophy. KW - Logic, Symbolic and mathematical KW - Logic of mathematics KW - Mathematics, Logic of KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Philosophy KW - Arithmétique. KW - Logique mathématique. KW - Fondements. KW - Philosophie. KW - Algebra, Abstract KW - Metamathematics KW - Set theory KW - Syllogism KW - Mathematical logic. KW - Mathematics. KW - Logic. KW - Philosophy and science. KW - Mathematical Logic and Foundations. KW - Mathematics, general. KW - Philosophy of Science. KW - Science and philosophy KW - Science KW - Argumentation KW - Deduction (Logic) KW - Deductive logic KW - Dialectic (Logic) KW - Logic, Deductive KW - Intellect KW - Psychology KW - Reasoning KW - Thought and thinking KW - Math KW - Methodology UR - https://www.unicat.be/uniCat?func=search&query=sysid:8558408 AB - Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene. ER -