Explanation and Proof in Mathematics: Philosophical and by Gila Hanna,Hans Niels Jahnke,Helmut Pulte

By Gila Hanna,Hans Niels Jahnke,Helmut Pulte

In the 4 a long time considering the fact that Imre Lakatos declared arithmetic a "quasi-empirical science," expanding cognizance has been paid to the method of evidence and argumentation within the box -- a improvement paralleled via the increase of desktop know-how and the mounting curiosity within the logical underpinnings of mathematics.  Explanantion and facts in Mathematics assembles views from arithmetic schooling and from the philosophy and background of arithmetic to bolster mutual expertise and percentage contemporary findings and advances of their interrelated fields.  With examples starting from the geometrists of the seventeenth century and old chinese language algorithms to cognitive psychology and present academic perform, participants discover the function of refutation in producing proofs, the numerous hyperlinks among test and deduction, using diagrammatic considering as well as natural good judgment, and the makes use of of facts in arithmetic schooling (including a critique of "authoritative" as opposed to "authoritarian" educating styles).

A sampling of the coverage:

  • The conjoint origins of facts and theoretical physics in historical Greece.

  • Proof as bearers of mathematical knowledge.

  • Bridging realizing and proving in mathematical reasoning.

  • The function of arithmetic in long term cognitive improvement of reasoning.

  • Proof as test within the paintings of Wittgenstein.

  • Relationships among mathematical evidence, problem-solving, and explanation.

Explanation and facts in Mathematics is sure to draw quite a lot of readers, together with mathematicians, arithmetic schooling pros, researchers, scholars, and philosophers and historians of mathematics.

Show description

Read Online or Download Explanation and Proof in Mathematics: Philosophical and Educational Perspectives PDF

Best logic books

18 Unconventional Essays on the Nature of Mathematics

This publication collects essentially the most fascinating contemporary writings which are tackling, from a number of issues of view, the matter of giving an accounting of the character, function, and justification of genuine mathematical practice–mathematics as really performed by means of actual dwell mathematicians. what's the nature of the gadgets being studied?

Computable Structures and the Hyperarithmetical Hierarchy (Studies in Logic and the Foundations of Mathematics)

This e-book describes a application of analysis in computable constitution conception. The aim is to discover definability stipulations similar to bounds on complexity which persist less than isomorphism. the implications observe to widely used different types of constructions (groups, fields, vector areas, linear orderings Boolean algebras, Abelian p-groups, versions of arithmetic).

Proceedings of the 13th Asian Logic Conference (Proceedings of the Asian Logic Conference)

This quantity presents a discussion board which highlights new achievements and overviews of modern advancements of the thriving good judgment teams within the Asia-Pacific zone. It includes papers by means of major logicians and in addition a few contributions in desktop technology logics and philosophic logics.

Introduction to Mathematical Logic, Sixth Edition (Discrete Mathematics and Its Applications)

The recent version of this vintage textbook, creation to Mathematical good judgment, 6th version explores the imperative issues of mathematical common sense. It covers propositional common sense, first-order common sense, first-order quantity conception, axiomatic set thought, and the speculation of computability. The textual content additionally discusses the key result of Gödel, Church, Kleene, Rosser, and Turing.

Additional resources for Explanation and Proof in Mathematics: Philosophical and Educational Perspectives

Example text

Download PDF sample

Rated 4.70 of 5 – based on 35 votes