Interweavings of Alan Turing＇s Mathematics and Sociology of Knowledge  

作　　者：Isabel Cafezeiro Ivan da Costa Marques 

机构地区：[1]Instituto de Computagao, Universidade Federal Fluminense, Rua Passo da Patria 24210-240, Brazil, and Programa dePos-Graduagao em Historia das Ciencias e das Ttecnicas e Epistemologia, Universidade Federal do Rio de Janeiro [2]Programa de Pos-Graduagao em Historia das Ciencias e das Ttecnicas e Epistemologia, Universidade Federal do Rio de Janeiro,Av Atlantica 22010-000, Brazil

出　　处：《Journal of Mathematics and System Science》2012年第7期420-429,共10页数学和系统科学（英文版）

摘　　要：This paper starts from the analysis of how Alan Turing proceeded to build the notion of computability in his famous 1936 text ＂On computable numbers, with an application to the Entscheidungsproblem＂. Looking in detail at his stepwise construction, which starts from the materialities to achieve a satisfactory level of abstraction, it is considered how his way of doing mathematics was one that constructs mathematical knowledge by evading a definite separation between matter and form; in this way, making the world and language come together. Following the same line of reasoning, it is argued in this paper that the abstract and the concrete, the deduction and the induction, the technical and the social as well as the objective and the subjective are unthinkable as pure entities. By considering the controversies and discussions from the mid-nineteenth century until now, it is shown that local （social） elements necessarily participate in what is usually considered ＂technical content＂ or ＂objectivity＂. While Alan Turing was a precursor of what today might be said to be an ＂anthropological approach to mathematical culture＂, unveiling and reviving approaches that enable the axis of authority for mathematics, logic and computing to be shifted, he also opened different paths for the construction of a variety of mathematical knowledge as well.

关 键 词：COMPUTABILITY Alan Tttring knowledge construction. 

分 类 号：TP393.03[自动化与计算机技术—计算机应用技术] O1-4[自动化与计算机技术—计算机科学与技术]