Author: William Arthur BrownellPublisher: Berkeley : University of California Press
ISBN:
Category : Mathematics
Languages : en
Pages : 254
Book Description
Arithmetical Abstractions
Author: William Arthur BrownellPublisher: Berkeley : University of California Press
ISBN:
Category : Mathematics
Languages : en
Pages : 254
Book Description
The Arché Papers on the Mathematics of Abstraction
Author: Roy T. CookPublisher: Springer Science & Business Media
ISBN: 1402042655
Category : Mathematics
Languages : en
Pages : 480
Book Description
This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut- or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies.
Detroit Journal of Education
Author: Office of Education Research Reports, 1956-65, ED 002 747-ED 003 960
Author: Educational Research Information Center (U.S.).Publisher:
ISBN:
Category : Education
Languages : en
Pages : 710
Book Description
Abstraction and Representation
Author: Peter DamerowPublisher: Springer Science & Business Media
ISBN: 9401586241
Category : History
Languages : en
Pages : 444
Book Description
This book deals with the development of thinking under different cultural conditions, focusing on the evolution of mathematical thinking in the history of science and education. Starting from Piaget's genetic epistemology, it provides a conceptual framework for describing and explaining the development of cognition by reflective abstractions from systems of actions.
Grounding Concepts
Author: C. S. JenkinsPublisher: OUP Oxford
ISBN: 0191552402
Category : Philosophy
Languages : en
Pages : 306
Book Description
Grounding Concepts tackles the issue of arithmetical knowledge, developing a new position which respects three intuitions which have appeared impossible to satisfy simultaneously: a priorism, mind-independence realism, and empiricism. Drawing on a wide range of philosophical influences, but avoiding unnecessary technicality, a view is developed whereby arithmetic can be known through the examination of empirically grounded concepts. These are concepts which, owing to their relationship to sensory input, are non-accidentally accurate representations of the mind-independent world. Examination of such concepts is an armchair activity, but enables us to recover information which has been encoded in the way our concepts represent. Emphasis on the key role of the senses in securing this coding relationship means that the view respects empiricism, but without undermining the mind-independence of arithmetic or the fact that it is knowable by means of a special armchair method called conceptual examination. A wealth of related issues are covered during the course of the book, including definitions of realism, conditions on knowledge, the problems with extant empiricist approaches to the a priori, mathematical explanation, mathematical indispensability, pragmatism, conventionalism, empiricist criteria for meaningfulness, epistemic externalism and foundationalism. The discussion encompasses themes from the work of Locke, Kant, Ayer, Wittgenstein, Quine, McDowell, Field, Peacocke, Boghossian, and many others.
Reports Made to the ... General Assembly of the State of Illinois
Author: IllinoisReports to the General Assembly of Illinois ...
Author: IllinoisReports Made to the Senate and House of Representatives of the State of Illinois
Author: IllinoisOffice of Education Research Reports, 1956-1965
Author: Educational Research Information Center (U.S.)Publisher:
ISBN:
Category : Education
Languages : en
Pages : 702
Book Description