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Concept Formation and Concept Grounding

Journal article
Authors Jörgen Sjögren
Christian Bennet
Published in Philosophia
Volume 42
Issue 3
Pages 827-839
ISSN 0048-3893
Publication year 2014
Published at Department of Pedagogical, Curricular and Professional Studies
Pages 827-839
Language en
Links dx.doi.org/10.1007/s11406-014-9528-...
Keywords Epistemology · Mathematics · Knowledge of theorems · The role of proof · Empiricism · Concept grounding · Concept formation
Subject categories Theoretical philosophy, Theory of science

Abstract

Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. But we also present some further problems with her view, concerning the role of proof for mathematical knowledge.

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