Concept Formation and Concept Grounding

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

HUMANIORA  -- Filosofi, etik och religion -- Filosofi (hsv//swe)

HUMANITIES  -- Philosophy, Ethics and Religion -- Philosophy (hsv//eng)

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap -- Didaktik (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences -- Didactics (hsv//eng)

Keyword

Epistemology

Mathematics

Knowledge of theorems

The role of proof

Empiricism

Concept grounding

Concept formation

Natural sciences

Naturvetenskap

Epistemology · Mathematics · Knowledge of theorems · The role of proof · Empiricism · Concept grounding · Concept formation

Publication and Content Type

ref (subject category)

art (subject category)