Dedekind's Abstract Concepts: Models and Mappings

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Philosophia Mathematica (3):nku021 (2014)
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Abstract

Dedekind's mathematical work is integral to the transformation of mathematics in the nineteenth century and crucial for the emergence of structuralist mathematics in the twentieth century. We investigate the essential components of what Emmy Noether called, his ‘axiomatic standpoint’: abstract concepts, models, and mappings.

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10.1093/philmat/nku021

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Author Profiles

Dirk Schlimm
McGill University
Wilfried Sieg
Carnegie Mellon University

Citations of this work

Dedekind's Logicism.Ansten Mørch Klev - 2015 - Philosophia Mathematica:nkv027.
Dedekind’s Map-theoretic Period.José Ferreirós - 2017 - Philosophia Mathematica 25 (3):318–340.
Pasch's empiricism as methodological structuralism.Dirk Schlimm - 2020 - In Erich H. Reck & Georg Schiemer (eds.), The Pre-History of Mathematical Structuralism. Oxford: Oxford University Press. pp. 80-105.
Dedekind's Logicism†.Ansten Mørch Klev - 2015 - Philosophia Mathematica 25 (3):341-368.

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References found in this work

Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
The Ways of Hilbert's Axiomatics: Structural and Formal.Wilfried Sieg - 2014 - Perspectives on Science 22 (1):133-157.
The concept of function up to the middle of the 19th century.A. P. Youschkevitch - 1976 - Archive for History of Exact Sciences 16 (1):37-85.

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