From Action to Mathematics per Mac Lane
From Wikipedia, the free encyclopedia
Throughout his Mathematics: Form and function, and especially in his chpt. I.11, the American mathematician Saunders Mac Lane informally discussed how mathematics is grounded in more ordinary concrete and abstract human activities. This entry, From Action to Mathematics per Mac Lane, sets out a summary of his views on the human grounding of mathematics.
These views, however informal, are a contribution to the philosophy and anthropology of mathematics.[1] Mac Lane can be seen as having anticipated, in some respects, the much richer and more detailed account of the cognitive basis of mathematics given in Lakoff and Núñez (2000). They argue that mathematics emerges via conceptual metaphors grounded in the human body, its motion through space and time, and in human sense perceptions.
The following table is adapted from one given on p. 35 of Mac Lane (1986). The rows are very roughly ordered from most to least fundamental. For a bullet list that can be compared and contrasted with this table, see section 3 of Where Mathematics Comes From.
Also see the related diagrams appearing on the following pages of Mac Lane (1986): 149, 184, 306, 408, 416, 422-28.
Mac Lane (1986) cites a related monograph by Gärding (1977).
[edit] Footnotes
- ^ On mathematics and anthropology, see White (1947) and Hersh (1997).
- ^ Also see the Basic Metaphor of Infinity of Lakoff and Núñez (2000), chpt. 8.
[edit] See also
- Conceptual metaphor
- Cognitive science
- Cognitive science of mathematics
- Embodied philosophy
- Foundations of mathematics
- Saunders Mac Lane
- Philosophy of mathematics
- Where Mathematics Comes From
[edit] Reference
- Gärding, Lars, 1977. Encounter with Mathematics. Springer-Verlag.
- Reuben Hersh, 1997. What Is Mathematics, Really? Oxford Univ. Press.
- George Lakoff and Rafael E. Núñez, 2000. Where Mathematics Comes From. Basic Books.
- Saunders Mac Lane, 1986. Mathematics: Form and Function. Springer Verlag.
- Leslie White, 1947, "The Locus of Mathematical Reality: An Anthropological Footnote," Philosophy of Science 14: 289-303. Reprinted in Hersh, R. , ed., 2006. 18 Unconventional Essays on the Nature of Mathematics. Springer: 304-19.