Idea analysis of algebraic groups: A critical comment on George Lakoff and Rafael núñez's where mathematics comes from
Philosophical Psychology 15 (2):185 – 195 (2002)
AbstractThe study that George Lakoff and Rafael Núñez call "idea analysis" and begin in their recent book Where mathematics comes from is intended to dissect mathematical concepts into their metaphorical parts, where metaphor is used in the cognitive-science sense promoted by Lakoff and Mark Johnson in Metaphors we live by and subsequent works by each of them and together. Lakoff and Núñez's analysis of the (modern) algebraic concept of group is based on the attribution to contemporary mathematics of what will be widely recognizable by their name for it, the folk theory of essences. I argue that this philosophical basis for their analysis is spurious and supply an alternative analysis of the same concept within their "metaphorical" paradigm but without essences. This analysis, which I hope is more viable than theirs, is intended to support the general applicability of the paradigm by freeing it from outmoded philosophical baggage.
Similar books and articles
The metaphoric origins of objectivity, subjectivity, and consciousness in the direct perception of reality.Stanley A. Mulaik - 1995 - Philosophy of Science 62 (2):283-303.
Book Review:Metaphors We Live By. George Lakoff, Mark Johnson. [REVIEW]Wayne C. Booth - 1983 - Ethics 93 (3):619-.
Mathematical and philosophical analyses.Robert Rogers - 1964 - Philosophy of Science 31 (3):255-264.
Agnostic Science. Towards a Philosophy of Data Analysis.D. C. Struppa - 2011 - Foundations of Science 16 (1):1-20.
Review of G. Lakoff and R. E. Núñez, Where Mathematics Comes From. [REVIEW]Gary M. Shute - 2005 - Minds and Machines 15 (1):118-123.
Added to PP
Historical graph of downloads