Examples of Mathematical Metaphors
Conceptual metaphors described in WMCF, in addition to the Basic Metaphor of Infinity, include:
- Arithmetic is motion along a path, object collection/construction;
- Change is motion;
- Sets are containers, objects;
- Continuity is gapless;
- Mathematical systems have an "essence," namely their axiomatic algebraic structure;
- Functions are sets of ordered pairs, curves in the Cartesian plane;
- Geometric figures are objects in space;
- Logical independence is geometric orthogonality;
- Numbers are sets, object collections, physical segments, points on a line;
- Recurrence is circular.
Mathematical reasoning requires variables ranging over some universe of discourse, so that we can reason about generalities rather than merely about particulars. WMCF argues that reasoning with such variables implicitly relies on what it terms the Fundamental Metonymy of Algebra.
Read more about this topic: Where Mathematics Comes From
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