support of their position. Mathematics, Form and Function (1986), an overview of mathematics intended for philosophers, proposes that mathematical concepts are ultimately grounded in ordinary human activities, mostly interactions with the physical world. Educators have taken some interest in what WMCF suggests about how mathematics is learned, and why students find some elementary concepts more difficult than others. However, even from an educational perspective, WMCF is still problematic. From the conceptual metaphor theory's point of view, metaphors reside in a different realm, the abstract, from that of 'real world', the concrete. In other words, despite their claim of mathematics being human, established mathematical knowledge — which is what we learn in school — is assumed to be and treated as abstract, completely detached from its physical origin. It cannot account for the way learners could access to such knowledge. WMCF is also criticized for its monist approach. First, it ignores the fact that the sensori-motor experience upon which our linguistic structure — thus, mathematics — is assumed to be based may vary across cultures and situations. Second, the mathematics WMCF is concerned with is "almost entirely... standard utterances in textbooks and curricula", which is the most-well established body of knowledge. It is negligent of the dynamic and diverse nature of the history of mathematics. WMCF's logo-centric approach is another target for critics. While it is predominantly interested in the association between language and mathematics, it does not account for how non-linguistic factors contribute to the emergence of mathematical ideas (e.g. See Radford, 2009; Rotman, 2008). 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. Example of metaphorical ambiguity WMCF (p. 151) includes the following example of what the authors term "metaphorical ambiguity." Take the set Then recall