Blending and Other Conceptual Operations in the Interpretation of Mathematical Proofs

Insights 1 from cognitive semantics suggest that conceptual mapping and combination processes play a role at several levels in natural language interpretation. It has been proposed by Lako (1987) and Johnson (1987) that such correspondence-making plays a role not only in communicative but in reasoning processes, and, in particular, mathematical reasoning. This proposal suggests that abstract mathematical concepts are grounded in experientially-based image schemas, and reasoning with the concepts proceeds according to the correspondences we make between the properties of the grounding schemas and the speci c con gurations arising in mathematical situations.