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Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (hereinafter WMCF) is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, WMCF seeks to found a cognitive science of mathematics, a theory of embodied mathematics based on conceptual metaphor.
Virtually all mathematical theorems today can be formulated as theorems of set theory. The truth of a mathematical statement, in this view, is represented by the fact that the statement can be derived from the axioms of set theory using the rules of formal logic.
In mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner. [1] Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne , [ 2 ] and remain in extensive use in the education theory.
The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning ' something learned, knowledge, mathematics ', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning ' mathematical science '. It entered the English language during the Late Middle English period through French and ...
In his article "Restructuring Lattice Theory" (1982), [1] initiating formal concept analysis as a mathematical discipline, Wille starts from a discontent with the current lattice theory and pure mathematics in general: The production of theoretical results—often achieved by "elaborate mental gymnastics"—were impressive, but the connections between neighboring domains, even parts of a ...
The Zermelo–Fraenkel axioms for set theory were formulated which provided a conceptual framework in which much mathematical discourse would be interpreted. In mathematics, as in physics, new and unexpected ideas had arisen and significant changes were coming.
A graphical representation of a Design Process using C-K Design Theory. C-K design theory or concept-knowledge theory is both a design theory and a theory of reasoning in design. It defines design reasoning as a logic of expansion processes, i.e. a logic that organizes the generation of unknown objects.
The term conceptual model refers to any model that is formed after a conceptualization or generalization process. [1] [2] Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is fundamentally a study of concepts, the ...