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Diagrammatic reasoning is reasoning by means of visual representations. The study of diagrammatic reasoning is about the understanding of concepts and ideas, visualized with the use of diagrams and imagery instead of by linguistic or algebraic means.
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
In contrast, diagrammatology is currently the term of choice for the arts and humanities, where it is closely associated with Charles Sanders Peirce's work on diagrammatic reasoning. In the introduction to his seminal 2011 work "Diagrammatology", Frederik Stjernfelt describes the reasoning behind his use of the term:
Let be a first-order language and be a theory over . For a model of one expands to a new language := {:} by adding a new constant symbol for each element in , where is a subset of the domain of .
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
Defeasible reasoning – Reasoning that is rationally compelling, though not deductively valid – from authority: if p then (defeasibly) q; Diagrammatic reasoning – reasoning by the mean of visual representations – reasoning by means of visual representations. Visualizing concepts and ideas with of diagrams and imagery instead of by ...
Use direct reasoning; Solve an equation [14] Also suggested: Look for a pattern [15] Draw a picture [16] Solve a simpler problem [17] Use a model [18] Work backward [19] Use a formula [20] Be creative [21] Applying these rules to devise a plan takes your own skill and judgement. [22] Pólya lays a big emphasis on the teachers' behavior.
In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. [1] It is said that commutative diagrams play the role in category theory that equations play in algebra. [2]