1999
DOI: 10.1075/pc.7.1.07net
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Linguistic formulae as cognitive tools

Abstract: Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a (partial) explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae (expressions used repetitively) in Greek mathematical texts. It is shown that (a) the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is fu… Show more

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Cited by 11 publications
(11 citation statements)
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“…So, too, are gestures; they are typically an integral part of a complete multimodal message (e.g., Engle, 1998). In much diagrammatic communication—think of maps, science diagrams, assembly instructions—the visual-spatial features of meaning form the core of the message; the words and symbols annotate (e.g., Netz, 1999). There are parallel cases for gesture; that is, the sequence of gestures form the core of the communication, and the words serve to annotate the gestures (e.g., Emmorey et al, 2000; Kirsh, 2013).…”
Section: Discussionmentioning
confidence: 99%
“…So, too, are gestures; they are typically an integral part of a complete multimodal message (e.g., Engle, 1998). In much diagrammatic communication—think of maps, science diagrams, assembly instructions—the visual-spatial features of meaning form the core of the message; the words and symbols annotate (e.g., Netz, 1999). There are parallel cases for gesture; that is, the sequence of gestures form the core of the communication, and the words serve to annotate the gestures (e.g., Emmorey et al, 2000; Kirsh, 2013).…”
Section: Discussionmentioning
confidence: 99%
“…Written text is spatially arranged to reflect the organization of thought, spaces between words and sentences, larger spaces between paragraphs. Greek text describing mathematics was written formulaically, fixed orders of semantic forms, often in rows, that formed tables for reasoning (Netz, 1999). Even babies do it; many discover ''in your face'' early on.…”
Section: Place In Spacementioning
confidence: 99%
“…A remarkable example, analyzed by Reviel Netz (1999), is the role of linguistic formulae in ancient Greek mathematics. Netz shows that, in contrast to deduction in modern mathematics, where one resorts to typographic symbols, thus opting for exploiting a visual resource, Greek mathematics made use of formulaic expressions of a linguistic resource presumably of oral origin.…”
Section: Language As Toolmentioning
confidence: 99%