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1 of 1 people found the following review helpful
5.0 out of 5 stars Very interesting book.
For someone who likes the history of science and mathematics is a lovely book. We lost throughout history the way of thinking of the Greek mathematicians. This book brings to light these issues in a clear way
Published 14 months ago by Sergio Ribeiro-Teixeira

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2 of 3 people found the following review helpful
2.0 out of 5 stars Overhyped
I could not find any "theory of the emergence of the deductive method" in this book, despite such promises on the dust jacket. It consists mostly of baroque analyses going absolutely nowhere. Trivial conclusions abound, along with fictional assertions that they are "surprising" (p. 19), here referring to the conclusion that in Greek mathematical texts...
Published 11 months ago by Viktor Blasjo


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1 of 1 people found the following review helpful
5.0 out of 5 stars Very interesting book., September 9, 2013
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This review is from: The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History (Ideas in Context) (Paperback)
For someone who likes the history of science and mathematics is a lovely book. We lost throughout history the way of thinking of the Greek mathematicians. This book brings to light these issues in a clear way
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2 of 3 people found the following review helpful
2.0 out of 5 stars Overhyped, November 27, 2013
This review is from: The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History (Ideas in Context) (Paperback)
I could not find any "theory of the emergence of the deductive method" in this book, despite such promises on the dust jacket. It consists mostly of baroque analyses going absolutely nowhere. Trivial conclusions abound, along with fictional assertions that they are "surprising" (p. 19), here referring to the conclusion that in Greek mathematical texts "the diagram is not directly recoverable from the text" (p. 19). Similarly, "the use of the diagram as a vehicle for logic ... might be considered a miracle" (p. 33), supposedly, until Professor Netz explains otherwise. Perhaps Netz can fool his mathematically ignorant colleagues in the Classics Department with this kind of sensationalism, but readers who know something about geometry will find his banal conclusions anything but "surprising" and "miraculous".

What little use I can imagine for this book comes from its discussions of how Greek mathematical thought is related to its mode of expression and representation. Some food for thought in this regard is the following.

"THEAANDTHEBTAKENTOGETHERAREEQUALTOTHECANDTHED
This is how the Greeks would write A+B=C+D, had they written in English. And it becomes clear that only by going beyond the written form can the reader realise the structural core of the expressions. Script must be transformed into pre-written language, and then be interpreted through the natural capacity for seeing form in language. Greek mathematical formulae are post-oral, but pre-written. They no longer rely on the aural; they do not yet rely on the layout." (p. 163)

"The lettered diagram is a distinctive mark of Greek mathematics. ... No other culture developed it independently." (p. 58) "The overwhelming rule in Greek mathematics is that propositions are individuated by their diagrams" (p. 38), contrary to the economy of using the same diagram for several propositions, and contrary even to plain sense, it would seem, in the use of completely functionless diagrams for number-theoretic propositions (p. 41).

But the diagrams were schematic only, with for example conic sections being crudely represented by circular arcs (p. 34). The diagrams were also static since "of the media available to the Greeks ... none had ease of writing and rewriting" (p. 14). Standard media were papyri and wax tablets, and, for larger audiences, such as Aristotle's lectures, "the only practical option was wood ... painted white" (p. 16). "None of these [ways of representing figures] is essentially different from a diagram as it appears in a book. ... The limitations of the media available suggest ... the preparation of the diagram prior to the communicative act---a consequence of the inability to erase." (p. 16) "This, in fact, is the simple explanation for the use of perfect imperatives in the references to the setting out---'let the point A have been taken'. It reflects nothing more than the fact that, by the time one comes to discuss the diagram, it has already been drawn." (p. 25)

"Many Greek mathematical works were originally set down within letters." (p. 13) Which is understandable since "in every generation ... a few dozens at most of active mathematicians ... thinly spread across the eastern Mediterranean ... had to discover each other. ... Alexandria may indeed be the exception to my rule---an exception not to be overestimated, since there were never more than a handful of Alexandrian mathematicians. They formed a literary tradition, not a school." (p. 291)
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The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History (Ideas in Context)
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