[FOM] Chinese and Indian logic -- Buckner's post

[José Félix Costa]

«Lukasiewicz says that only the logical principles stated in schematic terms
belong to logic, and not those given in concrete terms.»

I found at home a nice reference:

G. E. R. Lloyd, Adversaries and Authorities, Investigations into ancient
Greek and Chinese science, IDEAS IN CONTEXT, Cambridge University Press,
1996.

Otto Neugebaur (in his Exact Sciences in Antiquity, by the end of the
book --- ocurrences captured by the index) refers to the Lukasiewicz' paper
in the same terms as Buckner.

[Unfortunatly I have Needham's books in the south.]

But in what concerns the concept of proof, the Chinese got it!
The earliest Chinese text on mathematics is the Chou Pei Suan Ching. In this
text, a proof of the ''Theorem of Pythagoras'' is given. The proof is worked
out for the 3, 4, 5 triangle, but the idea of the proof is perfectly general
(Needham offers a translation of the proof).

J. Felix

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J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
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e-mail:   fgc at math.ist.utl.pt
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