[FOM] Lack of abstraction in LOGIC but not only

José Félix Costa fgc at math.ist.utl.pt
Mon Dec 5 06:57:15 EST 2005

Reacting to
«Lukasiewicz says that only the logical principles stated in schematic terms
belong to logic...»

This lack of abstraction to which Dean refers to, is also exhibited in
preclassic arithmetics and geometry. E.g., the following translation of
problem 14 of the Moscow Mathematical Papyrus, due primarily to Struve (I
got it from Richard Gillings, Mathematics in the Time of Pharaohs), makes
the point:

Method of calculating a truncated pyramid (in Egypt, Middle Kingdom):

If it is said to thee, a truncated pyramid of 6 *ellen* in height,
Of 4 *ellen* of the base, by 2 of the top,
Reckon thou with this 4, squaring. Result 16.
Double thou with this 4. Result 8.
Reckon thou this 2, squaring. Result 4.
Add together this 16, with this 8, and with this 4. Result 28.
Calculate thou 1/3 of 6. Result 3.
Calculate thou with 28 twice. Result 56.
Lo! It is 56! Thou has found rightly.

This gives you the formula of the frustrum V = h / 3 (a^2 + ab + b^2).

I will see what Joseph Needham says about Logic in China.(Science and
Civilisation in China).

Needham Research Institute
see Pt. 1. Language and Logic. Christoph Harbsmeier (1998)

J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm

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