ONT Re: Leibniz -- De Arte Combinatoria
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DAC. Note 4
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| From 'Of the Art of Combination' (cont.)
|
| 10. For a certain complexion to be determined, the greater whole must be
| divided into equal parts assumed as the smallest (that is, which now
| at any rate are not divided further), from which there is composed and
| by whose variation there varies the complexion -- i.e. the lesser whole.
| Because the lesser whole is greater or less as more parts enter into it
| at one time, the number of parts or unities to be taken together at one
| and the same time we shall call the "exponent", after the example of
| geometrical progression.
|
| For example, let the whole be ABCD. If the lesser wholes are to consist
| of two parts -- e.g. AB, AC, AD, BC, BD, CD -- the exponent will be two;
| if of three -- e.g. ABC, ABD, ACD, BCD -- the exponent will be three.
|
| 11. Given an exponent, we shall write the complexions as follows.
| If the exponent is two, we shall write "com2nation" (combination);
| if three, "con3nation" (conternation); if four "con4nation", &c.
|
| 12. "Complexions 'simpliciter'" are all the complexions computed
| for all the exponents; e.g. for the number four, fifteen.
| These are composed of four (by union), six (by com2nation),
| four (by con3nation), and one (by con4nation) ...
|
| Leibniz, DAC, p. 2.
|
| Leibniz, 'Logical Papers', A Selection Translated and
| Edited with an Introduction by G.H.R. Parkinson (ed.),
| Oxford University Press, London, UK, 1966.
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