ONT Re: Leibniz -- De Arte Combinatoria
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DAC. Note 3
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| From 'Of the Art of Combination' (cont.)
|
| 6. When we posit variations 'par excellence' we shall
| usually understand variability of order; for example,
| four things can be transposed in twenty-four ways.
|
| 7. The variability of a complexion we call "complexions";
| for example, four things can be joined to one another
| in fifteen different ways.
|
| 8. The number of things to be varied we shall call simply
| "number"; for example, four in the case imagined.
|
| 9. A "complexion" is the union of a smaller whole
| in a larger, as we have said in the preface.*
|
| *. [(Ed.) The reference is to A, vi, 1, 171 (No. 8)]:
|
| A whole, and therefore number or totality, can be broken into parts,
| as smaller wholes. This is the basis of "complexions", provided
| that you understand that in the different smaller wholes there
| are common parts. For example, let the whole be ABC; the
| smaller wholes, its parts, will be AB, BC, AC. It is also
| possible to vary the disposition of the smallest parts,
| or of those taken as the smallest (namely, unities)
| in relation to each other and to the whole; this
| is called "situation".
|
| 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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