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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