Re: Leibniz -- De Arte Combinatoria

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DAC.  Note 2

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| From 'Of the Art of Combination' (cont.)
|
| 3.  "Situation" ['situs'] is the locality of parts.
|
| 4.  Situation is either absolute or relative;  the former
|     is that of parts to whole, the latter is that of parts
|     to parts.  In the former, one considers the number of
|     places and their distance from the beginning and the end;
|     in the latter, no attention is paid either to beginning or
|     end, but one considers only the distance of a part from a
|     given part.  Hence the former is expressed by a line, or by
|     lines which do not enclose a figure or return upon themselves,
|     and best of all by a straight line;  the latter is expressed
|     by a line or lines which do enclose a figure, and best of all
|     by a circle.  In the former, the greatest attention is paid to
|     priority and posteriority;  in the latter, no such attention is
|     paid.  The former, therefore, would best be called "order",
|
| 5.  the latter, "vicinity";  the former, "disposition", the latter,
|     "composition".  In respect of order, therefore, the following
|     situations are different:  'abcd', 'bcda', 'cdab', 'dabc'.
|     In respect of vicinity, however, there is understood to
|     be no variation, but only one situation -- namely:
|
|                          b
|
|           a                             c
|
|                          d
|
| Hence the witty Taubmann, when he was dean of the
| philosophical faculty at Wittenberg, is said to have
| put the names of candidates for the Master's degree in
| a circular arrangement on the public programme, so that
| eager readers should not know who had "the swine's place".
|
| Leibniz, DAC, pp. 1-2.
|
| 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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