ONT Re: Hermeneutic Equivalence Classes
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| Leibniz, "Elements of a Calculus" (cont.)
|
| 15. When two terms are coincident, e.g. "man" and "rational animal", then
| their numbers, 'h' and 'ar', are in effect coincident (as 2 x 3 and 6).
| Since, however, the one term contains the other in this way, although
| reciprocally (for "man" contains "rational animal", and nothing besides;
| and "rational animal" contains "man", and nothing besides which is not
| already contained in "man"), it is necessary that the numbers 'h' and
| 'ar' (2 x 3 and 6) should also contain each other. This is the case,
| since they are coincident, and the same number is contained in itself.
|
| Furthermore, it is necessary that the one can be divided by the other,
| which is also the case; for if any number is divided by itself, the
| result is unity. So what we said in the previous article -- that
| when one term contains another the symbolic number of the former
| is divisible by the symbolic number of the latter -- also holds
| in the case of coincident terms.
|
| Leibniz, 'Logical Papers', pp. 21-22.
|
| Leibniz, G.W., "Elements of a Calculus" (April, 1679),
| G.H.R. Parkinson (ed.), 'Leibniz: Logical Papers', pp. 17-24,
| Oxford University Press, London, UK, 1966. (Couturat, 49-57).
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