ONT Re: Hermeneutic Equivalence Classes
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| Leibniz, "Elements of a Calculus" (cont.)
|
| 7. To make evident the use of symbolic numbers in propositions, it is
| necessary to consider the fact that every true universal affirmative
| categorical proposition simply shows ['significat'] some connexion between
| predicate and subject (a 'direct' connexion, which is what is always meant
| here). This connexion is, that the predicate is said to be in the subject,
| or to be contained in the subject; either absolutely and regarded in itself,
| or at any rate in some instance, i.e. that the subject is said to contain the
| predicate in a stated fashion. This is to say that the concept of the subject,
| either in itself or with some addition, involves the concept of the predicate,
| and therefore that subject and predicate are related to each other either as
| whole and part, or as whole and coincident whole, or as part to whole.
|
| In the first two cases the proposition is a universal affirmative;
| so when I say "All gold is metal" I simply mean that in the concept
| of gold the concept of metal is contained directly, since gold is
| the heaviest metal.
|
| Again, when I say, "Every pious man is happy", I mean simply this:
| that the connexion between the concepts of the pious man and of
| the happy man is such that anyone who understands perfectly the
| nature of the pious man will realize that the nature of the
| happy man is involved in it directly.
|
| But in all cases, whether the subject or predicate is a part
| or a whole, a particular affirmative proposition always holds.
|
| For example, some metal is gold; for although metal does not by itself
| contain gold, nevertheless some metal, with some addition or specification
| (e.g. "that which makes up the greater part of the Hungarian ducat") is of
| such a nature as to involve the nature of gold.
|
| There is, however, a difference in the method of containment between the
| subject of a universal and of a particular proposition. For the subject
| of a universal proposition, regarded in itself and taken absolutely, must
| contain the predicate; thus the concept of gold, regarded in itself and
| taken absolutely, involves the concept of metal, for the concept of gold
| is "the heaviest metal". But in a particular affirmative proposition,
| it is enough that the inclusion should hold with some addition. The
| concept of metal, regarded absolutely and taken in itself, does not
| involve the concept of gold; for it to do so, something must be
| added. This "something" is the sign of particularity; for
| there is some certain metal which contains the concept of
| gold.
|
| However, when we say later that a term is contained in a term or
| a concept in a concept, we shall understand "simply and in itself".
|
| Leibniz, 'Logical Papers', pp. 18-19.
|
| 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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