ONT Re: Hermeneutic Equivalence Classes
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| Leibniz, "Elements of a Calculus" (cont.)
|
| 8. Negative propositions merely contradict affirmatives, and assert
| that they are false. So a particular negative proposition simply
| denies that an affirmative proposition is universal. For example,
| when I say "Some silver is not soluble in common 'aqua fortis'", I
| simply mean that the universal affirmative proposition "All silver
| is soluble in common 'aqua fortis'" is false. For, if we believe
| certain chemists, there is a contrary instance, which they call
| "fixed silver" ['Luna fixa']. A universal negative proposition
| merely contradicts a particular affirmative. For example, if I
| say "No wicked man is happy", I mean that it is false that some
| wicked man is happy. So it is evident that negatives can be
| understood from affirmatives, and conversely, affirmatives
| from negatives.
|
| 9. Further, in every categorical proposition there are two terms.
| Any two terms, in so far as they are said to be in or not to
| be in, i.e. to be contained or not to be contained, differ
| in the following ways: that either one is contained in
| the other, or neither is. If the one is contained in
| the other, then either the one is equal to the other
| or they differ as whole and part. If neither is
| contained in the other, then either they contain
| something which is common, but not too remote,
| or they are totally different. However, we
| will explain this species by species.
|
| Leibniz, 'Logical Papers', pp. 19-20.
|
| 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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