ONT Re: Inquiry Into Symbolization
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| Note A. On A Limited Universe Of Marks
|
| Boole, De Morgan, and their followers, frequently speak of
| a "limited universe of discourse" in logic. An unlimited universe
| would comprise the whole realm of the logically possible. In such
| a universe, every universal proposition, not tautologous, is false;
| every particular proposition, not absurd, is true. Our discourse
| seldom relates to this universe: we are either thinking of the
| physically possible, or of the historically existent, or of
| the world of some romance, or of some other limited universe.
|
| But besides its universe of objects, our discourse also refers to
| a universe of characters. Thus, we might naturally say that virtue
| and an orange have nothing in common. It is true that the English
| word for each is spelt with six letters, but this is not one of the
| marks of the universe of our discourse.
|
| A universe of things is unlimited in which every combination of characters,
| short of the whole universe of characters, occurs in some object. In like
| manner, the universe of characters is unlimited in case every aggregate
| of things short of the whole universe of things possesses in common one
| of the characters of the universe of characters. The conception of
| ordinary syllogistic is so unclear that it would hardly be accurate
| to say that it supposes an unlimited universe of characters; but
| it comes nearer to that than to any other consistent view. The
| non-possession of any character is regarded as implying the
| possession of another character the negative of the first.
|
| In our ordinary discourse, on the other hand, not only are both universes limited, but,
| further than that, we have nothing to do with individual objects nor simple marks;
| so that we have simply the two distinct universes of things and marks related to
| one another, in general, in a perfectly indeterminate manner. The consequence
| is, that a proposition concerning the relations of two groups of marks is not
| necessarily equivalent to any proposition concerning classes of things; so
| that the distinction between propositions in extension and propositions in
| comprehension is a real one, separating two kinds of facts, whereas in the
| view of ordinary syllogistic the distinction only relates to two modes of
| considering any fact. To say that every object of the class S is included
| among the class of P's, of course must imply that every common character of
| the P's is a common character of the S's. But the converse implication is by
| no means necessary, except with an unlimited universe of marks. The reasonings
| in depth of which I have spoken, suppose, of course, the absence of any general
| regularity about the relations of marks and things. (CSP, SIL, 182-183).
|
| CSP, SIL, pages 182-186. (Cf. CE 4, pages 450-453, CP 2.517-531).
|
| Charles Sanders Peirce, "Note A. On A Limited Universe Of Marks" (1883),
| CSP (ed.), 'Studies in Logic, by Members of the Johns Hopkins University',
| Reprinted with an Introduction by Max H. Fisch & a Preface by Achim Eschbach,
| in 'Foundations of Semiotics, Volume 1', John Benjamins, Amsterdam, NL, 1983.
|
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 4, 1879-1884',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
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