ONT Re: Extension x Comprehension = Information
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| But since the object contains three elements,
| thing, image, form, we ought to have another kind
| of object besides the denotative and connotative.
| What is this?
|
| If we suppose ourselves to know no more of man than what is
| contained in the definition Man is the rational animal, then
| we might divide man into 'man risible' and 'man non-risible'.
|
| man
| ___________________|___________________
| / \
| man risible man non-risible
|
| And then the connotation of 'man' would be less than that
| of either 'man risible' or 'man non-risible'. And conversely
| 'man risible' and 'man non-risible' would have a less extension
| than 'man'. But we afterwards find that the class 'man non-risible'
| does not exist and is impossible. Henceforward the idea of man and
| that of risible man are changed. The 'extension' of risible man has
| become equal to that of 'men' and the comprehension of 'man' has become
| equal to that of 'risible man'. And how has this change in the relations
| of the terms been effected?
|
| Before the information we knew (let us say) that there were certain risible
| men whom we may denote by 'A' and there were other men who might or might not
| be risible whom we will denote by 'BB’'. We have now found that 'BB’' are also
| risible. When we said all men before we meant 'A + B + B’'; when we say all men
| now we mean the same. The extension of 'man' then has not changed. When we said
| risible men before we denoted 'A + B?' that is to say the whole of 'A' but none
| of 'B' for certain; but now when we say risible men we denote 'A + B + B’'.
| Hence the extension of risible men has 'increased', so as to become equal to
| that of 'men'. On the other hand the intension of 'risible man' is now as
| it was before, composed of 'risible', 'rational', and 'animal'; while the
| comprehension of 'man' which before contained only 'rational' and 'animal',
| now contains 'risible' also.
|
| CSP, CE 1, pages 275-276.
|
| Charles Sanders Peirce, "On the Logic of Science",
| Harvard University Lectures of 1865, pages 161-302 in:
|
|'Writings of Charles S. Peirce: A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.
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