[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

ECI.  Note 40

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| The last lecture was devoted to the fundamental inquiry
| of the whole course, that of the grounds of inference.
|
| We first distingushed three kinds of reference
| which every true symbol has to its object.
|
| In the first place, every true symbol is applicable to some real thing.
| Hence, every symbol whether true or not asserts itself to be applicable to
| some real thing.  This is the 'denotation' of the symbol.  All that we know
| of things is as denotative objects of symbols.  And thus all denotation is
| comparative, merely.  One symbol has more denotation than another or is
| more extensive when it asserts itself to be applicable to all the things
| of which the first asserts itself to be applicable and also to others.
|
| In the second place, every genuine symbol relates or purports to relate
| to some form embodied in its object.  This is its 'connotation'.  It is,
| in fact, only by means of this reference to a form that a symbol acquires
| its applicability to the thing.  The more form a symbol relates to, the
| greater its intension, comprehension, or connotation.
|
| Other things being equal, the greater the comprehension of
| a symbol the less its extension.  For since its denotation is
| created by its connotation, the more the latter is determined,
| the more the former is limited.  But this rule does not always
| hold good.  For just as there are real kinds in nature, that is
| to say classes which differ from all others in more respects than
| one, so there are symbols which imply that their collected objects
| are real kinds and thus they connote more forms than one, either of
| which would be sufficient to limit their extension to the extent to
| which it is limited.  Hence if a symbol changes in information it may
| change either its extension or comprehension without changing both and
| thus the reciprocal relation of extension and comprehension only holds
| good when the information is not changed.
|
| Information then may be defined as the amount of comprehension a symbol
| has over and above what limits its extension.  A symbol not only may have
| information but it must have it.  For every symbol must have denotation,
| that is, must imply the existence of some thing to which it is applicable.
| It may be a mere fiction;  we may know it to be fiction;  it may be intended
| to be a fiction and the very form of the word may hint that intention as in
| the case of abstract terms such as 'whiteness', 'nonentity', and the like.
| In these cases, we pretend that we hold 'realistic' opinions for the sake
| of indicating that our propositions are meant to be explicatory or analytic.
| But the symbol itself always pretends to be a true symbol and hence implies
| a reference to real things.
|
| Thus, no matter how general a symbol may be, it must have some connotation
| limiting its denotation;  it must refer to some determinate form;  but it
| must also connote 'reality' in order to denote at all;  but 'all' that
| has any determinate form has reality and thus this reality is a part
| of the connotation which does not limit the extension of the symbol.
|
| And so every symbol has information.
| To say that a symbol has information
| is as much as to say that it implies
| that it is equivalent to another
| symbol different in connotation.
|
| CSP, CE 1, pages 286-288.
|
| 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.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o