ONT Re: Extension x Comprehension = Information
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| Let us now return to the information. The information of a term
| is the measure of its superfluous comprehension. That is to say
| that the proper office of the comprehension is to determine the
| extension of the term. For instance, you and I are men because
| we possess those attributes -- having two legs, being rational,
| &c. -- which make up the comprehension of 'man'. Every addition
| to the comprehension of a term lessens its extension up to a certain
| point, after that further additions increase the information instead.
|
| Thus, let us commence with the term 'colour'; add to the comprehension
| of this term, that of 'red'. 'Red colour' has considerably less extension
| than 'colour'; add to this the comprehension of 'dark'; 'dark red colour'
| has still less [extension]. Add to this the comprehension of 'non-blue' --
| 'non-blue dark red colour' has the same extension as 'dark red colour',
| so that the 'non-blue' here performs a work of supererogation; it tells
| us that no 'dark red colour' is blue, but does none of the proper business
| of connotation, that of diminishing the extension at all. Thus information
| measures the superfluous comprehension. And, hence, whenever we make a symbol
| to express any thing or any attribute we cannot make it so empty that it shall
| have no superfluous comprehension. I am going, next, to show that inference is
| symbolization and that the puzzle of the validity of scientific inference lies
| merely in this superfluous comprehension and is therefore entirely removed by
| a consideration of the laws of 'information'.
|
| CSP, CE 1, page 467.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures of 1866, pages 357-504 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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