[CG] Re: Information = Comprehension × Extension

Information = Comprehension × Extension • Selection 1 • https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-exten… All, Our first text comes from Peirce's Lowell Lectures of 1866, titled “The Logic of Science, or, Induction and Hypothesis”. I still remember the first time I read these words and the light that lit up the page and my mind. ❝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”.❞ (Peirce 1866, p. 467) Reference — Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982. Resources — Inquiry Blog • Survey of Pragmatic Semiotic Information • https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-info… OEIS Wiki • Information = Comprehension × Extension • https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension C.S. Peirce • Upon Logical Comprehension and Extension • https://peirce.sitehost.iu.edu/writings/v2/w2/w2_06/v2_06.htm Regards, Jon cc: https://www.academia.edu/community/Lm0YXe cc: https://mathstodon.xyz/@Inquiry/113249701127551380