[CG] Re: Information = Comprehension × Extension

Information = Comprehension × Extension • Selection 2 • https://inquiryintoinquiry.com/2024/10/06/information-comprehension-x-exten… Re: Information = Comprehension × Extension • Selection 1 • https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-exten… Over the course of Selection 1 Peirce introduces the ideas he needs to answer stubborn questions about the validity of scientific inference. Briefly put, the validity of scientific inference depends on the ability of symbols to express “superfluous comprehension”, the measure of which Peirce calls “information”. Selection 2 sharpens our picture of symbols as “general representations”, contrasting them with two species of representation whose characters fall short of genuine symbols. ❝For this purpose, I must call your attention to the differences there are in the manner in which different representations stand for their objects. ❝In the first place there are likenesses or copies — such as “statues”, “pictures”, “emblems”, “hieroglyphics”, and the like. Such representations stand for their objects only so far as they have an actual resemblance to them — that is agree with them in some characters. The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less; for they stand for whatever they resemble and they resemble everything more or less. ❝The second kind of representations are such as are set up by a convention of men or a decree of God. Such are “tallies”, “proper names”, &c. The peculiarity of these “conventional signs” is that they represent no character of their objects. ❝Likenesses denote nothing in particular; “conventional signs” connote nothing in particular. ❝The third and last kind of representations are “symbols” or general representations. They connote attributes and so connote them as to determine what they denote. To this class belong all “words” and all “conceptions”. Most combinations of words are also symbols. A proposition, an argument, even a whole book may be, and should be, a single symbol.❞ (Peirce 1866, pp. 467–468) 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/V1EKBy cc: https://mathstodon.xyz/@Inquiry/113249701127551380