[CG] Re: Information = Comprehension × Extension

Information = Comprehension × Extension • Selection 4 • https://inquiryintoinquiry.com/2024/10/08/information-comprehension-x-exten… Re: Information = Comprehension × Extension • Selection 3 • https://inquiryintoinquiry.com/2024/10/07/information-comprehension-x-exten… All, Selection 3 showed how it was possible to combine symbols in such a way as to end up with species of representation outside the class of genuine symbols and introduced the concepts of “conjunctive terms” and “disjunctive terms” to describe two ways of doing this. The essence of wit being quickly grasping the middle term, Peirce's wit fastens on those terms to highlight the links between manners of representation and modes of inference. Selection 4 finds Peirce in the middle of articulating the connection between indexical reference and inductive inference, using examples of disjunctive terms as pivotal cases. ❝Accordingly, if we are engaged in symbolizing and we come to such a proposition as “Neat, swine, sheep, and deer are herbivorous”, we know firstly that the disjunctive term may be replaced by a true symbol. But suppose we know of no symbol for neat, swine, sheep, and deer except cloven-hoofed animals. There is but one objection to substituting this for the disjunctive term; it is that we should, then, say more than we have observed. In short, it has a superfluous information. ❝But we have already seen that this is an objection which must always stand in the way of taking symbols. If therefore we are to use symbols at all we must use them notwithstanding that. Now all thinking is a process of symbolization, for the conceptions of the understanding are symbols in the strict sense. ❝Unless, therefore, we are to give up thinking altogether we must admit the validity of induction. But even to doubt is to think. So we cannot give up thinking and the validity of induction must be admitted.❞ (Peirce 1866, p. 469) 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. Regards, Jon cc: https://www.academia.edu/community/VjvJbJ cc: https://mathstodon.xyz/@Inquiry/113249701127551380