[CG] Re: Information = Comprehension × Extension

Information = Comprehension × Extension • Selection 6 • https://inquiryintoinquiry.com/2024/10/10/information-comprehension-x-exten… Re: Information = Comprehension × Extension • Selection 1 • https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-exten… All, Selection 1 opens with Peirce proposing, “The information of a term is the measure of its superfluous comprehension”, and it closes with his offering the following promise. ❝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.❞ Summing up his account to this point, Peirce appears confident he's kept his promise. Promising on our own account to give it another pass, we'll let him have the last word — for now. ❝We have now seen how the mind is forced by the very nature of inference itself to make use of induction and hypothesis. ❝But the question arises how these conclusions come to receive their justification by the event. Why are most inductions and hypotheses true? I reply that they are not true. On the contrary, experience shows that of the most rigid and careful inductions and hypotheses only an infinitesimal proportion are never found to be in any respect false. ❝And yet it is a fact that all careful inductions are nearly true and all well-grounded hypotheses resemble the truth; why is that? If we put our hand in a bag of beans the sample we take out has perhaps not quite but about the same proportion of the different colours as the whole bag. Why is that? ❝The answer is that which I gave a week ago. Namely, that there is a certain vague tendency for the whole to be like any of its parts taken at random because it is composed of its parts. And, therefore, there must be some slight preponderance of true over false scientific inferences. ❝Now the falsity in conclusions is eliminated and neutralized by opposing falsity while the slight tendency to the truth is always one way and is accumulated by experience. The same principle of balancing of errors holds alike in observation and in reasoning.❞ (Peirce 1866, pp. 470–471) 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/L6RmB8 cc: https://mathstodon.xyz/@Inquiry/113249701127551380