Jon Awbrey<p>Information = Comprehension × Extension • Selection 1.2<br>• <a href="https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-extension-selection-1-a/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/10</span><span class="invisible">/05/information-comprehension-x-extension-selection-1-a/</span></a></p><p>❝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.</p><p>❝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”.❞</p><p>(Peirce 1866, p. 467)</p><p>Reference —</p><p>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.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Inference" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Inference</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/Abduction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Abduction</span></a> <a href="https://mathstodon.xyz/tags/Induction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Induction</span></a> <a href="https://mathstodon.xyz/tags/Deduction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Deduction</span></a> <a href="https://mathstodon.xyz/tags/LogicOfScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicOfScience</span></a> <br><a href="https://mathstodon.xyz/tags/Information" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Information</span></a> <a href="https://mathstodon.xyz/tags/Comprehension" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Comprehension</span></a> <a href="https://mathstodon.xyz/tags/Extension" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Extension</span></a> <a href="https://mathstodon.xyz/tags/InformationEqualsComprehensionTimesExtension" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>InformationEqualsComprehensionTimesExtension</span></a> <br><a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/Icon" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Icon</span></a> <a href="https://mathstodon.xyz/tags/Index" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Index</span></a> <a href="https://mathstodon.xyz/tags/Symbol" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Symbol</span></a> <a href="https://mathstodon.xyz/tags/PragmaticSemioticInformation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PragmaticSemioticInformation</span></a></p>