{ Information = Comprehension × Extension }

Posted on May 18, 2016 by Jon Awbrey

Another angle from which to approach the incidence of signs and inquiry is by way of Charles S. Peirce’s “laws of information” and the corresponding theory of information he developed from the time of his lectures on the “Logic of Science” at Harvard University (1865) and the Lowell Institute (1866).

When it comes to the supposed reciprocity between extensions and intensions, Peirce, of course, has another idea, and I would say a better idea, partly because it forms the occasion for him to bring in his new-fangled notion of “information” to mediate the otherwise static dualism between the other two.  The development of this novel idea brings Peirce to enunciate the formula:

\mathrm{Information} = \mathrm{Comprehension} \times \mathrm{Extension}

But comprehending what in the world that might mean is a much longer story, the end of which your present teller has yet to reach.  So, this time around, I will take up the story near the end of the beginning of Peirce’s own telling of it, for no better reason than that’s where I myself initially came in, or, at least, where it all started making any kind of sense to me.  And from this point we will find it easy enough to flash both backward and forward, to and fro, as the occasions arise for doing so.

Readings

This entry was posted in Abduction, Belief Fixation, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Peirce, Peirce's Categories, Pragmatism, Scientific Method, Semiotic Information, Semiotics, Sign Relations and tagged , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

13 Responses to { Information = Comprehension × Extension }

  1. phaneron0 says:
    September 15, 2016 at 9:25 am

    Jon:

    I hope you don’t mind me putting this here (for some reason it’s awaiting moderation at the blog you and I have been posting to).

    I was finding your comment helpful (I actually started in semiotics and then moved into statistics).

    We want or need communal inquiry so an acceptance of a common reality that different investigators can aim at, even though never get to, keeps the hope of communal inquiry alive.

    As for pragmatic things we strive for more than just not being frustrated by resistance from reality — rather we want our findings and claims that aim at … “beliefs which succeed for reasons connected to the way things are)” (Misak 2016).  “Peirce requires the success of belief to be connected to how things are” and “Ramsey makes full common cause with Peirce on the requirement that the success of a belief [ideally should] be connected to how things are” (Misak 2016).

    Misak, C. (2016).  Cambridge Pragmatism : From Peirce and James to Ramsey and Wittgenstein.  Oxford University Press.

    Keith O’Rourke

    Reply

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