Another angle from which to approach the incidence of signs and inquiry is by way of C.S. Peirce’s “laws of information” and the corresponding theory of information that 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:
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.