I am roughly at the halfway point of my comments on Peirce’s information formula, having just finished up the link between abductive inference and iconic reference.  The discussion of induction and indexicals will follow pretty much the same pattern, though there are a few wrinkles having to do with a number of interesting differences between Peirce’s early and later accounts of indices.

The rest of this post is slightly tangent to the topic at hand, but I couldn’t resist saying a few more words about the duality of information and control once other discussions brought the issue to mind.

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Viewing systems topics like change, control, dynamics, goals, objectives, optimization, process, purpose and so on in the light of the information dimension opens up a wide field of investigation.  It’s been my custom to cultivate that field layer by layer, working up from the most basic layer with a modicum of utility, namely, propositional calculus.  This is the layer of qualitative description underlying every layer of quantitative description.

Propositional calculus is the level of logic we’ve been using in our present discussion to describe various classes of entities populating a given universe of discourse.  Whether we call the corresponding descriptors predicates, propositions, or terms is of no importance for present purposes so long as we are using them solely as symbols in a symbolic calculus following a specific set of rules.

Extending the layer of propositional calculus from its coverage of static situations to the description of time-evolving states can be done fairly easily.  One follows the model of physics, where dealing with change made little progress until the development of differential calculus.  The analogous medium at the logical level is the differential extension of propositional calculus, or “differential propositional calculus”, for short.  See the following resource for a gentle introduction.

• Differential Propositional Calculus • Part 1 • Part 2

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.

Resources

• This Blog • Survey of Pragmatic Semiotic Information
• My Notes • Information = Comprehension × Extension
• C.S. Peirce • Upon Logical Comprehension and Extension

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science