Inquiry Into Inquiry

Re: Systems Science • Kent Palmer

The best way to get a handle on what Peirce meant by his formula,

is to study a suitable sample of critical passages from his Lectures of 1865–1866 on the Logic of Science.  The most instructive texts are those where he illustrates the abstract forms with concrete materials and minimal examples, simple but just complex enough to flesh out the most significant dimensions of the case.

I’ll be getting to that directly …

But I wanted to flag the following comment by Kent Palmer for future discussion, as doubt and uncertainty play a motivating role in both Peirce’s theory of inquiry and the revolution in our handling of information brought on by Shannon’s groundbreaking work.

Kent Palmer:

But then I noticed I had transformed Peirce’s formulation in order to make that connection and I was struck by doubt.  Notice doubt is at the level of hyper-intension defined by Tichy.  In fact, it is interesting that doubt is Cartesian and Husserl attempts to clarify doubt and refine it with his Epoche and Bracketing strategy.  But doubt is noetic not a noema.  Doubt is in the Husserlian hierarchy.  It turns out that doubt is fairly low in Husserl’s noetic Hierarchy because he starts with Meaning as Intentional Morphe forming hyle and comes down from there, exactly the opposite of Analytic Philosophy that starts with Extension and begrudgingly adds each level of intension.  Intentional morphe with hyle splits into noesis and noema.  Notice that the schema here is Form.

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Re: Systems Science • Kent Palmer

As a general rule Peirce avoided in advance many of the problems bedeviling later philosophies of science in the 20th Century.  Doing so came rather naturally to him as he rarely succumbed to the cycloptic species of reductionism afflicting so many modern isms.

In particular, it’s not so much that Peirce sought a way to jam together the extensions and intensions of concepts and other symbols, the stuffs empiricism and rationalism are made on, as that he grasped the whole body of information, the “synthetic unity of apperception” of which extensions and intensions are but the facets or lower dimensional projections.

That integral core of information borne by signs is the prize we’ll keep in view, stereoscopically, as we make our way into the texts of the 1860s.

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A Comprehensile Tale

Here’s a gloss on “comprehension” I copied from Runes some years ago, plus a bit of commentary I added at the time.

Comprehension.  The sum of characteristics which connote a class notion symbolized by a general term.  Also, the features common to a number of instances or objects.  Thus, the connotation (qv) or intension (qv) of a concept.  (Otto F. Kraushaar, in D.D. Runes (ed.) Dictionary of Philosophy, 1962).

Resource

• Information = Comprehension × Extension • Incidental Note 13

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Re: Information = Comprehension × Extension
Re: Systems Science • Kent Palmer

It may be useful to clear up a couple of technical points about Peirce’s terminology before getting to the main business.

Here I’m using extension and intension in the conventional sense that concerns the extension and intension of a concept or term.  We define a concept or term in extension by giving all the things falling under it.  We define a concept or term in intension by giving all the properties it implies or falls under.  The parallel morphology of the words “extension” and “intension” is pleasing enough to ear and eye that we usually just let it go at that, but punctilious pedants long ago noticed the fly in the ointment that an extension is a many, a set of things, while an intension is a one, a single property or quality, and so they insist on the technical term comprehension to signify a collection of intensions.  In practice, of course, context of application will determine how picky we need to be.

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Re: Survey of Pragmatic Semiotic Information
Re: Ontolog Forum • Joseph Simpson

I’ve been looking at the record of past discussions and thinking about what I’d like to accomplish this year.  Just off hand, I see a lot of discussion points I didn’t get a chance to give their due at the time and it looks like many of those are worth revisiting.  Some of the more troublesome points may seem tangential at first but they have a tendency to recur if not dealt with, so it’s critical to address them as best one can.

More to the main arc of this thread, I need to keep developing the implications of Peirce’s ideas about information, in particular, the way information integrates the extensional and intensional aspects of logic and thus helps to solve many old puzzles about the nature of scientific inference and inquiry in general.

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Peter Smith, on his Logic Matters blog, queried readers about the type/token distinction and its possible origins before Peirce.  I shared the following observations:

It doesn’t help with the question of semiogenesis, which is no doubt lost to the mists of history, but Peirce being Peirce naturally discerned three shades of signs in this respect:  Tone, Token, Type.  I collected a few excerpts here:

• Tone, Token, Type

The distinction between Original and Copy figures frequently in Plato, with echoes of still more ancient voices.  Aristotle on Categories gives an example where a word meaning both a live animal and its true-to-life image must be shorn of ambiguity prior to appearing in a court of logic.  Aristotle on Interpretation distinguishes objects from their copies, images, likenesses in the mind:

Words spoken are symbols or signs (symbola) of affections or impressions (pathemata) of the soul (psyche);  written words are the signs of words spoken.  As writing, so also is speech not the same for all races of men.  But the mental affections themselves, of which these words are primarily signs (semeia), are the same for the whole of mankind, as are also the objects (pragmata) of which those affections are representations or likenesses, images, copies (homoiomata).  (Aristotle, De Interp. i. 16^a4).

From a Peircean semiotic perspective we can distinguish an object domain and a semiotic plane, so we can have three types of type/token relations:  (1) within the object domain, (2) between objects and signs, (3) within the semiotic plane.  We could subtilize further but this much is enough for a start.

Type/token relations of type (1) are very common in mathematics and go back to the origins of mathematical thought.  These days computer science is rife with them.  I’ve seen a lot of confusion about this in Peircean circles as it’s not always grasped that type/token relations are not always all about signs.  It can help to speak of types versus instances or instantiations instead.

Aristotle covers type/token relations of types (2) and (3) in De Interp., the latter since he recognizes signs of signs in the clause, “written words are the signs of words spoken”.

Resources

• Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  Online.
• Limited Mark Universes • Peirce’s Note “On a Limited Universe of Marks”

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