Inquiry Into Inquiry

Re: Readings On Determination • 1

I keep coming back to Peirce’s early lectures on the logic of science because we see there the first inklings of his prospective theory of information, one of those ideas whose time was ripe enough but whose complete fruition lies yet in the future.  The ideas of constraint, definition, determination, information, and inquiry are naturally deeply intertwined.

Here is a link to my ongoing study of those lectures, focusing on the formula:

• Information = Comprehension × Extension

Definitions of Peirce’s various terms (content, sphere, etc.) may be found there.

Resources

• Collection Of Source Materials
• Survey of Definition and Determination

cc: Peirce List

Re: Peirce List (1) (2)

The concepts of definition and determination converge in their concern for setting bounds to the point where they coincide at a certain level of abstraction.  One avenue of approach to determination may then begin from a consideration of definition.

Reference

• Peirce, C.S. (1866), “The Logic of Science;  or, Induction and Hypothesis”, 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

• Collection Of Source Materials
• Information = Comprehension × Extension

cc: Peirce List

Re: Peirce List (1) (2)
Re: Jeffrey Downard (1) (2) (3)

Having been through this same discussion on many previous occasions I’ll try to sum up the more persistent confusions never ceasing to bedevil the subject.  Most of these arise from a failure to observe a number of critical distinctions.

1. There is above all the distinction between relations and tuples.  When it is necessary to emphasize the distinction I will describe relations as “relations in general” or “relations proper” while referring to tuples as “elementary relations”.

2. There is the corresponding distinction between sign relations and elementary sign relations or triples of the form

Relations are, generally speaking, much more complex structures than elementary relations, so classifying relations is a much more complex affair than classifying elementary relations.

The same goes for sign relations and elementary sign relations.  Almost all the literature you see on “classifying sign relations” actually goes no further than the much simpler task of classifying elementary sign relations.  Classifying sign relations, in the proper sense of the word, is a task for the future.

3. There is the distinction between formal or informational determination and causal or temporal determination.  The latter form of determination is a special case of the former.  A simple example of formal determination is found in such venerable phrases as “two points determine a line”.  Pairs of points do not cause lines or precede them in time.  Formal determination is defined at a higher level of abstraction than cause and time.

4. There is the distinction between dyadic forms of determination and triadic forms of determination.  Here we run into a verbal problem.  There is something about the word “determination” — possibly the grammatical category of “to determine” as a transitive verb with a lone direct object — that almost inexorably drags the mind down into the ruts of dyadic thinking, so it helps to use the more general and less biased idea of constraint.

   In this more general perspective, the family of concepts including correspondence, determination, law, relation, structure, and so on all fall under the notion of constraint.  Constraint is present in a system to the extent that one set of choices is distinguished by some mark from a larger set of choices.  That mark may distinguish the actual from the possible, the desired from the conceivable, or any number of other divisions depending on the subject in view.

   Thus we have a form of determination wherever we have a form of constraint.  One of the most general ways of expressing a constraint is in terms of the subset relation:

   • A dyadic relation is defined by the constraint where and are the domains of the relation
   • A triadic relation is defined by the constraint where are the domains of the relation
   • A sign relation is defined by the constraint where are the domains of the sign relation

Resources

• Collection Of Source Materials
• Survey of Definition and Determination

cc: Peirce List

Re: Peirce List (1) (2)

What I’m really after here has to do with the way a certain concept of determination figures into Peirce’s better definitions of a sign relation — “better” meaning definitions strong enough to bear the load of a consequential theory.

That is a very old business with me and there are developments of it still unfinished but lately I have noticed a number of related issues which are not as clear as they need to be.

So I’ll be trying to do something about that, by the by.

Resources

• Collection Of Source Materials
• Survey of Definition and Determination

cc: Peirce List

This is an anchor post for a set of readings on determination, focusing on the census of senses Peirce employed in his pragmatic approach to information, inquiry, science, and signs with a pinch of readings from other writers for historical and contemporary context.

I will start with a set of readings I collected some twenty years ago.  Once that groundwork is laid down, there is a set of ideas coming from the relational programming paradigm in computer science I think would mesh nicely with Peirce’s theory of information and could be extended to cover the triadic relations of his semiotics.

Resource

• Collection Of Source Materials

cc: Peirce List