Inquiry Into Inquiry

Re: Peirce List • Jerry Rhee • Tom Gollier • Edwina Taborsky

All through 1995 I worked on a graduate project in systems engineering at Oakland University developing my ideas about Inquiry Driven Systems.  I wrote a project report on Peirce’s treatments of analogy and inquiry incorporating a return to Dewey’s Sign of Rain story and I drew what I think is a slightly clearer picture of the logical inferences involved in the abductive and deductive steps.

The above Figure charts the progress of inquiry in Dewey’s Sign of Rain example according to the stages of reasoning identified by Peirce, focusing on the complex or mixed form of inference formed by the first two steps.

• Step 1 is an Abduction that abstracts a Case from the consideration of a Fact and a Rule.
•     In the Current situation the Air is cool.
•     Just Before it rains, the Air is cool.
•     The Current situation is just Before it rains.
• Step 2 is a Deduction that admits this Case to another Rule and so arrives at a novel Fact.
•     The Current situation is just Before it rains.
•     Just Before it rains, a Dark cloud will appear.
•     In the Current situation, a Dark cloud will appear.

What precedes is nowhere near a complete analysis of the Sign of Rain inquiry, even so far as it might be carried out within the constraints of the syllogistic framework, and it covers only the first two steps of the inquiry process, but maybe it will do for a start.

References

• Interpretation as Action : The Risk of Inquiry
• Dewey’s “Sign of Rain” • An Example of Inquiry
• Introduction to Inquiry Driven Systems • Inquiry

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8)

Re: Peirce List • Jerry Rhee • Tom Gollier • Edwina Taborsky

Given a working hypothesis, as abduced in the previous post, the next phase of inquiry uses deductive inference to expand the implied consequences of the abductive hypothesis, with the aim of testing its truth.  For this purpose, our inquirer must think of other things following from the consequent of his precipitate explanation.  Thus, he now reflects on the Case just assumed:

• Case :   The Current situation is just Before it rains.

He looks up to scan the sky, perhaps in a random search for further information, but since the sky is a logical place to look for details of an imminent rainstorm, symbolized in our story by the letter we may suppose our reasoner has already detached the consequent of the abduced Case, and has begun to expand on its further implications.  So let us imagine our up-looker has a more deliberate purpose in mind and his search for additional data is driven by the new-found, determinate Rule:

• Rule :   Just Before it rains, Dark clouds appear.

Contemplating the assumed Case in combination with this new Rule leads him by an immediate deduction to predict an additional Fact:

• Fact :   In the Current situation Dark clouds appear.

The reconstructed picture of reasoning assembled in this second phase of inquiry is true to the pattern of deductive inference.

References

• Interpretation as Action : The Risk of Inquiry
• Introduction to Inquiry Driven Systems • Inquiry

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8)

Re: Peirce List • Jerry Rhee • Tom Gollier • Edwina Taborsky

In passing from a sign-relational account to a propositional analysis of Dewey’s story there is an old mathematical trick, analogous to the method of adding fractions by expressing them over a common denominator, that comes in handy.

The general idea is that we introduce a new term to denote the Current situation.  In the example at hand, letting be the proposition that the Air is cool, we can express our hero’s initial observation by means of the following premiss:

• Fact :   In the Current situation the Air is cool.

Responding to an intellectual reflex of puzzlement about the situation, his resource of common knowledge about the world is impelled to seize on an approximate Rule:

• Rule :   Just Before it rains, the Air is cool.

This Rule can be recognized as having a potential relevance to the situation because it matches the surprising Fact, in its consequential feature

All of this suggests that the present Case may be one in which it is just about to rain:

• Case :   The Current situation is just Before it rains.

The whole mental performance, however automatic and semi-conscious it may be, that leads from a problematic Fact and a previously settled knowledge base of Rules to the plausible suggestion of a Case description, is what we are calling an abductive inference.

The above is the first part of a “Zeroth Order” logical analysis of Dewey’s Sign of Rain story that I’ve posted a number of times around the web.  The rest of the analysis can be found at the following location.

• Introduction to Inquiry Driven Systems • Inquiry

Reference

• Interpretation as Action : The Risk of Inquiry

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8)

Re: Peirce List • Tom Gollier

At this point in our paper, Sue and I had already introduced the rudiments of sign relations, as far as the common notions and continuities of thought underpinning the semiotic bridge from Aristotle to Peirce might be teased out, and we turned to the task of tracing the role of sign relations in the workings of a fully filled out inquiry process, with all its abductive, deductive, and inductive faculties intact.

The relation between theories of signs and theories of inquiry, as we find them in Aristotle, or Peirce, or name your favorite, or as we must find them at “the end of all our exploring”, are some of the things I’m still trying to understand but I can’t let my need to think I know much prevent me from learning more.

At any rate we do have a general outline from Peirce of how he thinks one cycle of inquiry goes, so what we tried to do in this case was to fit the semiotic roles into that hopper as best we could and see how far that afforded us any guidance in understanding the dynamics of Dewey’s story.

With that pre-ramble …

Any realistic practical situation will involve all sorts of objects, passed, pressing, and prospective.  Practical applications force us at any given moment to deal with an object domain that is a collection of many objects   Objects and objectives can be complex.  Objects can have sub-objects and super-objects.  Objectives can have sub-objectives and super-objectives, though we usually speak of goals and subgoals then.  The same goes for signs and interpretant signs, of course, which is what syntactic analysis and conceptual analysis are all about.

That overarching interest in practical applications is one of the reasons I’m always harping on the extensional formulation of a sign relation as a set where are sets of many elements.  The object domain is very like the universe of discourse in ordinary logic, while and are the systems of signs, public or private or whatever, that we use to talk and think about our present object domain.

So …

What makes the likelihood of rain a semiotic object in Dewey’s story is simply the fact that the ambulator interprets the cooling air as a sign of it.  We know the interpreter interprets the sign as a sign of that object by virtue of the fact that he forms an interpretent sign, the thought of the likelihood of rain, in his mind.

Reference

• Interpretation as Action : The Risk of Inquiry

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8)

Re: Peirce List • Tom Gollier

Let me dispel any notion that “the interpretant introduces the person as part of the object-sign-interpretant structure”.  We may have left it implicit or unclear in the text but the lower case “i” and the dashed lines in the figure were meant to suggest the agency of the interpreter and the circumstance that signs and interpretants reside nearer the personal sphere than the objects, generally speaking.  As a rule, for all sorts of reasons, primers in semiotics tend to start out talking about interpreters and only gradually abstract away to interpretants.  But I see now that it was faulty notation, as it’s more usual to read a lower case “i” as indicating a member of a local set I.  Next time I will use a Greek iota for the interpretive agent.

Reference

• Interpretation as Action : The Risk of Inquiry

cc: Peirce List (1) (2) (3) (4) (5) (6) (7)

Re: Peirce List • Tom Gollier

I know we’ve discussed the various meanings of the word object which make sense in Peirce’s semiotics and pragmatism generally, so let me just link to a recent comment I found in my search for previous mentions.

Keeping that variety of meanings in mind, a few more words may help to clarify the reading from last time.

• There are of course the usual run of behaviorist, causal, stimulus-response theories of “signal processing” and “verbal behavior” that have enjoyed their popularity and never-say-die revivals from the days of Charles Morris to B.F. Skinner, but Peirce’s semiotics includes them as degenerate species of the more solid genre he had in mind.
• Peirce’s definition of a triadic sign relation is cast at such a level of generality that nothing in it prevents a sign relation from having intentional objects in its object domain
• To say that coolness is a sign of rain is a perfectly natural statement in English, and I think it would be a more troubling narrowness to exclude it from sense.
• Semiotic objects are any objects of discussion or thought.  It should be obvious that we talk and think about future, imaginary, intentional, or “virtual” objects all the time.
• The fact that coolness might be a sign of many other things is exactly what calls for our peripatetic hero to abduce a hypothesis (rain?), to deduce a prediction (dark clouds?), and to test the prediction against further observations (look up!).  All of those features are why we chose Dewey’s story as an illustration of a full-blown inquiry.

Reference

• Interpretation as Action : The Risk of Inquiry

cc: Peirce List (1) (2) (3) (4) (5) (6) (7)

Re: Peirce List • Jerry Chandler

The simple question arises:  If an abductive step is taken by the inquirer, then what?

A very good question.  Susan Awbrey and I tried our hands at answering the What Next? question in the medium of analyzing Dewey’s “Sign of Rain” example.  Here is the relevant excerpt from “Interpretation as Action : The Risk of Inquiry”.

cc: Peirce List (1) (2) (3) (4) (5) (6)