ONT Re: Inquiry Into Inquiry
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Subj: Re: Inquiry
Date: Mon, 04 Sep 2000 22:36:02 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: Stand Up Ontology <standard-upper-ontology@ieee.org>
Example of Inquiry
The discussion of inquiry cries out for a concrete example.
Along these lines, the best point of departure that I can
think of is the following story of inquiry activities in
everyday life, as told by John Dewey.
| A man is walking on a warm day. The sky was clear the
| last time he observed it; but presently he notes, while
| occupied primarily with other things, that the air is cooler.
| It occurs to him that it is probably going to rain; looking up,
| he sees a dark cloud between him and the sun, and he then quickens
| his steps. What, if anything, in such a situation can be called
| thought? Neither the act of walking nor the noting of the cold
| is a thought. Walking is one direction of activity; looking and
| noting are other modes of activity. The likelihood that it will
| rain is, however, something 'suggested'. The pedestrian 'feels'
| the cold; he 'thinks of' clouds and a coming shower.
|
| John Dewey, 'How We Think', 1910, pages 6-7.
A good start at analyzing this example, surprisingly enough,
can be made within a primitive propositional and syllogistic
framework. In order to carry this out. I will first outline
a few terms of art from classical logic that can be used to
articulate the procedural stages of a generic inquiry process,
and then I will present my analysis of what is taking place,
logically speaking, to move this particular inquiry forward.
Basic Terminology
In the case of propositional logic, deduction comes down to an
application of the transitive law for conditional implications.
Contemplated on the scheme in Figure 1, deduction takes
a Case, the minor premiss X => Y, and puts it with
a Rule, the major premiss Y => Z, to arrive at
a Fact, the demonstrative conclusion X => Z.
Contrasted with this pattern, induction takes
a Fact of the form X => Z and matches it with
a Case of the form X => Y to guess that
a Rule of the form Y => Z is possibly in play.
Cast on this same template, abduction takes
a Fact of the form X => Z and matches it with
a Rule of the form Y => Z to guess that
a Case of the form X => Y is presently in view.
In its original usage a statement of Fact has to do with
a deed done or a record made, that is, a type of event that
is openly observable and not riddled with speculation as to
its very occurrence. In contrast, a statement of Case may
refer to a hidden or a hypothetical cause, that is, a type
of event that is not immediately observable to all concerned.
Obviously, the distinction is a rough one and the question
of which mode applies can depend on the points of view that
different observers adopt over time. Finally, a statement
of a Rule is called that because it states a regularity or
a regulation that governs a whole class of situations, and
not because of its syntactic form. So far in this discussion,
all three types of constraint are expressed in the form of
conditional propositions, but this is not a fixed requirement.
In practice, these modes of statement are distinguished by
the roles that they play within an argument, not by their
style of expression. When the time comes to branch out from
the syllogistic framework, we will find that propositional
constraints can be discovered and represented in arbitrary
syntactic forms.
In the normal course of a typical inquiry, the three basic types of
inference proceed in the order: Abduction, Deduction, Induction.
However, the same building blocks can be assembled in other ways
to yield different kinds of complex inferences. Of particular
importance for our purposes, reasoning by analogy is analyzed
as a combination of induction and deduction, in other words,
as the abstraction and application of a Rule.
For ease of reference, Figure 1 and the Legend beneath it
summarize the classical terminology for the three types
of inference and the relationships among them.
---------------------------------------------------------------------
| Z
| o
| |\
| | \
| | \
| | \
| | \ Rule
| | \
| | \
| | A > \
| | \ / \
| Fact | <-¤-D o Y
| | / \ /
| | I > /
| | /
| | /
| | / Case
| | /
| | /
| | /
| |/
| o
| X
|
| Figure 1. Basic Structure & Terminology
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Legend 1.
Deduction takes a Case, the minor premiss of the form X => Y,
matches it with a Rule, the major premiss of the form Y => Z,
then adverts to a Fact, the bound outcome of the form X => Z.
Induction takes a Case of the form X => Y,
matches it with a Fact of the form X => Z,
then adverts to a Rule of the form Y => Z.
Abduction takes a Fact of the form X => Z,
matches it with a Rule of the form Y => Z,
then adverts to a Case of the form X => Y.
Even more succinctly:
Abduction Deduction Induction
Premiss: Fact Rule Case
Premiss: Rule Case Fact
Outcome: Case Fact Rule
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OK, that will suffice to renew everybody's acquaintance
with this quaint old manner of speaking about syllogism.
Now it is time to give the Illustrated Classics Edition
of my favorite example of inquiry.
Analysis of Example
Returning to the "Rainy Day" story, we find our peripatetic
hero presented with a surprising Fact:
(Fact) C => A, "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) B => A, "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, C => A,
in its consequential feature A. All of this suggests that the
present Case may be one in which it is just about to rain:
(Case) C => B, "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 knowledge base
of Rules to the plausible suggestion of a Case description, is what
is usually called an abductive inference.
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, the inquirer needs
to think of other things that would follow from the consequence
of his precipitate explanation. Thus, he now reflects on the
Case just assumed:
(Case) C => B, "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 B, we may safely suppose that our reasoner
has already detached the consequence of the abduced Case, C => B,
and has begun to expand on its further implications. So let us
imagine that our up-looker has a more deliberate purpose in mind,
and that his search for additional data is driven by the new-found,
determinate Rule:
(Rule) B => D, "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) C => D, "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.
Whatever the case, our subject observes a Dark cloud, just as he would
expect on the basis of the new hypothesis. The explanation of imminent
rain removes the discrepancy between observations and expectations and
thereby reduces the shock of surprise that made this inquiry necessary.
Figure 2 gives a graphical illustration of Dewey's example of inquiry,
isolating for the purposes of the present analysis the first two steps
in the more extended proceedings that go to make up the whole inquiry.
---------------------------------------------------------------------
| A D
| o o
| \ * * /
| \ * * /
| \ * * /
| \ * * /
| \ * * /
| \ R u l e R u l e /
| \ * * /
| \ * * /
| \ * * /
| \ * * /
| F a c t B F a c t
| \ * /
| \ * /
| \ * /
| \ * /
| \ C a s e /
| \ * /
| \ * /
| \ * /
| \ * /
| \ * /
| \*/
| o
| C
|
| Figure 2. Dewey's "Rainy Day" Inquiry
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Legend 2.
A = the Air is cool,
B = just Before it rains,
C = the Current situation,
D = a Dark cloud appears.
A is a major term,
B is a middle term,
C is a minor term,
D is a major term, associated with A.
---------------------------------------------------------------------
In this analysis of the first steps of Inquiry,
we have a complex or a mixed form of inference
that can be seen as taking place in two steps:
1. The first step is an Abduction that abstracts a Case
from the consideration of a Fact and a Rule.
(Fact) C => A, In the Current situation the Air is cool.
(Rule) B => A, Just Before it rains, the Air is cool.
(Case) C => B, The Current situation is just Before it rains.
2. The next step is a Deduction that admits this Case
to another Rule and so arrives at a novel Fact.
(Case) C => B, The Current situation is just Before it rains.
(Rule) B => D, Just Before it rains, a Dark cloud will appear.
(Fact) C => D, In the Current situation, a Dark cloud will appear.
This is nowhere near a complete analysis of the Rainy Day inquiry,
even insofar as it might be carried out within the constraints of
the syllogistic framework, and it covers only the first two steps
of the relevant inquiry process, but maybe it will do for a start.
Moral of the Story: "Don't forget your umbrella!"
Jon Awbrey
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