ONT Re: Inquiry Into Inquiry
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John Collier wrote (JC):
Jon Awbrey wrote (JA):
JA: As far as automating induction goes, we should not expect
an inductive program to make up the data for us, no matter
how sophisticated it gets! Inductive tests can provide
measures of how well a theoretical construct fits a set
of data, but no fit is perfect, or even intended to be.
An inductive concept is supposed to present a simplification
of a complex reality, otherwise it would serve no function
over and above just staring at the data. In gauging the
slippage between concept and data, the degree of tolerance
acceptable in a given situation is a matter of discretionary
judgments that have to be made under field conditions.
JC: Selecting the data is an abductive step. Inductive machines have discovered Boyle's Law
and some other simple laws from data. Clark Glymour at Carnegie Mellon University is one
of the foremost researchers in this area. Less ambitious inductive methods are Minimum
Description Length (Jorma Rissinen, IBM), and Minmimum Message Length (Chris Wallace and
David Dowe, Mionash University). In my opinion the latter is more sophisticated now in
technique, and is beginning to converge on a general methodology that will work if any
thing will work for the inductive step. I've included in the inductive step so-called
eliminative induction (the Sherlock Holmes technique), which actually involves abduction
of hypotheses once one has the data. So there are really two abductive steps (at least),
one to isolate the relevant data, and the other to form hypotheses. The second seems to
be at least partially mechanizable, but the first, as you say, we are not even close to
realizing.
It all depends on how various observers define their sundry ductions, of course.
I kept up with the automated concept formation and machine learning literature
pretty tightly until about 1992, tapering off through 1996, and since then it
has been "Back to Peirce" all the way. As you know, there was a development
in his thinking about the precise structure of the triductive inquiry cycle,
though I regard the metamorphosis to be rather more natural and far less
radical than some writers make it out to be. Moreover, this evolution
was confluent with a general turn that was taking place throughout the
differentiating fields of mathematics throughout the 19th Century.
Accordingly, my strategy has been to try and follow these changes
with some care, however long and meandering a course it may be,
recapitulating in my gradation the phases of Peirce's transit.
Right now, I am still trying to establish a footing in the
syllogistic camp that was already staked out by Aristotle.
JA: When it comes to automating abductive reasoning, we should
observe the historical circumstance that it is often the most
"unlikely" set of hypotheses that turn out to form the correct
conceptual framework, at least when that likelihood has been
judged from the standpoint of the previous framework.
JC: Well, the likely ones have probably already been explored.
It's more than that, as what usually happens, when regarded retrospectively --
from a "Monday Morning Quarterback POV" -- is that the whole reference class,
sample space, and array of random variables that explicitly or implicitly
give one a sense of the odds of things in general has been altered in
a way that was just not assignable a likelihood from the preterite
frame of reference. This is just one of the reasons why a person
cannot do abduction the Bayesian way, no matter how many vehicles
get cranked out with "Abduction" in the headers but nothing but
Bayes in the bonnet.
JA: Aside from their responsibilities to the inquiry process,
abductive hypotheses can be freely generated in the most
creative manner possible. Breaking the mind-set of the
problem as stated and reformulating data descriptions
from new perspectives are just some of the allowable
strategies that are required for success.
JA: Abductive reasoning is the mode of operation which is involved
in shifting from one paradigm to another. In order to reduce
the overall tension of uncertainty in a knowledge base, it is
often necessary to restructure our perspective on the data in
radical ways, to change the channel that parcels out information
to us. But the true value of a new paradigm is typically not
appreciated from the standpoint of another model, that is, not
until it has had time to reorganize the knowledge base in ways
that demonstrate clear advantages to the community of inquiry
concerned.
JC: The reference to paradigms is interesting here. Kuhn's reflective
position was that different paradigms cross-classify. This makes
the problem of selecting data immediately related to the difficult
abduction step.
Yes.
JC: Kuhn thought that normal science works primarily by analogy,
not deduction or enumerative induction. This is a matter of
finding the Aristotelian "middle term". The difficult abductive
step involves rather more than this, since the first and last terms
are also open.
Not sure. I'm still in the muddle o' medias res myself.
But I do have a passel of charts and graphs on this bit,
which you just know you're gonna get to see. But just
for teaser of coming attractions, look at this picture:
| Z
| o
| |\
| | \
| | \
| | \
| | \ Rule
| | \
| | \
| | A > \
| | \ / \
| Fact | <-¤-D o Y
| | / \ /
| | I > /
| | /
| | /
| | / Case
| | /
| | /
| | /
| |/
| o
| X
|
| Figure 1. Basic Structure & Terminology
We usually think of each duction as being produced from a vertext
to its opposite side, thinking of the vertex as an index of its
two incident considerations, which correspond to the premisses
of the inference in question. But suppose that we contemplate
the possibility of a reasoning process F that takes a Fact ZX
and produces a middle term Y, in effect, posing the Rule ZY
and the Case YX at a single moment. More on this later.
| Z
| o
| |\
| | \
| | \
| | \
| | \ Rule
| | \
| | \
| | \
| | \
| Fact | F--¤--> o Y
| | /
| | /
| | /
| | /
| | / Case
| | /
| | /
| | /
| |/
| o
| X
|
| Figure 2. Factorization of a Fact
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