ONT Re: Inquiry Into Inquiry
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~ARCHIVE~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Subj: Theory of Inquiry, Types of Inference, Missing the Bus
Date: Fri, 18 May 2001 13:00:20 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: Arisbe <arisbe@stderr.org>,
SemioCom <semiocom@listbot.com>,
Standardize Unto Others <standard-upper-ontology@ieee.org>
CC: Cathy Legg <cathy@coombs.anu.edu.au>,
Arien Malec <arien_malec@yahoo.com>
Inquiry SIG,
Because it took me literally a half an hour to find this
thread under the subject line where I left it last, I am
restarting it under a title more reflective of its topic.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Theory of Inquiry, Types of Inference, Missing the Bus
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Note 1
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Subj: Theory of Inquiry
Date: Sat, 29 Apr 2000 15:06:01 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: Peirce Discussion Forum <peirce-l@lyris.acs.ttu.edu>
Arien Malec wrote:
AM: When Chomsky questioned whether for Peirce inductive procedures provide
only post hoc guidance to abduction (note that I'm moving to a paraphrase
of selected quotations from a paper I haven't read), I suspect he is asking
whether the familiar sort of induction (generalization from sample to whole)
plays a part in abduction, or whether that sort of reasoning is post hoc.
Jon Awbrey wrote:
JA: Can you tell me which statements that Chomsky made are the ones that you
interpret to say that he questions "whether for Peirce inductive procedures
provide only post hoc guidance to abduction"? I either missed them or read
them in another way.
Cathy Legg wrote:
CL: I guess I'm having trouble getting my head around how
induction could play this this sort of role, given that
abductions arise when a phenomenon appears surprising and
irregular. Would this be a possible example -- I'm waiting
for my morning bus and it doesn't arrive: surprise. I then
think -- in the past sometimes my bus hasn't arrived when it's
a public holiday I've forgotten about: this case should be the
same (induction), I then form the hypothesis that it is a public
holiday (abduction).
Jon Awbrey wrote:
JA: Here is my analysis of your "Missing the Bus"
problem, to the extent that it can be represented
within the constraints of "propositional models"
or "sentential logic".
JA: C = Current situation, that is, your current situation under
the circumstances of the problem in question, represented by
a "circle" in a venn diagram. This is just a cheap propositional
gimmick for covering, to some extent, the indexical characterisitics
of the situation in question without resorting to using variables
that range over domains of "individual situations".
JA: Next, consider the alternative possibilities:
Proposition X = [C => A]
= [In the Current situation, the bus Arrives]
Proposition Y = [C => ~A]
= [In the Current situation, the bus does Not Arrive]
JA: As it happens, X is your expectation, while Y is your observation.
This difference between your expectation and your observation is
what you affectively experience as a surprise.
JA: Let me stress this. The observed fact is Y, but what renders it
surprising is its difference from X, and this occurs on the point
of detaching its consequent.
JA: Incidentally, it is this "differential" aspect of inquiry
that led me, starting about a decade ago, to begin to develop
a "differential logic", extending "propositional calculus" in
almost precisely the same way that differential calculus extends
analytic geometry.
JA: But let us get back to your situation.
JA: The way that induction enters this situation
is as a component of previous cycles of inquiry
that led to the formation of a rule, even if it is
only a "probable approximate rule", more or less to
the following effect:
Proposition K = [B => A]
= [In the Best case scenario, the bus Arrives]
JA: It does not affect the analysis at all if you have in mind another
sort of descriptor than "best", say, "normal", "ordinary", or so on,
so long as you acknowledge the conducive function or the mediating role
of any middle term like B.
JA: When you get to the bus stop, you are actually in a somewhat confused,
indeterminate, uncertain, or vague state of mind, in the sense that
you have probably not even stopped to ask yourself the question:
JA: Question Q = [Is it really true that J?]
where:
Proposition J = [C => B]
= [The Current situation is a Best case scenario]
JA: Consequently, you have walked, or ran, as is frequently the case,
right into your current situation, operating under the influence
of something like the following form of automatic deduction:
(Case J): C => B
(Rule K): B => A
-------------------
(Fact X): C => A
JA: And this is just where we came in, with the discrepancy between
the expected fact X : C => A and the observed fact Y : C => ~A.
JA: The surprise that you meet with, instead of the bus, might lead you
question all sorts of things. Any number of speculations might come
to mind. Among the more rational possibilities, the surprise might
cause you to inquire into any and all of the premisses that fed into
the above deduction, if not the axioms of the logic that you happen
to be employing at the time.
JA: But let us suppose that you focus on the case C => B, as it is most
frequently the case that is the cause of the problem, and therefore,
in accord with a higher order induction in the inquiry into inquiry,
it is most frequently the case that rational people consider first.
JA: And so, after reflecting on the situation, and eliciting certain features
of how your habitual reasoning processes fed into it, quasi modo intuitio,
you decide to vary the description of the case, in this case, from saying
that C => B to asking whether it might not be true that C => ~B, that is,
asking yourself, "Can it be that the current situation is not actually the
best (modal, normal, ordinary, usual, ...) case, and that this is the cause
of my expectation being disappointed?"
JA: Oops! I've run out of time for today, so I will have to look at the
rest later, but I think that the foregoing is the gist of how I see
the process of inquiry working its way out in situations like these.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Note 2
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Subj: Re: Theory of Inquiry
Date: Tue, 02 May 2000 02:34:14 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: Peirce Discussion Forum <peirce-l@lyris.acs.ttu.edu>
JA: I am replying to my own previous reply to you as a way of
continuing my analysis of your example, to the extent
that it can be represented in propositional terms.
JA: I am going to introduce a type of diagram that I often
use in articulating these sorts of logical situations.
JA: To present what we have so far in this style of depiction,
I can summarize the analysis I have already given as follows:
| A (A)
| o o
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ B (B) /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \ * * /
| \ /
| \*/
| o
| C
|
| Figure 1. Missing the Bus
|
| A = Arriving bus situations,
| B = Best case situations,
| C = Current situation.
It is my guess that something like this style of geometric figure
was used by Aristotle, and may have been a common sort of picture
at the time, at least, this is the impression that I get from the
way that he uses two different styles of language for indicating
the various kinds of logical relationships that are relevant to
the fundamental types of reasoning situation that he discusses.
For instance, Aristotle often uses the geometric label of the
line segment AB to indicate the premiss B => A. Of course,
this may just be a fluke of Greek grammar, or of its later
transcription.
The point elements in these diagrams represent the "propositions"
that one is contemplating with respect to domain of objects, persons,
situations, and so on. Alternatively, one may treat them as the "terms"
of the problem: Major, Middle, Minor, and so on.
The line elements in these diagrams represent the "logical relations"
that are being considered between certain pairs of propositions, or else
the premisses that are being contemplated between various pairs of terms,
where roughly vertical lines indicate "implications", the antecedent lower
and the consequent higher, and where roughly horizontal placements indicate
relationship of "alteration" (change) or "alternation" (diversity), that is,
the situation among a number of alternatives, exclusive or inclusive, that
are available for changing or choosing among.
The language that labels various line elements (premisses or relations)
as Cases, Facts, or Rules was added later, but I will use it freely to
talk about the different roles of premisses within the various forms
of reasoning.
One other thing, I often use the equivalent notations:
(A) = ~A = A' = Not A.
Among other things, this gives the following equivalence:
"A => B" = "(A (B))".
OK, I think that will be enough of a set up to get this going.
| Data:
|
| Alternative Facts: (C (A)) versus ( C ((A))), that is, (C A)
| Alternative Cases: (C (B)) versus ( C ((B))), that is, (C B)
| Alternative Rules: (B (A)) versus ((B)((A))), that is, (A (B))
We have the surprising Fact C => (A), represented by the line segment (A)C.
The reason that this Fact is surprising is that we automatically expected
a different Fact, namely, C => A. And, assuming the current situation C,
which we always do -- since this whole intervention of C is just a gimmick
for supplying a pivot to our thought -- we were led moreover to expect A,
the arrival of the bus.
If we stop to think about it, we realize that there is a middle term that
we have been taking for granted, say B, the benign situation, the best case
scenario (assuming that the best case means catching the bus), or perhaps
the modal, normal, ordinary, or usual case, if you like those terms better.
The name "reflection" seems to fit the process by which we can become aware
of the previously automatic, implicit, and probably unconscious deduction
that led to a current expectation, the one that is subject to conflict with
a current observation, thereby generating a dilemma, a problem, or a surprise.
Nota Bene. Actually, I use the word "problem" more specifically
to refer to a difference between an intention and an observation,
but that is another, yet related story.
In the process of reflecting on the "program" of a habitual deduction, we become
able to identify the intermediate and the middle terms that go "into it", and at
this point we become able to contemplate their deliberate variation. In this way,
we pass from the class of propositions that are schematized by "B" to one or two
in the class of propositions that are summarized by "~B", thereby guessing a new
Case, for example, that the current situation has the marks of a public holiday,
or C => H, where H => ~B, and is thus not beneficial for our immediate purposes.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~EVIHCRA~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤