[Inquiry] Re: Examples Of Inquiry

[Jon Awbrey]

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EOI.  Note 11

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Cathy Legg's "Missing The Bus" Example (cont.)

Here is my analysis of Cathy Legg's "Missing the Bus" problem,
to the extent that it can be represented within the constraints
of propositional models, sentential logic, or zeroth order logic.

Let "C" represent the Current situation, that is,
the intinerant inquirer's current situation under
the circumstances of the problem in question, also
depicted 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, but without having to resort
to the use of variables that range over domains of
"individual situations".

Next, let us contemplate the alternative possibilities,
formulated here as Proposition X versus Proposition Y.

   X  =  [C => A]   =  [In the Current situation, the bus Arrives]

   Y  =  [C => ~A]  =  [In the Current situation, the bus does Not Arrive]

As it happens, X is one's expectation, while Y is one's observation.
This difference between one's expectation and one's observation is
what one affectively experience as a surprise.

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 the alternative consequents, A versus ~A.

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.

But let us get back to the situation at the bus stop.

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 as
formulated in Proposition K:

   K  =  [B => A]  =  [In the Best case scenario, the bus Arrives]

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.

When our traveller gets to the bus stop, it is most likely
that she is in a slightly confused, indeterminate, uncertain,
or vague state of mind, in the sense that she has probably not
even stopped to ask herself the question we'll call Question Q:

   Q  =  [Is it really true that J?], where:

   J  =  [C => B]  =  [The Current situation is a Best case scenario]

Consequently, she has walked, or ran, as is frequently the case,
right into the current situation, operating under the influence
of something like the following train of an automatic deduction:

   Case J:  C => B
   Rule K:  B => A
  -----------------
   Fact X:  C => A

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.

The surprise that one meets with, instead of the bus,
might lead one to question all sorts of things.  Any
number of speculations might come to mind.  Among the
more rational possibilities, the surprise might cause
one to inquire into any and all of the premisses that
fed into the above deduction, if not the axioms of the
logic that one happens to be implementing at the moment.

But let's suppose that one lights 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 of the inquiry into inquiry,
it is most frequently the Case that empirical people consider first.

And so, after reflecting on the situation, and eliciting certain features
of how one's habitual reasoning processes fed into it, quasi modo intuitio,
one decides 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 oneself, "Can it be that the current situation is not actually the
best (modal, normal, ordinary, usual, ...) case, and that this may be the
cause of my expectation being disappointed?"

Jon Awbrey

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