Induction

[Detlef Morgenstern]

Dear Sergio,

it's getting interesting! You wrote:

(http://www.wco.com/~sanna/casc/archive/msg00099.html)

> You're right that abduction is used in this sequence, but I
> think it is not the most "dangerous" part of the reasoning
> (which seems to be item b). Here's an analysis of the sequence:
>
> a) Direct observation
> b) Induction
>     b.1) "All white powder I have seen before was
>           the result of chalk powder"
>     b.2) "I'm seeing now white powder",
>     b.3) "So, I'm seeing chalk powder"
> c) Conclusion of Inductive inference
> d) Abduction
>     d.1) "All teachers I've seen so far had hands dirt with
>           chalk powder"
>     d.2) "I'm seing a hand dirt with chalk powder"
>     d.3) "He must be a teacher"
> e) Conclusion of Abductive inference

At a first glance, there seems to be some relatedness of character between
induction and deduction. I want to show that abduction is more a kind of
deduction than similar to induction.

Section b) appears to be a mix of induction and deduction. And there is a
hidden step (b1.3=b2.1):

b1) Induction
    b1.1) "All white powder I have seen before was
           the result of chalk powder"
    b1.2) "Some white powder is chalk powder"
    b1.3) "All white powder is chalk powder"
b2) Deduction
    b2.1) "All white powder is chalk powder"
    b2.2) "I'm seeing now white powder",
    b2.3) "So, I'm seeing chalk powder"

If d) is somehow similar to b) then this comes from d) being similar to b2).

To better demonstrate what I mean, I will inspect the microstructure of
induction, deduction and abduction. All this starts from the observation of
some property (Y) of instances of type (X):

(X)              (Y)
chalk powder     is white
teachers         have hands powdered with chalk

Two cases must be considered.

(Case 1)
Induction:
 Observe:
   I.1) Observation: "There exist (X)es having property (Y)."
 Compress:
   I.2) Rule:        "Some (X)es have property (Y)."
 Generalise:
   I.3) Rule:        "All (X)es have property (Y)."

Deduction:
 Know:
   D.1) Rule:        "All (X)es have property (Y)."
 Observe:
   D.2) Observation: "I see an (X)."
 Infer:
   D.3) Conclusion:  "It must have property (Y)."

Abduction:
 Know:
   A.1) Rule:        "All (X)es have property (Y)."
 Invert:
   A.2) Rule:        "Some instances with the property (Y) are (X)es."
 Generalise:
   A.3) Rule:        "All instances with the property (Y) are (X)es."
 Observe:
   A.4) Observation: "I see an instance having property (Y)."
 Infer:
   A.5) Conclusion:  "It must be an (X)."

(Case 2)
Induction:
 Observe:
   I.1) Observation: "There exist (X)es having property (Y)."
 Compress:
   I.2) Rule:        "Some instances with the property (Y) are
                      (X)es."
 Generalise:
   I.3) Rule:        "All instances with the property (Y) are (X)es."

Deduction:
 Know:
   D.1) Rule:        "All instances with the property (Y) are (X)es."
 Observe:
   D.2) Observation: "I see an instance with the property (Y)."
 Infer:
   D.3) Conclusion:  "It must be an (X)."

Abduction:
 Know:
   A.1) Rule:        "All instances with the property (Y) are (X)es."
 Invert:
   A.2) Rule:        "Some (X)es have property (Y)."
 Generalise:
   A.3) Rule:        "All (X)es have property (Y)."
 Observe:
   A.4) Observation: "I see an (X)."
 Infer:
   A.5) Conclusion:  "It must have property (Y)."

> You put abduction as if it was a IF/THEN pair, which is only
> used for deductions. Abduction is inference to the best
> explanation. It is very related to induction, because it is
> an equally "weak" method.

Both deduction and abduction follow the same pattern:
   Rule -> Observation -> Conclusion
For me, they are of the same structure. I should even say, abduction **is**
deduction: Deduction from an inverted generalised rule.

Induction is completely different from both in that it proceeds
   Observation -> Rule

About the dangers/weaknesses:

Induction:
Generalisation is the weak point in induction. The generalised  rule will be
falsified as soon as there will be an observation of an (X) not having
property (Y) (case (1)) or an observation of property (Y) with an instance
other than (X) (case (2)).

Deduction:
Cannot be stronger than its weakest point: the rule which it must rely on.
And this rule is provided by induction...

Abduction:
Generalisation (same as in induction), and dependence upon strength of the
rule (provided by induction).

I would not rank weaknesses. But what can be seen clearly (if you are not a
sceptic) is that this framework is infected with weakness by generalisation,
and only by it. All the other "micromethods" only propagate this weakness.

> It is not really easy to decide for one method (deduction or
> induction/abduction). Both have advantages and disadvantages.
> One way to try to decide is to choose the method with greatest
> psychological plausibility.

> Probably the best option would be a well balanced mixture of
> all methods.

And some deeper investigation in what I called "micromethods". Induction,
deduction and abduction are built of common building blocks.

Regards,

Detlef