John Josephson (jj@cis.ohio-state.edu)
Sat, 19 Oct 1996 14:35:51 -0400

Ryszard Michalski wrote:

> If you want to be consistent with recent research findings, what you call
> induction should be called inductive generalization.

> Induction is a general form of inference, opposite of deduction.

The work "induction" has had no consistent use, either recently or
historically. Sometimes writers have meant all inferences that arenít
deductive, sometimes they have specifically meant inductive
generalizations, and sometimes they have meant next-case inductions as
in the philosophical "problem of induction" raised by David Hume. C. S.
Peirce seems to have used the term to mean: testing a hypothesis by
generating predictions and evaluating those predictions empirically. It
will be best, I think, for researchers, especially those who read this
mailing list, to make appropriate distinctions to minimize confusion.
We should write "inductive generalization" if thatís what we mean.

Possibly it would be best to completely avoid using the term "induction"
unqualified, e.g., as it occurs in the proposed title of the workshop.

Alternatively, we might just be careful to reserve the unqualified term
as a general category for all non-deductive inferences. However, I
think you can make a good case that abductions, inductive
generalizations, next-case predictions, and probably other members of
the inference zoo, whether defined formally or informally, can be
deductive at the same time as they are abductions, etc., etc. For
example an inductive generalization (as sample-to-population inference)
becomes deductive as soon as the sample grows to include the whole
population, or, for smaller samples, if you explicitly assume a premise
that `the sample is representative.'

Abductions (as best-explanation inferences) can all be viewed as
instances of the deductive form:

{E(i)} are all of the possible explanations for D.
Some explanation for D must be correct.
not E (i) (for-all i not-equal j).
Therefore, E(i).

Thus, all abductions are deductions! Moreover, any inference
whatsoever, even irrational and stupid inferences, can be construed as
deductive inferences with missing premises, that is they are
"enthymemes." The stupid inference `p, therefore q,' can always be
viewed as a deductive inference with the hidden premise `p implies q.'

The lesson is, apparently, that the set of non-deductive inferences is
empty, depriving the word "induction," of any fly poop of meaning when
used unqualified as a name for non-deductive inferences. But wait!
Perhaps we can mean by "induction" any inference, conceived as having
some reasonable persuasive force, that gets its persuasive force other
than by being a deductive inference. That is, "inductive inferences" are
justified inferences whose justifications are other than deductive.
"Deduction," "abduction," "inductive generalization," and so on, are
categories of Justifications for inferences, not categories of
inferences as such. A given instance of inferential reasoning, a single
inferential step, might belong to more than one category at the same
time, depending on which justifications can be given on itís behalf, and
especially, which justifications give it force. "non-deductive"
inferences are those inferences that have non-deductive justifications.

Significance: Let us avoid the unqualified use of the term "induction,"
but if we must use it, let us agree to mean any inference with
non-deductive justification (which is not the same as inferences with no
deductive justification).

.. john josephson