# reverse deduction, etc.

John Josephson (jj@cis.ohio-state.edu)
Mon, 21 Oct 1996 08:10:43 -0400

> According to a popular view, both abduction and induction embody --
> as logical inference operations -- a form of "reversed" deduction:
> together with the background knowledge, the hypothesis should
> entail a given set of observations.

This view might be popular, but, as I have argued as vigorously as I
can, itís wrong. Abduction, as inference to the best explanation,
infers an explanation, but an explanation need not deductively entail
the item explained. (For example, the flu hypothesis explains the body
aches, but often people have flu without body aches, so having flu does
not imply body aches.) Inductive generalizations need not be reverse
deduction either. Consider statistical generalizations from samples to
populations. 50% of the observed smidgets are squidgets, so I induce
that approximately 50% of all smidgets are squidgets; but the fact that
50% of all smidgets are squidgets does not imply that, in the next
observed sample, 50% of all smidgets will be squidgets.

Conclusion: neither abduction not inductive generalization are
essentially reverse deduction.

> Abduction is used to generate, according
> to some general theory a reason -- an explanation -- for the truth
> of the observation in terms of hypotheses which are typically
> specific to the situation and individual objects at hand.

Abduced explanations might be specific or not. Sometimes a patient's
symptoms are explained; sometimes an empirical generalization is
explained by an underlying causal mechanism (e.g., universal gravitation
explains the orbits of the planets).

> Each separate observation will get its own explanation, not necessarily
> related to the explanations of other observations, and not intended
> to account for other (later) observations.

The flu hypothesis explains both the body aches, and the nasal
discharge. If the patient develops a cough, the flu hypothesis will
explain that too.

.. john