🚀 go-pugleaf

In article <526@thor.wright.EDU> vdasigi@silver.UUCP (Venu Dasigi) recalls
Peirce's beautiful characterisation of deduction, induction and abduction:

>Starting with
>
>1. A --> B (if a sample is from this bag, the sample is white.)
>2. A (this sample s is from this bag.)
>3. B (the sample s is white.)
>
>Deduction amounts to concluding 3 from 1 and 2.
>Induction amounts to concluding 1 from 2 and 3.
>Abduction amounts to concluding 2 from 1 and 3.

The formulation of induction given here, brings into mind a problem that
has been bothering me for some time. Given premises A and B, why should
I prefer the inductive conclusion A --> B over B --> A (any white sample
is from this bag)? The same problem arises with the prototypical
crows-argument: seeing a number of black crows might amount to the
inductive conclusion, that everything that is black is a crow. Of
course, this hypothesis would be falsified by the observation of a black
non-crow, rendering the set of premises non-symmetrical. But it seems to
me that any set of premises of the form
	{A(a)&B(a), A(b)&B(b), ...}
give equal evidence for two possible inductive hypotheses:
	forall(x) A(x) --> B(x), and
	forall(x) B(x) --> A(x).
Perhaps the introduction of a typed logic could help: if A is treated as
a type, the inductive conclusion would be
	forall(x:A) B(x)

Any comments on this?
--Peter

Peter A. Flach                             Institute for Language Technology
UUCP: ..!mcvax!kubix!flach                 and Artificial Intelligence (ITK)
BITNET: flach@htikub5                      Tilburg University,   PObox 90153
(+31) (13) 66 3119                         5000 LE  Tilburg, the Netherlands