alf@ttds.UUCP (Thomas Sj|land) (09/25/84)
> That's a little like saying, "The girl next to me is blonde. The > girl next to her is blonde. Therefore all girls are blonde." (Or, > "3 is a prime, 5 is a prime; therefore all odd numbers are prime.") > > An observation of 2 (or 3, or 20, or N) samples does *not* an inductive > proof make. In order to have an inductive proof, you must show that > the observation can be extended to ALL cases. So true. It has been said before, but still... Mathematical induction is logically valid, philosophical induction is not. Several philosophers in the past have made a carreer in explaining why you cannot PROVE that the natural "laws" are valid tomorrow, but why it is still reasonable (or not in some cases) to BELEIVE that they will be. That common-sense reasoning is often so succesful in beleiving unprovable propositions is why philosophers are at all interested in the problem. Any "deductive" system that tries to "prove" that a given state in the environment will look so and so when "extrapolated" for some parameter has to make the assumption that the natural laws are constant (or at least predictable) over space and time. That includes ourselves when we try to perform reasoning in any natural science (except mathematics or logic). Mathematical induction is something completely different since it does not try to extrapolate from specific recordings of the state of the "real world" into yet unknown states, but merely performs "all-introduction". This distinction is important and to me it seems to indicate that AI has the same knowledge theoretical problem that physics and probability theory has. Can a theorem prover be claimed to say anything about the real world ? Is it just good heuristics to claim that logic should be used for AI, or is there something more to it ? Sorry to have bored those who know all this..
SHEBS@UTAH-20.ARPA (09/26/84)
From: Stan Shebs <SHEBS@UTAH-20.ARPA>
There's another name for "induction" on one case: generalization. Lenat's
AM and the Boyer-Moore theorem prover are both capable of doing
generalizations, and there are probably others that can do it also.
Not too hard really; if you've set up just the right formalism,
generalization amounts to easily-implemented syntactic mutations (now
all we need is a program to come up with the right formalisms!)
stan shebs