Induction

[Freddy Offenga]

Dear Detlef and Sergio,

I've tried to follow your interesting debate about induction,
which was posted under the subject 'Biological Foundations'.
In this message I'm going to reply to some of the things
you've said.

Sergio:
     The most important principle of cognitive systems is
     inductive generalization, the ability one intelligent
     entity has of perceiving regularities in the world and
     grouping them into cohesive structures.

As I've learned, this is called 'enumerative induction'.
"Enumerative induction is spoken of when discussing the crea-
tion of generalizations on the basis of several instances of a
certain regularity" (Haselager, 1997).

Detlef:
     Can we refer to some unified "algorithm" of inductive
     generalization? Frustration arises from the attempt to
     find this algorithm on a higher level ("symbols", "frame-
     works", "clauses"). We drown in complexity. I think, the
     brain doesn't apply this kind of conscious high-level
     generalization. It is some very, very basic - atomic -
     feature of the brain. It's "built in" on the hardware
     level.

So, we do not concentrate too much on the high-level (knowled-
ge level), but go from the low (implementational level) to the
mid-level (the formal level).
I think this way we're closing one 'gap', while creating more
distance between the high and mid levels. I agree that we
should avoid 'drowning in complexity', but we _have_ to make
connections with the higher 'mental' states, otherwise the
formal level wouldn't make much sense.

Currently I see CasC as a powerful formal idea from which the
mental states somehow could 'emerge'. In other words, there is
a strong formal foundation probably with a good connection to
the implementational level (biological plausible), but the
psychological, sensible part isn't clear at all.

Detlef:
     I think, the abstracting capability is not concentrated
     in "a couple of modules which scan and compact our know-
     ledge database", it is a completely distributed feature
     at the "logical gate" level.

I've reached the same conclusion and it raises the following
question: is this a contradiction of the modularity of the
mind (Fodor), because the 'modules' are (in CasC terms) just
huge patterns which only _seem_ to perform special tasks?
Or maybe it's no problem at all, because we're only dealing
with the central systems here. 

Detlef:
     In many cases, we induce a law, having sensed *different*
     cause->effect associations, which did not repeat at all.
     We want to find out *what is common* to them even if they
     look very different. This, I think, is the powerful side
     of induction. Limiting it to repeated (in space and time)
     occurrence of similar sensations, we throttle its power
     nearly to the idle.

If we can find the 'common' things you talk about, why do you
still say the associations are _different_ ?
The sensors doesn't change, so we can always relate 'new'
things to 'old' (common) things.

Detlef:
     We should be able to describe intelligence in terms of
     logic manipulations. Foundations of intelligence cannot
     be illogical, or logic-free. When we aim at finding a
     "basic principle", we need not look outside logic. I
     think we must completely move the focus. Instead of
     permanently adding complexity to logic on the higher
     (complex) levels, we must revise its firmware, introdu-
     cing some new "particle" symmetry.

And not ignore the 'complex' levels as I tried to explain.
The nice thing about the symbolic view is that there is a
close connection to mental states. The symbols mean something,
the are about something. There are causal relations between
them and they relate to input/output.
It's nice to see that your 'functional compression' shifted to
'inductive compression'. Something like going from Fodor's
input systems to the central systems.

Sergio:
     Generally we don't have a single cause_x1 for a single
     effect_x1. We have a set of causes with a probabilistic
     relationship between them and those causes may give rise
     to a set of effects. The brain seems very good at deci-
     ding which of the causes are relevant *in the current
     context*.

This is probably the hard question, since it relates to the
(unsolved) "frame problem" in cognitive science (more about
this in some of my future messages).

Sergio:
     The great problem of induction is that the process of
     increasing abstraction is not always sound. From a set of
     regular occurrences (patterns) we usually have *dozens*
     of possible abstractions. Induction alone is very dange-
     rous because it leads to "mysticisms". On top of inducti-
     on we must put other methods (like deduction, analogical
     reasoning, etc) to try to restrict the wrong "ascending
     paths" of the reasoning.

Do you mean it's a problem, because induction generates too
much possible rules (plausible hypothesis generation) and some
"mysterious" proces must select the right one? (evaluation of
hypothesis).

Friendly greetings,


Freddy Offenga

F.Offenga at student.kun.nl
Software Engineer and Student Cognitive Science at:
Katholieke Universiteit Nijmegen, The Netherlands