6.2 Analogy and Induction

   Induction and analogy are obviously closely related. In induction one assumes the future will
be similar to the past, and tries to guess which of a set of past patterns will continue into the
future. In analogy one assumes that similar entities will have similar patterns, and directs pattern
recognition on this basis. The difference is that in analogy, one is merely trying to locate patterns
in some entity x, by analogy to some entity x%. In induction, on the other hand, one assumes that
a complete catalogue of patterns has already been recognized, and one tries to make a coherent
model out of these patterns. The two processes complement each other.
   Many AI researchers view analogical reasoning with a great deal of skepticism. For instance,
Bipin Indurkhya has argued that
          One naturally asks: Given some state of background knowledge, what justification is
there, if any, that similarities in certain respects determine similarities in other respects? …an
inference from analogy cannot be justified on the basis of existing similarity between the source
and the target alone. The justification, if any, must come from the background knowledge in
some other form…. Once it is realized that an inference based only on some existing similarity
between the source and the target — and nothing else — is about as justified as a random
inference, one learns to exercise extreme caution in deriving an inference from analogy. One
seeks justification in other places; it must be some other piece of knowledge, some piece of fact,
which "justifies" why the existing similarities determine the inferred ones. And if no such
justification can be found, the so-called analogical inference is to be properly discarded. (1988,
pp. 224-25)
In the notation introduced above, the "source" is x% and the "target" is x. The point is that, in
general, there is no reason to believe that the existence of some similarities between x and x%
implies the existence of other similarities.
Indurkhya thinks this implication must be drawn from "facts" and "background information."
   Really, there are two questions here. The first is, when is it justifiable to assume that the
existence of a degree D1 of similarity between x and x% implies a degree D2 of similarity
between x and x%. In other words, how can one tell when reasoning by analogy is justifiable at
all; and when is it justifiable, how can one tell to what extent? The other is, how is it possible to
tell, based on the type of similarity between x and x%, what kinds of further similarities to look
for. That is: in Step 2 of the analogy algorithm, is there some way to determine what sorts of
patterns (y,z) should be looked at on the basis of the similarities used for the computation?
Indurkhya, expressing a view which is widespread in the AI community, states that both of these
questions should be answered by reference to "background knowledge".
   Does this requisite background knowledge perhaps come from deduction? This may be true in
certain instances. But, as we shall see, deductive reasoning is only useful when it is paired with
analogical reasoning. The analogies used in executing deductive reasoning cannot all be
executed on the basis of background information obtained by deduction.
    Does the background knowledge come from experience? If so, it does not come directly from
raw, unprocessed sense perception; it comes out of the process of induction. Induction requires
pattern recognition. And I suggest that effective general pattern recognition requires analogy.
From this it follows thatthe background information Indurkha requires cannot come entirely from
experience: either it comes from some other source or it is not always necessary.
    However, although induction may not be used to justify every particular analogy, it may still
be used to justify analogy in general. This may sound contradictory, but the paradox is only
apparent. Not all the analogies used in inductive reasoning can be justified inductively. However,
if analogies that are not justified by induction are used anyway, and they happen to work, then
the tendency to take habits implies that analogy can be expected to work in the future.
I find this argument rather convincing. On the basis of ample real-world experience, we know
that analogy has often worked in the past. We have obtained useful results from it so often that
its effectiveness must be considered a very intense pattern in the past. Therefore, by the tendency
to take habits — by induction — it is relatively likely that analogy will work in the future. Hence it
is advisable to reason by analogy.
    Another way to phrase this is to postulate a "spatial" tendency to take habits, to the effect that
analogy does in fact tend to work more often than it would in a randomly selected universe
obeying the temporal tendency to take habits. This strategy seems much less elegant than in the
temporal, inductive tendency to take habits; it has more of an ad hoc flavor. But it does yield the
desired result.
Kaynak: A New Mathematical Model of Mind

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