I am trying to understand categorical logic from reading Pei Wangs very
interesting paper, A Logic of Categorization. Since I am a total
newbie to the field I have some probably dumb questions. But at the risk
of making a fool of myself let me ask them to members of the list.
Lets use --> as the arrow symbol commonly used to represent an
inheritance relation of the type used in categorical logic, where A --> B,
roughly means category A is a species (or instance) of category B.
Category B, in addition to what we might normally think as a
generalization, can also be a property (meaning Bs category would be that
of concepts having property B).
I understand how the deduction inference rule works.
DEDUCTION INFERENCE RULE:
Given S --> M and M--> P, this implies S --> P
This make total sense. If S is a type of M, and M is a type of P, S is a
type of P.
But I dont understand the rules for induction and abduction which are as
following:
ABDUCTION INFERENCE RULE:
Given S --> M and P --> M, this implies S --> P to some degree
INDUCTION INFERENCE RULE:
Given M --> S and M --> P, this implies S --> P to some degree
The problem I have is that in both the abduction and induction rule --
unlike in the deduction rule -- the roles of S and P appear to be
semantically identical, i.e., they could be switched in the two premises
with no apparent change in meaning, and yet in the conclusion switching S
and P would change in meaning. Thus, it appears that from premises which
appear to make no distinctions between S and P a conclusion is drawn that
does make such a distinction. At least to me, with my current limited
knowledge of the subject, this seems illogical.
It would appear to me that both the Abduction and Induction inference
rules should imply each of the following, each with some degree of
evidentiary value
S --> P
P --> S, and
S <--> P, where <--> represents a similarity relation.
Since these rules have been around for years I assume the rules are right
and my understanding is wrong.
I would appreciate it if someone on the list with more knowledge of the
subject than I could point out my presumed error.
Edward W. Porter
Porter & Associates
24 String Bridge S12
Exeter, NH 03833
(617) 494-1722
Fax (617) 494-1822
[EMAIL PROTECTED]
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