ONT Re: Information = Comprehension x Extension -- Discussion

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ICE.  Discussion Note 39

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One of the ways of trying to make sense of such outlandish notions as
"currently noted property of x" and "discourse relative property of x"
is to augment suitably basic 2-adic relations with an extra parameter --
let us say, "instance of" and "implier of" on the logical side of the
ledger, and "element of" and "subset of" on the set-theoretic account --
thus ending up with 3-adic relations that we might symbolize this way:

   Relative instantiation.   j : x is y

   Relative implication.     j : x => y

   Relative membership.      j : x in y

   Relative inclusion.       j : x =c y

In each case, we can leave the interpretation of
the "interpretive parameter" j relatively loose
for the moment, tying it to its own context of
interpretation, not to be recursive about it,
but just to be flexible in a pragmatic way.

For example, j might be taken as an agent, a community, or a context,
and the context might be cultural, discursive, environmental, or any
other factor affecting the interpretation of signs that anyone might
think to conceive.

Under the "agent interpretation", one might then read these expressions,
just by way of giving some possible illustrations, in any of these ways:

   Relative instantiation.   j : x is y.   "j says x is y"

   Relative implication.     j : x => y.   "j knows x implies y"

   Relative membership.      j : x in y.   "j thinks x is a member of y"

   Relative inclusion.       j : x =c y.   "j believes x is a subset of y"

At the outset our task would be to identify the formal, generic, or structural
principles that are common to the whole variety of specialized interpretations,
only after that project was well under way trying to enumerate their diversity.

Jon Awbrey

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