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Revision as of 17:02, 16 August 2011
, 17:02, 16 August 2011→6.30. Connected, Integrated, Reflective Symbols: + raw text
===6.30. Connected, Integrated, Reflective Symbols===
===6.30. Connected, Integrated, Reflective Symbols===
<pre>
Triadic relations need to be recognized as the minimal subsistents or staple elements of continuity that are capable of keeping the symbols for generalized objects or "hypostatic abstractions" viable in practice. In order to remain fully functioning in all the ways that initially make them useful, abstract terms have to stay connected in each of the many directions of relationship that make their use both flexible and stable, namely, (1) attached to the substantive particulars of their denotations, (2) dedicated to the associational and definitional connotations that constitute their law abiding participation in a commonwealth of other abstract terms, (3) relevant to the ongoing understanding of inquiring agents and interpretive communities. Anything less, any attempt to use staple structural elements of lower arity than triadic bonds is bound to corrupt in time the dimensional solidity of these symbolic amalgamations.
In order for its knowledge to be reflective, an intelligent system must have the ability to reason about sign relations, not only the ones in which it operates but also the ones in which it might participate. A natural way of approaching this task is to consider the domain of sign relations set within the embedding framework of n place relations, since resourcefulness with relations in general is something that a reasonably competent knowledge based system will need anyway.
Now here is a class of mathematical objects, n place relations, that are worthy of some thought, no matter what application might be intended, and given the levels of combinatorial complexity that their study raises, it is likely that suitable software will need to play a role in their investigation.
One of the ways that the design principles declared above bear on the application to n place relations is as follows. In order to support reasoning about general classes of relations, and sign relations in particular, a computational system (or implemented formal system) must have signs or names that are available to refer to the subject matter of particular relations and symbols or formulas that are able to represent predicates of relations. If these references and representations are to avoid all the various ways of becoming logically empty and effectively vacuous — something they can do (1) by failing to have sufficient denotation from the very outset or (2) by exceeding the conceptual and computational bounds needed to maintain consistency and tractability at any subsequent stage of processing their indications — then ...
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===6.31. Generic Orders of Relations===
===6.31. Generic Orders of Relations===
