ONT Re: Zeroth Order Ontology
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ZOO. Discussion Note 7
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I've been referring to our formal systems L_1 and L_2 as "formal languages"
or as "spaces". Sometimes I'm careful to treat their elements as symbols,
indicated through the use of quotation marks, and sometimes I leave that
to context and the reader's own recognizance of their formal character.
Indeed, the only thing that led me to start using quotes was the need
to mark the empty string, which I could've circumvented through the
use of a special notation like "!e!". The fact is that it doesn't
really matter yet whether we regard these elements as signs or as
objects, since that is a relational role distinction, and for the
moment our formal language is not really about anything. In the
present setting, the term "formal language" means nothing more
than a finitely-generated set. In short, we are still playing
a glass bead game, with "uninterpreted formal tokens" (UFT's).
The thing that we do have, perhaps as a kind of proto-meaning,
is the relator-catalyzed clumping together of expressions into
exclusive and exhaustive "formal equivalence classes" (FEC's).
You may well anticipate that we'll eventually treat these FEC's
as "logical equivalence classes" (LEC's) of some sort or another.
At any rate, whether presently or prospectively, we will discover
but a limited success in pinning down anything like a putatively
absolute meaning for any expression in any language, being able
at best to say that all of the signs in each equivalence class
share the "same meaning" in a sense that has to be specified.
Even though we are still working at the level of a formal arithmetic,
we may still notice that distinctive characteristics of this type of
system are already in force at this primitive stage, namely, the use
of "equational rules of transformation" for what will eventually get
interpreted as "inference". The distinctive feature of equations is
their reversibility. In effect, no information is gained or lost in
the process of carrying out the transformation in question. In this
type of formal setting, the mere fact of representation is of little
use in itself without a facility for quickly recognizing equivalence
classes of signs, which in turn depends on the ease with which signs
are transformed into interpretant signs while preserving with surety
their equivalence classes. Ease and facility are pragmatic features.
Jon Awbrey
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