ONT Re: Apposite Purposes Of Logical Languages Objectified (APOLLO)
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Logic, as a normative aim, sights itself through objective signs.
What is an objective sign? It is a bit like an objective lens.
The object of an objective sign
is to signify its object as
objectively as possible.
What does that mean?
It is only what we are always already trying to do in formal,
logical, or mathematical inquiries, where we are trying to
arrive at conceptions of objects that are as independent
of particular languages, media, and representations
as we possibly can.
An objective inquiry aims to acquire a comprehension of its object
that will be as abstract, categorical, generic, invariant, objective --
just to mention a few of the words that are thrown in this direction --
as possible, taking into account all of the evident limitations of
finitely informed creatures such as ourselves.
But how does one track or apply any traction to such an elusive object?
How does one get an "abstract grip", or find enough "abstract traction"
to draw out the outlined trace of a "language independent tract" (LIT)?
By avoiding all language, all perspective, all representation, and
by eschewing as utterly ineffably as possible all the bits whereof?
Hardly.
It is more by taking in as many different languages,
points of view, and ways of representing the object
as possible that we gradually move toward acquiring
a recognition of it that approximates a relation of
independence with respect to any particular setting.
This is not a new aim, not a new problem, and many intellectual tools
have been developed over the millennia to help us deal with its tasks,
though each new encounter with the need to carry it out one more time
undoubtedly presents a variety of novel aspects that demand an act of
generalization or an act of specialization upon the tools that we own.
One of these standard tools has acquired the name of "Category Theory",
whereof I must not be silent, anon.
Jon Awbrey
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