ONT Re: Zeroth Order Ontology
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ZOO. Discussion Note 6
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By way of supplying additional motivation for the grueling rigors ahead,
of starting from such minimal resources and trying to bootstrap our way
up to a full-function logical utility, let me mention two more reasons
that I have for doing things this way. No doubt some people imagine
themselves already pre-convinced of the worthwhileness of bottom-up
methods, but it has been my experience that no sooner do you show
people just far down the bottom might be than they start turning
blue in the face and clambering for the airy heights once more.
Ontological Insecurity About Variables.
Taking the arithmetic approach to algebra solved a problem that
used to give me high anxiety about the practice of mathematics,
and that is the worries that I used have about the ontological
status of variables. I'll discuss this remedy for perplexity
when it naturally arises, in the process of supplementing the
arithmetic initials with the algebraic initials of the system.
Unity of Syntax, Semantics, Pragmatics.
If we take up Peirce's theme of "logic as semiotic",
it means that we see both the operations of knowledge
representation and the methods of logical inquiry that
lead us to the knowledge in question as taking place in
the embedding of the appropriate triadic sign relations.
But any natural species of triadic relations tends to
become very complex very quickly, and so it has been
the norm, historically speaking, almost immediately
to seek some way to reduce the intellectual load,
the usual way being to focus on only one or two
dimensions of the full sign relation at a time.
This may be necessary in practical terms, but
it has the effect that we lose a grasp of the
integral nature of the character and dynamics
of the semiotic structures and functions that
are required to support knowledge operations,
incuding both representation and reasoning.
One way to make up for this deficiency is
to study simple enough systems that we
can still grasp all three dimensions
in a connected way. That is one of
the things that I hope to do here.
Jon Awbrey
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