ONT Re: Extensions Of Logical Graphs
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I have a little over three decades worth of unfinished business here --
so many things I've been trying to say about what logic means to me
and incidentally why the spin that Peirce put on the subject makes
such a huge difference in our prospects for actually being able to
apply logic to problems of real significance and solid substance
in human terms -- so give me a while to get the thing organized.
The first thing that comes to mind is the practical need to integrate two different aspects
of logical reasoning. Language is diverse here -- some will cast the distinction as a split
between "assertive" and "evaluative" uses of logical syntax, others will encounter the issue
in the form of a discursive wrangle between "declarative" and "procedural" styles of reasoning,
whether it concerns cognitive theorizing or computational practice. I ran into this problem on
both of these apparent fronts, and had wrestled with it for quite a while before I realized that
Peirce had already finessed the whole issue from the very beginning of his systematic logical work.
I will quit dancing around and just say it straight out -- there are ideas and methods in Peirce's
1870 paper, "Description of a Notation for the Logic of Relatives", that mark the high point of our
age's logical power. There are ideas about the analysis of logical expressions and the extensions
of logical calculi that relegate the so-called "discovery" of quantifiers at a later date to the
status of a passing afterthought or an incidental corollary. And yet the significance of many of
these advances, screened through the anachronistic glasses of a modern POV and all the illusions
of its progressive fallacies, is currently lost to the contemporary scene and the benighted sight
of most players on it with regard to the overall purpose of logic. It gets worse. As I see it,
many of the features of our current "families of notation" (FON's), novelties that are genarally
pointed out as its proudest improvements -- like changing Peirce's and Mitchell's Sum and Product
symbols for quantification to rotated "E" and "A" symbols -- are literally great steps backward
when it come to their effects on the logical issues that I mentioned, those of integrating the
descriptive and the functional aspects of any applied and computationally implemented logic.
We will all have to find our own ways of staying sane ...
I will try this for a while and see how it works out ...
Have to break ...
Jon Awbrey
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