SUO: Propositional Equation Reasoning Systems (PERS)
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| Ergo in numero quo numeramus repetitio unitatum facit pluralitatem;
| in rerum vero numero non facit pluralitatem unitatum repetitio,
| vel si de eodem dicam "gladius unus mucro unus ensis unus".
|
| Therefore in the case of that number by which we number, the repetition of ones makes a plurality;
| but in the number consisting in things the repetition of ones does not make a plurality,
| as, for example, if I say of one and the same thing, "one sword, one brand, one blade".
|
| Boethius (Anicius Manlius Severinus Boetius, c.480-524 A.D.),
| 'De Trinitate' ('The Trinity Is One God Not Three Gods'), in:
| 'The Theological Tractates', Trans. H.F. Stewart & E.K. Rand,
| New Edition, Loeb Classical Library, Harvard/Heinemann, 1973.
Arisbeans, PORToses, SemioCompères, & SUOphists,
Especially Jerry, Jim, John, Mary, Matthew, Pat:
This is "yet another promissory note" (YAP^N),
in deed, the continuance if not the extension
of numerous, and yet unremunerous, older IOU's
that I have been wont to issue, to publish, or
to utter, from time to time, on the same score,
but I will tender it here, anyway, in spite of
the not inconsiderable nuisance factor, I know,
in doing so, if only to keep reminding myself,
for one, of what I ought to due about it all.
I am reminded of the prospect of this project
by that recent discussion of axioms and rules,
and by the collateral issue of model-theoretic
versus proof-theoretic manners, methods, modes,
just plain ways of doing logic and mathematics.
One of the things that a host of people tend to forget,
maybe because its ways are far less developed than the
customary, far more frequented ways of doing things,
is the availability of yet another way of reasoning,
in which all of the inference steps are reversible,
unlike what I dub "implicational reasoning systems",
like that two-lane blank-top that paves its way via
modus ponens & modus tollens. This other way of ways
leads on to "equational reasoning systems", here using
the term "equational" in a dual sense to suggest that
their domains are designed to encompass equivalences
in a natural way and that these realms are ruled via
equivalential "rules of inference" (ROI's). Moreover,
perhaps this is a residual from the early days of Lisp,
when the folk wisdom was that codes and data were really
designed to be wielded as one blade, one brand, one sword,
so to speak, and it was only the role that one cast them in,
persistent over the ages or transient from moment to moment,
the hand that hefted them, so to spike, that determined the
axe-cidental, inessential, and interrupretive distinction.
I have to break away here.
I will give examples anon.
Talk to you later,
Jon Awbrey
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