ONT Re: Question Of Logic
Jon Awbrey wrote:
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
> Joe, Seth:
>
> | Logical principles of inference are merely rules for the illative transformation
> | of the symbols of the particular system employed. If the system is essentially
> | changed, they will be quite different. (CP 2.599).
>
> Yes, but Peirce would be rather acutely aware that the significant features
> of transformations on any space, whether algebraic, geometric, or syntactic,
> would be its invariant properties, the kinds of "objective qualities" that
> are not affected by the vicissitudes of the arbitrary metamorphoses in its
> conventionally arbitrated bases of representation.
Jon is surely correct on this, and the surrounding context for those
sentences actually seems as if designed to make that clear. Here is a part
of that context, the point at issue there being that it is one thing to
reason and quite another to represent an argument logically for purposes of
critical assessment.
==========quote Peirce=========
[A reasoner] does not, in strict accuracy, reason in any form of syllogism.
For his reasoning moves in first intentions, while the forms of logic are
constructions of second intention. They are diagrammatic representations of
the intellectual relation between the facts from which he reasons and the
fact which he infers, this diagram necessarily making use of a particular
system of symbols -- a perfectly regular and very limited kind of language.
It may be a part of a logician's duty to show how ordinary ways of speaking
and of thinking are to be translated into that symbolism of formal logic;
but it is no part of syllogistic itself. Logical principles of inference
are merely rules for the illative transformation of the symbols of the
particular system employed. If the system is essentially changed, they will
be quite different. (CP2.599, 1902)
========end quote===============
The reason for the reference to syllogistic is that Peirce was illustrating
the point with use of two different figures of the syllogism. (Also, Peirce
sometimes uses the word "syllogistic" and its cognates in its original
sense, which just meant any deductive form: the Aristotelian form so-called
is actually just a special case of syllogism, in that sense.) The same
point could be made by contrasting the transformation rules of his
Existential Graphs system and, say, those appropriate to his earlier
Entitative Graph system, which differed from the later system chiefly in
treating conjoint inscription on the sheet of assertion as conjunction
rather than inclusive alternation. Or, more to the point, perhaps, the
difference between the Existential Graph system and any of the variations on
the algebraic type of notation as regards transformation rules since one of
the motives of developing the graph system was to be able to develop a
notation for logical representation that required no inference principles
that were required merely to compensate for the peculiarities of the
notation itself, such as, say, the principle that enables you to switch the
positions of p and q in conjunctive expressions, which is simply gratuitous
in the graphical system he developed.
I trust that someone will correct me if I am wrong, but my understanding is
that logic as usually construed since Peirce cannot even distinguish between
an inference principle (rule) which is an artifact required only because of
a peculiarity of the notation and a principle required by logical
considerations regardless of notation.
Joseph Ransdell
ransdell@door.net