On 9/18/2019 4:20 AM, Jon Awbrey wrote:
> communication, can be difficult.?? Sometimes people do not even recognize the
> existence of other paradigms, disciplines, cultures, long before it comes to
> the question of their value.?? Readers of Peirce know he often uses important
> words in more primordial senses than later came into fashion.?? Other times his
> usage embodies a distinct analysis of the concept in question.?? More than once
> I've found myself remarking how Peirce "anticipates" some strikingly "modern"
> idea in logic, mathematics, or science, only to find its roots lay deep in
> the history of thought.?? Whether he anticipates a future sense or preserves
> an ancient sense is not always easy to answer.
I had to go back a bit to remind myself why I restarted this thread,
but at least it supplies plenty of material for future study on the
difficulties of cross-paradigm communication.
At any rate, while I still have them in mind, I wanted to add to the record
a few exhibits on Peirce's definition of logic as "formal semiotic" and in
another place his description of logic as "semiotic, the quasi-necessary,
or formal, doctrine of signs".
Here's two variants of a paragraph where Peirce defines logic as "formal semiotic".
Selections from C.S. Peirce, "Carnegie Application" (1902)
Cf: C.S. Peirce : On the Definition of Logic
No. 12. On the Definition of Logic
Logic will here be defined as formal semiotic. A definition
of a sign will be given which no more refers to human thought
than does the definition of a line as the place which a particle
occupies, part by part, during a lapse of time. Namely, a sign
is something, A, which brings something, B, its interpretant sign
determined or created by it, into the same sort of correspondence
with something, C, its object, as that in which itself stands to C.
It is from this definition, together with a definition of "formal",
that I deduce mathematically the principles of logic. I also make
a historical review of all the definitions and conceptions of logic,
and show, not merely that my definition is no novelty, but that my
non-psychological conception of logic has virtually been quite
generally held, though not generally recognized. (NEM 4, 20-21).
No. 12. On the Definition of Logic [Earlier Draft]
Logic is formal semiotic. A sign is something, A, which brings
something, B, its interpretant sign, determined or created by it,
into the same sort of correspondence (or a lower implied sort) with
something, C, its object, as that in which itself stands to C. This
definition no more involves any reference to human thought than does
the definition of a line as the place within which a particle lies
during a lapse of time. It is from this definition that I deduce the
principles of logic by mathematical reasoning, and by mathematical
reasoning that, I aver, will support criticism of Weierstrassian
severity, and that is perfectly evident. The word "formal" in
the definition is also defined. (NEM 4, 54).
Charles S. Peirce (1902), "Parts of Carnegie Application" (L 75), published in
Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce,
vol. 4, 13-73. http://www.iupui.edu/~arisbe/menu/library/bycsp/L75/l75.htm
Here's a passage where Peirce explains his sense of "formal" or "quasi-necessary".
Selection from C.S. Peirce, "Ground, Object, and Interpretant" (c. 1897)
Cf: C.S. Peirce : Logic as Semiotic
Logic, in its general sense, is, as I believe I have shown,
only another name for semiotic (...), the quasi-necessary,
or formal, doctrine of signs. By describing the doctrine
as "quasi-necessary", or formal, I mean that we observe
the characters of such signs as we know, and from such an
observation, by a process which I will not object to naming
Abstraction, we are led to statements, eminently fallible,
and therefore in one sense by no means necessary, as to what
must be the characters of all signs used by a "scientific"
intelligence, that is to say, by an intelligence capable of
learning by experience. As to that process of abstraction,
it is itself a sort of observation.
The faculty which I call abstractive observation is one which
ordinary people perfectly recognize, but for which the theories
of philosophers sometimes hardly leave room. It is a familiar
experience to every human being to wish for something quite
beyond his present means, and to follow that wish by the question,
"Should I wish for that thing just the same, if I had ample means
to gratify it?" To answer that question, he searches his heart,
and in doing so makes what I term an abstractive observation.
He makes in his imagination a sort of skeleton diagram, or outline
sketch, of himself, considers what modifications the hypothetical
state of things would require to be made in that picture, and then
examines it, that is, observes what he has imagined, to see whether
the same ardent desire is there to be discerned. By such a process,
which is at bottom very much like mathematical reasoning, we can reach
conclusions as to what would be true of signs in all cases, so long as
the intelligence using them was scientific.
C.S. Peirce, Collected Papers, CP 2.227
From an unidentified fragment, c. 1897
Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1-6,
Charles Hartshorne and Paul Weiss (eds.), vols. 7-8, Arthur W. Burks (ed.),
Harvard University Press, Cambridge, MA, 1931-1935, 1958. Volume 2 :
Elements of Logic, 1932.