Francesco, Edwina, and Jon AS,
FB
"Subject and Object are the same thing except for trifling distinctions" (EP
2:494)
Yes! And they're the same as the "arguments" of relations by
logicians today. This quotation and the others cited by Francesco
confirm the point I was trying to make: From age 12 to 74, Peirce
was a logician. Every version of logic that he used or invented
had a precise mapping to his algebra of 1885, to his later EGs,
and to the most widely used logics today.
Peirce was also a professional lexicographer. Note his letter
to the editor of the Century Dictionary, Benjamin E. Smith, who
had also been one of his students at Johns Hopkins:
The task of classifying all the words of language, or what's the
same thing, all the ideas that seek expression, is the most
stupendous of logical tasks. Anybody but the most accomplished
logician must break down in it utterly; and even for the strongest
man, it is the severest possible tax on the logical equipment and
faculty.
Implication: Over the years, Peirce had described his logics and
the versions designed by other logicians in various ways. He also
explored other versions in his Gamma graphs, 3-valued logic, modal
logics, and metalanguage. But his first-order logic was equivalent
to the core (Alpha + Beta) of existential graphs, and to "classical
first-order logic" today. For the history, see "Peirce the logician"
by Hilary Putnam: http://jfsowa.com/peirce/putnam.htm
When trying to relate different terminologies by Peirce and others,
always ask how or whether they could be mapped to FOL. If they
can't, then ask what extensions or variations would be needed.
ET
I'm trying to emphasize... that Peircean semiotics is not
expressed simply in language and/or logic, but in its pragmatic
application to material life.
My concern is that much of the focus of our examination of Peirce
is often on terminology, on which term he used for..___. Since
Peirce often changed these terms, then, to me, they are not the
vital ground of Peircean semiosis and even sidesteps the fundamental
nature of Peircean semiotics - which is its pragmaticism.
I completely agree. But Peirce's logic was constant while his
terminology was changing. Peirce put far more emphasis on mapping
logic to and from perception and action than anyone else. But his
terminology was idiosyncratic. His logic is the foundation for
relating his terminology to any versions in use today.
That foundation is key to bringing Peirce into the 21st century.
Logicians, philosophers, and computer scientists today will never
study Peirce unless we can show exactly how his writings relate
to what they're doing now and what they still need to do.
JAS
my own purpose in focusing so much on Peirce's concepts and
terminology in logic as semeiotic is not for its own sake, but
primarily for the purpose of making our ideas clear.
Yes. That was Peirce's motivation throughout his career. And logic
was always his primary tool, as he said explicitly in 1877.
JAS
Peirce defined pragmatism as "no attempt to determine any truth
of things," but rather "merely a method of ascertaining the meanings
of hard words and of abstract concepts" (CP 5.464, EP 2:400; 1907).
Yes. And remember his comment to Benjamin Smith.
JAS
no one on the List is advocating "Platonic idealism."
Why keep bringing it up?
I was citing Peirce's "three universes": possibility, actuality,
and the necessitated. Mathematical entities are "real possibles"
in Peirce's terms. For an analysis of Peirce's ideas about these
issues, I recommend an article by Susan Haack:
https://www.researchgate.net/publication/247935387_Peirce_and_Logicism_Notes_Towards_an_Exposition_1993
On page 9, she wrote
at CP 4.118 (1893) Peirce speaks of "the Platonic world of pure
forms with which mathematics is always dealing," and in the
prospectus for his 12-volume _Principles of Philosophy_ (c. 1893)
he entitles the third volume, _Plato's World: an Elucidation of
the Ideas of Modern Mathematics_. But at 4.161 (c. 1897) we read...
If this is Platonism, it is Platonism of a very distinctively
Peircean stripe.
Edwina
I think one can get trapped in the isolation of words and should
instead, consider their function in the actual world.
Yes. But Peirce claimed that math and logic, formal and informal,
are the foundation for all the sciences and all the ways of thinking
and acting in the world. (See his 1903 classification.)
William James could not fully understand Peirce because he did
not know logic. WJ was never able to understand Peirce's
logic and his distinction between pragmatism and pragmaticism.
In the excerpts below, note that nearly every sentence uses logical
terminology. (This excerpt happens to be something I was recently
reading, but you can find many more examples in all his writings.)
John
___________________________________________________________________
5.448. Perhaps a more scientific pair of definitions would be that
anything is general in so far as the principle of excluded middle does
not apply to it and is vague in so far as the principle of contradiction
does not apply to it.†1 Thus, although it is true that "Any proposition
you please, once you have determined its identity, is either true or
false"; yet so long as it remains indeterminate and so without identity,
it need neither be true that any proposition you please is true, nor
that any proposition you please is false. So likewise, while it is
false that "A proposition whose identity I have determined is both true
and false," yet until it is determinate, it may be true that a
proposition is true and that a proposition is false.†P1
†P1 These remarks require supplementation. Determination, in general,
is not defined at all; and the attempt at defining the determination of
a subject with respect to a character only covers (or seems only to
cover) explicit propositional determination. The incidental remark
[447] to the effect that words whose meaning should be determinate would
leave "no latitude of interpretation" is more satisfactory, since the
context makes it plain that there must be no such latitude either for
the interpreter or for the utterer. The explicitness of the words would
leave the utterer no room for explanations of his meaning. This
definition has the advantage of being applicable to a command, to a
purpose, to a medieval substantial form; in short to anything capable of
indeterminacy. (That everything indeterminate is of the nature of a
sign can be proved inductively by imagining and analyzing instances of
the surdest description. Thus, the indetermination of an event which
should happen by pure chance without cause, /sua sponte/, as the Romans
mythologically said, /spontanément /in French (as if what was done of
one's own motion were sure to be irrational), does not belong to the
event — say, an explosion — /per se/, or as explosion. Neither is it by
virtue of any real relation: it is by virtue of a relation of reason.
Now what is true by virtue of a relation of reason is representative,
that is, is of the nature of a sign. A similar consideration applies to
the indiscriminate shots and blows of a Kentucky free fight.) Even a
future event can only be determinate in so far as it is a consequent.
Now the concept of a consequent is a logical concept. It is derived
from the concept of the conclusion of an argument. But an argument is a
sign of the truth of its conclusion; its conclusion is the rational
interpretation of the sign. This is in the spirit of the Kantian
doctrine that metaphysical concepts are logical concepts applied
somewhat differently from their logical application. The difference,
however, is not really as great as Kant represents it to be, and as he
was obliged to represent it to be, owing to his mistaking the logical
and metaphysical correspondents in almost every case. Another advantage
of this definition is that it saves us from the blunder of thinking that
a sign is indeterminate simply because there is much to which it makes
no reference; that, for example, to say, "C.S. Peirce wrote this
article," is indeterminate because it does not say what the color of the
ink used was, who made the ink, how old the father of the ink-maker
[was] when his son was born, nor what the aspect of the planets was when
that father was born. By making the definition turn upon the
interpretation, all that is cut off. [Cf. 3.93.]
At the same time, it is tolerably evident that the definition, as it
stands, is not sufficiently explicit, and further, that at the present
stage of our inquiry cannot be made altogether satisfactory. For what
is the interpretation alluded to? To answer that convincingly would be
either to establish or to refute the doctrine of pragmaticism. Still
some explanations may be made. Every sign has a single object, though
this single object may be a single set or a single continuum of objects.
No general description can identify an object. But the common sense of
the interpreter of the sign will assure him that the object must be one
of a limited collection of objects. Suppose, for example, two
Englishmen to meet in a continental railway carriage. The total number
of subjects of which there is any appreciable probability that one will
speak to the other perhaps does not exceed a million; and each will have
perhaps half that million not far below the surface of consciousness, so
that each unit of it is ready to suggest itself. If one mentions
Charles the Second, the other need not consider what possible Charles
the Second is meant. It is no doubt the English Charles Second.
Charles the Second of England was quite a different man on different
days; and it might be said that without further specification the
subject is not identified. But the two Englishmen have no purpose of
splitting hairs in their talk; and the latitude of interpretation which
constitutes the indeterminacy of a sign must be understood as a latitude
which might affect the achievement of a purpose. For two signs whose
meanings are for all possible purposes equivalent are absolutely
equivalent. This, to be sure, is rank pragmaticism; for a purpose is an
affection of action.
What has been said of subjects is as true of predicates. Suppose the
chat of our pair of Englishmen had fallen upon the color of Charles II's
hair. Now that colors are seen quite differently by different retinas
is known. That the chromatic sense is much more varied than it is
positively known to be is quite likely. It is very unlikely that either
of the travelers is trained to observe colors or is a master of their
nomenclature. But if one says that Charles II had dark auburn hair, the
other will understand him quite precisely enough for all their possible
purposes; and it will be a determinate predication.
The October remarks [i.e. those in the above paper] made the proper
distinction between the two kinds of indeterminacy, viz.:
indefiniteness and generality, of which the former consists in the
sign's not sufficiently expressing itself to allow of an indubitable
determinate interpretation, while the [latter] turns over to the
interpreter the right to complete the determination as he please. It
seems a strange thing, when one comes to ponder over it, that a sign
should leave its interpreter to supply a part of its meaning; but the
explanation of the phenomenon lies in the fact that the entire universe
— not merely the universe of existents, but all that wider universe,
embracing the universe of existents as a part, the universe which we are
all accustomed to refer to as "the truth" — that all this universe is
perfused with signs, if it is not composed exclusively of signs. Let us
note this in passing as having a bearing upon the question of
pragmaticism. [Cf. 4.539.]
The October remarks, with a view to brevity, omitted to mention that
both indefiniteness and generality might primarily affect either the
logical breadth or the logical depth of the sign to which it belongs.
It now becomes pertinent to notice this. When we speak of the depth, or
signification, of a sign we are resorting to hypostatic abstraction,
that process whereby we regard a thought as a thing, make an
interpretant sign the object of a sign. It has been a butt of ridicule
since Molière's dying week, and the depth of a writer on philosophy can
conveniently be sounded by his disposition to make fun of the basis of
voluntary inhibition, which is the chief characteristic of mankind. For
cautious thinkers will not be in haste to deride a kind of thinking that
is evidently founded upon observation — namely, upon observation of a
sign. At any rate, whenever we speak of a predicate we are representing
a thought as a thing, as a substantia, since the concepts of substance
and subject are one, its concomitants only being different in the two
cases. It is needful to remark this in the present connexion, because,
were it not for hypostatic abstraction, there could be no generality of
a predicate, since a sign which should make its interpreter its deputy
to determine its signification at his pleasure would not signify
anything, unless nothing be its significate. — From "Basis of
Pragmaticism," 1906, following somewhat after 554.
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