Jon AS and Gary R,
JAS: The new thread title is alarmist hyperbole.
GR: I strongly agree
My word 'danger' is mild compared to the vehement denunciation that
Peirce would pronounce if anybody would introduce a contradiction
in his system of semeiotic. Peirce-List should be alarmed.
Among Peirce's many comments about logic and metaphysics,
the metaphysician who is not prepared to grapple with all the
difficulties of modern exact logic had better put up his shutters
and go out of the trade. (CP 1.624)
metaphysics ought to be founded on logic. To found logic on
metaphysics is a crazy scheme. (CP 2.168)
In exact logic (which includes EGs), one contradiction destroys the
entire theory. But a theory can be saved by stepping back through
the proof to determine which assumption is at fault and replacing or
revising that assumption.
That proof (copy below) depends on three assumptions:
1. In every triad, the First represents something in the universe of
possibility. The Second, in actuality. The Third, in necessity.
2. Every sign that is a First can refer only to possible objects
(in the universe of Possibility). A First can never, by itself,
refer to any particular object in the universe of actuality. But
as a possibility, it may be used to describe something actual that
has been independently determined by some Index (which is a Second).
3. As a widening of a Rheme and a logical Term, a Seme must include
predicates. Peirce said it also includes percepts, icons, and
images. But two options about other kinds of "widening" were
being debated. Option A: Nothing else. Option B: The subject
phrase of a sentence in English or other language.
Points #1 and #2 are definitions in Peirce's system of categories,
which is the foundation of his semeiotic. If any contradiction is
inserted or implied, the foundation collapses.
The debate so far is about two options for widening Rheme to Seme.
Option A claims that a Seme includes only signs that Peirce had
explicitly discussed. But option B claims that a paragraph in an
early draft implies the subject of a sentence in ordinary language.
For option A: In CP 4.538, the definition of Seme includes Term
and Logical Term. Both of them are predicates (Firsts). That
paragraph does not contain the ambiguous word 'subject'. And
in CP 4.539 ff, Peirce said "A percept is a Seme" and discussed
other image-like signs that are also Firsts: an icon in the triad
icon, index, symbol; or a mark in the triad Mark/Tone, Token, Type.
In 1903, Peirce used the word 'quasi-predicate' for such signs.
For option B: Seme is defined in a draft that Peirce did not include
in the final version of CP 4.538:
The first member of the triplet, the “Seme,” embraces the logical
Term, the Subject or Object of a sentence, everything of any kind,
be it a man or a scribed character, such as h or Pb, which will
serve or is supposed to serve, for some purpose, as a substitute
for its Object. (R 295, p. 26ff)
In this paragraph, the phrase "The logical Term, the Subject" implies
a predicate, as in option A. But the remainder of the sentence seems
to imply the subject phrase of a sentence, which would have an index
or indexical whose object would be something in the universe of
actuality, not possibility.
Why didn't Peirce use this definition in the final version?
Did he explicitly reject it? Did he just overlook it?
Or did he think it might be misleading?
Consider the implications: The subject of a sentence in English
contains some word that serves as an index (a proper name) or
some indexical words that make it refer to something that exists
in actuality. But any sign that refers to an actual entity is
a Second, such as an Index, Token, Actisign, or Sinsign.
At this point, we have two options for resolving the debate:
Option A uses the definition of Seme as a logical Term, which
is a predicate that may occur in subject or predicate position
of a syllogism. That option preserves the consistency of Peirce's
semeiotic. To avoid any ambiguity about the word 'subject', he
decided to remove that word from the final version (CP 4.538).
But option B assumes that the draft version in R 295 is more
significant than the final version in CP 4.538. It also assumes
that the ambiguous word 'subject' should not be considered as a
logical subject (which is a predicate), but as a reference to some
actual existent (a Second) rather than a possibility (a First).
This choice causes a contradiction in the foundation of the system
of semeiotic.
Which option would Peirce himself intend?
As he said, "metaphysics ought to be founded on logic".
Since option B leads to a contradiction, it's "a crazy scheme".
John
______________________________________________________________________
The derivation of the contradiction can be summarized in three points:
1. In CP 4.538, Peirce said that the triad Term, Proposition, Argument
had to be widened, and he proposed a new triad Seme, Pheme, Delome.
In 4.539, he discussed issues about percepts, which showed why the
category Seme needed to go beyond purely symbolic Terms.
2. But Jon claimed that Subject would be an appropriate widening.
He was misled by an ambiguity in the word 'subject': as a logical
term, it's a predicate, which is a Rheme, which is a Seme; but as
a grammatical subject, it would refer to something actual.
3. But that triad would contradict the foundation of Peirce's system.
A Seme is a First. It represents a pure possibility, such as a
Mark/Tone, Potisign, or Qualisign. But a grammatical subject in
language refers to something that exists. It's a Second, such
as a Token, Actisign, or Sinsign. To claim that a grammatical
subject could be a Seme would mix Firstness and Secondness,
and create a contradiction in the center of the system.
The reason why Jon was misled is that the word 'subject' without
any qualifiers is ambiguous. A Term in Aristotle's syllogisms may
be used in either subject position or predicate position. As a
Term without an indexical word in front (a, some, any, every...),
it would be a predicate, which is a Seme.
But a grammatical subject refers to something that exists (or is
assumed to exist) in the Universe of Discourse. That kind of
subject would be a Second. It would be a Pheme, not a Seme.
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