Edwina, Gary R, and Jon AS,
Finally, this thread has reached the dénoument, when the pieces
fall into place and the mysterious knots are untied.
Every so-called Modified EG (MEG) is false. The file brutus.png
shows how to replace MEGs with ordinary EGs that satisfy all of
Peirce's criteria. That method, when explained in Peirce's exact
words, resolves the outstanding issues about what is proper or
ultimate in various contexts.
But first, I'll comment on notes by Edwina and Gary R.
ET
I see Peirce's work as evolving so that... I don't see Peirce
abandoning much at all. And when he finds himself as having clearly
been in error, he tends to explicitly state that along with his
corrected view... Peirce is constantly experimenting; but, in
my opinion, one needn't take an experiment late in his life as
necessarily "abandoning" those undertaken earlier.
I strongly agree. For logic, Peirce began with the 19th c. version
of Aristotelian-Scholastic logic when he was 13 and Boolean logic
a few years later. During the next 60+ years, major breakthroughs
occurred in 1870, 1885, and 1897. After each one, he went through
variations and interpretations. But unless he explicitly corrected
some error, he didn't reject the earlier versions.
The rock-solid stability of classical first-order logic from 1885
makes it the Rosetta Stone for relating Peirce's writings about
logic and semeiotic at every period of his life. It's also essential
for relating his writings to every version of logic from Aristotle
to the present. Peirce explained EGs in several different ways, but
the first-order core, the rules of inference, and the translations
from one version to another never changed.
GR
it seems to me that one remains squarely in the realm of logic as
semeiotic when one is working with EGs because, as now repeatedly
noted: "All that existential graphs can represent is propositions,
on a single sheet, and arguments on a succession of sheets, presented
in temporal succession." CSP
I agree. But logic as semeiotic is the foundation. Without it, you
get word hash with no criteria for evaluation or correction.
GR quoting CSP
CSP: The system of Existential Graphs (at least, so far as it is
at present developed) does not represent every kind of Sign. For
example, a piece of concerted music is a sign; for it is a medium
for the conveyance of Form. But I know not how to make a graph
equivalent to it.
In CP 2.643, Peirce wrote "the various sounds made by the instruments
of an orchestra strike upon the ear, and the result is a peculiar
musical emotion, quite distinct from the sounds themselves."
As I showed with the graph of a musical score, it's easy to map
the notes from a score to any notation for FOL. But the emotions
produced by Jascha Heifetz and the kid next door are very different.
The musical score can't explain the emotion, but it can be useful
as a map for analyzing the performance. Perhaps the note at bar 17,
as the kid played it, was grating, and the transition to the next
note was abrupt, off tempo, and slightly flat. Yet a professional
violinist, in some context, might deliberately play a note that way.
Context and purpose are critical for interpreting anything.
Music illustrates the distinction between the discrete subjects and
predicates in the logic, and the continuous sound, which you or your
cat may perceive as streams of quasi-subjects and quasi-predicates.
(A cat that likes music: http://minervaclassics.com/harpcat1.jpg )
JAS
In Peirce's "proper" or "ultimate" analysis of Propositions, "pure"
predicates are the only predicates. Anything that refers to content
in the universe of discourse--i.e., anything that can only be
understood by an interpreting Quasi-mind that has had previous
Collateral Experience with it--is a Subject; it belongs to the
Object of the Proposition.
No. That claim is false for many reasons. First of all, The words
'proper' and 'ultimate' are both relative terms that depend on context.
And the contexts for those two words have nothing in common.
CP has 124 occurrences of 'proper'. Some of them narrow the meaning
of a word, such as 'proper name' or 'history proper'. The others
occur with words like 'for' or 'with' that refer to some context.
For example, consider the chair you're sitting on. Sitting is its
*proper* use. But you could also use it for many other purposes.
You might stand on it to change a light bulb, or you might use it
to hold some books you're putting on a shelf.
The "ultimate" analysis of the chair depends on whether you're talking
with a carpenter, a chemist, or a nuclear physicist. The first two
might give you useful advice for some purposes, but not for sitting.
If the physicist starts talking about quarks and leptons, that might
be ultimate, but it's not proper for any use of a chair.
As for the quotation, "when we have carried analysis so far as to
leave only a continuous predicate, we have carried it to its ultimate
elements" -- that kind of "ultimate" is rarely proper for any useful
application.
To illustrate that point, let's turn to the MEGs. Each one has
a teridentity or a ligature of multiple teridentities, which falsely
state that some wildly different things are identical. For example,
the MEG for "Brutus kills Caesar" has a teridentity, which states
that there is a single entity in the universe of discourse, which
happens to be identical to Brutus, Caesar, and the act of killing.
That proposition is false.
The attached brutus.png shows how to generate correct EGs by
following Peirce's directions. At the top is the simplest way to
translate "Brutus kills Caesar" to the EG, Brutus———Kills———Caesar .
This EG has a dyad -kills- with two unattached pegs, and two logical
subjects, each with its own line of identity: Brutus——— and Caesar——— .
The second EG in brutus.jpg has one more logical subject, which is
the gerund 'killing' (a nominalization) with a line of identity that
is also attached to a triad named Rel. I'm using the name Rel for the
pure predicate that Peirce defined in NEM 3:886, 3rd line from the top.
As Peirce said, Rel is a pure predicate. With Rel, the second EG states
"Brutus stands in the relation 'killing' to Caesar."
All four EGs state the same proposition. But the roles of Brutus and
Caesar in the first and second are shown only by their position on the
left or the right. To show the roles explicitly, linguists often use
"case relations" or "thematic roles", such as Agent and Patient in
EG #3. In that EG, the monad Killing- is attached to a teridentity,
which is attached to two dyads, -Agent- and -Patient-.
Those dyads are linguistically primitive, but they are not logically
"pure". To "purify" the EG, they can be converted to the monads
Agency- and Patiency- by nominalization (hypostatic abstraction).
Then those monads would be connected to the pure predicate Rel
in the fourth EG at the bottom of brutus.png.
In summary, all four EGs in brutus.png state exactly the same
proposition as the English "Brutus kills Caesar." the first EG has
two logical subjects, and one impure predicate (which represents
content in the UoD). The second has three logical subjects and one
pure predicate named Rel. The third has three logical subjects and
two predicates that express linguistic content: -Agent- and -Patient-.
The fourth has five logical subjects and two pure predicates.
Re ultimate analyses: The second and fourth EGs are ultimate in the
logical sense of having only pure predicates. The third is ultimate
in the linguistic sense of showing the case roles. The fourth is
ultimate in both the logical sense and the linguistic sense.
Re proper analyses: That depends entirely on context. Note the
word 'proper' in NEM 3:885: "the proper way in logic is to take as
the subject whatever there is if which sufficient knowledge cannot
be conveyed in the proposition itself, but collateral experience on
the part of its interpreter is requisite."
That quotation mentions the experience of the interpreter. That would
be content in the Universe of Discourse, which is never expressed in
pure predicates. And the purpose of that conversion is relevant only
in the context of communication with some interpreter.
Conclusions:
1. Although all four analyses state the same proposition, they would
be "proper" for different purposes. The first EG is probably the
most useful for ordinary communication and reasoning. The second
EG would be useful when it's necessary to refer to the act of
killing: "Some senators thought that the killing was justified."
But the third and fourth would be "proper" only for a theoretical
study in logic or linguistics.
2. All the examples in this note and in my previous note show the
clear distinction between logical subjects and predicates: subjects
always have a line of identity with a free end that had previously
been attached to some peg of a predicate; and predicates always
have one or more unattached pegs.
3. The Modified EGs are false, but most of them could be converted to
correct EGs by using the pure predicate Rel. But 'to' and 'from'
are not pure predicates because they refer to something in the UoD.
The preposition 'to' could be nominalized as Direction-toward, and
'from' could be Direction-away.
4. As Peirce experimented with new ways of stating his ideas, his newer
terminology remains consistent with the older versions, unless he
explicitly corrected them. But sometimes the newer terms are more
general than the older ones. It's essential to check the examples
and definitions to determine how the old and new terms are related.
5. Points #2 and #4 imply that the earlier words 'quasi-predicate' and
'quasi-subject' apply to the nonsymbolic icons or images when they
are used as predicates or subjects. Although Peirce did not discuss
them in connection with EGs, he used the word 'index' in a way that
is similar to the use of an EG line of identity. A quasi-predicate
would have something like an unattached peg; a quasi-subject would
have something like an index that can point to a peg.
6. Point #5 implies that the "widening" of the word 'rheme' to 'seme'
in seme/pheme/delome would include both quasi-predicates and logical
predicates. It's also likely that pheme would also be widened to
include propositions stated by images combined with something that
served as an index.
7. The sharp distinction between subjects and predicates implies that
a seme could never refer to a logical subject or a quasi-subject.
Since Peirce had frequently used the word 'subject', it's unlikely
that he forgot to mention it as the "widening" of the word 'seme'.
But it's quite likely that he forgot the word 'quasi-predicate',
which he had only used in one MS, several years earlier.
Some implications of these conclusions:
JAS
The "proper way" is Peircean, not Aristotelian,
The method of replacing an arbitrary verb that connects the subject
and predicate with the copula -is- was specified by Aristotle, and
it was taught in every textbook in the 19th c. CP has over 300
occurrences of "Aristot" from every period of Peirce's writings.
Peirce certainly added new revisions and extensions. But Peirce
and all his readers had studied Aristotle. According to his ethics
of terminology, he always used Aristotle's terminology in the same
way it had been translated to Latin and then to English.
JAS
The trichotomy that had to be "much widened" was
term/proposition/argument;
Note the first sentence of CP 4.538: "A familiar logical triplet
is Term, Proposition, Argument." Familiar for his readers always
meant Aristotelian logic as taught in every 19th c. textbook.
That sentence also had a footnote, presumably by Hartshorne & Weiss,
which added the synonyms rheme and dicisign. Since the editors
understood Peirce's frequent references to Aristotle, I trust their
judgment in writing that footnote.
The English word 'term' is derived from the Latin 'terminus',
which refers to both "ends" of an Aristotelian proposition:
the subject and the predicate.
From slide 15 of http://jfsowa.com/talks/aristo.pdf :
The four sentence patterns:
Universal affirmative: Every S is P.
Particular affirmative: Some S is P.
Universal negative: No S is P.
Particular negative: Some S is not P.
In syllogisms, the letter S represents the subject term; P,
the predicate term; and M, the middle term. All three letters
represent exactly the same words or phrases.
But -- and this is a huge **BUT** -- the subject term is always
preceded by the word 'every', 'some', 'no' (or something equivalent),
and the predicate never has those words. When translated to an EG,
every subject term has a line of identity, and every predicate term
has the equivalent of an unattached peg.
If you want to understand Peirce precisely, you must study the
sources that he studied *and* the sources he assumed that his
audience or readers had studied. It also helps to study modern
logic, since many logicians from the 20th and 21st c. have also
had good ideas that help clarify some of the issues.
JAS: The additional step that I am taking is to recognize...
JFS: If Peirce did not explicitly take that step, don't put words
in his mouth.
JAS: But I did not put words in his mouth; I said quite plainly
that I was taking an additional step.
The phrase 'the additional step' is a claim that it's implied by
or justified by something Peirce wrote. If that step seems to be
clear or obvious, there may be some reason why Peirce never took it.
There are two possibilities: (1) he didn't find that step useful
or relevant, or (2) you may have missed some relevant obstacle.
Peirce never wrote the triad subject/proposition/argument, and it
contradicts both the Aristotelian term/proposition/argument and
his own rheme/dicisign/argument. By repeating it, you're claiming
to know what Peirce would have or might have said. That puts words
in Peirce's mouth that he would have spit out in disgust.
At the end of this note are three quotations, which I have analyzed
in whole or in part above. I'm including them here just to emphasize
that they are totally irrelevant to the claims about the words 'proper'
and 'ultimate' and to the claims about subjects and predicates.
John
______________________________________________________________________
CSP: I regard everything to which the assertion relates and to
which reference can be removed from the predicate, although what is
referred to be a quality, relation, state of things, etc. as a Subject.
(R 611)
CSP: But the proper way in logic is to take as the subject whatever
there is of which sufficient knowledge cannot be conveyed in the
proposition itself, but collateral experience on the part of its
interpreter is requisite ... The result is that everything in a
proposition that possibly can should be thrown into the subjects,
leaving the pure predicate a mere form of connection ... (NEM 3:885)
CSP: When we have analyzed a proposition so as to throw into the
subject everything that can be removed from the predicate, all that it
remains for the predicate to represent is the form of connection between
the different subjects as expressed in the propositional form ... when
we have carried analysis so far as to leave only a continuous predicate,
we have carried it to its ultimate elements. (SS 71-72)
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