List, Frank, Ben:
This discussion has very deep roots into the foundations of CSP's
thinking, at least in my opinion. Pragmatically, the situation of the
logic of grammatical terms and it relationships to formal logics is an
unresolved issue, at least from my perspective. CSP's writings open up
several conundrums which deserve inquiry by modern logicians. I
explore examples and draw a novel conclusion wrt the role of units in
term logic.
Why do I feel this way?
Consider the sentence:
The verb "fought" establishes a relation BETWEEN Peter and Harry.
The nature of this relation depends on the identity of BOTH Peter and
Harry.
(It differs from the sentence, "Tom fought Bill", these two sentences
lack a common TERM.)
Consider the following two grammatical issues:
Does this sentence, "Peter fought Harry.", contain a predicate?
Or, is it an example of what CSP refers to as a "conjunctive copula"?
Consider the sentence:
Harry fought Peter and contrast it with it's "twin", Peter fought
Harry.
Does it have the same logical meaning as the first sentence?
Does the distinction between the two sentences convey information?
If not, why not?
If the switch of the order of the terms of this sentence changes the
meaning of the sentence, how is it related to grammar? More broadly,
one can ask the question, what is the role of the concept of ORDER in
grammar in contrast with its roles in logics and mathematics.
NB: contrast this sentence with CSP's usage of the sentence "Cain
kills Abel".
Apparently, CSP is using the term "conjunctive copula" to signify a
form of a proposition such that the two grammatical nouns are of equal
rank. Is this the case or not? What are other possible meanings for
this strange term?
In modern logical terminology, these example sentences can be referred
to as a "two place predicate". This grammatical usage is analogous to
the mathematical usage of n-dimensional spaces such that the
distinctive nature of each predicate is ignored and the meaning of
each variable TERM is taken as an undefined value.
In other words, the material nature of the identity is annihilated in
the n-dimensional logic of mathematics.
Note the difference between this example and CSP use of blank spaces
in a logical proposition of three terms and its extension to a fourth
term:
"___ sells ___ to ___."
"___ sells ___ to ___ for ."
Also, compare this usage with CSP's description of the mapping of an
icon to a rhema in which it compares the generative relation of this
map to chemical radicals!
In my view, a clear and distinct meaning for the relationships among
relatives necessarily requires a clear and distinct cognitive stance
with respect to the identity of the term. [ergo, a "family tree" of
meanings of terms]
In this regard, contrast with 3.420-421 wrt relative rhema. (see The
Existential Graphs of CSP, D. Roberts, p.21-25 for discussions).
The question I would pose to a philosophically-oriented logician is
simple: Does the concept of a propositional term infer a unit of
measure or not? If the concept of a unit is necessary, then is the
meaning of the proposition made distinct by the distinction between
the identities of the logical units, ergo, Peter and Harry?
I can summarize this line of thought by a general proposition for the
logic of terms as units of meaning as in the
"Quali-sign-Sin-sign-legi-sign, icon-index-symbol, rheme, dicisign,
argument" format for logic by CSP, but now expressed in mereological
terms of parts of the whole:
"The union of the units unifies the unity." [ergo, a fight, ergo,
beta-graphs.]
In a metaphysical LOGIC:
"The union of the units unifies the unity of the universe." [ergo,
existence]
Cheers
Jerry
(BTW, the notion of a logical "term" was introduced rather late in
the history of logic, perhaps by Peter of Spain? It was derived from
the notion of "terminals" as parts of a sentence.)
On Nov 8, 2015, at 3:03 PM, Franklin Ransom wrote:
Ben, Gary F,
I like Gary's suggestion about "throwing everything" into the
predicate or into the subject. However, not quite everything gets
thrown in, right? There still needs to be some bare minimum subject
if everything gets thrown into the predicate, and some bare minimum
predicate if everything gets thrown into the subject. I'm not sure
this works.
Ben, I thought to myself of that possibility, namely of erasing the
subject and letting the rhema or term remain. But I don't see how
propositions and arguments can really be like terms in this sense,
since propositions certainly require subjects and arguments do
because they require premisses in the form of propositions.
But, I was looking through Natural Propositions to make sure I
understood the "throwing everything in" idea, and I found a quote
from Peirce that Frederik included in his text that seems pertinent.
NP, p.84, quoted from "Pragmatism", 1907, 5.473:
The interpretant of a proposition is its predicate; its object is
the things denoted by its subject or subjects (including its
grammatical objects, direct and indirect, etc.).
So this says that the subject-term represents the object of the
proposition, while the predicate-term represents the interpretant of
the proposition. We should probably imagine that interpretants don't
all come down to being cases of predicate-terms. But if we consider
that the conclusion of an argument is the argument's interpretant,
and comes in the form of a proposition, and that such proposition
itself can be interpreted by way of its predicate, then propositions
and arguments can ultimately be interpreted as predicate terms. A
term, in this way, as an interpretant, signifies all the characters
of the propositions and arguments leading to it, while denoting, by
way of its determination from such determining signs, the object(s)
of the determining signs. What do you think?
Franklin
On Sun, Nov 8, 2015 at 2:14 PM, Benjamin Udell <bud...@nyc.rr.com>
wrote:
Gary F., Franklin,
Gary, you wrote,
I’m not sure what Peirce meant by saying in 1893 that every
proposition and every argument can be regarded as a term, or what
advantage a logician would gain by regarding them that way.
[End quote]
In "Kaina Stoicheia" III. 4. (EP 2:308), 1904,
http://www.iupui.edu/~arisbe/menu/library/bycsp/stoicheia/stoicheia.htm
[1]
Peirce says:
[....] If we erase from an argument every monstration of its special
purpose, it becomes a proposition; usually a copulate proposition,
composed of several members whose mode of conjunction is of the kind
expressed by "and," which the grammarians call a "copulative
conjunction." If from a propositional symbol we erase one or more of
the parts which separately denote its objects, the remainder is what
is called a _rhema_; but I shall take the liberty of calling it a
_term_. Thus, from the proposition "Every man is mortal," we erase
"Every man," which is shown to be denotative of an object by the
circumstance that if it be replaced by an indexical symbol, such as
"That" or "Socrates," the symbol is reconverted into a proposition,
we get the _rhema_ or _term_ "_____ is mortal." [....]
[End quote]
Somewhere Peirce also notes that a proposition is a medadic term.
Best, Ben
On 11/8/2015 1:48 PM, g...@gnusystems.ca wrote:
Franklin,
I’m not sure what Peirce meant by saying in 1893 that every
proposition and every argument can be regarded as a term, or what
advantage a logician would gain by regarding them that way. But to
me it sounds like a precursor of his (much later) observation that
one can analyze a proposition by “throwing everything” into the
predicate _OR_ by throwing everything into the subject. Maybe his
comment in the Regenerated Logic also works in both directions.
In the Kaina Stoicheia passage, when Peirce says that the
“totality of the predicates of a sign” is “called its logical
_depth_,” and that the “totality of the subjects … of a sign
is called the logical _breadth,_” the sign he is referring to has
to be a proposition, because only propositions include subjects and
predicates. Each subject and each predicate can be called a
“term,” but it’s the breadth and depth of the whole sign, the
proposition, that Peirce is defining here, not the breadth or depth
of the terms (which is what he defined in ULCE). And, as you say,
propositions and arguments also have information (which for Peirce
is the logical product of breadth and depth).
Gary f.
} The birth and death of the leaves are the rapid whirls of the eddy
whose wider circles move slowly among the stars. [Tagore] {
[2]http://gnusystems.ca/wp/ [2] }{ _Turning Signs_ gateway
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