Jerry, Frank, list,
Responses interleaved below.
On 11/9/2015 1:56 PM, Jerry LR Chandler wrote:
[JC] 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.)
BU: They lack a common subject term. They have the predicate term
"fought" in common.
[JC] 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"?
BU: The sentence contains the predicate term "fought".
By "conjunctive copula" Peirce meant "and" connecting propositions.
[From "Kaina Stoicheia"] 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."
[end quote]
For example, "All A is B. All B is C. Ergo all A is C"
becomes "All A is B, *and* all B is C, *and* all A is C."
[JC] 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?
BU: It has a different meaning. I'm not sure what you mean by "logical
meaning." The word "fought" has the same meaning in both sentences.
Taken _/separately/_, each sentences has the logical form 'c fought d.'
Maybe that is what you mean by "same logical meaning." But if they're
taken together, (for example as in "Harry fought Peter or Peter fought
Harry") then one letter needs to be assigned to Peter in both sentences
and the other letter needs to be assigned to Harry in both sentences.
[JC] Does the distinction between the two sentences convey information?
BU: Yes.
[JC] 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?
BU: As syntax.
[JC] 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.
BU: I don't know.
[JC] 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?
BU: No. He means a conjunction of two or more propositions.
[JC] 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.
BU: I don't understand your meaning.
[JC] 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?
BU: I'm not sure what you mean by "propositional term." I don't see how
the concept of proposition involves a unit of measure. Do you mean
counting? Counting of propositions or of something else?
[JC] 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,
BU: I don't know what you're getting at with the idea of thinking of
them as units. They're multiform and often complex.
Best, Ben
[JC] 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:
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