Copulant?

Ben, List:

Thanks for the interesting post on the notion of "copulant".

Perhaps you can give your views on the origin of this term.

The Mac dictionary gives the definition of copula as derived from two  
parts,

co  as together

+ apere, fasten.

The grammatical usage of the term "copula", as I understand it, is to  
fasten together the subject with whatever.
A copula does not require a property, or does it?

Obviously, the term copulate as for sexual intercourse, also makes  
sense in this historical setting.

When Peirce writes:

"The copulants are likewise indispensable and have the property of  
being a continuant"

several meanings are possible,

At the moment I think that he is using the term copulant not in the  
sense of the verbal form, but rather as some sort of ill - defined  
extender of the sentence.  Concomitantly, the usage of the term,  

Re: Copulant?

Ben, List:

>[Jerry] Thanks for the interesting post on the notion of "copulant".

You're welcome. Let me take the opportunity to immediately say that, where I said that I think that there are
pure copulants, and pure symbols, I have to retract the part about pure symbols. I would need a definition
of pure symbol, so that I could say whether there are pure copulants which aren't pure symbols or vice
versa. Even if I came up with a plausible definition of "pure symbol," I still couldn't readily argue that
it's what Peirce thought or would have thought.

>[Jerry] Perhaps you can give your views on the origin of this term.
> The Mac dictionary gives the definition of copula as derived from two parts,
> co  as together
> + apere, fasten.
> The grammatical usage of the term "copula", as I understand it, is to fasten together the subject with whatever.
> A copula does not require a property, or does it?

In ordinary grammar, words like "is" and "was" are the copula. If being is a property, then still it's not a
property in the usual sense. Anyway, if by "property" one means quality, attribute, modification,
accident, then being is not considered a property. I don't know whether a word like "seems" in a sentence
like "It seems blue" is typically considered a copula from a grammatical viewpoint, but I wouldn't be
surprised if there's been disagreement about it. In a case like "seems" the predicate "blue" is called the
"predicate complement" just like in the case of words like "is." 

Peirce says that the copulant sign is neither descriptive nor denominative and that it can, on the other
hand, incorporate descriptives and denominatives. If the resultant proposition is universal
("Ax[Sx-->Px]"), then as a whole the proposition is a copulant. If the resultant proposition is
particular ("Ex[Sx&Px]"), then as a whole the proposition is a descriptive. I'm not sure of his view on
singular propositions but by that pattern they would not be copulants. And a copulant, says Peirce, can be
found in the descriptive and drawn out -- the "and" in "Ex[Sx&Px]" for instance, it rains *and* hails, it

Re: Copulant?

Dear Ben, Jerry--

For me the copula expresses the ontological relationship of the subject and 
predicate of a proposition.  This relationship can be of three types --  
identity, otherness or equivalence.   Something can only be identical with 
itself or its own form -- with all else it is both irreducibly other and in 
some way equivalent or continuous in meaning.  For me time (and thought) 
come closest to examples of pure equivalence,  space (inertia and will) of 
pure otherness and  form (organization or feelings) of pure selfness.  I 
think this is close to what Peirce had in mind as well.

For me the expression "pure symbol" is ambiguous.  I don't think there are 
pure symbols in the sense that a symbol (however pure) does not include the 
iconic and indexical functions which are part and parcel of all triadic 
relations and hence of all signs or representations.   OTOH if by pure one 
has in mind a practical question as to what degree a particular sign is used 
symbolically (i.e. depends solely upon imputation of it's connotative and 
denotative functions)  as opposed to actual similarity of form (as does an 
iconic sign) or  actual spatial-temporal correlation (as does an indexical 
sign) than I would say there are indeed relative degrees of symbolic purity 
among signs.  There are analogous ambiguities that arise in the discussion 
of iconic signs and "mere" similarities -- or indexical signs and mere 
correlations.

I suspect that all of the so called "things" that populate the potential, 
actual or representational world we inhabit are themselves forms of one of 
these three fundamental and irreducible modes of being or relations.   What 
we call "things" are in reality representations of forms actualized in 
otherness.   I do believe that things exists apart from our representation 
of them, but I'm not convinced we have yet ascertained the fundamental, 

Re: Copulant?

Jerry, list,

I should correct myself a bit. 

1. I said: "The pure copulant marks the point in analysis where further analysis finds no more descriptives
or denominatives, but only further copulants, expressing further logical relations, expandible
indefinitely and tautologously, thirdness irreducible to secondness or firstness, and bringing into
view an end of that vein of inquiry, since one there sees, with the pragmatic or "third" degree of clarity,
that in the final analysis all would agree that there's nothing left but logical relations further
expandable infinitely and tautologously. There's nothing left whereby to explicate the term or
proposition which one began analyzing."

I should say that there's nothing further to find whereby to explicate either the original term or _the
continuant (the pure copulant) itself_. Arriving at a continuant is like arriving at a repeating decimal
-- expand it as much as you like, still you'll find nothing new. 

2. Sorrentino used the word "copula" in mentioning the copula. I think that it amused him that a word
suggestive of sex happens to denote words which freeze the prose.

3. I said : "One would need to squeeze a copulant out of '...transact...' by saying something like '...are
transactors...'. 

I didn't mean to suggest that that completed the analysis. As to "creating water," this might be analyzed
into something involving "...causes water." Peirce regards "causes" as a copulant. 

4. I said, "They're intension-switchers or intension-transformers". That's probably not precisely
correct, since predicates can be defined extensionally and in many abstract situations one does define
them extensionally, but it's at least something like whatever is correct. It's one thing to consider the
attribution/distribution/frequency etc. of properties/qualities/predicates and it's another
thing to consider structures of identity and otherness among subjects (objects).  There's a distinction

RE: reality/unreality of species

RE: [peirce-l] using the “Y” with Peirce¨s “ground” in the center

AW: [peirce-l] RE: [peirce-l] using the “Y” with Peirce¨s “ground” in the center

Re: Copulant?

Dear Jim

>[Jim] For me the copula expresses the ontological relationship of the subject and predicate of a
proposition.  This relationship can be of three types --  identity, otherness or equivalence.   

The copula as a relationship of identity is not between subject and predicate but instead between two
subjects which are really one. Otherness is non-identity between subjects, unless by "otherness" you
mean something broader, like "elseness" or "notness."  We often express identity and otherness by
polyadic predicates. However, identity and otherness are not qualities or attributes in any usual sense.

If what you have are identity, non-identity, and equivalence, then what about non-equivalence? You
really have four there. However, you seem to be thinking more about continuity than equivalence, and it
might be better to say "continuity" instead of "equivalence." And I suspect that by "otherness" you mean
something broader than non-identity of subjects.

>[Jim] Something can only be identical with itself or its own form -- with all else it is both irreducibly
other and in some way equivalent or continuous in meaning.  For me time (and thought) come closest to
examples of pure equivalence,  space (inertia and will) of pure otherness and  form (organization or
feelings) of pure selfness.  I think this is close to what Peirce had in mind as well.

It's like you're trying to turn Peirce's "quality, reaction, representation" into a trichotomy where one
can see "self, other, mediation," which seems simpler and where self and other appear as extremes between
which mediation mediates. But in speaking of "identity" you seem to be characterizing firstness from a
kind of secondness viewpoint. With Peirce's conception of quality, you get an idea of WHAT it is that has
this natural selfness and self-identity. And it's a vagueness rather than sheer identity, sheer
identity opposed to sheer otherness like black and white squares on a checkerboard.

>[Jim] For me the expression "pure symbol" is ambiguous.  I don't think there are pure symbols in the sense
that a symbol (however pure) does not include the iconic and indexical functions which are part and parcel
of all triadic relations and hence of all signs or representations.   OTOH if by pure one has in mind a
practical question as to what degree a particular sign is used symbolically (i.e. depends solely upon
imputation of it's connotative and denotative functions)  as opposed to actual similarity of form (as
does an iconic sign) or  actual spatial-temporal correlation (as does an indexical sign) than I would say
there are indeed relative degrees of symbolic purity among signs.  There are analogous ambiguities that
arise in the discussion of iconic signs and "mere" similarities -- or indexical signs and mere correlations.

Going by Peirce's characterizations of pure icon and nearly pure index, a pure symbol would be one that
signifies via the effect which it will have on its interpretant without conveying information or coming
as a compulsory directive fact. By itself, a word like "and" seems not to convey information like "red" or
to come as a compulsory fact (except in compelling attention to the signs conjoined by it), and, maybe, as
with the index, there is only the "nearly pure" version. In any case it's hard to think how even the most
nearly pure symbol could work without getting involved more mediately with lots of information and
facts. So it seems like you can have (at least nearly) pure symbols as long as you don't mean symbols
divorced and utterly remote from all involvement with icons and indices. But these are the same lines of
thought as are involved in thinking about Peirce's pure copulant, the continuant, with its tautologous
expansion, canceling out of colors, like Ahab's pasteboard mask or like Hephaistos's chains thrown by
the gathered gods on his wife Aphrodite and Ares in (pun intended) copulation (A & A were ashamed at being
caught, and their fellow Olympians mercilessly laughed and ridiculed them). The problem still remains,
what would be the difference between a pure copulant and a (nearly?) pure symbol? Peirce was going to the
trouble of working out systematic distinctions, and he would take an equality between those two kinds of
sign as meaning a mistake somewhere -- how could pure versions of symbol and copulant be the same thing if
symbol and copulant are defined differently?

>[Jim] I suspect that all of the so called "things" that populate the potential, actual or
representational world we inhabit are themselves forms of one of these three fundamental and
irreducible modes of being or relations.   What we call "things" are in reality representations of forms
actualized in otherness.   I do believe that things exists apart from our representation of them, but I'm
not convinced we have yet ascertained the fundamental, potential forms of actuality.

Incorrigible Platonist! Seeking a subtler form for your Platonism? More seriously speaking, I think that
what Peirce does is to try to make room for various tendencies, including your tendency and the actualist
tendency which says, "find the forms? The actuality finds _you_, its blind compulsion breaking in on you,
often whether you like it or not."

>[Jim] Nothing original or perhaps even useful in my formulation, but each time I read one of Ben's
interesting explorations I'm inspired to make another go at it myself.  Nor do I claim mine is an accurate
account of Peirce's position  -- merely my imperfect and idiosyncratic interpretation.

>[Jim] Thanks to you both for a stimulating discussion.

Thanks for your stimulating response. And I got to play some more with the copula pun.

Best, Ben

---
Message from peirce-l forum to subscriber gspp-peirce-l <at> m.gmane.org

Re: Copulant?

Ben,  List:

Thank you for your thoughts; you always bring an element of surprise  with your writings - which nearly always stimulates new thoughts and often a chuckle or smile.

Your latest post was no exception.  Happily,  I found it less persuasive than you usually are.

First, I am perplexed by the POSSIBILITY of impure symbols.

As a mark or sign, a symbol simply is a scribbling on one media or another - a mark may be scribbled by a painter, a poet, a mathematician or a chemist - as an expression of sentience.  It is not necessary that the mark have any meaning or signification.

I find no identifiable sentience that that motivates a distinction between one mark and another.  Perhaps I am rejecting the grammatical notion that all nominates may take an adjective with such talk, but I think not.  For example, such statements as "The short mark was shorter than the middle mark and the middle mark was shorter than the longest mark" is a perfectly reasonable statement in my mind.  In addition, it is logically crisp and decisive.  Perhaps you have some examples that might help me in the search for sentience?

[Jerry] Perhaps you can give your views on the origin of this term.

The Mac dictionary gives the definition of copula as derived from two =

parts,

co  as together

+ apere, fasten.

The grammatical usage of the term "copula", as I understand it, is to =

fasten together the subject with whatever.

A copula does not require a property, or does it?

{Ben] In ordinary grammar, words like "is" and "was" are the copula. If being =

is a property, then still it's not a property in the usual sense. =

Anyway, if by "property" one means quality, attribute, modification, =

accident, then being is not considered a property.

The concept of fastening things together can include such verbals as "is" or "was".

But the question I seek to explore is the other direction of implication, that is,

Is the concept of fastening together something more than the concept of containment in the sense of Leibniz, 

or the sense of membership as in set theory / Russell.

For example, consider the sentences:

Jim wrestled Bill.

The orgasms were simultaneous.

in terms of the definition of a predicate - that is, from the roots, 

prae, 'beforehand' and 'dicare' make known.

The roots of the term 'predicate' are vital in the predicate logic of sets.

Is Bill a property of Jim?

Is her orgasm a property of his orgasm?

The existence of the state of being fastened together, being copulated, seems rather different from the concept of presupposing that something was said beforehand, that is, in Leibniz's sense, the container and the contained.

Peirce says that the copulant sign is neither descriptive nor =

denominative and that it can, on the other hand, incorporate =

descriptives and denominatives

Ben, when you write, 

When you write: 

. If the resultant proposition is =

universal ("Ax[Sx-->Px]"), then as a whole the proposition is a =

copulant. If the resultant proposition is particular ("Ex[Sx&Px]"), then =

as a whole the proposition is a descriptive. I'm not sure of his view on =

singular propositions but by that pattern they would not be copulants. =

And a copulant, says Peirce, can be found in the descriptive and drawn =

out -- the "and" in "Ex[Sx&Px]" for instance, it rains *and* hails, it =

rains *concurrently with* its hailing, it rains *concurrently with its =

concurrence with* hailing, etc.

the logical symbolism presupposes set theory.  That is fine, but I am interested in precisely how and why chemical notation does not follow the rules of set theory.  My aim is give an explication of the difference between a predicate and a copula in ordinary grammar.

I am uncertain by what you mean when you write: 

Exploring a bit, I find that not all =

logical relations seem to expand, upon analysis, to such simple =

right-out-of-the-gate repeaters, but analysis does lead to their =

expansion to regular tautologous repetitions eventually. The infinite =

expandibility into tautologous repetition is the mark of the continuant.

By expansion, do you mean extension to more terms in the same proposition? 

(For example, one object and multiple, perhaps unbounded, number of properties / relations?)

Or, do you mean expansion as more statements of propositions?

(For example, composing a sorite from an unbounded number of propositions?)

Or, do you mean the regularity of expansion by iterative or repetitive processes?

(For example, a continued fraction?)

{Ben] What comes to =

light as the copula grows and becomes complicated are logical relations =

(to which I for my part would add probabilitative, information, etc., =

relations).=20

Exactly!  But how does this possibility distinguish between copula and predicates?

We are on the same wavelength - what happens when increases occur? emergences? or repetitions?

When Peirce writes:

"The copulants are likewise indispensable and have the property of =

being a continuant" several meanings are possible,

At the moment I think that he is using the term copulant not in the =

sense of the verbal form, but rather as some sort of ill - defined =

extender of the sentence. Concomitantly, the usage of the term, =

continuant, appears to be not in the mathematical sense of continuity, =

but rather also as the sense of extending the sense.

At this point the picture becomes very fuzzy when I try to decipher =

what a "pure copulant" might be such that it is not explicable.

I think that Peirce really is alluding to the grammatical copula. He =

mentions subjects and predicates -- using the words "subject" and =

"predicate" -- in connection with the copulative (The Essential Peirce =

Volume 2, Page 485, in Peirce's Letter to Lady Welby December 25, 1908).

Yes, I have re-read this letter several times.  It is one source of my concerns.

=

[Ben] In grammar, a copula is a way of predicating a predicate of a subject.

Well, could be. Would it not also be true that:

'In grammar, a predicate is a way of copulating a subject with it properties?"

The analysis of the copulant either finds it to be a pure copulant or =

analyzes it down to some combination of pure copulant with descriptives =

&/or denominatives.

???

If things are fastened together, they are fastened together.  

Perhaps one could substitute the concept of the completed copulation for the notion of purity?

The pure copulant marks the point in analysis where =

further analysis finds no more descriptives or denominatives, but only =

further copulants, expressing further logical relations, expandible =

indefinitely and tautologously, thirdness irreducible to secondness or =

firstness, and bringing into view an end of that vein of inquiry, since =

one there sees, with the pragmatic or "third" degree of clarity, that in =

the final analysis all would agree that there's nothing left but logical =

relations further expandable infinitely and tautologously.

I wish I could understand what it is that you wish to communicate with this sentence.

In particular, if things are completely fastened together (mathematicians call such an object a complete graph)

then the totality of possible relations exist.

There's =

nothing left whereby to explicate the term or proposition which one =

began analyzing.

[Ben] One has already squeezed out of it all the denominative =

seeds and all the descriptive juice and has settled into a repetitious =

logical sequence which just continues on and on.

I love this sentence.  It would do nicely as a substitute for my breakfast O.J.      

One has reached the =

continuant, the pure copulant. (That's the case although, in turn, one =

may have at that point not yet squeezed all the implicit copulants out =

of the extracted denominatives and descriptives).

Is it necessary to intertwine the notions of completeness with the notion of purity, or is a matter of taste? 

I disagree with Peirce's association of logical relations with the =

universal quantity per se -- I would associate them with a logical =

quantity which is essentially the universe of discourse, the total =

population, the gamut, etc., _as_ a logical quantity, but it lacks a =

technical name. But I very much hold with associating =

predicate-formative and propositional-formative functors such as "not" =

and "and" (e.g., from "red," the "not" forms the predicate "not-red") =

with the kind of copula which joins subject to predicate. This is about =

attribution as opposed to the attribute -- the predication as opposed to =

the predicate -- etc. It is about a kind of transformation of the =

predicate (e.g., from "red" to "not-red") which does not end up =

referencing the same quality or particular kind of the same quality -- =

it is not about adverbs of manner or other ways of "further modifying" a =

same qualitative predicate. Instead it's about transformations of the =

predicate as marking a division of a universe of discourse, switching, =

for instance, in the case of "not" from that which is red to that which =

is not red. I mean, "not red" is not a species of "red." "Probably red" =

is not a species of "red." And so on. I think it can also be a "switch" =

to a distributional frequency, amount of distinctness (information), =

etc. They're intension-switchers or intension-transformers. Ultimately, =

in my view, a major division of research, usually regarded as "applied" =

mathematics but also simultaneously as deep or nontrivial mathematics, =

is about these sorts of relations -- the deductive mathematical theories =

and areas of logic, information, probability, optimization, and whatever =

else deals with such "valuations" of propositions, predicates, etc. and =

draws deductive conclusions, particularly non-reversibly deductive =

conclusions. (Deductive math of info theory, however, for historical =

reasons, has considerable overlap into abstract algebra and so is less =

likely to fit entirely within the foregoing characterization.) =20

Ben - I am not yet ready to tackle the semantic fillers of the alphabetic forms of symbolic logic.

Perhaps we can return to this paragraph at a latter date.

[Jerry] In the previous exchange on the usage of the symbol "Y" and the =

usage of the term "Cenopythagorean" as alternative forms of firstness, =

secondness and thirdness, the possibility of a further abstraction =

emerged.  For example, the usage of the "y" symbol may suggest the =

potential coherence of man, mind and nature in a true statement / =

proposition.  But this usage of the terms copulant and continuant =

appear, in my mind, to suggest otherwise.

I don't know, it's quite vague to me what you have in mind there.

This may not be helpful to you, but I am thinking of natural relations within natural Porphyrean trees.

(A "y" is a component of a tree.  Trees can be viewed as "y"s composed together.)

[Jerry] This distinction is important for the logic of chemical =

sentences. I would note that chemical discourse depends on at least two =

uses of the concept of a verb.

One usage is to connect the name to the properties:  Water is ice, =

liquid or steam.

The second usage is to connect the structures to one another, Hydrogen =

and oxygen transact to create water.

Heretofore, I have associated the prior statement as a predication =

that associated the nomination with the exact properties of the =

nominate.

The later statement associated the parts with the exact structure of =

the whole in the sense of to fasten together, a copulation of the two =

elements to create a new nominate.

Not every verb is a copula or a copulant.

Huh?

I thought that was what I was communicating with my two examples from chemistry.

One example is a predication.

The nomination, water, prae speaks of the essential forms, the necessary attributes of water, ice, liquid and steam.

The other is a perplex copulation of parts into a whole by fastening them together.

Or, have I misread your intent?

One would need to squeeze a =

copulant out of "...transact..." by saying something like "...are =

transactors..." The "are" is a copulant, and in the universality of the =

proposition is the copulance of the proposition as a whole.

But, 'trans' is the relation between this and that, here or there, transfer, transport, etc.

Is it the implication of a an exact dynamics that you find troublesome? 

Your questions and comments are interesting as always!

Thanks.  I hope this response does not bore you! 

Cheers

Jerry 

---
Message from peirce-l forum to subscriber gspp-peirce-l <at> m.gmane.org

Sale at Indiana U. Press & latest Transactions