Ed,
I used the verb 'give' as an example of an obligatory triad: any act of giving must have three participants. The mapping to three dyadic relations is a purely syntactic transformation that replaces the verb "give" with a gerund 'giving' and three linguistic dyads. But the node labeled 'giving" (in any notation, linear or graphic) still has three links. If you delete any of those three, the semantics is incomplete.
As another example, consider the sentence "I dropped the box on the floor". The verb 'drop' happens to have three connections, but only two are obligatory. You can replace that sentence with two semantically complete sentences: "I dropped the box" and "the box landed on the floor."
In that example, each sentence, by itself, is syntactically and semantically complete. The verb 'give' is semantically an obligatory triad; there must always be three participants. But the verb 'drop' only requires two participants for a complete sentence. The verb 'land' only requires one -- the sentence "The plane landed" only has one participant for the verb to make a syntactically and semantically complete sentence.
C. S. Peirce observed that relations that express intentions (by humans or other sentient beings) require a third participant who has or had the intention that caused or explained the dyadic relation that links the other two.
For example, an act of giving may be performed by sending a package in the mail. But the package is not gift unless it contains a card that explains why it was sent. That obligatory Thirdness is essential to show the intention.
John
----------------------------------------
From: "Edward Barkmeyer" <ebarkmeyer(a)thematix.com>
John's last paragraph:
JFS> For example, "A gives B to C" my be replaced by three dyads and a monad: "Giving(X) and Agent(X,A) and Patient(X,B) and Recipient(X,C)". In this translation of an obligatory triad to a monad and three dyads, the act of giving X has three parts that must occur at the same time.. You can't perform the different dyads in separable actions.
This is the standard dyadic form for the description of an arbitrary 'event'/'situation'. The event is an instance of some class of events/situations, which is usually a separate monadic predicate. In John's example, Giving(X). Each of the 'roles' in the event (active or passive) is a dyadic predicate of the form <role>(<event>, <participant>). And, not coincidentally, this is exactly the 5th normal form rendering of a complex relation (which is a DBMS representation of a 'situation').
Cf: C.S. Peirce • On the Definition of Logic
https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-on-the-definition-of-l…
Selections from C.S. Peirce, “Carnegie Application” (1902)
<QUOTE CSP>
No. 12. On the Definition of Logic
Logic will here be defined as formal semiotic. A definition of a sign will be given
which no more refers to human thought than does the definition of a line as the place
which a particle occupies, part by part, during a lapse of time. Namely, a sign is
something, A, which brings something, B, its interpretant sign determined or created
by it, into the same sort of correspondence with something, C, its object, as that
in which itself stands to C. It is from this definition, together with a definition
of “formal”, that I deduce mathematically the principles of logic. I also make a
historical review of all the definitions and conceptions of logic, and show, not
merely that my definition is no novelty, but that my non-psychological conception
of logic has virtually been quite generally held, though not generally recognized.
(NEM 4, 20–21).
No. 12. On the Definition of Logic [Earlier Draft]
Logic is formal semiotic. A sign is something, A, which brings something, B,
its interpretant sign, determined or created by it, into the same sort of
correspondence (or a lower implied sort) with something, C, its object,
as that in which itself stands to C. This definition no more involves
any reference to human thought than does the definition of a line as
the place within which a particle lies during a lapse of time.
It is from this definition that I deduce the principles of logic
by mathematical reasoning, and by mathematical reasoning that,
I aver, will support criticism of Weierstrassian severity, and
that is perfectly evident. The word “formal” in the definition
is also defined. (NEM 4, 54).
</QUOTE>
Reference
=========
Charles S. Peirce (1902), “Parts of Carnegie Application” (L 75), published in
Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce,
vol. 4, 13–73. Online ( https://arisbe.sitehost.iu.edu/menu/library/bycsp/L75/l75.htm ).
BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Jon, list
A few comments on your outline of the Sign. I think one has to be
careful not to set up a Saussurian linguistic dyad.
I refer you to Robert Marty's '76 definitions of the Sign' - which
are quotes from Peirce's work. I'll refer to several of them:
"Genuine mediation is the character of a Sign. A sign is anything
which is related to a Second thing, its Object, in respect to a
Quality, in such a way as to bring a Third thing, its Interpretant,
into relation to the same Object.....1902. 2.92
And '"A definition of a sign will be given which no more refers to
human though that does the definition of a line as the place which a
particle occupies, part by part, during a lapse of time. 1902. NEW IV
pp 20-2
And 'Every sign stands for an object independent of itself, but it
can only be a sign of that object in so far as that object is itself
of the nature of a sign or thought. 1903. CP 1-53
"A sign is plainly a species of medium of communication' 1905. MS283
p 125
"Signs ...are triadic" 1909 6.344
"A sign is an object which stands for another to some mind"
I have several points.
First - Peirce uses both the term 'Representamen' for this mediative
process - as well as the term 'sign'. Second- He also understands the
'sign' as a complete triadic process such that this irreducible triad
can be considered an existential entity. That is, the full triad, the
Sign, has three correlates or relational parts: ;that in itself, that
with the object; and that with the interpretant.
A full active triad, in my view, can be understood in many ways: I'd
consider a cell as a full active triad, and thus, as both a Sign [the
triad] and engaged in that triadic mediative process using the
internal representamen/sign to carry out this mediation.
Edwina
On Wed 01/12/21 11:45 AM , Jon Awbrey jawbrey(a)att.net sent:
Cf: Triadic Relations • 3
https://inquiryintoinquiry.com/2021/11/08/triadic-relations-3/ [1]
Examples from Semiotics
=======================
The study of signs — the full variety of significant forms of
expression —
in relation to all the affairs signs are significant “of”, and
in relation
to all the beings signs are significant “to”, is known as
“semiotics” or the
theory of signs. As described, semiotics treats of a 3-place
relation among
signs, their objects, and their interpreters.
The term “semiosis” refers to any activity or process involving
signs.
Studies of semiosis focusing on its abstract form are not concerned
with every concrete detail of the entities acting as signs, as
objects,
or as agents of semiosis, but only with the most salient patterns of
relationship among those three roles. In particular, the formal
theory
of signs does not consider all the properties of the interpretive
agent
but only the more striking features of the impressions signs make on
a
representative interpreter. From a formal point of view this
impactor
influence may be treated as just another sign, called the
“interpretant
sign”, or the “interpretant” for short. A triadic relation of
this type,
among objects, signs, and interpretants, is called a “sign
relation”.
For example, consider the aspects of sign use involved when two
people,
say Ann and Bob, use their own proper names, “Ann” and
“Bob”, along with
the pronouns, “I” and “you”, to refer to themselves and each
other. For
brevity, these four signs may be abbreviated to the set {“A”,
“B”, “i”, “u”}.
The abstract consideration of how A and B use this set of signs
leads to the
contemplation of a pair of triadic relations, the sign relations L_A
and L_B,
reflecting the differential use of these signs by A and B,
respectively.
Each of the sign relations L_A and L_B consists of eight triples of
the form
(x, y, z), where the “object” x belongs to the “object
domain” O = {A, B},
the “sign” y belongs to the “sign domain” S, the
“interpretant sign” z
belongs to the “interpretant domain” I, and where it happens in
this case
that S = I = {“A”, “B”, “i”, “u”}. The union S ∪
I is often referred to
as the “syntactic domain”, but in this case S = I = S ∪ I.
The set-up so far is summarized as follows:
• L_A, L_B ⊆ O × S × I
• O = {A, B}
• S = {“A”, “B”, “i”, “u”}
• I = {“A”, “B”, “i”, “u”}
The relation L_A is the following set of eight triples in O × S ×
I.
• { (A, “A”, “A”), (A, “A”, “i”), (A, “i”,
“A”), (A, “i”, “i”),
(B, “B”, “B”), (B, “B”, “u”), (B, “u”,
“B”), (B, “u”, “u”) }
The triples in L_A represent the way interpreter A uses signs.
For example, the presence of (B, “u”, “B”) in L_A says A
uses “B”
to mean the same thing A uses “u” to mean, namely, B.
The relation L_B is the following set of eight triples in O × S ×
I.
• { (A, “A”, “A”), (A, “A”, “u”), (A, “u”,
“A”), (A, “u”, “u”),
(B, “B”, “B”), (B, “B”, “i”), (B, “i”,
“B”), (B, “i”, “i”) }
The triples in L_B represent the way interpreter B uses signs.
For example, the presence of (B, “i”, “B”) in L_B says B
uses “B”
to mean the same thing B uses “i” to mean, namely, B.
The triples in the relations L_A and L_B are conveniently arranged
in the form of relational data tables, as shown below.
Table A. L_A = Sign Relation of Interpreter A
https://inquiryintoinquiry.files.wordpress.com/2020/05/sign-relation-la-int…
[2]
Table B. L_B = Sign Relation of Interpreter B
https://inquiryintoinquiry.files.wordpress.com/2020/05/sign-relation-lb-int…
[3]
Resources
=========
Survey of Relation Theory
https://inquiryintoinquiry.com/2021/11/08/survey-of-relation-theory-5/
[4]
Survey of Semiotics, Semiosis, Sign Relations
https://inquiryintoinquiry.com/2019/10/29/survey-of-semiotics-semiosis-sign…
[5]
Regards,
Jon
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Cf: Triadic Relations • 1
https://inquiryintoinquiry.com/2021/11/07/triadic-relations-1/
| Of triadic Being the multitude of forms is so terrific that
| I have usually shrunk from the task of enumerating them;
| and for the present purpose such an enumeration would be
| worse than superfluous: it would be a great inconvenience.
|
| C.S. Peirce, Collected Papers, CP 6.347
( https://inquiryintoinquiry.com/2012/06/14/c-s-peirce-of-triadic-being/ )
All,
A “triadic relation” (or “ternary relation”) is a special case of a polyadic or
finitary relation, one in which the number of places in the relation is three.
One may also see the adjectives 3-adic, 3-ary, 3-dimensional, or 3-place being
used to describe these relations.
Mathematics is positively rife with examples of triadic relations
and the field of semiotics is rich in its harvest of sign relations,
which are special cases of triadic relations. In either subject, as
Peirce observes, the multitude of forms is truly terrific, so it's best
to begin with concrete examples just complex enough to illustrate the
distinctive features of each type. The discussion to follow takes up
a pair of simple but instructive examples from each of the realms of
mathematics and semiotics.
Resources
=========
• Relation Theory
https://oeis.org/wiki/Relation_theory
• Triadic Relations
https://oeis.org/wiki/Triadic_relation
• Sign Relations
https://oeis.org/wiki/Sign_relation
• Survey of Relation Theory
https://inquiryintoinquiry.com/2021/11/08/survey-of-relation-theory-5/
Regards,
Jon
