outline of trikonic |>*k: diagrammatic trichotomic gary richmond city university of new york new...
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Outline of trikonic |>*k: Diagrammatic Trichotomic
Outline of trikonic |>*k: Diagrammatic Trichotomic
Gary RichmondCity University of New York
New York, USA
Gary RichmondCity University of New York
New York, USA
Reduction Thesis
All relations ofmore than three elements
are reducibleto triadic relations,
but triadic relationsare not reducible to dyadic and monadic
relations.
triad
monad
dyad
Valencies
gives to
xx yy
zz
A Thief of PeirceP. 198
A Thief of PeirceP. 200
Complex Valental Graphs
Composition: “+”
Icosahedral formsIcosahedral forms Icosahedral formsIcosahedral forms
2312311ns
2ns
3ns
Three Peircean categories
ideas (in the Platonic sense)1
2 brute events
3habits(or, more exactly, habit-taking)
Three Universes of Experience:
1ns, ideas
3ns, habits
2ns, brute events
(“Airy nothings,” mere possibility ofbeing actualized, so, “floating” at the top)
(Tending to bring 1ns & 2ns into relationship in futuro, so, “to the right”)
(Brute actions and reactions, existential & earthbound, so, “sinking” to the diagram’s bottom)
habitsbrute events
ideaspossibility1
23
Universal Categories:
necessity
actuality
ideasideashabitshabits
brute eventsbrute events
unit (in itself)
correlate(to another)
medium(bringing into relation)
1
23
“the beginning...fresh, original, spontaneous, free.”
“determined, terminated, ended, correlative, object, necessitated, reaction.”
“medium, becoming, developing,bringing about.”
C.S. Peirce“Trichotomic” in EP I:280
1
23
feeling1
23
Existential Categories:
thought
action-reaction
ideasideashabitshabits
brute eventsbrute eventsnecessity
actuality
possibility
may be (VAGUE, )1
23
Logical Modalities:
will necessarily beif…(GENERAL, )
actually is(SPECIFIC, )
feelingthought
action-reaction
ideasideashabitshabits
brute eventsbrute eventsnecessity
actuality
possibility
semeiotic grammarsemeiotic grammar
Sign ElementsSign Elements
sign (representamen)
interpretant
object
9-adic Sign Relations
qualisign (tone)legisign (type)sinsign (token)
as to the sign itself:as to the sign itself:
iconsymbol
index
in relation to the object:in relation to the object:
in relation to the interpretant:in relation to the interpretant:rheme (propositional function)
dicisign (proposition)argument
10-adic Classification of
Signs
11
1111
22
1111
33
1111
22
2211
22
2222
33
2222
33
3311
33
3322
33
3333
33
2211
9-adic Sign Relations
qualisign (tone)legisign (type)
sinsign (token)
as to the sign itself:as to the sign itself:
iconsymbol
index
in relation to the object:in relation to the object:
in relation to the interpretant:in relation to the interpretant:rheme (propositional function)
dicisign (proposition)argument
Dicent Indexical Sinsign:
analytical vector
2
2
2
—the wind’s direction.
It is asserted—
—that the weathervane indicates—
—sinsigndicent—
—indexical—
10-ADIC CLASSIFICATION OF SIGNS:
QUALISIGN
RHEMATIC
ICONIC
SYMBOLIC
SYMBOLIC
SYMBOLIC
ICONIC
ICONIC
RHEMATIC
RHEMATIC
RHEMATIC
RHEMATIC
RHEMATIC
LEGISIGN
LEGISIGN
LEGISIGN
LEGISIGN
LEGISIGN
LEGISIGN
DICENTIC
DICENTIC
DICENTIC
SINSIGN
SINSIGN
SINSIGN
INDEXICAL
INDEXICAL
INDEXICAL
INDEXICAL
11
1111
22
1111
33
1111
22
2211
22
2222
33
2222
33
3311
33
3322
33
3333
33
2211ARGU-
MENTATIVE
10-ADICCLASSIFICATION
OFSIGNS:11
1111
22
1111
33
1111
22
2211
22
2222
33
2222
33
3311
33
3322
33
3333
33
2211
9-ADIC SIGN RELATIONS:
qualisign (tone)legisign (type)
sinsign (token)
as to the sign itself:as to the sign itself:
iconsymbol
index
as to the object:as to the object:
rheme (propositional function)
dicisign (proposition)argument
as to the interpretant:as to the interpretant:
Theoretical Grammar:SIGN ELEMENTS:
signsigninterpretantinterpretant
objectobject
mathematicssciences of discovery: |> philosophy (as cenoscopic):
sciences: |> sciences of review special sciencespractical sciences
phenomenology (as trichotomic)|> metaphysicsnormative sciences: esthetics theoretical grammar:
|> logic (as semeiotic): |> rhetoric (methodeutic)ethics critic
Classification of the Sciences
Vectorsprocessorder
representation
analysis
determination
aspiration
1
2
3
Semeiosis:determination vector
—the sign—
—for an interpretant.
The object determines—
2/1/3
representation vector
—creates a sign (e.g., a diagram). . .
An interpreter (e.g., a scientist). . .
. . .of a complex object.
3/1/2
Evolution:
Chance sporting
Achieved structural modification
New-habit taking
processvector
Inquiry:
Abduction (hypothesis formation)
Induction (actual experiment)
processvector
Deduction (of implicationsof hypothesis for testing)
In Relation to Testbeds:Hypotheses are formed as to possible goals, tools, projects which might be of value to a community . . .
. . . so that decisions to actually test particular tools, projects, etc. are put into effect and tests are made.
. . . by use of a suite of meta-tools like |>*k/GRASS, the implications for testing are argumentatively laid out . . .
de Moor, Keeler, Richmond ICCS02 paper
process vector
F u r t h e r P r o s p e c t s
Further Prospectsaspiration vector
F u r t h e r P r o s p e c t s
|>*K in virtual community development:
. . . tends to achieve its purposes.
A virtual community . . .
. . . through its use of stakeholder-selected theories, methods, tools, etc. . . .
Copyright ©Gary Richmond