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