The Self-transcending
Construction of Emergence
Jeffrey Goldstein, Ph.D.
Adelphi University
Garden City, New York
USA
goldstei@adelphi.edu
EXAMPLES OF EMERGENCE
life consciousness speciation project teams
multi-organisms artificial life the Internet
magnetism superfluidity
superconductivity
additional computational functionality
dissipative structures
optimal options prices
perception of color attractors and their basins
drug interactions
leadership behavior
software “bugs” temperature
cities
wars scientific revolutions creative ideas
Self-transcending
Constructions
in Neo-emergentism
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Drives Behind Emergence:
Candidates
Blumenbach: Bildungstrieb
Spencer: Increasing Heterogeneity
Bergson: Creative Evolution/Elan Vital
Alexander: Nisus (Connatus from Spinoza)
Whitehead: Processual
De Chardin: Eschatological
Thermodynamics: Self-organization Based
On Minimum or Maximum Entropy
Production or So-called Fourth Law of
Thermodynamics (information theoretic)
Construction, not Process
• Not a Metaphysics Based on the
Already Given (Structures, Dynamics,
Properties)
• Not Subjugation to Process or
Temporal Flow
• Non-Oppositional
• Based on Constructional Resources
and Operations
• Free Act of Creativity but Not Order for
Free
Reiser’s Transfinite
Aggregates
Bennett’s
Logical
Depth
Fontana’s and
Buss’s
Computational
Constructions
Crutchfield’s
Calculi of
Emergence
Anderson’s
Constructionist
Hypothesis
?
Cohen’s/Stewart’s
Existence Theorem
for Emergent
Phenomena
Holland’s Sets of
Equations that
Change Cardinality
Piaget’s LogicoMathematical
Constructions
Reiser’s Transfinite
Aggregates
Bennett’s
Logical
Depth
Fontana’s and
Buss’s
Computational
Constructions
Crutchfield’s
Calculi of
Emergence
Anderson’s
Constructionist
Hypothesis
Gödel and
Turing:
Limitative
Theorems
Piaget’s LogicoMathematical
Constructions
Cohen’s/Stewart’s
Existence Theorem
for Emergent
Phenomena
Holland’s Sets of
Equations that
Change Cardinality
Reiser’s Transfinite
Aggregates
Bennett’s
Logical
Depth
Fontana’s and
Buss’s
Computational
Constructions
Crutchfield’s
Calculi of
Emergence
Anderson’s
Constructionist
Hypothesis
Cantorian Antidiagonalization”
Cohen’s/Stewart’s
Existence Theorem
for Emergent
Phenomena
Holland’s Sets of
Equations that
Change Cardinality
Piaget’s LogicoMathematical
Constructions
Reiser’s Transfinite
Aggregates
Bennett’s
Logical
Depth
Fontana’s and
Buss’s
Computational
Constructions
Crutchfield’s
Calculi of
Emergence
Anderson’s
Constructionist
Hypothesis
Selftranscending
Constructions
“STC”
Piaget’s LogicoMathematical
Constructions
Cohen’s/Stewart’s
Existence Theorem
for Emergent
Phenomena
Holland’s Sets of
Equations that
Change Cardinality
Formalism of STC (incl. Negation) -ADAPTED FROM SIMMONS
Construction of anti-diagonal sequence to transcend
cardinality of rational numbers:
Definition 1: R is a 3-place relation among x,y,z represented
as D1 and D2 making-up vertical and horizontal arrays of
rationals
Definition 2: A diagonal F is constructed on D1 and D2 so that
the mapping is a bijection D1 --> D2
Definition 3: G is the value of the diagonal F in R
Definition 4: STC is an anti-diagonal of F in R so that
(STCxyz =¬ Gxyz)
NOTE: ¬
IS A NEGATION OPERATOR WHICH ALLOWS STC
TO TRANSCEND CARDINALITY OF RATIONALS
BIAS AGAINST CONSTRUCTION
 SCIENCE VERSUS ART
 EVOLUTION VERSUS DESIGN
•CONSTRUCTION SEEMS TO IMPLY
CONSTRUCTOR
•CONTINUITY OF EVOLUTION
VERSUS DISCONTINUITY OF
CONSTRUCTION
 BERGSON: ELAN VITAL VERSUS MACHINE
• CONSTRUCTIONS ARE THOUGHT OF AS
PREDICTABLE AND DEDUCIBLE
Construction, not Process
• Not a Metaphysics Based on the Already Given
(Structures, Dynamics, Properties)
• Not Subjugation to Process or Temporal Flow
• Non-Oppositional
• Based on Constructional Resources and
Operations
• Free Act of Creativity but Not Order for Free
CONSTRUCTIONAL SOURCES OF
NOVELTY IN NEO-EMERGENTISM
RECURSIVE OPERATIONS, E.G.,
FUNCTIONAL ITERATION,
CROSSOVER,
RECOMBINATION..
NEGATION OPERATIONS
(CHANGING VALUES ON
RECURSION)
INTRODUCTING RANDOMNESS
INTO SYSTEM
RECURSION
Constrained Generating Procedures (Holland)
f c :Ic x Sc Sc (where fc is defined so that
fc (t+1) = fc(Ic(t)Sc(t)); I = possible input
combinations at time t, S = states of system
at time t
RECURSION
FUNCTIONAL ITERATION
(FEIGENBAUM’S ROUTE TO CHAOS)
xn  f ( f (... f ( f ( x0 ))...))  f ( x0 )
n
f n is the nth iterate of f
Holland’s Genetic Recombination
Using Negation and Randomness
AND/OR MUTATION
Crossover and Mutation Negate Previous
Combination at Every Iteration
Formalism of STC (incl. Negation) -ADAPTED FROM SIMMONS
Construction of anti-diagonal sequence to transcend
cardinality of rational numbers:
Definition 1: R is a 3-place relation among x,y,z represented
as D1 and D2 making-up vertical and horizontal arrays of
rationals
Definition 2: A diagonal F is constructed on D1 and D2 so that
the mapping is a bijection D1 --> D2
Definition 3: G is the value of the diagonal F in R
Definition 4: STC is an anti-diagonal of F in R so that
(STCxyz =¬ Gxyz)
NOTE: ¬
IS A NEGATION OPERATOR WHICH ALLOWS STC
TO TRANSCEND CARDINALITY OF RATIONALS
Thou sendeth forth Thy spirit, they are created;
And
Thou renewest the face of the earth.
– Psalm 104:30
Whose Name stands for “I am that I am” says,
Look, I am doing a new thing;
It springs forth right now, do you not perceive it?
I create a path out of the wilderness
And rivers out of the desert.
-Isaiah 43:19