Creativity and Rationality: Interrelationships and

Implications for Education.

Mark H. Bickhard

Lehigh University

mark@bickhard.name

http:/bickhard.ws/

Abstract

Representation and cognition emerge out of interaction systems in a manner that tightly integrates cognition and motivation. This basis forces a variation and selection constructivism — an evolutionary epistemology — for learning and development. In complex organisms such as human beings, it is adaptive not only to develop ways of generating potentially useful new variations, but also to learn about the selection principles — to learn about what counts as error. Creativity is at the core of the generation of variations, and rationality is the direction in which the learning of kinds of errors and of how to avoid those errors proceeds. Creativity and rationality are interrelated cognitive skills and cognitive motivations, and education optimally nurtures the development of both.

Overview

• Representation

• Knowing Levels

• Representation and Motivation

• Learning and Development

• Rationality and Critical Principles

• Creativity and Rationality

RepresentationA Naturalistic Model

• Far From Equilibrium Systems– Require maintenance of far from

equilibrium conditions

• Self Maintenant Systems– Candle Flame

• Recursively Self Maintenant Systems– Bacterium

Function

• Contributions to the maintenance of far from equilibrium conditions

• Function is in the service of the continued existence of the system– System relative notion– Heart of Parasite

• Etiological Model– Epiphenomenal

Truth Value

• Functional presupposition of interactions– Swimming is functional if oriented up a sugar

gradient– Swimming is not functional if oriented down a

sugar gradient

• Conditions of appropriateness presupposed– Implicit– Can be false — swimming up a saccharin gradient

• Functional presuppositions have truth value

More Complex Representation

• Resources– Frog: Multiple interaction possibilities– Differentiation of indication of interaction

potentialities from selection of interaction to engage in

– Indications also have truth value

• Indications are conditional– Branches and iterations of conditional

interaction possibilities

Complex Representation II

• Small manipulable object– Web of conditional interaction possibilities– Mutually reachable possibilities

• Manipulations and scans

– Invariances

Complex Representations III

• Abstractions– Number as heuristic– Second representational level

• Reflective Abstraction

Knowing Levels

• Unbounded hierarchy of potentialities for new properties to be represented

• Iteration of the representational aboutness relationship

Piaget and Pragmatism

• Object representation model borrowed from Piaget

• Abstraction model adapted from Piaget• Can borrow from Piaget because both

models are interaction based• Generally within the framework of

Peirce’s Pragmatism– Unlike most models of representation

Problems with Representation

• Encoding or correspondence models of representation

• Unbounded correspondences– Which correspondence?

• Problem of representational error– Two possibilities; must model three conditions

• Problem of system detectable error– Radical skeptical argument

Motivation

• What is the problem of motivation?– To energize organism into action?– Cannot be: organism is far from

equilibrium: if it ceases to interact, it ceases to exist

– Organism are necessarily always doing something, even if it’s sleeping

• Motivation: Selection of what to do next

Representation and Motivation

• Representation emerges in indications of interactive potentialities — for the sake of the selection of next interactions

• Selection occurs among the indicated potentialities– Such selection is a motivational phenomenon

• Representation and motivation are different aspects of the same problem of interaction selection

• They are not separate systems

Learning and Development

• Signet ring models of representation: transduction, induction

• World impresses itself into passive mind

• The world cannot impress an interaction system into a passive mind

• So, if representation emerges in interaction, learning cannot be passive

Evolutionary Epistemology

• Interaction systems must be constructed and, without prescience, tried out to see if they work

• Learning must involve an evolutionary epistemology of constructive variations and selections

Development

• In complex organisms, constructions will be in the context of and making use of previous constructions

• Construction is recursive– And means of construction are also recursive — a

meta-recursiveness

• Therefore, construction is historistic: what is possible or easy may depend on what has been constructed before

Development II

• Therefore trajectories of construction are important

• Learning is the study of construction in the moment

• Development is the study of the historistic dependencies and properties of evolutionary epistemological constructions

Constraints on Development

• Inherent constraints: algebra before calculus• Construction constraints: components before

integrations of components• Knowing levels: must be ascended in

sequence• Nurturing developmental trajectories

– Scaffolding and self-scaffolding• Nurturing of self scaffolding

Learning Error

• Advantageous to learn selection principles — kinds of error– Safer, more economical, to test constructions

internally

• Knowledge of selection principles must itself be fallibilistically constructed– Kinds of error about error knowledge– Epistemic values– Climbs the knowing levels hierarchy

Critical Principles

• If articulable, principles of error serve as principles of criticism

• Thus, critical principles

• Hierarchy of critical principles

Negative Knowledge

• Critical principles constitute knowledge of error possibilities

• They frame the search for ways to avoid error

• They frame the knowledge of what errors are being avoided, if it is known how to avoid them

• That is, they frame positive knowledge

Rationality =? Logic

• Rationality commonly equated with logic• But logics cannot construct other logics

more powerful than themselves• History of logic has involved the

construction of more powerful logics• Therefore, if rationality were equated to

logic, the history of logic would be irrational

Rationality as Positive Knowledge

• Rational knowledge is usual considered to be positive knowledge

• Critical principles serve as backbone for positive knowledge

• Negative knowledge of critical principles guides search for and understanding of positive knowledge

Rationality and Critical Principles

• Critical principles are the negative knowledge skeleton of positive knowledge

• The tendency to develop critical principle hierarchy and positive knowledge that satisfies those values is the tendency toward rationality

• Rationality is a developmental tendency in any domain in which it is possible to learn about error

Rationality and Logic

• What about logic?• Critical principles regarding inference

and argument• Positive knowledge of how to avoid

those errors constitutes what we call logic– Tarski, Mowstowski, Sher: logic studies

invariances of automorphisms

What about constructions?

• We learn more about error• We get better at heuristic constructions within

framework of critical principles• Such constructions are generative• They solve problems, satisfy constraints,

modify problems in the service of other constraints– Such as consistency: Einstein and blackbody

radiation

Creativity and Rationality

• Creativity is the construction-knowledge aspect of evolutionary epistemology

• Rationality is the selection-knowledge aspect of evolutionary epistemology

• Creativity and rationality are differing aspects of the same developmental process and tendency– They should be nurtured together

Selected Implications

• Representation is emergent:– Cognition does not have to involve the processing

or combinations of elements that are already representations

– Dynamic activity with representations emergent as “foam”

– What emergents resonate with or influence other processes, criteria?

• They will capture and dominate resultant processes

– Dennett’s “fame” - depends on what else is going on

Selected Implications II

• Play and creativity– Play relaxes critical suppressions– Feynman’s sailing paper plates

• Yielded mathematics critical to his later Noble prize

Selected Implications III

• Creative cultures– All seem to have involved openness of

discussion and criticism– Including criticisms of criticisms– Selects for better results and for better

creative heuristics in their creation– And for creativity of critical principles

Selected Implications IV

• Issues of personality– Anything I might think of

• Is not valuable• Is not legitimate• Is dangerous to my self esteem to reveal• Would be hubris to take seriously• And so on and on

– Suppression of creative generations by sense of personal error rather than by domain relevant critical principles

Selected Implications V

• Social processes of creativity and rationality can involve divisions of labor– Nurturing creative generation– And nurturing strong selection principles– And nurturing selections of, criticisms of,

selection principles