Conceptions of creativity and a key creative moment

in the history of Western philosophy

Professor Michael Beaney

Department of Philosophy, University of York

Beijing Normal University, 19 December 2011

Plan1) definition of creativity: 3 requirements

(i) originality; (ii) value; (iii) intentionality

2) conceptions of creativity (i) combinational; (ii) explorational; (iii) transformational

3) case study: Frege’s invention of modern logic(i) originality; (ii) value; (iii) intentionality

4) implications: Frege and creativity (i) combinational; (ii) explorational; (iii) transformational

Kong Zi and Zhuangzi

The Master said, ‘If one learns from others but does not think, one will be bewildered. If, on the other hand, one thinks but does not learn from others, one will be in peril.’(Analects, II, 15)

My life flows between confines, but knowledge has no confines. If we use the confined to follow after the unconfined, there is danger that the flow will cease; and when it ceases, to exercise knowledge is purest danger.(Zhuangzi, ch. 3: ‘What matters in the nurture of life’)

1 Definition of creativity creativity = ability to create, i.e. to produce

something new or original (out of existing material)

product must be valuable process must be intentional; i.e. product must

be the result of a deliberate process

creativity is the ability to produce something new, where there is value in the product and intentionality in the process

1 (i) Originality

(1) originality sometimes distinguished from creativity creativity involves working within constraints;

originality involves changing constraints (Jon Elster) ‘mere’ originality may not be creativity, but seems

a necessary ingredient [cf. Daoist youwei vs. wuwei]

(2) originality relative distinction between psychological (P-) and historical

(H-) creativity (Margaret Boden) two people may be equally P-creative but one may

have historical priority

1 (ii) Value value also relative

Objection: evil actions, lacking value, can be creativee.g. torture, 9/11 bombings

Responses:(1) value to some people reply: we can still grudgingly recognize ingenuity

(2) identify more carefully where the ingenuity liese.g. the planning involved

1 (iii) Intentionality

(1) Objection: luck often plays a major rolee.g. Goodyear’s discovery of vulcanization; Fleming’s discovery of penicillin

Response: “you make your own luck” Goodyear and Fleming had ongoing projects

(2) Question: can computers be creative? quick answer: no, because they lack intentionality longer answer: they can nevertheless be a

constitutive part of creativity (just like luck)

2 Conceptions of creativity

Margaret Boden, The Creative Mind (1990, 2004); ‘What is creativity?’ (1994)

3 conceptions: combinational; explorational; transformational

Key idea: conceptual space: a domain of thinking

governed by a set of rules and principles “the generative system that underlies that domain

and defines a certain range of possibilities: chess moves, or molecular structures, or jazz melodies” (1994, p. 79)

2 (i) Combinational creativity combining old ideas in new ways (e.g. unicorn)

Boden’s main objection: ignores ‘radical originality’ first-time novelty: something that occurs for the

first time, but generated by same rules as other things

radical originality: what could not have arisen before, in the sense that there was no generative system by means of which it could have been generated

radical originality at the heart of genuine creativity, according to Boden

2 (ii) Explorational creativity exhibited in exploring a generative system

e.g. Bach’s music; Euclidean geometry influence of Chomskyan generative linguisticsLinguistic creativity: ability to construct and understand

new sentences, explained by grasp of rules Boden’s example: “The pineapples are in the bathroom

cabinet, next to the oil paints that belonged to Machiavelli.” Dickens’ description of Scrooge as “a squeezing, wrenching,

grasping, scraping, clutching, covetous old sinner”

not genuine creativity, according to Boden

2 (iii) Transformational creativity exhibited when a generative system is transformed

by rejecting one or more of its constituent rules e.g. dropping the parallel postulate to yield non-Euclidean

geometry; Schoenberg’s dropping of the home-key constraint to yield atonal music

so Schoenberg more creative than BachObjection: whether TC more valuable than EC

depends on product e.g. linguistic creativity not just a matter of generation

merely breaking a rule not creative (cf. originality)

2 (ii) and (iii) Exploration and transformation in creativity

Boden’s considered view: genuine creativity involves transformation after thorough exploration

e.g. Schoenberg’s early tonal period; geometers’ attempts to prove Euclid’s fifth axiom

Objection: exploration is not necessary for transformation (David Novitz)

e.g. Picasso’s cubism, influenced by African tribal carvings

Response: some sense of limitations of earlier system(s) needed to stimulate innovation

and certainly required to appreciate its value

2 (iii) Transformation: Picasso’s cubism

‘Head of a Woman’ (1909)

African carving from Ivory Coast

Kong Zi

The Master said, ‘A man is worthy of being a teacher who gets to know what is new by keeping fresh in his mind what he is already familiar with.’ (Analects, II, 11)

The Master said, ‘The gentleman is devoted to principle but not inflexible in small matters.’ (Analects, XV, 37)

Gottlob Frege (1848-1925) German mathematician,

logician and philosopher

taught at Jena 1874-1917

1)Begriffsschrift (1879)2)Die Grundlagen der

Arithmetik (1884)3)Grundgesetze der

Arithmetik (1893, 1903)

Logicism and creativity arithmetic can be derived from logic

Dao produced [sheng] the One.The One produced the two.The two produced the three.And the three produced the ten thousand things …(Daodejing 42)

3 Case study: Frege’s invention of modern logic the single most important event in the

development of analytic philosophy Frege’s logic was new, valuable and intentional,

so satisfies all the key requirements for creativity

Frege’s logic is a powerful generative system, and the philosophy that was developed to support and apply it is a sophisticated conceptual space

case study can thus throw light on creativity and provide a test of conceptions and claims

3 (i) Frege’s originality

Key idea: invention of quantifier notation ( and ) allowed formalization of sentences with

quantifier phrases, even sentences with multiple quantifiers

The two simplest cases:(1) All Ps are Ls.(1’) If anything is a P, then it is an L.(1*) x (Px Lx).

(2) Some Ps are Ls.(2*) x (Px & Lx).

3 (ii) The value of Frege’s logic far more powerful than previous systems of logic

integrated the two main existing systems, syllogistic theory and propositional logic

Boolean logic could handle each but not together

Example:(3) Every philosopher respects some logician.

Two readings:(3a) (x) (Px (y) (Ly & Rxy)).(3b) (y) (Ly & (x) (Px Rxy)).

3 (iii) Intentionality Frege’s aim to make explicit the logical relations

between both concepts and propositions“[My Begriffsschrift is] intended to serve primarily to test in the most reliable way the validity of a chain of inference and to reveal every presupposition that tends to slip in unnoticed, so that its origin can be investigated” (BS, pref.)

Frege well aware of his logic’s novelty and value based on his use of function-argument analysis

“I believe that the replacement of the concepts subject and predicate by argument and function will prove itself in the long run.” (Ibid.)

4 Frege and creativity as a case study, Frege’s logic can be regarded as a

paradigm example of creativity Frege’s own views can be investigated as

contributions to debates about creativity

1)Frege himself criticizes combinational creativity, though compositional views are also present

2)Frege’s logic a generative system, ‘explored’ in Frege’s logicist project

3)Frege’s logic and philosophy exhibit transformational creativity, but Boden’s account needs qualification

4 (i) Frege and combinational creativity

(1) Frege’s critique of combinational theories of concepts [cf. ‘Bai ma bu shi ma’]

criticizes Boolean (combinatorial) logicExamples: ‘blogician’; ‘deathbed’ vs. ‘lifeboat’

(2) Frege’s compositional theory of meaning(P1) The reference of a sentence is

determined by the reference of its parts.(P2) The sense of a sentence is composed of

the senses of its parts.

4 (ii) Frege and explorational creativity Frege’s philosophical aim to demonstrate

logicism – the thesis that arithmetic is reducible to logic

1) rules of inference logical (cf. mathematical induction) {BS}

2) number concepts definable logically {GL}3) arithmetical propositions provable by logic {GG}

once basic rules, concepts and axioms in place, system can then be ‘explored’ but more like Euclidean geometry than classical

music

4 (iii) Frege and transformational creativity

(1) Frege’s invention of modern logic transformational in establishing a new generative system

but not simply a matter of rejecting a rule of an earlier logical system, nor did Frege ‘explore’ an earlier system

application of function-argument analysis from mathematics to logic: “let’s treat concepts as functions”

(2) Frege’s philosophy then developed to support and apply that logic

all of Frege’s characteristic doctrines flow from this transformation of key concepts, such as that of concept

itself (understood as a kind of function)

4 (ii) and (iii) Exploration and transformation in Frege’s logic

Two paradigms of analytic philosophy(1) Existential statements

(0a) Unicorns do not exist.(0b) The concept unicorn is not instantiated.(0c) ¬(x) Fx.

offers diagnosis of ontological argument

(2) Theory of descriptions (Bertrand Russell)(Ka) The present King of France is bald.(Kb) There is one and only one King of France, and whatever is King of France is bald.(Kc) (x) (Kx & (y) (Ky y = x) & Bx).

Conclusion1) definition of creativity: 3 requirements

(i) originality; (ii) value; (iii) intentionality

2) conceptions of creativity (i) combinational; (ii) explorational; (iii) transformational

3) case study: Frege’s invention of modern logic(i) originality; (ii) value; (iii) intentionality

4) implications: Frege and creativity (i) combinational; (ii) explorational; (iii) transformational

Kong Zi

A gentleman who studies is unlikely to be inflexible.(Analects, I, 8)

谢谢