COGNITIO: Revista de Filosofia
ISSN 1518-7187
Indexação: The Philosopher`s Index; Citas Latinoamericanas en Ciencias Sociales y Humanidades (CLASE)
Banco de Traduções
Tradução de artigo publicado no Número 3, Novembro de 2003
Maria Eunice Quilici Gonzalez gonzalez@marilia.unesp.br
Post-Graduate Programme in Cognitive
Science and Philosophy of Mind, Philosophy
Department,
UNESP, Av. Hygino Muzzi Filho 737,
Marília, SP, 17525-900, BRAZIL
Original in Portuguese.
[tr. to English by the author]
Abstract: We investigate the nature of Creative reasoning focusing on Peirce’s notion of abductive reeasoning and on the main premisses of the Self-Organization Paradigm developed in Cognitive Science. As an initial hypothesis we characterise Creativity as a selforganizing process in which abductive reasoning occurs allowing the expansion of well structured conceptual spaces. As originally characterised by Peirce, abduction - in contrast with deduction and induction - provides a mode of logic inference upon which creative reasoning is based. It starts which the perception of anomalies or apparently unsolvable problems: surprise and doubts initiate the abductive process of search of those possible hypotheses that, if proved true, could resolve the problems in question. We argue that, as a kind of heuristics, abduction constitutes a guide for the process of expansion of conceptual spaces. This process can be considered a part of the establishment of order parameters in the flow of distributed information available to self-organizing systems. In this sense, promising contributions of Philosophy and Cognitive Science to studies of Creativity could be given with the understanding of how self-organizing processes involving abductive reasoning may take place in dynamic systems which process parallel information.
Keywords : abductive reasoning, conceptual space, creativity, neural networks, order parameters, selforganization
Introduction
The contrast between creative and mechanistic processes of information has always been a common characteristic of objections addressed to the mechanistic approach to the mind proposed by cognitive science. Thus, for example, in the early stages of artificial intelligence we find such a contrast in Turing's well known article Computing Machinery and Intelligence where he addresses Lady Lovelace's remarks on the impossibility of computers to be creative.
She argues that computers can do only what their programs allow them to do, and in this sense they do not constitute good instruments to understand creative thinking. Even though her remarks seem to be intuitively true they leave unexplained the nature of creativity and the reason why a programmed system, like a computer, could not be creative.

2
Turing does not seem to completely answer Lovelace's objection to his mechanistic approach to the mind, but he brings an important element into the discussion (relating surprise and creative thinking) when he insists that computers often surprise him in his expectation about their performances.
The suggestion proposed by Turing, and developed by researchers like Newell and Simon
(1972), Gonzales (1984), Boden (1996) and others, is that creativity is directly related to problem solving activity in which explorations in the problem space lead to the expansion of conceptual spaces. This expansion releases the feeling of surprise often present in creative thinking.
General heuristics have been described to guide search processes; they include strategies for examining, comparing, altering and combining concepts, strings of symbols, and the heuristics themselves. However critics insist that, despite their general appearance, heuristics are shaped for specific purposes and computers incorporating them will only do what their programs tell them to do: no real creativity is involved in their activities, so the history goes. But, what kind of creativity is under discussion in this context? The natural answer is that the kind of creativity under discussion is the one which we humans experience in our everyday life, at the individual and social level, when new and original ideas, theories and artistic productions are recognised as of some value. In this sense, creativity involves an element of subjectivity that makes it difficult to be analysed from an objective perspective. In this context Popper (1959) stresses:
"The question of how it happens that a new idea occurs to a man - whether it is a musical theme, a dramatic conflict, or a scientific theory - may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge.... My view of the matter, for what it is worth, is that there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process. My view may be expressed by saying that every discovery contains "an irrational element", or "a creative intuition", in Bergson's sense."
Popper 's hypothesis that the process of generation of new ideas involves an element of irrationality and therefore that it cannot be the object of scientific or logic investigations found several adepts amongst philosophers and scientists who left the subject to empirical psychologists to investigate. In opposition, Hanson (1958) developed a logic theory of scientific discovery based upon Peirce's concept of abductive inference. As originally characterised by
Peirce (1931-1958), abduction - in contrast with deduction and induction - provides a mode of inference upon which creative reasoning is based (CP, 5.170). As is going to be explained, this type of reasoning constitutes a form of heuristics which has been applied in Artificial
Intelligence.
Without ignoring possible subjective elements involved in certain creative processes, we are going to argue that creativity can be characterised in terms of self-organizing processes in which abductive inference may take place. We shall explain our hypothesis in 3 steps:
(1) based on the classification proposed by Boden (1996) we will present two senses in which creativity is traditionally characterised focusing on their structural characteristics. In both senses we will indicate the presence of abductive reasoning as an important characteristic of creativity;
(2) the main steps of abductive inference, as proposed by Peirce (1931-1958), shall be described with indications of its relevance for a logical approach to creativity. This kind of inference is described as a particular form of activity of dynamic self-organizing systems.
(3) Enlarging the context in which the concept of creativity is investigated we shall consider a variety of creative systems including minds, social processes and robots. The main premises

3 of the self-organization paradigm (SOP) will then be discussed in order to illustrate the dynamics of such creative systems.
1- Two Senses of Creativity
In What Is Creativity?, Margaret Boden defines creativity in terms of exploration and transformation of conceptual spaces. These are, as she stresses, multidimensional structures organized in accordance with principles that unify a domain of thinking. Such principles constitute "... the generative system that underlies that domain and defines a certain range of possibilities..." Explorations in different domains of thinking often lead to the expansion and, sometimes to useful transformations in their structure providing the basis for novelties.
An important contribution to the study of creativity in the domain of cognitive science is given by Boden's analysis of how exploration in conceptual spaces may lead to relevant novelties in the domain of music, visual arts, literature and science. In science, for instance, she investigates Mendeleyev's creative process with the proposal of the periodic table in the 1860s: initially he classified chemical elements in rows and columns according to their similar observable properties and behaviour. In his processes of classification he left some gaps, predicting that in the future new appropriate elements could be discovered to fill them. Several years latter such elements were discovered whose properties satisfied his predictions and, moreover his table led to a more powerful classification of elements in terms of atomic number. This, in turn, explained the gaps originally left by Mendeleyev in his original classification.
Examples like the above illustrate situations in which mapping and explorations in conceptual spaces may lead to the expansion and generation of new ideas. Sometimes changes in conceptual spaces may lead to radical transformations, and not just expansions, in the constraints that define them. In this context, Boden (1996) describes the structural changes found in the development of post-Renaissance Western music based on the generative system known as tonal harmony:
"From its origins to the end of the nineteenth century, the harmonic dimensions of this space were continually tweaked to open up the possibilities ... implicit in it from the start. Finally, a major transformation generated the deeply unfamiliar (yet closely related) space of atonality."
After investigating the steps of the process of undermining the notion of " home key", which gave rise to atonal music, Boden stresses that the final, culminating, transformation realised by
Schoenberg led to different constraints such as the usage of every note in the chromatic scale to structure his atonal music: a constraint was dropped out giving place to new ones which allowed new forms of harmonic modulations to be created.
In summary, the essential contribution given by Boden to the understanding of the origins of new ideas consists of making clear that conceptual exploration leading to the expansion or sometimes to the negation of their generative structure can be seen as a form of creativity. In this context, she suggests two senses in which creativity should be described. The first focuses on ideas which characterise a creative individual mind in its uniqueness: “A valuable idea is Pcreative if the person in whose mind it arises could not have had it before; it does not matter how many times other people have already had the same idea."(Boden, 1996)
In contrast, the second sense of creativity stresses its historical characteristics: "A valuable idea is H-creative if it is P-creative and no one else, in all human history, has ever had it before"
(Boden, 1996).
The proper Analysis of H-creative ideas requires investigations of collective thoughts in relation to which such ideas should be considered as creative ones. Such investigations have not

4 been developed in cognitive science, but the present day research in the area indicates a promising future. As Schaffer (1996, p.16) stresses, recent investigations on creativity and discovery "starts to look less individual and specific, and more like a lengthy process of hard work and negotiation within a set of complex social networks".
Acknowledging the role played by cultural values in the classification of ideas as creative or not (given that worthless new ideas are not considered creative), Boden, however, is mainly concerned with the question of "what does it mean to say that an idea could not have arisen before?". She distinguishes ideas that are merely novel ones - that can be produced by the same set of generative rules which produced other familiar ideas (as in Mendeleyev's classificatory procedures) - from radical and genuinely original ideas that cannot be produced in this familiar way (like Schoenberg's atonal music). The existence of such new ideas presupposes the overcoming of limitations in the pre-existing conceptual area in which they would not find their natural space.
A variation of this classification can be considered in relation to the distinction between invention and discovery. Genuine inventions are those which could not have been found before their appearances - as happened with thr invention of atomic bomb, computers, etc. A discovery, in turn, presupposes the existence of the object that is uncovered- as happened with the discovery of the law of gravitation, neutrino, the complexity of the human brain, etc. However, even the most creative inventions or discoveries presuppose the existence of some implicit form of order from which, and thanks to which, they emerge. As Boden (1996) stresses:
"... the ascription of creativity always involves tacit or explicit reference to some specific generative system ... It follows that constraints - far from being opposed to creativity - make creativity possible. To throw away all constraints would be to destroy the capacity for creative thinking. Random processes alone, if they happen to produce anything interesting at all, can result only in first-time curiosities, not radical surprises."
In this sense, creative thinking seems to presuppose: (a) some form of recognition of the principles and regularities that structure and, consequently, constrain a well established conceptual space, and (b) a subsequent movement to overcome them, whenever problems or anomalies are detected. As we are going to see in the next section, these two steps involved in creative thinking constitute the basis of abductive reasoning
2- Reasons Versus Motivations: An Introduction to Abductive Reasoning
In their studies on the logic of creative processes, Peirce (1931-58) and Hanson (1958, 1963,
1965) stressed the distinction between reasons to suggest a new hypothesis (as a possible solution to a certain problem), and the motivations that make an individual choose specific strategies to solve such a problem.
Motivations, differently from reasons to propose an idea, are not susceptible to logical analysis, because they involve subjective elements, preferences and tastes that reflect the complexity of our cultural history, which is differently instantiated in different individuals.
Without ignoring the relevance of motivations in the process of creation, Peirce and Hanson focus on the reasoning behind creativity. According to them, the mind is a dynamical system whose main activity is the production of habits. As Peirce affirms, strong habits constitute beliefs:
"For belief, while it lasts, is a strong habit, and as such, forces the man to believe until some surprise breaks up the habit." (CP 5.524).
Creative thinking seems to oscillate between strong, well established, beliefs and doubts or surprises that break them initiating the process of origins of new beliefs which will substitute the

5 previous ones. The process of breaking and abandoning a belief does not happen merely by chance, but requires some experience which will conflict with expectations:
"The breaking of a belief can only be due to some novel experience" (CP 5.524).
This novel experience mentioned by Peirce produces in the mind a surprising effect which may be active or passive. The first occurs "... when what one perceives positively conflicts with expectations" ; the second occurs "...when having no positive expectations but only the absence of any suspicion of anything out of the common something quite unexpected occurs, - such as a total eclipse of the sun which one had not anticipated" (CP 8.315)
Surprise - produced by the perception of an anomaly - constitutes the first step of abductive inference considered by Peirce as responsible for creative thinking. Under the effect of a surprise, which confronts expectations produced by well established beliefs, doubts stimulate the mind to inquiry until they disappear and well settled beliefs take place again. In this process, explanatory hypotheses are considered that could transform the surprising situation in a "matter of course".
In a well known passage, Peirce (CP 5.189) suggests the following logic description characteristic of abductive reasoning:
The surprising fact, C, is observed.
But if A were true, C would be a matter of course.
Hence, there is reason to suspect that A is true.
Abductive inference underlying the reasons supporting creative thinking does not provide absolute guarantees about its correctness. It constitutes only a useful heuristic to guide the mind in its attempt to free itself from doubts. Peirce (CP 5.173) stresses that an abduction is a kind of natural instinctive faculty:
"This Faculty is at the same time of general nature of instinct, resembling the instincts of animals in its so far surpassing the general powers of our reason and for its directing us as if we were in the possession of facts that are entirely beyond the reach of our sense. It resembles instinct too in its small liability to error: for though it goes wrong oftener than right, yet the relative frequency with which is right is on the whole the most wonderful thing in our constitution."
Despite its instinctive character, abduction is considered by Peirce as " ... the only logical operation which introduces any new ideas" (CP 5.171) In this sense, would Peirce restrict creativity to the domain of the human mind? The answer seems to be no. Creativity would not be an exclusive property of humans, but could well be spread around our natural world. Peirce suggests that "...there may be some natural tendency toward an agreement between the ideas which suggests themselves to the mind and those which are concerned in the laws of nature."
(CP 1.81).
The element common to all creative systems seems to be the process of generating new habits, which, according to Peirce, is present in the most primitive forms of organization existing in nature. In living beings, the ability to create and change habits allows organisms to act in order to further their own survival and to adjust their behaviour in accordance with environmental requests, changing the environment and being affected by it in a circular feedback way. Changes in habits happen when the organism is confronted with new, surprising, events that initiate abductive reasoning.
In summary: according to Peirce and Hanson the role played by abductive reasoning in creative thinking is directly related to generation, changes and expansions of a domain of beliefs understood as a form of habit. Such expansions happen whenever creative minds are confronted

6 with problems: the mind, in its tendencies to operate with well stabilised forms of beliefs, sometimes experiences the perception of anomalies or unsolvable problems in the domain of existing beliefs. Surprises and doubts initiate the abductive process of search for those possible hypotheses that, if true, could resolve the problem in question. Thus, as a kind of heuristics, abduction constitutes a guide for the expansion of conceptual spaces.
This characterization of the process of creativity seems to be similar to the one suggested by
Boden, as presented in the previous section, according to which creative ideas emerge out of the process of expansion of conceptual spaces. In both - Peirce's and Boden's characterizations, creative ideas represent a way out of problematic situations whose solution requires a dynamic mechanism to approach and to change well established beliefs. As we are going to see in the next section, examples of this kind of mechanism can be found in self-organizing neural networks.
3- Self-organization and Creativity
If creativity always involves a set of well structured habits or beliefs delimited by constraints in relation to which surprising facts can be experienced, how are these constraints produced in the first place? In this section we are going to investigate this question from the self-organization paradigm (SOP).
As pointed out in Gonzales (2000), even though the notion of self-organization has been the subject of philosophical analysis centuries ago (Aristotle, Kant, Peirce and Bergson, for example, have discussed this notion in the context of living organisms), it was with the cybernetic movement, and more recently with connectionism (Kohonen, 1988, 1997), that this concept was illustrated empirically.
A fundamental hypothesis of SOP is that there are two basic types of self-organization known as primary and secondary (Debrun, 1996).
Primary self-organization characterises those processes in which organic or inorganic elements initally separated (or with independent behaviours) interact in such a way that they become co-ordinated and interdependent. Such a process occurs, ideally, without the presence of a central control or any kind of pre-established program, set of rules or laws. It is “...selforganizing in the sense that it changes from separated parts to parts joined ” (Ashby, 1962).
Examples of self-organization, in this first sense, are found in processes of pattern formation in neural networks. These patterns emerge from the interaction of a large number of neuron like units that send excitatory and inhibitory signals to one another. In this process, the activity of individual units produces a collective effect which, in turn, affects the behaviour of individual elements. Even though each singular unit plays a role in the organizational dynamics of the net, the property that really matters to its final organization is a collective , self-organizing, one.
From the information distributed over the units, and with the help of self-organizing processes operating upon them, an order parameter may emerge in the net. As characterised by
Haken (1999), order parameters result from the interaction between low-level components. They constitute high-level patterns which, once created, constrain and control the behaviour of the low-level components. These, in turn, may change, in a circular feed-back way, the high-level order parameters.
As pointed out in Gonzales (2000), the self-organizing dynamics of order parameters formation distinguishes models of artificial neural nets from those AI models elaborated in traditional Von Neumann machines. Initially, the net's units have little or no relevant interdependent relations amongst themselves. With training, primary self-organization may take

7 place; each unit is affected by other units, forming patterns of connectivity. Their organizations emerge mainly from the dynamics of competition, co-operation and adjustment established between the net's units and informational patterns in the environment.
Temporarily, different forms of organization may emerge from the primary process of selforganization, but only one of them will evolve. In order to do that neural nets have to acquire the ability to create and to change habits - understood as stable tendencies to repeat specific patterns of behaviour - in a secondary sense of the term self-organization.
Secondary self-organization, then, includes the primary one, adding to it the ability to create and to change habits through learning mechanisms. In the case of living organisms, the ability to create and to change habits allows them to act in order to further their own survival and to adjust their behaviour in accordance with environmental requests, changing the environment and being affected by it in a kind of circular feedback way.
A relevant point to be considered here is that, in accordance with the suppositions of the SOP, habits can be established amongst elements without the influence of a central control. However, in the primary sense there is no guarantee that these tendencies will be developed. When circular feedback mechanisms are present, and order parameters are formed in order to control the behaviour of established organizations, then secondary self-organization applies.
Taking into consideration these two notions of self-organization, the central hypothesis of the present paper is that creativity is a self-organizing process in which abductive reasoning occurs allowing the expansion of well structured search spaces.
Our starting point is the fact that the theory of self-organization provides many examples of cases where a system with a well established order parameter (i.e. a stable behavioural pattern that constitutes a habit) can suddenly jump to a different state after encountering a disturbance.
This sensitivity to perturbations is a central characteristic of dynamical systems that are on the verge of changing the order parameter. We submit that Peirce´s conception of creativity as involving abductive reasoning that gets triggered by surprises can be understood from this dynamic perspective. Through secondary self-organization a system behaves within the confines of a stable set of order parameters (habits). Under certain circumstances the appearance of surprises provides sufficient perturbation for the system to change its behavioural mode into an entirely new and different stable pattern. Thus, abduction as breaking a habit in response to surprises becomes understood as a self-reorganization of the system into a new order parameter in response to perturbations by the environment.
Taking this perspective provides some interesting results. First of all, the question as to how a system can generate hypotheses that are ´ frequently right
´, as Peirce puts it, is no longer a mystery. It is, ultimately, the collective interaction of the components of the system in response to aspects of the environment that results in the higher level order parameter. Thus, the new order parameter (i.e. the abduced hypothesis or habit) arises out of the history of the interactions of components within the system as well as out of the history of the system’s interactions with the environment. Indeed, from this perspective it is hard to see how the resulting order parameter could not be relevant, grounded as it is in the process of ongoing couplings between the system and its surroundings.
Secondly, the behaviour produced by a system governed by the new order parameter can be creative in the sense that it need not be related to the old ones in a straightforward way. Even initially small changes in the order parameter can ultimately give rise to wildly different stable behavioural patterns. A small difference in the behaviour of the organism (under the influence of the perturbation) can lead to different feedback from the environment which leads to slightly different behaviour once again, leading to different feedback, etc. This circularly coupled process

8 can set off a cascade of organism-environment interactions that lead to behavioural patterns that have no direct connection to the behaviours that were displayed before the disturbance. In
Boden´s terminology of conceptual spaces, it can be said that responses to perturbations can lead to such radically different behavioural patterns that they transcend the confines of the traditional conceptual space, thus necessitating a transformation of the conceptual space in order to encompass the new behaviour. Note, again, that there is no reason to wonder how the new behavioural pattern (despite its originality) can be adaptive, since both the organism and the environment have added their share to it, collectively sculpturing it, so to speak, into its final stable form.
We have argued that through self-organization, different habits are created by organisms allowing them to act in the environment in order to preserve their existence. As the dynamics of perception - action evolves, organisms are inevitably confronted with anomalies or problems.
Creative organisms adjust (or sometimes change radically) their habits to solve those problems using abduction as a possible guide to realise this process of adjustment. If we accept this hypothesis as a possible way of describing creativity in living creatures, could we extend its domain to encompass artificial systems such as robots?
To conclude this paper we are going to investigate possible applications of creativity in robotenvironment systems like Roboser (Verschure et al, 1996), which incorporates circular feedback and self-organizing mechanisms. This system contains a light-sensitive robot which moves around, propelled by external sources of light, on a flat surface. As it is designed, Roboser has a mechanism of aversion to any sort of physical contact, so that while it is attracted to light, it will run away whenever its body touches any object.
Now, would it be correct to suppose that Roboser is a creative system? At first glance, the answer is no; according to our common sense notion of creativity presented in the introduction of this paper, it does not make sense to talk about creativity in robots because they are pre-wired systems with no freedom to choose any particular item available in the world. However, if we include in them, as is the case with Roboser, circular feedback and self-organization mechanisms, then we are tempted to answer with a ´qualified no´.
Given that Roboser does not seem to possess criteria of relevance for distinguishing between appropriate and inappropriate habits, it becomes difficult to establish when Roboser can genuinely be called to be surprised with a new event while it is moving around. However, if a set of habits is fixed in Roboser's systems, then such habits could function as constraints in relation to which novelties could appear.
It seems to us that Roboser, despite being a relatively simple system, has the ability to respond to perturbations with new and sometimes strongly different forms of behaviour. From the perspective of Roboser´s history of interactions with the environment, some new behavioural patterns that are clearly distinct from its previous behaviours. However, the question remains whether such new behaviours can be called P-creative in Boden´s sense.
A further doubt we have arises because Roboser´s universe is missing an essential ingredient for H-creativity (and for mentality in general, but we reserve that issue for another paper). After all, Roboser is alone . Without a society of fellow-robots, all being slightly different in terms of their histories of primary and secondary self-organizational processes, Boden´s criterion for Hcreativity is simply inapplicable.
As suggested in section 1, a proper analysis of creativity seems to require investigations of the domain of collective behaviour, in relation to which criteria for the classification of creative (or

9 non creative) behavioural patterns could be established. In humans, this classification is grounded in their socio-cultural environment: we support certain attitudes and reject others on the basis of our own cultural values. Given that Roboser does not exist in such a collective dimension, how could its actions/hypotheses be considered creative or non creative? Therefore, we believe that a focus on the dynamics of socio-cultural aspects of creativity will have to be a necessary next step in the investigation of self-organization, abduction and creativity. The work by Vygotsky, we submit, could provide a fruitful foundation for this enterprise and should play a more central role in cognitive scientific research of creativity.
Further directions for research include a way to quantify the difference between changing, expanding and transforming conceptual spaces (specifically in the context of robotics), an investigation of the proper (control) parameter settings under which the above mentioned significant changes in order parameters can occur, and an examination of the set of parameter settings which qualify as providing a physical equivalent to mentalistic notions such as ´surprise´ and ´problem´.
Acknowledgements
We thank Prof. Lauro Frederido B. da Silveira for his stimulating ideas on Peirce's abductive reasoning which have motivated us to produce this essay. We also thank our colleagues from
CLE, UNICAMP, for all the invaluable discussions on self-organization; and Brazilian agencies
FUNDUNESP, CAPES, CNPQ and FAPESP for funding this research. Finally, we would like to thank the Dutch NICI-research institute for allowing one of the authors a prolonged stay in
Marilia, Brasil.
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