Kelly's "Geometry of Psychological Space" and its Significancefor Cognitive Modeling
Mildred L G Shaw & Brian R Gaines
Knowledge Science Institute, University of Calgary
Calgary, Alberta, Canada T2N 1N4
{mildred, gaines}@cpsc.ucalgary.ca
(from The New Psychologist, 23-31, October, 1992)
Abstract
Introduction
Psychological Geometry
Constructs and Concepts
A Visual Language for the Logic
The Repertory Grid
Conclusions
References
Abstract
Personal construct psychology is a theory of individual and group psychologicaland social processes that takes a constructivist position in modeling humanknowledge but bases this on a positivist scientific position that characterizesconceptual structures in axiomatic terms. It provides a fundamental frameworkfor both theoretical and applied studies of knowledge acquisition andrepresentation. This paper presents Kelly's original intuitions underlyingpersonal construct psychology and links these to its foundational role incognitive and computational knowledge representation.Introduction
George Kelly was a clinical psychologist who lived between 1905 and 1967,published a two volume work defining personal construct psychology in 1955, andwent on to publish a large number of papers further developing the theory, manyof which have been issued in collected form (Maher, 1969). Figure 1 attemptsto encapsulate the historic forces at work in psychology, logic, cognitivescience and artificial intelligence before and after Kelly's work.
Figure 1 The intellectual setting of personal construct psychology
Personal construct psychology can be seen to be an heir to Europeanlogical positivism and American pragmatism, taking an alternative path tobehaviorism that is similar in many respects to what later became termedcognitive science. In this Kelly was preceded by Vygotsky in the USSRwhose bookThought and Languageappeared in 1934 but was suppresseduntil 1962 (Wertsch, 1985; Vygotsky, 1989). Luria, who had been a student ofVygotsky invited Kelly to Moscow in 1961 where he delivered a particularlyclear statement of the formal principles of personal construct psychology inthe light of reactions to his earlier book (Kelly, 1969). Kelly was working ona second book when he died of which, unfortunately, only the preface has beenpublished (Kelly, 1970), and he also began to become involved with the computersimulation of personality (Kelly, 1963). However, his work never became partof the mainstream cognitive science literature although it has attractedwidespread attention and application in management, education and clinicalpsychology (Shaw, 1981).
Kelly was a keen geometer with experience in navigation and an interest inmulti-dimensional geometry. When he came to formalize his theory he took ashis model Euclid'sElementsand axiomatized personal constructpsychology as afundamental postulatetogether with elevencorollaries, terming the primitives involveselementsandconstructs. Kelly took far more than a vocabulary from Euclid. TheElementswere the normative model for the science that arose out of theGreek enlightenment, and fulfilled a similar role in the second enlightenmentfor Descartes, Kant and others (Russell, 1946). The careful definition ofterms, with attention to exact and overt presuppositions, and then thedevelopment of a rigorous deductive sequence with precise specification ofhypothesis and constructions, provided an intellectual model that we followtoday. Indeed in the post-modern literature the modern age has beencharacterized as based on theethics of geometry(Lachterman, 1989).
Kelly presented his theory as ageometry of psychological space(Kelly,1969), and his conceptual framework is very clear if seen in these terms. Itmay seem strange to base cognitive science on geometry rather than logic untilone remembers that the reasoning structure of theElementswas the basisfor both Greek and modern logic, and that geometry and logic in acategory-theoretic framework are equivalent (Mac Lane, 1971). What Kellyachieved through the use of geometry was an intensional logic, one in whichpredicates are defined in terms of their properties rather than extensionallyin terms of those entities that fall under them. In his time there were noadequate formal foundations for intensional logic--it was not until 1963 thatHintikka (1963) published the model sets formulation that gave intensionallogic itspossible worldsformal foundations.
PsychologicalGeometry
Kelly's "fundamental postulate" for personal construct psychology was that:"A person's processes are psychologically channelized by the way in which heanticipates events." (Kelly, 1955, p.46)
This was stated as a postulate to emphasize that it was presented as aconvenient viewpoint from which to understand human behavior, not imputed to anunderlying physiological or psychological reality. The basis of Kelly'sapproach to psychotherapy was that this was also a convenient viewpoint fromwhich someone could understand, and modify, their own behavior. He saw allpeople as "personal scientists" in anticipating the world, and attempted todevelop techniques where this anticipatory modeling activity was reflexivelyapplied to the self. His first corollary, the construction corollary,states:
"A person anticipates events by construing their replications." (p.50)
This emphasis on the role in behavior of a view to the future is whatdistinguishes Kelly's approach to psychology. He saw people as driven by theneed to cope with coming events in the world and all other aspects of behavioras deriving from this:
"A person's processes, psychologically speaking, slip into the grooves whichare cut out by the mechanisms he adopts for realizing his objectives." (p.49)
These grooves provide templets for construing events which he termed "personalconstructs":
"Man looks at his world through transparent templets which he creates and thenattempts to fit over the realities of which the world is composed." (pp.8-9)
"Constructs are used for predictions of things to come, and the world keeps onrolling on and revealing these predictions to be either correct or misleading.This fact provides the basis for the revision of constructs and, eventually, ofwhole construct systems." (p.14)
Kelly introduces the notion of apsychological spaceas a term for aregion in which we may place and classify elements of our experience. It isimportant to note that he did not suppose this space to pre-exist as a world ofsuch elements, but rather to come into being through a process of constructionby which we create a space in which to place elements as we come to construethem. He sees us as creating dimensions in personal psychological space as away of providing a coordinate system for our experience, and emphasizes thatthe topology of the space comes into existence as it is divided:
"Our psychological geometry is a geometry of dichotomies rather than thegeometry of areas envisioned by the classical logic of concepts, or thegeometry of lines envisioned by classical mathematical geometries. Each of ourdichotomies has both a differentiating and an integrating function. That is tosay it is the generalized form of the differentiating and integrating act bywhich man intervenes in his world. By such an act he interposes a differencebetween incidents -- incidents that would otherwise be imperceptible to himbecause they are infinitely homogeneous. But also, by such an intervening act,he ascribes integrity to incidents that are otherwise imperceptible becausethey are infinitesimally fragmented. In this kind of geometrically structuredworld there are no distances. Each axis of reference represents not a line orcontinuum, as in analytic geometry, but one, and only one, distinction.However, there are angles. These are represented by contingencies oroverlapping frequencies of incidents. Moreover, these angles of relationshipbetween personal constructs change with the context of incidents to which theconstructs are applied. Thus our psychological space is a space withoutdistance, and, as in the case of non-Euclidian geometries, the relationshipsbetween directions change with the context." (Kelly, 1969)
It is this emphasis on the space itself being created by a process of makingdistinctions rather than being defined by the elements distinguished that givespersonal construct psychology its intensional nature:
"the construct is a basis of making a distinction...not a class of objects, oran abstraction of a class, but a dichotomous reference axis" (Kelly, 1970)
Figure 2 shows the main features of Kelly's notion of psychological space. Aconstruct is a dichotomous reference axis. It defines a family of planesorthogonal to it that divide the space:
"To catch a glimpse of psychological space we may imagine a system of planes,each with two sides or aspects, slicing through a galaxy of events" (Kelly,1970)
However, only part of the space that is divided is used in placing elements:
"A construct is convenient for the anticipation of a finite range of eventsonly. A personal construct system can hardly be said to have universalutility. Not everything that happens in the world can be projected upon allthe dichotomies that make up a person's outlook. . . The geometry of the mindis never a complete system." (Kelly, 1970)
This division defines the dichotomous poles of the construct:
"Each construct involves two poles, one at each end of its dichotomy. Theelements associated at each pole are like each other with respect to theconstruct and are unlike the elements at the other pole" (Kelly, 1955)
Even though Kelly's geometry is not metrically defined, he has no problems inusing the defined constructs to generate a metric as shown in Figure 3:
"imagine a system of planes, each with two sides or aspects, slicing through agalaxy of events...If the set is moved into all possible positions it generatesa paracartesian hyperspace with its relatively concrete scalar axes" (Kelly,1970)
It is possible to develop a complete theory of cognition, action, learning andintention with the geometry.
Figure 2 The geometry of psychological space
Figure 3 Scales in psychological space
Constructsand Concepts
One obvious question about Kelly's use of the term "construct" was how itdiffers from the more conventional term "concept." He discusses this in thefollowing terms:"We use the termconstructin a manner which is somewhat parallel to thecommon usage of `concept.' However, if one attempts to translate ourconstructinto the more familiar term, `concept,' he may find someconfusion. We have included, as indeed some recent users of the term `concept'have done, the more concretistic concepts which nineteenth-centurypsychologists would have insisted on calling `percepts.' The notion of`percept' has always carried the idea of its being a personal act--in thatsense, ourconstructis in the tradition of `percepts.' But we also seeourconstructas involving abstraction--in that sense ourconstructbears a resemblance to the traditional usage of `concept.' ...Now when we assume that the construct is basically dichotomous, that itincludes percepts, and that it is a better term for our purposes than the term`concept,' we are not quarreling with those who would use it otherwise. Withinsome systems of logic the notion of contrast as something distinct fromirrelevancy is not part of the assumptive structure. We, on the other hand aresimply assuming that this is the way people do, in fact, think." (Kelly, 1955,p.70)
The dichotomous aspect of constructs is the most significant aspect of thedifference between Kelly's constructs and current usage of the term, `concept.'Hisdichotomy corollarystates this:
"A person's construction system is composed of a finite number of dichotomousconstructs." (p.59)
and it is a consequence of the two-sided nature of a distinction represented inthe geometry. The range of convenience captures the notion of relevancy andthe distinction within it then generates a natural opposition. That peopletend to conceptualize the world in terms of restricted sorts that are thendichotomized is a phenomenon identified in antiquity (Lloyd, 1966) and commonacross many cultures (Maybury-Lewis & Almagor, 1989).
Since the term "concept" is used in psychology and in knowledge representationin somewhat different ways, it is useful to define it clearly in these contextsfor the purposes of this paper. A psychological concept is defined to be thatmental entityimputedto a distinction making agent as enabling it tomake a particular distinction. Note that concepts are separated both from thedistinctions they support and the entities they distinguish, and are notreified but seen as imputed to the agent. They are themselves distinctionsmade by an observer--possibly, a reflective observer. Concepts are statevariables we impute to a knowledgeable agent. This definition also correspondsto Anglin's: