Levels of abstraction in logic and human action: A theory of discontinuity in the structure of mathematical logic, psychological behaviour, and social organization

164 Pages·1978·28.013 MB·English

by  Elliott Jaques with R.O. Gibson and D. J. Isaac

LEVELS OF
.U3STRACIR )N
1LN IDGIC
AND HI TMAN
‘Cr
liott Jaques
RiLiGibN011 And I), Lisiraci
L E V E L S O F
4 A B S T R A C T I O N I N
L O G I C A N D H U M A N
A C T I O N
A theory of discontinuity in the
structure of mathematical logic,
psychological behaviour, and social
organization
Editor: Elliott Jaques
with
R. 0. Gibson
and
D. J. Isaac
Heinemann • London
Preface and Acknowledgments
Heinemann Educational Books Ltd
LONDON EDINBURGH M E L B O U R N E A U C K L A N D This book is a combination of original papers and reprints.
TORONTO H O N G KONG S I N G A P O R E
The reprints and their sources are as follows:
KUALA LUMPUR N E W DELHI N A I R O B I
JOHANNESBURG L U S A K A I B A D A N Chapter 4: 'Experimental Treatment of Discontinuity Theory
KINGSTON of Human Development': D. J. Isaac and B. M. O'Connor,
Human Relations, Vol. 22, No. 5, 1969, pp. 427-55.
Chapter 5: 'Use of Loss of Skill under Stress, to Test a Theory
of Psychological Development': D. J. Isaac and B. M.
O'Connor, Human Relations, Vol. 26, No. 4, 1973, pp. 488 ff.
Chapter 6: 'Separation of Two Adult Populations': D. J. Isaac
and B. M. O'Connor, Human Relations (to be published).
Chapter 7: 'Discontinuity Theory of Psychological Develop-
ment': D. J. Isaac and B. M. O'Connor, Human Relations,
Vol. 29, No. 1, 1975, pp. 41-61.
ISBN 0 435 82280 2
Chapter 16: 'Stratification of Work and Organizational
Design': Ralph Rowbottom and David Billis, Human Rela-
© Elliott Jaques, R. 0. Gibson, and D. J. Isaac 1978
tions, Vol. 30, No. 1, 1977.
First published 1978
Chapter 15: 'Stratified Depth Structure of Bureaucracy':
Elliott Jaques; and
Chapter 19: 'Levels of Abstraction in Mental Activity': Elliott
Jaques; both in A general theory of bureaucracy, Elliott Jaques;
Heinemann Educational Books/Halsted Press, 1976.
The quotations from G. A. Miller's Psychology, the science of
mental life, arc included by permission of Hutchinson Publishing
Group Limited.
Various parts of the manuscript have been typed by Mrs C.
Borg-Skelton, Miss R. Fowler, Mrs M. Lewis, Mrs C. S.
Sparks and Miss NI. Stevens.
Published by
Heinemann Educational Books Ltd
48 Charles Street, London WI X 8AH
Printed in Great Britain by
Butler & Tanner Ltd, Frome and London
Contents
INTR D o N
I Structure ()I' the Book 3
Elliott Jaques
2 The System of Levels and Components 1 2
Elliott Jaques
3 Speculations on Deductive and Inductive Logic
and Knowledge 2 6
Elliott Jaques
PART A : EXPERIMENTAL WORK
ON DISCONTINUITY I N
PSYCHOLOGICAL
DEVELOPMENT
4 Experimental Treatment olDiscontinuity Theory of
Psychological Development 3 7
D. J. Isaac and B. M. O'Connor
5 Use of Loss of Skill under Stress to Test a Theory of
Psychological Development 7 0
D. J. Isaac and 13. M. O'Connor
6 Separation of Two Adult Populations Identified
with Two Levels of Psychological Development 8 1
D. J. Isaac and B. M. O'Connor
PART B: ABSTRACT RELATIONS
STRUCTURE
7 A Discontinuity Theory of Psychological Develop-
ment 95
D. J. Isaac and 13. M. O'Connor
PART C: CONVERSION T O SYSTEM
OF TRUTH TABLES
8 Conversion from the Relational to the Contrast
System 123
R. 0. Gibson and D. J. Isaac
vi C o n t e n t s
9 Truth Tables as a Formal Device in the Analysis of
Human Actions 132
Introduction
R. 0. Gibson and D. J. Isaac
10 Development of Truth Tables and 'Levels' 161
R. 0. Gibson
I I The Null Set 170
R. 0. Gibson
PART D: T R U T H TABLES A N D
LEVELS OF ABSTRACTION
12 S -R and F-T 1 7 7
R. 0. Gibson
13 'Fermat's Last Theorem' as an Expression of Duality 189
R. 0. Gibson
14 'The Two Cultures' and 'Levels of Abstraction' 1 9 9
R. 0. Gibson
PART E: DISCONTINUITY THEORY
IN HUMAN ACTIVITY
15 Stratified Depth Structure of Bureaucracy 2 0 9
Elliott Jaques
16 Stratification of Work and Organizational Design 2 2 4
Ralph Rowbottom and David Bill is
17 Assessment of Individual Capacity 2 5 1
Gillian Stamp
18 Five Levels of Mental Handicap 2 7 1
Ian Macdonald
19 Levels of Abstraction in Mental Activity 2 7 8
Elliott Jaques
BIBLIOGRAPHY 3 0 1
INDEX 3 0 5
1
Structure of the Book
Elliott Jaques
The fact that qualitative changes may occur in the state of
material things, and that those changes may occur suddenly,
is an ordinary part of everyday experience: falling snow may
change to a water droplet as it touches the ground; a stationary
object moves when touched; a dark wire lights up when
electrically activated. The natural sciences take such changes
for granted, it being expected that at certain critical points
changes in quality will occur with changes in the quantity of
given properties of a substance—its temperature, velocity,
electrical resistance, and so on. In short, continuous change in
quantity may be accompanied at certain decisive points by
discontinuity in state.
The most commonly used examples are, of course, quantum
theory on the one hand, and on the other hand changes in state
ofwater, from ice to water to steam to super-heated steam: with
continuous change in quantity in temperature sudden rapid
changes occur in density at critical temperatures, the qualita-
tive changes in density being manifested in change in
appearance.
In the social sciences, discontinuity in state with change in
quantity has been far less taken for granted. It is, indeed, only
in the Marxist theory of dialectical materialism that the notion
of change in quality with change in quantity appears in any
systematic way—although unfortunately linked to a highly
improbable historical materialistic view of the development of
one type of society from another. Apart from that attempt at
an explanation of social history, there have been occasional
references from time to time to the possibility of discontinuity
in so-called levels of abstraction. Little in the way of systematic
4 L e v e l s of Abstraction in Logic and Human Action Structure of the Book 5
work has been done, however; the results which are available Background
are summarized by Gillian Stamp in Chapter 17. The present work began in 1961 and came about through a
The most familiar quantitative expression of continuity chance meeting and discussion between John Isaac and myself.
theory in the social sciences is the normal distribution curve. At that time he had been working with the idea that significant
It is this normal distribution which is usually looked for in discontinuities showed up in levels of abstraction in mathe-
systematic studies. What is less commonly recognized is that matics and in scientific theory. His concern was with the
the normal distribution curve implies a single-parameter, or education of science students; he had become aware of possible
single-property, description of psychological and social pheno- discontinuities in levels of abstraction, through such observa-
mena. It is precisely this single-parameter notion which tions as the fact that some students were so concretely orientated
dominates the outlook in the social sciences. that they could never quite encompass the fact that a triangle
The less common outlook—that of multiple parameters, or was a mental construct and not a physical thing.
discontinuity—would express itself in multi-modality of dis- At the time he had already worked out with Roland Gibson
tribution. Multi-modality has never been a very popular inter- a preliminary analysis of geometry in terms of six discrete
pretation of distribution arrays. There has been a marked levels (later changed to five), ranging from primitive behaviour
tendency to smooth out the peaks and valleys so as to get a in a three-dimensional space to the development of the highly
uni-modal normal distribution. A useful example is that of the abstract hodological geometries. This work is reported in Gib-
many rat-learning experiments in which, despite the fact that son's article in Chapter 10. At the same time I had become
the data point to two different populations of rats in the sense interested in the idea of an underlying structure of discrete
that one group seems to be using a higher level of abstraction levels of managerial organization, and we were aware of a
in solving the maze-running problem, the interpretation is strong commonality in our approach—his to teaching and
stated in terms of higher ability only, rather than in terms of science and mine to organization structure.
higher ability having led to a change in quality to a different Since that time we have continued to exchange views and
type or quality of ability in the 'smarter' group of rats.' ideas. Isaac has pursued a programme of experimental work
It will be argued in this book that multiple parameters are with Brian O'Connor, and latterly has generalized his results
as ordinary a feature of human phenomena as they are of all in collaboration with Gibson through an analysis of the struc-
other natural phenomena, and that, under ordinary conditions, ture of mathematical logic. A series of publications has resulted
discontinuity will characterize the properties and development from this work, and it is the collection of these publications
of human characteristics. This idea is generally accepted in the which forms the centre-piece of this book.
notion of stages in individual development as in the extensive
work of Piaget and other developmental psychologists. We shall Structure of the Book as a Statement of Scientffic Methods
try to show, however, that these discontinuities are manifest The book falls into five main parts— A to E— which are
also in individual differences which divide populations into systematically connected as shown in the accompanying dia-
multi-modally distributed groups. This manifestation of discon- gram. The circular five-stage process which is represented gives
tinuities in individual differences has extensive implications for a picture of scientific methodology in its most general sense in
action; that is to say, it contains all the components of scientific
the analysis of psychological and social processes.
method, in contrast to many theories of method which con-
See, for example, Tolman, E. C. (1951) 'Cognitive Maps in Rats and
centrate on only one or a few components.
Men', in Behaviour and Psychological Man: University of California Press,
This general statement of scientific methodology comprises:
pp. 256-9.
the interaction between initial hunches, hypotheses, theories
(B) and the data collected in the context of those ideas (A) ;
Structure al the Book 7
6 L e v e l s of Abstraction in Logic and Human Action
In Part D the logical systematic testing is carried through
then the conversion of the elaborated theory and data (C) into
by means of a systematic analysis of truth table logic. The use
logical terms (D) where they can be systematically and rigor-
of truth tables is the methodology for the analysis, from which
ously examined for logical consistency. This logical testing is
is constructed an internally coherent system of five levels of
reinforced by practical testing and application (E), processes
abstraction. These five levels, derived from independent logical
D and E interacting in the same way as A and B. Probability
analysis, arc found to match the levels which were demon-
statements may be derived from the D—E interaction, linking
strated experimentally.
again with empirical data in A.
From Part D to Part E the two-way movement is between
the abstract and the concrete (hut at a higher level ofgeneraliza-
Logical System of dualities, Abstract
tion). mirroring the two-way movement between A and B
method structures, and relation
components structure which also connects data and abstraction. D and E constitute
Discontinuity a qualitative dimension, as a counterpart to the quantitative
Truth Conversion theory of character of the A and B interaction. In Part E are presented
table paper psychological
development a number of di fferent examples of how the experimentally and
(D) (C) (B) logically derived levels of abstraction are manifested in the
structure of mental capacity and in hierarchical social or-
Qualitative D & E A & 8 Quantitative ganization. Logically the relation is between universal principle
dimension interact interact dimension
• • and the specific instance, a relationship which introduces the
notion of probability. It is via probability that Part E returns
Applied Probability Experimen al to Part A, in the sense that probability provides the general
papers papers context for the empirical statistical analysis of data.
)E) This movement through Parts A, B, C, D and E, and back
Applications Statistical data from E to A, will he found to characterize the analyses of levels
of abstraction in mathematical logic in Chapter 9.
The organization of the book reflects this general methodo-
The Experimental Work and Discontinuity Theory
logy. It begins with the A—B empirical—theoretical interaction.
The chapters by Isaac and O'Connor in Part B describe the
For clarity of presentation, and not for reasons of empiricist
experimental work which was undertaken to explore two con-
philosophy, it presents first the purely statistical data in Part A,
nected hypotheses about discontinuity in psychological de-
reprinting a series of experimental papers by Isaac and
velopment showing up in two different types of multi-modality.
O'Connor. From these raw data an abstract relation structure
The first hypothesis was that discontinuity in ability in
is derived in Part B, described in the Isaac and O'Connor
problem-solving would manifest itself in the emergence with
`Discontinuity Theory of Psychological Development'. The
age of an increasing number of modes in the distribution of
relationship between Parts A and B is that of empirical data
scores indicating level of performance—giving a series of dis-
and an abstraction within which those data were sought and
crete levels of ability, five in all."
found, and the abstraction further elaborated. It is a quantita-
It may he noted in Chapter 4 that the original hypothesis was that there
tive dimension.
would be six prime levels of abstraction. As the experimental work proceeded,
Part C takes the material from A and B and puts it through
however, this hypothesis was changed to five levels rather than six. There
a conversion process. It introduces a system of dualities, struc- then emerged the more general conception of five fundamental levels, but
ture, and components, which allows the experimental material reappearing as a coherent set in higher- and lower-level contexts as described
to be converted to the general system of mathematical logic. on page 22.
Structure of the Book 9
8 L e v e l s of Abstraction in Logic and Human Action
The second hypothesis was that not only would there be a development is described in Chapter 7. That chapter elaborates
series of discontinuous levels, but that a different mode of work fifteen components, or modes of functioning. These fifteen
would emerge with each level. Each of the lower-level modes components occur because each of the lower levels of abstrac-
would reappear at each higher level, creating a number of tion reappears in a more complex context at each successively
different methods or styles of problem-solving at the higher higher level of abstraction. There is thus one component at
levels. There would thus be one additional mode of problem- level one, two at level two, and so on up to five components at
solving at each level; with the resulting pattern of fifteen com- level five, giving fifteen components in all. The fifteen com-
ponents described in Chapters 8 and 9: ponents arc shown in later chapters to correspond to fifteen
basic dualities in the analysis of mathematical logic (Chapter
Level 5 A 5 B5 C5 D5 ES 8), and to fifteen styles of work-capacity (Chapter 17).
Level 4 A 4 B4 C4 D4
Level 3 A 3 B3 C3 Conversion to Truth Tables and Logical Analysis
The experimental work and its derived discontinuity theory are
Level 2 A 2 B2
converted for use in truth table analysis by the structure of
Level I A l bi-polar relationships and contrasts described in Chapter 8.
The content of the fifteen modes of functioning is here further
Both these hypotheses have been strongly supported by the generalized, and by formulation in terms of relationships and
experimental work. A point of great significance is that the contrasts lays the foundation for the relational statements and
problems were administered in a manner characteristic.of real- dualities of mathematical logic. The notion is introduced of
life work, rather than like the artificial conditions of intelligence interplay in movement back and forth between confusion and
testing. There were two important features: discrimination. This notion is later expressed in the interaction
between T (discrimination) and F (confusion) in the truth table
(a) the subject was given no practice sessions to familiarize him
analysis.
with the type of problem, but rather was required to dis-
The full system is then presented in Chapter 9, which sets
cover for himself the nature of the problem as well as how
out the creative analysis, carried out by Gibson and Isaac, of
to solve it;
a structure of discontinuous levels inherent in mathematical
(b) the available information did not remain constant; the
logic as a complete system.
problem required instead the accumulation of information
How this analysis was intuitively pursued is described by
and experience, the amount of information being well
Gibson in Chapter 10. The succeeding chapters 11, 12 and 13
beyond what could possibly be consciously remembered.
describe some general applications of the analysis to such
In a brilliant experimental design, Isaac and O'Connor diverse problems as the possible resolution of Fermat's last
have vividly described in Chapter 4 how, when the problem- theorem, the humanizing ofstimulus-response psychology, and
solvingsituations were administered under the usual intelligence a formulation of the two-culture issue. The question of Fermat's
test conditions of a familiar frame of reference, a uni-modal last theorem is resolved in the following sense:
distribution of scores was obtained. It was only with the switch All models of the levels-structure itself, that is all models or
to the unfamiliarity which characterizes problem-solving in formulations of the authors' sociological perspective, neces-
everyday life that multi-modality was revealed. sarily mirror one another. Fermat's last theorem taken as a
Confirmed by the experimental work described in Chapters postulate, in the arithmetic model, corresponds to the parallel
4, 5 and 6, a general theory of discontinuity in psychological postulate in the geometry model. But the geometrical case is
10 L e v e l s of Abstraction in Logic and Human Action Structure of the Book I I
generally regarded to have been established as postulational; existence of multi-modality in the distribution of work-capacity
hence the impossibility of proving Fermat's last theorem. in human populations.
Applications The Argument and its General Implications
The final chapters are included to illustrate the five-level con- Finally, a comment on Chapters 2 and 3. In these chapters I
ceptual scheme in practice. Chapter 15 (Jaques) describes the have tried to summarize the argument of the book, and to show
general pattern of discontinuity in structure of levels of bureau- the striking resemblances in results emerging independently
cratic organization, and how this structure was discovered. from the experimental work, the logical 'analysis', and the
Chapter 16 by Rowbottom and Billis describes their formula- applied field work. I have tried, further, to draw certain broad
tion of the work content of the various levels of bureaucratic implications from the work: in particular with respect to the
organization. understanding of deductive and inductive logical processes, and
The remaining chapters by Stamp, Macdonald and Jaques, the contextual theory of meaning. For the reader who is not too
all have to do with human work-capacity. It is these papers familiar with mathematical logic, it is hoped that these chapters
which serve to give psychological content to the more abstract will serve as a useful introduction to the logical 'analysis' which
conceptions developed in the experimental work and logical forms the core of the argument.
analysis.
Chapter 17, by Gillian Stamp, presents an extension of the
Isaac and O'Connor work into the assessment of work-capacity.
She gives the evidence for the existence of five levels of capacity.
At each succeeding level a new style or mode of .working
emerges, alongside the preceding modes, all functioning at a
higher level as a result of being integrated within a more general
context. This research points to the same fifteen components
which appear in the experimental work and the logical analysis,
each of the fifteen modes suggesting a psychological meaning
for the fifteen components.
In Chapter 18, Ian Macdonald describes his work with
mentally handicapped individuals. The five levels he has de-
veloped for the assessment of their general capabilities were
quite independently derived from field work with nurses,
doctors and others concerned with the problem of how to make
such assessments. It was the striking similarity in feel between
those five levels and the five levels obtained from normal
populations and logical analysis, that led to the idea of the
possible existence of a range of more and more abstract contexts -
within which the five levels of abstraction can be expressed (see
Chapter 2).
Chapter 19 (Jaques) outlines some of the original thinking
which gave rise to the hypothesis that the regular discontinuity
found in bureaucratic hierarchies is a straight reflection of the