Fragments of Behaviour: The Extensional Stance: Text
David Longley
FRAGMENTS OF BEHAVIOUR:
EXTRACT 5: FROM 'A System Specification for PROfiling BEhaviour'
Full text is available at:
http://www.uni-hamburg.de/~kriminol/TS/tskr.htm
SECTION B: Methodological (Evidential) Behaviourism
The Perspective From 'The Extensional Stance
'Suppose that each line of the truth table for the
conjunction of all [of a person's] beliefs could be
checked in the time a light ray takes to traverse the
diameter of a proton, an approximate "supercycle" time,
and suppose that the computer was permitted to run for
twenty billion years, the estimated time from the "big-
bang dawn of the universe to the present. A belief
system containing only 138 logically independent
propositions would overwhelm the time resources of this
supermachine.'
C. Cherniak (1986)
Minimal Rationality p.93
'Cherniak goes on to note that, while it is not easy to
estimate the number of atomic propositions in a typical
human belief system, the number must be vastly in excess
of 138. It follows that, whatever its practical benefits
might be, the proposed consistency-checking algorithm is
not something a human brain could even approach. Thus,
it would seem perverse, to put it mildly, to insist that
a person's cognitive system is doing a bad job of
reasoning because it fails to periodically execute the
algorithm and check on the consistency of the person's
beliefs.'
S. Stich (1990)
The Fragmentation of Reason p.152
'I should like to see a new conceptual apparatus of a
logically and behaviourally straightforward kind by
which to formulate, for scientific purposes, the sort of
psychological information that is conveyed nowadays by
idioms of propositional attitude.'
W V O Quine (1978)
In the extract from Cherniak, the point being made is that as the
number of discrete propositions increase, the possible combinations
increases dramatically, or, as Shafir and Tversky 1992 say:
'Uncertain situations may be thought of as disjunctions
of possible states: either one state will obtain, or
another....
Shortcomings in reasoning have typically been attributed
to quantitative limitations of human beings as
processors of information. "Hard problems" are typically
characterized by reference to the "amount of knowledge
required," the "memory load," or the "size of the search
space"....Such limitations, however, are not sufficient
to account for all that is difficult about thinking. In
contrast to many complicated tasks that people perform
with relative ease, the problems investigated in this
paper are computationally very simple, involving a
single disjunction of two well defined states. The
present studies highlight the discrepancy between
logical complexity on the one hand and psychological
difficulty on the other. In contrast to the "frame
problem" for example, which is trivial for people but
exceedingly difficult for AI, the task of thinking
through disjunctions is trivial for AI (which routinely
implements "tree search" and "path finding" algorithms)
but very difficult for people. The failure to reason
consequentially may constitute a fundamental difference
between natural and artificial intelligence.'
E. Shafir and A. Tversky (1992)
Thinking through Uncertainty: Nonconsequantial Reasoning
and Choice
Cognitive Psychology 24,449-474
>From a pattern recognition or classification stance, it is known that
as the number of predicates increase, the number of linearly separable
functions becomes proportionately smaller as is made clear by the
following extract from Wasserman (1989) when discussing the concept of
linear separability:
'We have seen that there is no way to draw a straight
line subdividing the x-y plane so that the exclusive-or
function is represented. Unfortunately, this is not an
isolated example; there exists a large class of
functions that cannot be represented by a single-layer
network. These functions are said to be linearly
inseparable, and they set definite bounds on the
capabilities of single-layer networks.
Linear separability limits single-layer networks to classification
problems in which the sets of points (corresponding to input values)
can be separated geometrically. For our two-input case, the separator
is a straight line. For three inputs, the separation is performed by a
flat plane cutting through the resulting three-dimensional space. For
four or more inputs, visualisation breaks down and we must mentally
generalise to a space of n dimensions divided by a "hyperplane", a
geometrical object that subdivides a space of four or more
dimensions.... A neuron with n binary inputs can have 2 exp n
different input patterns, consisting of ones and zeros. Because each
input pattern can produce two different binary outputs, one and zero,
there are 2 exp 2 exp n different functions of n variables.
As shown [below], the probability of any randomly selected function
being linearly separable becomes vanishingly small with even a modest
number of variables. For this reason single-layer perceptrons are, in
practice, limited to simple problems.
n 2 exp 2 exp n Number of Linearly Separable Functions
1 4
2 16 14
3 256 104
4 65,536 1,882
5 4.3 x 10 exp 9 94,572
6 1.8 x 10 exp 19 5,028,134
P. D. Wasserman (1989)
Linear Separability: Ch2. Neural Computing Theory and Practice
In later sections evidence is presented in the context of clinical vs.
actuarial judgment that human judgement is severely limited to
processing only a few variables. Beyond that, non- linear fits become
more frequent. This is discussed later in the context of connectionist
'intuitive',inductive inference and constraints on short-term or
working memory span (c.f. Kyllonen & Christal 1990 - "Reasoning
Ability Is (LIttle More Than) Working-Memory Capacity?!"), but it is
worth mentioning here that in the epilogue to their expanded re-print
of their 1969 review of neural nets 'Perceptrons - An Introduction to
Computational Geometry', after reiterating their original criticism
that neural networks had only been shown to be capable of solving 'toy
problems', ie problems with a small number of dimensions, using 'hill
climbing' algorithms, Minsky and Papert (1988) effectively did a
'volte face' and said:
'But now we propose a somewhat shocking alternative:
Perhaps the scale of the toy problem is that on which,
in physiological actuality, much of the functioning of
intelligence operates. Accepting this thesis leads into
a way of thinking very different from that of the
connectionist movement. We have used the phrase "society
of mind" to refer to the idea that mind is made up of a
large number of components, or "agents," each of which
would operate on the scale of what, if taken in
isolation, would be little more than a toy problem.'
M Minsky and S Papert (1988) p266-7
and a little latter, which is very germane to the fragmentation of
behaviour view being advanced in this volume:
'On the darker side, they [parallel distributed
networks] can limit large-scale growth because what any
distributed network learns is likely to be quite opaque
to other networks connected to it.'
ibid p.274
This *opacity* of aspects, or elements, of our own behaviour to
ourselves is central to the theme being developed in this volume,
namely that a science of behaviour must remain entirely extensional
and that there can not therefore be a science or technology of
psychology to the extent that this remains intensional (Quine
1960,1992). The discrepancy between experts' reports of the
information they use when making diagnoses (judgments) is reviewed in
more detail in a later section, however, research reviewed in Goldberg
1968, suggests that even where diagnosticians are convinced that they
use more than additive models (ie use interactions between variables -
which statistically may account for some of the non-linearities),
empirical evidence shows that in fact they only use a few linear
combinations of variables (cf. Nisbett and Wilson 1977, in this
context).
As an illustration of methodological solipsism (intensionalism) in
practice consider the following which neatly contrasts subtle
difference between the methodological solipsist approach and that of
the methodological or 'evidential' behaviourist.
Several years ago, a prison psychologist sought the views of prison
officers and governors as to who they considered to be 'subversives'.
Those considered 'subversive' were flagged 1, those not considered
subversive were flagged 0. The psychologist then used multiple
regression to predict this classification from a number of other
behavioural variables. From this he was able to produce an equation
which predicted subversiveness as a function of 4 variables: whether
or not the inmate had a firearms offence history, the number of
reports up to arrival at the current prison, the number of moves up to
arrival where the inmate had stayed more than 28 days, and the number
of inmate assaults up to arrival.
Note that the dependent variable was binary, the inmate being
classified as 'subversive' or 'not subversive'. The prediction
equation, which differentially weighted the 4 variables, therefore
predicted the dependent variable as a value between 0 and 1. Now the
important thing to notice here is that the behavioural variables were
being used to predict something which is essentially a propositional
attitude, ie the degree of certainty of the officers beliefs that
certain inmates were subversive.
The methodological solipsist may well hold that the officer's beliefs
are what are important, however, the methodological behaviourist would
hold that what the officers thought was just *an approximation of what
the actual measures of inmate behaviour represented*, ie his thoughts
were just vague, descriptive terms for inmates who had lots of
reports, assaulted inmates and had been moved through lots of prisons,
and were probably in prison for violent offences. What the officers
thought was not perhaps, all that important, since we could just go to
the records and identify behaviours which are characteristic of
troublesome behaviour and then identify inmates as a function of those
measures (cf. Williams and Longley 1986).
In the one case the concern is likely to be with developing better and
better predictors of what staff THINK, and in the other, it becomes a
matter of simply recording better measures of classes of behaviour and
empirically establishing functional relations between those classes.
In the case of the former, intensional stance, one becomes interested
in the *psychology* of those exposed to such factors (ie those exposed
to the behaviour of inmates, and what they *vaguely or intuitively
describe it as)*. From the extensional stance (methodological
behaviourist) defended in these volumes, such judgments can only be a
**function** of the data that staff have had access to. From the
extensional stance, one is simply interested in recording *behaviour*
itself and deducing implicit relations. Ryle (1949) and many
influential behaviourists since (Quine 1960), have, along with Hahn
(1933) suggested that this is our intellectual limit anyway:
'It is being maintained throughout this book that when
we characterize people by mental predicates, we are not
making untestable inferences to any ghostly processes
occurring in streams of consciousness which we are
debarred from visiting; we are describing the ways in
which those people conduct parts of their predominantly
public behaviour.'
G. Ryle
The Concept of Mind (1949)
Using regression technology as outlined above is essentially how
artificial neural network software is used to make classifications, in
fact, there is now substantial evidence to suggest that the two
technologies are basically one and the same (Stone 1986), except that
in neural network technology, the regression variable weights are
opaque to the judge, cf. Kosko (1992):
'These properties reduce to the single abstract property
of *adaptive model-free function estimation*:Intelligent
systems adaptively estimate continuous functions from
data without specifying mathematically how outputs
depend on inputs...A function f, denoted f: X Y, maps
an input domain X to an output range Y. For every
element x in the input domain X, the function f uniquely
assigns the element y to the output range Y.. Functions
define causal hypotheses. Science and engineering paint
our pictures of the universe with functions.
B. Kosko (1992)
Neural Networks and Fuzzy Systems: A Dynamical Systems
Approach to Machine Intelligence p 19.
The rationale behind Sentence Management as outlined in the paper
'What are Regimes?' (Longley 1992) and in section D below, is that the
most effective way to bring about sustained behaviour change is not
through specific, formal training programmes, but through a careful
strategy of apposite allocation to activities which *naturally require
the behavioural skills* which an inmate may be deficient in. This
depends on standardised recording of activity and programme behaviour
*throughout sentence* which will provide a *historical and actuarial,
record of attainment.* This will provide differential information to
guide management's decisions as how best to help inmates lead a
constructive life whilst in custody, and, hopefully, after release.
Initially, it will serve to support actuarial analysis of behaviour as
a practical working, inmate, and management, information system. In
time, it should provide data to enable managers to focus resources
where they are most required (ie provide comprehensive regime
profiles, which highlight strong and weak elements). Such a system is
only interested in what inmates 'think' or 'believe' to the extent
that what they 'think' and 'believe' are specific skills which the
particular activities and programmes require, and which can therefore
be systematically assessed as criteria of formative behaviour
profiling. What is required for effective decision making and
behaviour management is a history of behavioural performance in
activities and programmes, much like the USA system of Grade Point
Averages and attendance. All such behaviours are the natural skills
required by the activities and programmes, and all such assessment is
criterion reference based.
The alternative, intensional approach, of asking staff to identify
risk factors from the documented account of the offence, and
subsequently asking staff to look out for them in the inmate's prison
behaviour may well only serve to shape inmates to inhibit
(conditionally suppress) such behaviour, especially if their
progression through the prison system is contingent on this. However,
from animal studies of acquisition-extinction-reacquisition, there is
no evidence that such behaviour inhibition is likely to produce a
*permanent* change in the inmate's behaviour in the absence of the
inmate *learning new behaviours*. Such an approach is also blind to
base rates of behaviours. Only through a system which encouraged the
acquisition of *new* behaviours can we expect there to be a change in
risk, and even this would have to be *actuarially* determined. For a
proper estimate of risk, one requires a system where inmates can be
assessed with respect to standard demands of the regime. The standard
way to determine risk factors was to derive these from *statistical*
*analysis,* not from *clinical (intensional) judgement*.
Much of the rationale for this stance can be deduced from the
following. Throughout the 20th century, psychologists' evaluation of
the extent to which reasoning can be formally taught has been
pessimistic. From Thorndike (1913) through Piaget (see Brainerd 1978)
to Newell (1980) it has been maintained that:
'the modern.....position is that learned problem-solving
skills are, in general, idiosyncratic to the task.'
A. Newell 1980.
Furthermore, it has been argued that whilst people may in fact use
abstract inferential rules, these rules can not be formally taught to
any significant degree. They are learned instead under natural
conditions of development and cannot be improved by formal
instruction. This is essentially Piaget's position.
The above is, in fact, how Nisbett et al (1987) opened their SCIENCE
paper '*Teaching Reasoning*'. Reviewing the history of the concept of
formal discipline which looked to the use of latin and the classics to
train the 'muscles of the mind', Nisbett et. al provided some
empirical evidence on the degree to which one class of inferential
rules can be taught. They describe these rules as 'a family of
pragmatic inferential rule systems that people induce in the context
of solving recurrent everyday problems'. These include "causal
schemas", "contractual schemas" and "statistical heuristics". The
latter are clearly instances of inductive rather than deductive
inference.
Nisbett et. al. clearly pointed out that the same can not be said for
the teaching of deductive inference (i.e. formal instruction in
deductive logic or other syntactic rule systems). With respect to the
teaching of logical reasoning, Nisbett et. al. had the following to
say:
'Since highly abstract statistical rules can be taught
in such a way that they can be applied to a great range
of everyday life events, is the same true of the even
more abstract rules of deductive logic? We can report no
evidence indicating that this is true, and we can
provide some evidence indicating that it is not.....In
our view, when people reason in accordance with the
rules of formal logic, they normally do so by using
pragmatic reasoning schemas that happen to map onto the
solutions provided by logic.'
ibid. p.628
Such 'causal schemas' are known as 'intensional heuristics' (Agnoli
and Krantz 1989) and have been widely studied in psychology since the
early 1970s, primarily by research psychologists such as Tversky and
Kahneman (1974), Nisbett and Ross (1980), Kahneman, Slovic and Tversky
(1982), Holland et. al (1986) and Ross and Nisbett (1991).
A longitudinal study by Lehman and Nisbett (1990) looked at
differential improvements in the use of such heuristics in college
students classified by different subject groups. They found
improvements in the use of statistical heuristics in social science
students, but no improvement in conditional logic (such as the Wason
selection task). Conversely, the natural science and humanities
produced significant improvements in conditional logic. Interestingly,
there were no changes in students studying chemistry. Whilst the
authors took the findings to provide some support for their thesis
that reasoning can be taught, it must be appreciated that the findings
at the same time lend considerable support to the view that each
subject area inculcates its own particular type of reasoning, even in
highly educated individuals. That is, the data lend support to the
thesis that training in particular skills must look to training for
transfer and application within particular skill areas. This is
elaborated below in the context of the system of Sentence Management.
Today, formal modelling of such intensional processes is researched
using a technology known as 'Neural Computing' which uses inferential
statistical technologies closely related to regression analysis.
However, such technologies are inherently inductive. They take samples
and generalise to populations. They are at best pattern recognition
systems.
Such technologies must be contrasted with formal deductive logical
systems which are algorithmic rather than heuristic (extensional
rather than intensional). The algorithmic, or computational, approach
is central to classic Artificial Intelligence and is represented today
by the technology of relational databases along with rule and
Knowledge Information Based System (KIBS) which are based on the First
Order Predicate Calculus, the Robinson Resolution Principle (Robinson
1965,1979) and the long term objectives of automated reasoning (e.g.
Wos et. al 1992 and the Japanese Fifth Generation computing project) -
see Volume 2 and 3.
The degree to which intensional heuristics can be suppressed by
training is now controversial (Kahneman and Tversky 1983; Nisbett and
Ross 1980; Holland et al. 1986; Nisbett et al 1987; Agnoli and Krantz
1989; Gladstone 1989; Fong and Nisbett 1991; Ploger and Wilson 1991;
Smith et al 1992). In fact, the degree to which they are or are not
may be orthogonal to the main theme of this paper, since the main
thrust of the argument is that behaviour science should look to
deductive inferential technology, not inductive inference. Central to
the controversy, however, is the degree to which the suppression is
sustained, and the degree of generalisation and practical application
of even 'statistical heuristics'. For example, Ploger and Wilson
(1991) said in commentary on the 1991 Fong and Nisbett paper:
'G. T. Fong and R. E. Nisbett argued that, within the
domain of statistics, people possess abstract rules;
that the use of these rules can be improved by training;
and that these training effects are largely independent
of the training domain. Although their results indicate
that there is a statistically significant improvement in
performance due to training, they also indicate that,
even after training, most college students do not apply
that training to example problems.
D. Ploger & M. Wilson
Statistical reasoning: What is the role of inferential rule training?
Comment on Fong and Nisbett.
Journal of Experimental Psychology General; 1991 Jun Vol
120(2) 213-214
Furthermore, Gladstone (1989) criticises the stance adopted by the
same group in an article in American Psychologist (1988):
'[This paper]' criticizes the assertion by D. R. Lehman
et al. that their experiments support the doctrine of
formal discipline. The present author contends that the
work of Lehman et al. provides evidence that one must
teach for transfer, not that transfer occurs
automatically. The problems of creating a curriculum and
teaching it must be addressed if teachers are to help
students apply a rule across fields. Support is given to
E. L. Thorndike's (1906, 1913) assessment of the general
method of teaching for transfer.'
R. Gladstone (1989)
Teaching for transfer versus formal discipline.
American Psychologist; 1989 Aug Vol 44(8) 1159
What this research suggests is that whilst improvements can be made by
training in formal principles (such as teaching the 'Law of Large
Numbers'), this does not in fact contradict the stance of Piaget and
others that most of these inductive skills are in fact learned under
natural lived experience ('erlbnis' and 'lebenswelt' Husserl 1952, or
'Being-in-the-world' Heidegger 1928). Furthermore, there is evidence
from short term longitudinal studies of training in such skills that
not only is there a decline in such skills after even a short time,
but there is little evidence of application of the heuristics to novel
problem situations outside the training domain. This is the standard
and conventional criticism of 'formal education'. Throughout this
work, the basic message seems to be to focus training on specific
skills acquisition which will not so much generalise to novel
contexts, but find application in other, similar if not identical
contexts.
Most recently, Nisbett and colleagues have looked further at the
criteria for assessing the efficacy of cognitive skills training:
'A number of theoretical positions in psychology
(including variants of case-based reasoning, instance-
based analogy, and connectionist models) maintain that
abstract rules are not involved in human reasoning, or
at best play a minor role. Other views hold that the use
of abstract rules is a core aspect of human reasoning.
The authors propose 8 criteria for determining whether
or not people use abstract rules in reasoning. They
examine evidence relevant to each criterion for several
rule systems. There is substantial evidence that several
inferential rules, including modus ponens, contractual
rules, causal rules, and the law of large numbers, are
used in solving everyday problems. Hybrid mechanisms
that combine aspects of instance and rule models are
considered.'
E. E. Smith, C. Langston and R. E. Nisbett:
The case for rules in reasoning.
Cognitive Science; 1992 Jan-Mar Vol 16(1) 1-40
We use rules, it can be argued, when we apply extensionalist
strategies which are of course, by design, domain specific. Note that
in the history of logic it took until 1879 to discover Quantification
Theory. Furthermore, research on deductive reasoning itself suggests
strongly that the view developed in this volume is sound:
'Reviews 3 types of computer program designed to make
deductive inferences: resolution theorem-provers and
goal-directed inferential programs, implemented
primarily as exercises in artificial intelligence; and
natural deduction systems, which have also been used as
psychological models. It is argued that none of these
methods resembles the way in which human beings usually
reason. They [humans] appear instead to depend, not on
formal rules of inference, but on using the meaning of
the premises to construct a mental model of the relevant
situation and on searching for alternative models of the
premises that falsify putative conclusions.'
P. N. Johnson-Laird
Human and computer reasoning.
Trends in Neurosciences; 1985 Feb Vol 8(2) 54-57
'Contends that the orthodox view in psychology is that
people use formal rules of inference like those of a
natural deduction system. It is argued that logical
competence depends on mental models rather than formal
rules. Models are constructed using linguistic and
general knowledge; a conclusion is formulated based on
the model that maintains semantic information, expresses
it parsimoniously, and makes explicit something not
directly stated by the premise. The validity of the
conclusion is tested by searching for alternative models
that might refute the conclusion. The article summarizes
a theory developed in a 1991 book by P. N. Johnson-Laird
and R. M. Byrne.'
P. N. Johnson-Laird & R. M. Byrne
Precis of Deduction.
Behavioral and Brain Sciences; 1993 Jun Vol 16(2) 323-
380
That is, human reasoning tends to focus on content or intension. As
has been argued elsewhere, such heuristic strategies invariably suffer
as a consequence of their context specificity and constraints on
working memory capacity.
--
David Longley
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David Longley
FRAGMENTS OF BEHAVIOUR:
EXTRACT 3: FROM 'A System Specification for PROfiling BEhaviour'
Full text is available at:
http://www.uni-hamburg.de/~kriminol/TS/tskr.htm
There is a logical possibility that in restricting the subject matter
of psychology, and thereby the deployment of psychologists, to what
can only be analysed and managed from a Methodological Solipsistic
(cognitive) perspective, one will render some very significant results
of research in psychology irrelevant to applied *behaviour* science
and technology, unless taken as a vindication of the stance that
behaviour is essentially context specific. As explicated above,
intensions are not, in principle, amenable to quantitative analysis.
They are, in all likelihood, only domain or context specific. A few
further examples should make these points clearer.
Many Cognitive Psychologists study 'Deductive Inference' from the
perspective of 'psychologism', a doctrine, which, loosely put,
equates the principles of logic with those of thinking. Yet the work
of Church (1936), Post (1936) and Turing (1937) clearly established
that the principles of 'effective' computation are not psychological,
and can in fact be mechanically implemented. However, researchers in
'Cognitive Science' such as Johnson-Laird and Byrne (1992) have
reviewed 'mental models' which provide an account for some of the
difficulties and some of the errors observed in human deductive
reasoning (Wason 1966). Throughout the 1970s, substantial empirical
evidence began to accumulate to refute the functionalist (Putnam 1967)
thesis that human cognitive processes were formal and computational.
Even well educated subjects it seems, have considerable difficulty
with relatively simple deductive Wason Selection tasks such as the
following:
_____ _____ _____ _____
| | | | | | | |
| A | | T | | 4 | | 7 |
|_____| |_____| |_____| |_____|
Where the task is to test the rule "if a card has a vowel on one side
it has an even number on the other".
Or in the following:
_____ _____ _____ _____
| | | | | | | |
| A | | 7 | | D | | 3 |
|_____| |_____| |_____| |_____|
where subjects are asked to test the rule 'each card that has an A on
one side will have a 3 on the other'. In both problems they can only
turn over a maximum of two cards to ascertain the truth of the rule.
Similarly, the majority have difficulty with the following,
similar problem, where the task is to reveal up to two hidden
halves of the cards to ascertain the truth or falsehood of the rule
'whenever there is a O on the left there is a O on the right':
_____________ _____________ ____________ ____________
| ||||||| | ||||||| ||||||| | ||||||| |
| O ||||||| | ||||||| ||||||| O | ||||||| |
|______||||||| |______||||||| |||||||______| |||||||______|
(a) (b) (c) (d)
Yet computer technology has no difficulty with these examples of the
application of basic deductive inference rules (modus ponens and modus
tollens). The above require the application of the material
conditional. [1] is falsified by turning cards A and 9, [2] by turning
cards A and 7, and [3] by turning cards (a) and (d). Logicians, and
others trained in the formal rules of deductive logic often fail to
solve such problems:
'Time after time our subjects fall into error. Even some
professional logicians have been known to err in an
embarrassing fashion, and only the rare individual takes
us by surprise and gets it right. It is impossible to
predict who he will be. This is all very puzzling....'
P. C. Wason and P. N. Johnson-Laird (1972)
Psychology of Reasoning
Furthermore, there is impressive empirical evidence that formal
training in logic does not generalise to such problems (Nisbett et al
1987). Yet why is this so if, in fact, human reasoning is, as the
cognitivists, have claimed, essentially logical and computational?
Wason (1966) also provided subjects with numbers which increased in
series, asking them to identify the rule. In most cases, the simple
fact that all examples shared no more than simple progression was
skipped, and whatever hypotheses they created were held onto even
though the actual rule was subsequently made clear. This persistence
of belief, and rationalisation of errors despite debriefing and
exposure to contrary evidence, is well documented in psychology, and
is a phenomenon which methodologically is, as Popper makes clear in
the leading quote to this paper, at odds with the formal advancement
of knowledge. Here is what Sir Karl Popper (1965) had to say about
this matter:
'My study of the CONTENT of a theory (or of any
statement whatsoever) was based on the simple and
obvious idea that the informative content of the
CONJUNCTION, ab, of any two statements, a, and b, will
always be greater than, or at least equal to, that of
its components.
Let a be the statement 'It will rain on Friday'; b the
statement 'It will be fine on Saturday'; and ab the
statement 'It will rain on Friday and it will be fine on
Saturday': it is then obvious that the informative
content of this last statement, the conjunction ab, will
exceed that of its component a and also that of its
component b. And it will also be obvious that the
probability of ab (or, what is the same, the probability
that ab will be true) will be smaller than that of
either of its components.
Writing Ct(a) for 'the content of the statement a', and
Ct(ab) for 'the content of the conjunction a and b', we
have
(1) Ct(a) <= Ct(ab) => Ct(b)
This contrasts with the corresponding law of the
calculus of probability,
(2) p(a) => p(ab) <= p(b)
where the inequality signs of (1) are inverted. Together
these two laws, (1) and (2), state that with increasing
content, probability decreases, and VICE VERSA; or in
other words, that content increases with increasing
IMprobability. (This analysis is of course in full
agreement with the general idea of the logical CONTENT
of a statement as the class of ALL THOSE STATEMENTS
WHICH ARE LOGICALLY ENTAILED by it. We may also say that
a statement a is logically stronger than a statement b
if its content is greater than that of b - that is to
say, if it entails more than b.)
This trivial fact has the following inescapable
consequences: if growth of knowledge means that we
operate with theories of increasing content, it must
also mean that we operate with theories of decreasing
probability (in the sense of the calculus of
probability). Thus if our aim is the advancement or
growth of knowledge, then a high probability (in the
sense of the calculus of probability) cannot possibly be
our aim as well: THESE TWO AIMS ARE INCOMPATIBLE.
I found this trivial though fundamental result about
thirty years ago, and I have been preaching it ever
since. Yet the prejudice that a high probability must be
something highly desirable is so deeply ingrained that
my trivial result is still held by many to be
'paradoxical'.
K. Popper
Truth, Rationality, and the Growth of Knowledge
Ch. 10, p 217-8
CONJECTURES AND REFUTATIONS (1965)
Modus tollens and the extensional principle that a compound event can
only be less probable (or equal) to its component events independently
is fundamental to the logic of scientific discovery, and yet this,
along with other principles of extensionality (deductive logic) seem
to be principles which are in considerable conflict with intuition, as
Kahneman and Tversky (1983) demonstrated with their illustration of
the 'Linda Problem'. In conclusion, the above authors wrote, twenty
years after Wason's experiments on deductive reasoning and Popper's
(1965) remarks on Conjectures and Refutation':
'In contrast to formal theories of belief, intuitive
judgments of probability are generally not extensional.
People do not normally analyse daily events into
exhaustive lists of possibilities or evaluate compound
probabilities by aggregating elementary ones. Instead,
they use a limited number of heuristics, such as
representativeness and availability (Kahneman et al.
1982). Our conception of judgmental heuristics is based
on NATURAL ASSESSMENTS that are routinely carried out as
part of the perception of events and the comprehension
of messages. Such natural assessments include
computations of similarity and representativeness,
attributions of causality, and evaluations of the
availability of associations and exemplars. These
assessments, we propose, are performed even in the
absence of a specific task set, although their results
are used to meet task demands as they arise. For
example, the mere mention of "horror movies" activates
instances of horror movies and evokes an assessment of
their availability. Similarly, the statement that Woody
Allen's aunt had hoped that he would be a dentist
elicits a comparison of the character to the stereotype
and an assessment of representativeness. It is
presumably the mismatch between Woody Allen's
personality and our stereotype of a dentist that makes
the thought mildly amusing.. Although these assessments
are not tied to the estimation of frequency or
probability, they are likely to play a dominant role
when such judgments are required. The availability of
horror movies may be used to answer the question "What
proportion of the movies produced last year were horror
movies?", and representativeness may control the
judgement that a particular boy is more likely to be an
actor than a dentist.
The term JUDGMENTAL HEURISTIC refers to a strategy -
whether deliberate or not - that relies a natural
assessment to produce an estimation or a prediction.
.Previous discussions or errors of judgement have
focused on deliberate strategies and on
misinterpretations of tasks. The present treatment calls
special attention to the processes of anchoring and
assimilation, which are often neither deliberate nor
conscious. An example from perception may be
instructive: If two objects in a picture of a three-
dimensional scene have the same picture size, the one
that appears more distant is not only seen as "really"
larger but also larger in the picture. The natural
computation of real size evidently influences the (less
natural) judgement of picture size, although observers
are unlikely to confuse the two values or to use the
former to estimate the latter.
The natural assessments of representativeness and
availability do not conform to the extensional logic of
probability theory.'
A. Tversky and D. Kahneman
Extensional Versus Intuitive Reasoning:
The Conjunction Fallacy in Probability Judgment.
Psychological Review Vol 90(4) 1983 p.294
The study of Natural Deduction (Gentzen 1935;Prawitz 1971; Tenant
1990) as a psychological process (1983) is really just the study of
the performance of a skill (like riding a bicycle in fact), which
attempts to account for why some of the difficulties with deduction
per se occur. The best models here may turn out to be connectionist,
where each individual's model ends up being almost unique in its fine
detail. There is a problem for performance theories, as Johnson Laird
and Byrne (1991) point out:
'A major difficulty for performance theories based on
formal logic is that people are affected by the content
of a deductive system..yet formal rules ought to apply
regardless of content. That is what they are: rules that
apply to the logical form of assertions, once it has
been abstracted from their content.'
P. N. Johnson-Laird and R. M. J. Byrne (1991)
Deduction p.31
The theme of this volume up to this point has been that methodological
solipsism is unlikely to reveal much more than the shortcomings and
diversity of social and personal judgment and the context specificity
of behaviour. It took until 1879 for Frege to discover the Predicate
Calculus (Quantification Theory), and a further half century before
Church (1936), Turing (1937) and others laid the foundations for
computer and cognitive science through their collective work on
recursive function theory. From empirical evidence, and developments
in technology, it looks like human and other animal reasoning is
primarily inductive and heuristic, not deductive and algorithmic.
Human beings have considerable difficulties with the latter, and this
is normal. It has taken considerable intellectual effort to discover
formal, abstract, extensional principles, often only with the support
of logic, mathematics and computer technology itself. The empirical
evidence, reviewed in this volume is that extensional principles are
not widely applied except in specific professional capacities which
are domain-specific. In fact, on the simple grounds that the discovery
of such principles required considerable effort should perhaps make us
more ready to accept that they are unlikely to be spontaneously
applied in everyday reasoning and problem solving.
For further coverage of the 'counter-intuitive' nature of deductive
reasoning (and therefore its low frequency in everyday practice) see
Sutherland's 1992 popular survey 'Irrationality', or Plous (1993) for
a recent review of the psychology of judgment and decision making. For
a thorough survey of the rise (and possibly the fall) of Cognitive
Science, see Putnam 1986, or Gardner 1987. The latter concluded his
survey of the Cognitive Revolution within psychology with a short
statement which he referred to as the 'computational paradox'. One
thing that Cognitive Science has shown us is that the computer or
Turing Machine is not a good model of how people reason, at least not
in the Von-Neumann Serial processing sense. Similarly, people do not
seem to think in accordance with the axioms of formal, extensional
logic. Instead, they learn rough and ready heuristics which they which
they try to apply to problems in a very rough, approximate way.
Accordingly, Cognitive Science may well turn to the work of Church,
Turing and other mathematical logicians who, in the wake of Frege,
have worked to elaborate what effective processing is. We will then be
faced with the strange situation of human psychology being of little
practical interest, except as a historical curiosity, an example of
pre-Fregian logic and pre-Church (1936) computation. Behaviour science
will pay as little attention to the 'thoughts and feelings' of 'folk
psychology' as contemporary physics does to quaint notions of 'folk
physics'. For some time, experimental psychologists working within the
information processing (computational) tradition have been working to
replace such concepts such as 'general reasoning capacity' with more
mechanistic notions such as 'Working Memory' (Baddeley 1986):
'This series of studies was concerned with determining
the relationship between general reasoning ability (R)
and general working-memory capacity (WM). In four
studies, with over 2000 subjects, using a variety of
tests to measure reasoning ability and working-memory
capacity, we have demonstrated a consistent and
remarkably high correlation between the two factors. Our
best estimates of the correlation between WM and R were
.82, .88., .80 and .82 for studies 1 through 4
respectively.
...
The finding of such a high correlation between these two
factors may surprise some. Reasoning and working-memory
capacity are thought of differently and they arise from
quite different traditions. Since Spearman (1923),
reasoning has been described as an abstract, high level
process, eluding precise definition. Development of good
tests of reasoning ability has been almost an art form,
owing more to empirical trial-and-error than to a
systematic delineation of the requirements such tests
must satisfy. In contrast, working memory has its roots
in the mechanistic, buffer-storage model of information
processing. Compared to reasoning, short-term storage
has been thought to be a more tractable, demarcated
process.'
P. C. Kyllonen & R. E. Christal (1990)
Reasoning Ability Is (Little More Than) Working-Memory
Capacity
Intelligence 14, 389-433
Such evidence stands well with the logical arguments of Cherniak which
were introduced in Section A, and which are implicit in the following
introductory remarks of Shinghal (1992) on automated reasoning:
'Suppose we are given the following four statements:
1. John awakens;
2. John brings a mop;
3. Mother is delighted, if John awakens and cleans his room;
4. If John brings a mop, then he cleans his room.
The statements being true, we can reason intuitively to
conclude that Mother is delighted. Thus we have deduced
a fact that was not explicitly given in the four
statements. But if we were given many statements, say a
hundred, then intuitive reasoning would be difficult.
Hence we wish to automate reasoning by formalizing it
and implementing it on a computer. It is then usually
called automated theorem proving. To understand
computer-implementable procedures for theorem proving,
one should first understand propositional and predicate
logics, for those logics form the basis of the theorem
proving procedures. It is assumed that you are familiar
with these logics.'
R. Shinghal (1992)
Formal Concepts in Artificial Intelligence: Fundamentals
Ch.2 Automated Reasoning with Propositional Logic p.8
Automated report writing and automated reasoning drawing on actuarial
data is fundamental to the PROBE project. In contrast to such work
using deductive inference, Gluck and Bower (1988) have modelled human
inductive reasoning using artificial neural network technology (which
are heuristic, based on constraint satisfaction/approximation, or
'best fit' rather than being 'production rule' based). That is, it is
unlikely that anyone spontaneously reasons using truth-tables or the
Resolution Rule (Robinson 1965). Furthermore, Rescorla (1988), perhaps
the dominant US spokesman for research in Pavlovian Conditioning, has
drawn attention to the fact that Classical Conditioning should perhaps
be seen as the experimental modelling of inductive inferential
'cognitive' heuristic processes. Throughout this paper, it is being
argued that such inductive inferences are in fact best modelled using
artificial neural network technology, and that such processing is
intensional, with all of the traditional problems of intensionality:
'Connectionist networks are well suited to everyday
common sense reasoning. Their ability to simultaneously
satisfy soft constraints allows them to select from
conflicting information in finding a plausible
interpretation of a situation. However, these networks
are poor at reasoning using the standard semantics of
classical logic, based on truth in all possible models.'
M. Derthick (1990)
Mundane Reasoning by Settling on a Plausible Model
Artificial Intelligence 46,1990,107-157
and perhaps even more familiarly:
'Induction should come with a government health warning.
A baby girl of sixteen months hears the word 'snow' used
to refer to snow. Over the next months, as Melissa
Bowerman has observed, the infant uses the word to refer
to: snow, the white tail of a horse, the white part of a
toy boat, a white flannel bed pad, and a puddle of milk
on the floor. She is forming the impression that 'snow'
refers to things that are white or to horizontal areas
of whiteness, and she will gradually refine her concept
so that it tallies with the adult one. The underlying
procedure is again inductive.'
P. N. Johnson-Laird (1988)
Induction, Concepts and Probability p.238: The Computer
and The Mind
David Longley
FRAGMENTS OF BEHAVIOUR:
EXTRACT 6: FROM 'A System Specification for PROfiling BEhaviour'
Full text is available at:
http://www.uni-hamburg.de/~kriminol/TS/tskr.htm
ASSESSING AND EVALUATING 'WHAT WORKS'
As briefly mentioned in earlier sections, over recent years, there
have been some moves to introduce formal 'Cognitive Skills' programmes
both in the Canadian Correctional System (Porporino et. al. 1991) and
more recently, within the English system. Empirical studies to date
have focused on very small numbers in treatment and 'comparison'
groups, and have produced equivocal results when the dependent
variable is taken as reconviction rate.
In brief, based on the published data, efficacy of the Canadian
Cognitive Skills Training can not be described as robust, nor can it
be said that the programme's content per se significantly influences
recidivism. The objective here is not to be negative, there may be
further unpublished evidence which puts the programme in a more
favourable light. However, I think it important to point out that on
the basis of the evidence reported in the Porporino et al (1991) paper
we should look at the claims made for the efficacy of the Cognitive
Skills programme with a degree of caution. The published results can
in fact be taken to suggest something equally positive if considered
from the alternative perspective of Sentence Management.
The Porporino et al. paper suggests that those who are motivated to
change (those who volunteered) did almost as well as those who
actually participate in the Cognitive Skills programme. If this is
true, it would seem to be further justification for adopting the
Attainment based Sentence Management system as an infrastructure for
Inmate Programmes. If further evidence can be drawn upon to
substantiate the published claims for the efficacy of 'Cognitive
Skills', that evidence could be used to vindicate the proposed
strategy of an integrated use of the natural demands of all activities
and routines to inculcate new skills in social behaviour and problem
solving. Sentence Management is designed to provide the Service with a
means of integrating all of the currently used assessment systems in
use across activities. It is important to appreciate that the criteria
it looks to assess inmates with respect to, are the very criteria
which activity supervisors are already using to assess inmates, be
these NVQ Performance Criteria, or the 'can do' statements of an RSA
english course. Attainment Criteria per se, can not therefore be
dismissed lightly. The Sentence Management system is designed to
enable staff throughout the system to pull together assessment
material in a common format, it has not been designed to ask anything
new of such staff, although they can add additional criteria to those
they already use if they wish.
Effective programmes must produce evidence of behaviour change, and
not merely self-report, ie verbal behaviour change. We require
measures of attainment with respect to the preset skill levels which
programme staff have been contracted to deliver. All programmes must
have predetermined goals or objectives and these can be specified
independently of any participating inmates. If there is evidence that
the special programmes approach has special merit which excludes them
from the remarks made so far (which, from the review of programmes
below must be viewed with caution), we should not lose sight of the
fact that special programmes are likely to be seen as treatment
programmes, and that they can only occupy inmates for a small
proportion of their time in custody. If there is evidence to justify
the efficacy of special programmes addressing how inmates think, we
should look carefully to what education and other skill based
programmes are designed to deliver. There is much to be said for
adopting an approach to inmate programmes which is education, rather
than treatment based, and one which looks to all that the regime has
to offer as an infrastructure.
The following is how the Canadian group describe the objectives of
their 'Cognitivist' approach:
'The basic assumption of the cognitive model is that the
offender's thinking should be a primary target for
offender rehabilitation. Cognitive skills, acquired
either through life experience or through intervention,
may serve to help the individual relate to his
environment in a more socially adaptive fashion and
reduce the chances of adopting a pattern of criminal
conduct.
Such a conceptualization of criminal behaviour has
important implications for correctional programming. It
suggests that offenders who are poorly equipped
cognitively to cope successfully must be *taught* rather
than *treated*. It suggests that emphasis be placed on
teaching offenders social competence by focusing on:
thinking skills, problem-solving and decision making;
general strategies for recognizing problems, analysing
them, conceiving alternative non-criminal solutions to
them;
ways of thinking logically, objectively and rationally
without overgeneralizing, distorting facts, or
externalizing blame;
calculating the consequences of their behaviour - to
stop and think before they act;
to go beyond an egocentric view of the world and
comprehend and consider the thoughts and feelings of
other people;
to improve interpersonal problem-solving skills and
develop coping behaviours which can serve as effective
alternatives to anti-social or criminal behaviour;
to view frustrations as problem-solving tasks and not
just as personal threats;
to develop a self-regulatory system so that their pro-
social behaviour is not dependent on external control.
to develop beliefs that they can control their life;
that what happens to them depends in large measure on
their thinking and the behaviour it leads to.
To date we have been able to examine the outcome of 40
offenders who had been granted some form of conditional
release and were followed up in the community for at
least six months. On average, the follow up period was
19.7 months. We also gathered information on the outcome
of a comparison group of 23 offenders who were selected
for Cognitive Skills Training but had not participated.
These offenders did not differ from the program
participants on a number of characteristics and were
followed-up for a comparable period of time.
.....offenders in the treatment group were re-admitted
for new convictions at a lower rate that the comparison
group during the follow-up period. Specifically, only
20% of the treatment group were re-admitted for new
convictions compared to 30% of the offenders in the
comparison group. It is interesting to note that the
number of offenders who were returned to prison without
new convictions (eg technical violations, day-parole
terminations) is similar yet marginally larger in the
treatment group. It is possible that the Cognitive
Skills Training participants may be subjected to closer
monitoring because of expectations regarding the
program.'
F. Porporino, L. Fabiano and Robinson
Focusing on Successful Reintegration:Cognitive Skills
Training for Offenders - July 1991
The authors tell us that seven of the 23 in the comparison group were
reconvicted for a new offence, whilst eight of the 40 offenders in the
treatment group were reconvicted for a new offence. However, looking
at returns to prison for violations of parole etc., the authors say:
'It is interesting to note that the number of offenders who were
returned to prison without new convictions (eg technical violations,
day-parole terminations) is similar yet marginally larger in the
treatment group'.
Furthermore, when the authors compared the predicted reconviction rate
(52%) for these groups with the actual rates (20% and 30% for the
treatment and comparison groups respectively) the low rate of
reconviction in the comparison group led them to conclude:
'motivation for treatment in end of itself may be
influential in post-release success'.
In fact, the conclusion can be stated somewhat more strongly. Imagine
this was a drugs trial. The comparison group, like the treatment
group are all volunteers. They all wanted to be in the programme, they
all, effectively, wanted to take the tablets. Some, however, didn't
get to join the programme, they didn't 'get to take the tablets', but
other than that did not differ from the treatment group. In the
Porporino study, those inmates comprised the comparison group. When
the reconviction data came in, it showed that those in the comparison
group were pretty much like those in the treatment group. The
treatment, ie 'the Cognitive Skills' training, had virtually no
effect. The comparison group is remarkably like the treatment group in
not being reconvicted for a new offence. In fact, if five of the
comparison group had reconvicted rather than seven, the reconviction
rate would have been the same (20%) for both groups.
TREATMENT COMPARISON
Readmissions with New Convictions 20% 30.4%
(8/40) (7/23)
Readmissions without New Convictions 25% 21.7%
(10/40) (5/23)
No Readmissions 55% 47.9%
(22/40) (11/23)
Apart from the fact that the numbers being analysed are extremely
small, the fact that the authors take these figures to justify
statements that Cognitive Skills, ie an intensive 8-12 week course,
focusing on what inmates 'think', a course that focuses apparently on
changing 'attitudes' rather than 'teaching new/different behaviours',
is causally efficacious in bringing about reductions in recidivism is
questionable. The comparison group it must be appreciated, were all
volunteers, only differing from the treatment group in that they did
not get to participate in the programme. But only 30% of them (7/23)
were reconvicted for a new offence, compared to 20% (8/40) in the
treatment group. Compared to the expected reconviction rate for those
in either group (52%) might reasonably be led to the conclusion that
those in the comparison group did very well compared to those who
actually participated in the programme. The above pattern of results
casts some doubt as to how important the content of the Cognitive
Skills Programme was at all. The fact that the percentages in the 'No
Readmissions' and the 'Readmissions Without New Reconvictions' lends
support to this view.
These (Canadian) studies have also presented evidence for short term
longitudinal changes in 'Cognitive Skills' performance for those
participating in the programme (and somewhat surprisingly, sometimes
in the comparison groups). These changes may however be comparable in
kind to the changes observed in the more formal education studies
surveyed by Nisbett et al. (1987). The whole notion of formal training
in abstract 'Cognitive Skills' might in fact be profitably critically
evaluated in the context of such research programmes, along with the
more substantial body of research into the heuristics and biases of
natural human judgment ('commonsense') in the absence of
distributional data. Other studies, e.g. McDougall, Barnett, Ashurst
and Willis (1987), although more sensitive to some of the
methodological constraints in evaluating such programs, still give
much greater weight to their conclusions than seems warranted by
either the design of their study or their actual data. For instance,
in the above study, an anger control course resulted in a
'significant' difference in institutional reports in a three month
follow up period at the p<0.05 level using a sign test. However, apart
from methodological problems, acknowledged by the authors, the
suggestion that the *efficacious component* was cognitive must, in the
light of the arguments of Meehl and others below, on the simple logic
of hypothesis testing, be surely be seen to be indefensible. On the
basis of their design, one might, cautiously, suggest that there is
some evidence that participating in the programme had some effect
(possibly, as p<0.05), but precisely what it was within the course
which was efficacious can not be said given the design of the study.
As readers will come to appreciate, this is a pervasive problem in
social science research, and is yet another example of 'going beyond
the information given'. The force of Meehl's and Lakatos' arguments in
the light of such failures to refrain from inductive speculation on
the basis of minimal evidence should not be treated lightly. It is a
problem which has reached epidemic proportions in psychology as many
of the leading statisticians now lament (Guttman 1985, Cohen 1990),
the above studies are in fact quite representative of the general
failure of psychologists as a group to appreciate the limits of the
propositional as opposed to the predicate calculus as a basis for
their methodology. Most of the designs of experiments adopted do not
allow researchers to draw the conclusions that they do from their
studies. In the above study, the best one could say is that behaviour
improved for those inmates who participated in a program. Logically,
one simply cannot say more.
At the same time that 'Cognitive Skills' programmes are being
developed in the English Prison system, an attempt is being made to
introduce a naturalistic approach to behavioural skill development,
and assessment, 'cognitive skills' being but one class of these
behaviours. Such skills are generally taught within education, as
elements of particular VTC CIT courses or even some of the domestic
activities such as wing cleaning. This is the system of 'Sentence
Management' which looks to inculcate skills under the relatively
natural conditions of inmate activities and the day to day routines.
Through a combination of continuous assessment of behaviour, target
negotiation and contracting and apposite allocation of inmates, the
system aims to maximise transfer of skills acquisition by *teaching for
transfer* (Gladstone 1989) and compensating for deficits.
The Methodological Plight of Intensional (Cognitive) Psychology
Inductive inferential technology par excellence, ie Neyman-Pearson
hypothesis testing, or more accurately, conclusions drawn from using
that technology, has not been without its critics, and it is on this
point that we end this section. The conclusion to be drawn from the
following may well be that the most valuable contribution of
specialists are their skills in deductive rather than inductive logic.
Rather than training staff in the use of heuristics, we should perhaps
be providing them with specific formal roles, ie functions, which
require the practice of formal deductive skills. Here is how Meehl
(1978) reviewed the standard (inductive) methodological approach
adopted by most psychologists:
'I suggest to you that Sir Ronald has befuddled us,
mesmerised us, and led us down the primrose path. I
believe that the most universal reliance on merely
refuting the null hypothesis as the standard method for
corroborating substantive theories in the soft areas is
a terrible mistake, is basically unsound, poor
scientific strategy, and one of the worst things that
ever happened in the history of psychology'.
P. E. Meehl
Theoretical Risks and Tabular Asterisks:
Sir Karl and Sir Ronald and The Slow Progress of Soft Psychology.
J Consulting and Clinical Psychology 1978,45,4,p806-34
The contrasting approach of point prediction refutation is the
falsificationism of Sir Karl (Popper). In 1967, Meehl made the point
very clearly:
'I conclude that the effect of increased precision,
whether achieved by improved instrumentation and
control, greater sensitivity in the logical structure of
the experiment, or increasing the number of
observations, is to yield a probability approaching 1/2
of corroborating our substantive theory by a
significance test, *even if the theory is totally
without merit*. That is to say, the ordinary result of
improving our experimental methods and increasing our
sample size, proceeding in accordance with the
traditionally accepted method of theory-testing by
refuting a directional null hypothesis, yields a prior
probability = 1/2 and very likely somewhat above that
value by an unknown amount. It goes without saying that
successfully negotiating and experimental hurdle of this
sort can constitute only an extremely weak corroboration
of any substantive theory, quite apart from currently
disputed issues of the Bayesian type regarding the
assignment of prior probabilities to the theory itself.
So far as I am able to discern, this methodological
truth is either unknown or systematically ignored by
most behaviour scientists. I do not know to what extent
this is attributable to confusion between the
substantive theory T and the statistical hypothesis H1,
with the resulting mis-assignment of the probability (1-
p) complementary to the significance level p attained,
to the "probability" of the substantive theory; or to
what extent it arises from insufficient attention to the
truism that the point-null hypothesis H0 is [quasi]
always false. It seems unlikely that most social science
investigators would think in their usual way about a
theory in meteorology which "successfully predicted"
that it would rain on the 17th of April, given the
antecedent information that it rains (on the average)
during half the days in the month of April.
But this is not the worst of the story. Inadequate
appreciation of the extreme weakness of the test to
which a substantive theory T is subjected by merely
predicting a directional statistical difference d > 0 is
then compounded by a truly remarkable failure to
recognize the logical asymmetry between, on the one
hand, (formally invalid) "confirmation" of a theory via
affirming the consequent in an argument of form [T > H1,
H1, infer T], & on the other hand the deductively tight
REFUTATION of the theory *modus tollens* by a falsified
prediction, the logical form being: [T > H1, ~H1, infer
~T].
While my own philosophical predilections are somewhat
Popperian, I dare say any reader will agree that no
full-fledged Popperian philosophy of science is
presupposed in what I have just said. The destruction of
a theory *modus tollens* is, after all, a matter of
deductive logic; whereas that the "confirmation" of a
theory by its making successful predictions involves a
much weaker kind of inference. This much would be
conceded by even the most anti-Popperian "inductivist".
The writing of behavior scientists often reads as though
they assumed - what it is hard to believe anyone would
explicitly assert if challenged - that successful and
unsuccessful predictions are practically on all fours in
arguing for and against a substantive theory.'
P. E. Meehl (1967)
Theory Testing in Psychology and Physics: A Methodological Paradox.
Philosophy of Science, p.111-2 June 1967
Rozeboom (1960), Bolles (1962), Bakan (1966) and Lykken (1968) made
similar points throughout the 1960s. Cohen (1990), in a remarkably
well written paper reviewed the dire situation as follows:
'Over the years, I have learned not to make errors of
the following kinds:
When a Fisherian null hypothesis is rejected with an
associated probability of, for example, .026, it is
*not* the case that the probability that the null
hypothesis is true is .026 (or less than .05, or any
other value we can specify). Given our framework of
probability as long-run relative frequency -as much as
we might wish it to be otherwise - this result does not
tell us about the truth of the null hypothesis, given
the data. (For this we have to go to Bayesian or
likelihood statistics, in which probability is not
relative frequency but degree of belief.) What it tells
us is the probability of the data, given the truth of
the null hypothesis - which is not the same thing, as
much as it may sound like it.
If the p value with which we reject the Fisherian null
hypothesis does not tell us the probability that the
null hypothesis is true, it certainly cannot tell us
anything about the probability that the *research* or
alternative hypothesis is true. In fact, there *is* no
alternate hypothesis in Fisher's scheme: Indeed, he
violently opposed its inclusion by Neyman and Pearson.
Despite widespread misconceptions to the contrary, the
rejection of a given null hypothesis gives us no basis
for estimating the probability that a replication of the
research will again result in rejecting that null
hypothesis.
Of course, everyone knows that failure to reject the
Fisherian null hypothesis does not warrant the
conclusion that it is true. Fisher certainly knew and
emphasized it, and our textbooks duly so instruct us.
Yet how often do we read in the discussion and
conclusions of articles now appearing in our most
prestigious journals that "there is no difference" or
"no relationship"?
The other side of this coin is the interpretation that
accompanies results that surmount the .05 barrier and
achieve the state of grace of "statistical
significance". "Everyone" knows that all this means is
that the effect is not nil, and nothing more. Yet how
often do we see such a result to be taken to mean, at
least implicitly, that the effect is *significant*, that
is, *important, large*. If a result is *highly*
significant, say p<0.001, the temptation to make this
misinterpretation becomes all but irresistible.
Let's take a close look at this null hypothesis - the
fulcrum of the Fisherian scheme - that we so earnestly
seek to negate. A null hypothesis is any precise
statement about a state of affairs in a population,
usually the value of a parameter, frequently 0. It is
called a "null" hypothesis because it means "nothing
doing". Thus, "The difference in the mean score of U.S.
men and women on an Attitude Toward the U.N. scale is
zero" is a null hypothesis. "The product-moment r
between height and IQ in high school students is zero"
is another. "The proportion of men in a population of
adult dyslexics is .50" is yet another. Each is a
precise statement - for example, if the population r
between height and IQ is in fact .03, the null
hypothesis that it is zero is false. It is also false if
the r is .01, .001, or .000001!.
A little thought reveals a fact widely understood by
statisticians: The null hypothesis, taken literally (and
that's the only way you can take it in formal hypothesis
testing), is always false in the real world. It can only
be true in the bowels of a computer processor running a
Monte carlo study (and even then a stray electron may
make it false. If it is false, even to a tiny degree, it
must be the case that a large enough sample will produce
a significant result and lead to its rejection. So if
the null hypothesis is always false, what's the big deal
about rejecting it?'
J. Cohen (1990)
What I Have Learned (So Far)
American Psychologist, Dec 1990 p.1307-1308
Lykken (1968) had simply pointed out:
'Most theories in the areas of personality, clinical,
and social psychology predict no more than the direction
of a correlation, group difference, or treatment effect.
Since the null hypothesis is never strictly true, such
predictions have about a 50-50 chance of being confirmed
by experiment when the theory in question is false,
since the statistical significance of the result is a
function of the sample size.'
It is this contrast between testing, ie falsifying, a
theory or hypothesis by such a weak criterion as the
above, compared to making point predictions (testing
conjunctions of statements by modus tollens) as Popper
urges that led Meehl to write his paper on Theoretical
Risks and Tabular Asterisks in 1978, lamenting on the
slow progress in soft psychology which is the
consequence of not appreciating how weak a test the
Neyman-Pearson actually procedure is.'
But perhaps the worst of it that although Cohen (1962)
undertook a power (power=1-beta, where beta is the
likelihood of a type II error) survey of the articles in
the 1960 volume of the Journal of Abnormal and Social
Psychology in which he found that the median power to
detect a medium effect size under representative
conditions was only .46 (ie worse than chance),
Sedlmeier and Gigerenzer (1989) published a paper
entitled "Do studies of Statistical Power Have an Effect
on the Power of Studies." in which they replicated the
study on the 1984 Journal of abnormal Psychology and
found that the median power under the same conditions
was .44, a little worse than the original .46. Apart
from no improvement over the years, and providing
substantial empirical evidence for what Lakatos has to
say below, what does this mean? Cohen had this to say:
'When I finally stumbled onto power analysis, and
managed to overcome the handicap of a background with no
working math beyond high school algebra (to say nothing
of mathematical statistics), it was as if I had died and
gone to heaven. After I learned what noncentral
distributions were and figured out that it was important
to decompose noncentrality parameters into their
constituents of effect size and sample size; I realized
that I had a framework for hypothesis testing that had
four parameters; the alpha significance criterion, the
sample size, the population effect size, and the power
of the test. For any statistical test, any one of these
was a function of the other three. This meant for
example, that for a significance test of a product-
moment correlation, using a two-sided .05 alpha
criterion and a sample size of 50 cases, if the
population correlation is .30, my long-run probability
of rejecting the null hypothesis and finding the sample
correlation to be significant was .57, a coin flip. As
another example, for the same alpha=.05 and population
r=0.30, if I want to have .80 power, I could determine
that I needed a sample size of 85.'
J. Cohen (1990) p.1308
And this was Lakatos' earlier conclusion:
'The requirement of continuous growth...hits patched-up,
unimaginative series of pedestrian "empirical"
adjustments which are so frequent, for instance in
modern social psychology. Such adjustments may, with the
help of so-called "statistical techniques" make some
"novel" predictions and may even conjure up some
irrelevant grains of truth in them. But this theorising
has no unifying idea, no heuristic power, no continuity.
They do not add up to a genuine research programme and
are on the whole, worthless..
After reading Meehl (1967) and Lykken (1968) one wonders
whether the function of statistical techniques in the
social sciences is not primarily to provide a machinery
for producing phoney corroborations and thereby a
semblance of "scientific progress" where, in fact, there
is nothing but an increase in pseudo-intellectual
garbage.'
I Lakatos (1978) p88-9
Falsification and the methodology of scientific research programs
The Methodology of Scientific Research Programs: Imre Lakatos
philosophical papers (vol 1 pp 139-67) Eds. Worrall & Currie.
Guttman (1976;1985) has made similar remarks within the professional
statistical literature:
'Many practitioners have become disillusioned with
declarative inference, especially that of hypothesis
testing. For example, according to Carver 'statistical
significance testing has involved more fantasy than
fact. The emphasis on statistical significance over
scientific significance in education and research
represents a corrupt form of the scientific method.
Educational research would be better off if it stopped
testing its results for statistical significance'. The
'significance' testing referred to here is largely
according to Neyman-Pearson theory. We shall marshall
arguments against such testing, leading to the
conclusion that it be abandoned by all substantive
science and not just by educational research and other
social sciences which have begun to raise voices against
the virtual tyranny of this branch of inference in the
academic world.'
L. Guttman (1985)
The Illogic of Statistical Inference for Cumulative Science
Applied Stochastic Models and Data Analysis Vol 1, 3-10
Things have not changed much recently:
'It is not at all clear why researchers continue to
ignore power analysis. The passive acceptance of this
state of affairs by editors and reviewers is even more
of a mystery. At least part of the problem may be the
low level of consciousness about effect size: It is as
if the only concern about magnitude in much
psychological research is with regard to the statistical
test result and its accompanying p value, not with
regard to the psychological phenomenon under study.'
J. Cohen (1992)
A Power Primer: Quantitative Methods in Psychology:
Psychological Bulletin 112,1,155-159
If not via the classic, albeit 'hybrid' (Gigerenzer 1993), methodology
of inductive inferential hypothesis testing, what practical form can a
naturalistic science and technology of behaviour take? The solution
being urged in the PROBE project is a) historical, b) descriptive and
c) deductive. It requires psychologists to simply record and
extensionally analyse a history of behaviour (including 'de dicto'
content-clauses) categorised according to finite reference classes
(specific valid values) in conjunction with dates, times and
locations. In effect, to adopt a Quinean (1960,1992), Observation
Statement/Observation Categorical testing, and relational approach to
the analysis of behaviour. The majority of staff employed by the
Prison Service are already performing tasks which could be classed as
work in behaviour management. However, what is required is a service
in behaviour analysis using behaviour science and technology. If
psychologists limited themselves to recording and analysing behaviour
*as functions of the regime* in which they occur (Ross and Nisbett
1991), the Service would have an effective science and technology of
behaviour, and a clear framework for both recruitment and staff
training. In recent years, a good number of academics have recommended
some such approach. Cohen (1990) for instance had the following to
say:
'Despite my career-long identification with statistical
inference, I believe, together with such luminaries as
Meehl (1978), Tukey (1977), and Gigerenzer (Gigerenzer
and Murray 1987), that hypothesis testing has been
greatly overemphasized in psychology and in the other
disciplines that use it. It has diverted our attention
from crucial issues. Mesmerized by a single all-purpose,
mechanized, "objective" ritual in which we convert
numbers into other numbers and get a yes-no answer, we
have come to neglect close scrutiny of where the numbers
came from....So, how should I use statistics in
psychological research? First of all, descriptively.
John Tukey's (1977) Exploratory Data Analysis is an
inspiring account of how to effect graphic and numerical
analyses of the data at hand so as to understand them.
The techniques, although subtle in conception, are
simple in application, requiring no more than paper and
pencil (Tukey says if you have a hand-held calculator,
fine).......he manages to fill 700 pages with techniques
of "mere" description, pointing out in the preface that
the emphasis on inference in modern statistics has
resulted in a loss of flexibility in data analysis.'
J. Cohen (1990) American Psychologist Dec p.1310
As Gigerenzer (1987, 1988, 1993) has pointed out, some of the
bewilderment one experiences in teaching statistics mentioned at the
beginning of this volume can be accounted for by Latent Inhibition,
i.e. students have largely been *badly taught* as undergraduates. In
1986, Meehl proposed a thesis which he urges us to take literally:
'Thesis: Owing to the abusive reliance upon significance
testing - rather than point or interval estimation,
curve shape, or ordination - in the social sciences, the
usual article summarizing the state of the evidence on a
theory (such as appears in the Psychological Bulletin)
is nearly useless.....I think it is scandalous that
editors still accept manuscripts in which the author
presents tables of significance tests without giving
measures of overlap or such basic descriptive statistics
as might enable the reader to do rough computations,
from means and standard deviations presented, as to what
the overlap is.'
P. E. Meehl (1986)
What Social Scientists Don't Understand
in Metatheory in Social Science: Eds D. W. Fiske & R. A.
Shweder p.325
However, the main difficulty lies perhaps in the context specificity
of all learning, - the failure of Leibniz's Law within epistemic
contexts. In the Sentence Management system, such intensionalist
opacity is averted by making all observations of behaviour relative to
demands of the environment specified under Function 17 of the
Governors Contract, specified a priori, on RM-1s. The analytical and
management technology is declarative, criterion referenced, deductive,
and extensional. Its detailed presentation is deferred to Volume 2
which almost exclusively presents the findings as Tukey box plots and
other descriptive statistics.
David Longley
FRAGMENTS OF BEHAVIOUR:
EXTRACT 14: FROM 'A System Specification for PROfiling BEhaviour'
Full text is available at:
http://www.uni-hamburg.de/~kriminol/TS/tskr.htm
Quantifers in natural language refer to the positions in statements
taken by pronouns. They allow us to keep track of who, or what, we are
talking about. In formal, predicate (functional) logic, they demystify
the whole process of deductive inference. In a finite universe of
discourse (which is what we have in PROBE as a database of inmates),
existential (y) quantification can be replaced by a finite series of
disjunctions (V ie ORs), just as universal (z) quantification can be
replaced by a finite series of conjunctions (U ie ANDs). Our queries
can be conceived as clauses written in disjunctive or conjunctive
normal form. When applied to the database, cases either do or do not
meet the specified conditions for class membership, and this serves as
our basis for actuarial analysis of behaviour. Since our database is
finite, we can in fact venture into considering the application of
probability quantifiers (e.g. Vickers 1988), ie the relative frequency
of individuals which meet the conditions of our logical conditions.
'The major motivating principle of probability quantifiers is
the development of probability within pure or general logic
to the extent that this is possible. The great difficulty of
precisely defining general logic can perhaps be avoided by
agreeing that however it is defined, the semantics of first-
order logic as developed by Frege and Tarski fall quite
within its confines. Then, as the above remarks suggest, the
question is just to what extent such notions as "the
proportion of objects falling under a concept" or "the
proportion of assignments satisfying a formula" can be given
a meaning in general logic.'
J. M. Vickers (1988)
Chance & Structure: An Essay on the Logical Foundations of
Probability
Probability quantifiers:principles and semantics p.153
Once this way of working with a data base becomes familiar, it is a
simple set of steps from relative frequencies to joint probabilities
and correlations, regressions and the rest of descriptive statistics
which all Prison Psychologists receive systematic training in as part
of their induction MSc training. It should also be clear that work
within the PROBE system is work in the application of extensional
logic to a specific domain within which the Prison Service employs
Behaviour Scientists to provide a technical service within. That
specificity, or specialism is defined by the selection, analysis and
use of the behaviour predicates and functions within a particular
universe of discourse.
In the case of breaches of prison rules, each instance of an
infraction is identified by the paragraph of the prison rules broken.
In turn, further aspects of the infraction can be recorded such as the
date, time and location, resulting in an n-place predicate. Individual
names, or identifiers are syntactically referred to as constants, with
arbitrary individuals being represented as variables. These are
jointly referred to as terms. A term, without variables is known as a
ground term. When we describe an individual, the descriptor is a
predicate of order n, where n is the number of terms which follow. The
predicate and its terms, together, are known as an atom. A ground
atom, is an atom without variables. Semantically, the set of ground
terms is known as the Herbrand Universe, ie the cases within our CASE
based data base which are inmates. The Herbrand base for any retrieval
we may write is the set of ground atoms that we can construct from the
predicates available (often confusingly called variables) and the
ground term in the Herbrand Universe. This encompasses all we can say
about the inmates in our database. A Herbrand Interpretation is a
subset of the Herbrand base, i.e. those assigned the value true.
Ultimately, these notions will be important when we come to use AI
techniques such as the resolution principle to milk implicit
inferences from within our database. Note, that according to the
thesis being developed in these volumes, it is only the failure of
Leibniz's Law within epistemic (intensional) contexts which makes any
of this seem remotely difficult. What we are generally concerned with
is the creation of well formed formulae, simple atomic propositions or
predicates, which when combined by logical connectives, amount to
compound propositions, or complex predicates. Such predicates are
generally described as one-place, two-place or higher indicating how
many argument positions they require. For example, age is one place
predicate, whilst associate_of, is a two place predicate. The PROBE
data dictionary (Volume 5) lists one-place, unary or monadic
predicates. Two place predicates are also referred to as relations.
Two place predicates, known as binary relations do not exist in the
schema. Individual inmates can be regarded as unary relations, a
strange notion, but one which allows one to treat individuals as
classes.
An example or two may help to make the above more concrete at this
point. Age, NIC score, report rate and index offences will suffice to
illustrate the value of working solely extensionally with relations
and classes. Comparison of the distribution of inmates by age group is
one of the population measures provided to the field week as part of
weekly analysis of the Long Term prison system. Such population
parameters readily highlight unplanned discrepancies in allocation.
That there is a functional relationship between NIC score and age, or
age and rate of disciplinary infractions was used in Volume 2 to
highlight how such relations can be used by management in the interest
of maintaining control.
Relations are clearly basic to relational data bases, and it should be
noted that one of the great changes brought about by relativity theory
was that Newtonian monadic predicates were replaced by relations
(Churchland 1989). The logic of relations with quantifiers is perhaps
the greatest breakthrough in human thought to date, and is still one
of the most difficult to fully appreciate. Frege's 'Concept Writing
Script' (his 'Begriffsschrift' or Predicate Calculus) effectively
introduced for the first time, cognition or reasoning, as a formal,
mechanical process. Here is how Carnap (1933) introduced the notion of
the new logic:
'The new logic is distinguished from the old not only by the
form in which it is presented but chiefly also by the
increase of its range....The only form of statements
(sentences) in the old logic was the predicative form:
"Socrates is a man," "All (or some) Greeks are men." A
predicate-concept or property is attributed to a subject-
concept. Leibniz had already put forward the demand that
logic should consider sentences of relational form. In a
relational sentence such as, for example, "a is greater than
b," a relation is attributed to two or more objects, (or, as
it might be put, to several subject-concepts). Liebniz's idea
of a theory of relations has been worked out in the new
logic. The old logic conceived relational sentences as
sentences of predicative form. However, many inferences
involving relational sentences thereby become impossible. To
be sure, one can interpret the sentence "a is greater than b"
in such a way that the predicate "greater than b" is
attributed to the subject a. But the predicate then becomes a
unity; one cannot extract b by any rule of inference.
Consequently, the sentence "b is smaller than a" cannot be
inferred from this sentence. In the new logic, this inference
takes place in the following way: The relation "smaller than"
is defined as the "converse" of the relation "greater than."
The inference in question then rests on the universal
proposition: If a relation holds between x and y, its
converse holds between y and x. A further example of a
statement that cannot be proved in the old logic: "Wherever
there is a victor someone is vanquished." In the new logic,
this follows from the logical proposition: If a relation has
a referent, it also has a relatum. Relational statements are
especially indispensable for the mathematical sciences. Let
us consider as an example the geometrical concept of the
three-place relation "between" (on an open straight line).
The geometrical axioms "If a lies between b and c, b does not
lie between c and a" can be expressed only in the new logic.
According to the predicative view, in the first case we would
have the predicates "lying between b and c" and "lying
between c and a". If these are left unanalyzed, there is no
way of showing how the first is transformed into the second.
If one takes the objects b and c out of the predicate, the
statement "a lies between b and c" no longer serves to
characterise only one object, but three. It is therefore a
three-place relational statement....
Restriction to predicate-sentences has had disastrous effects
on subjects outside logic. Perhaps Russell is right when he
made this logical failing responsible for certain
metaphysical errors.....Above all, we may well assume that
this logical error is responsible for the concept of absolute
space. Because the fundamental form of a proposition had to
be predicative, it could only consist in the specification of
the position of a body. Since Leibniz had recognized the
possibility of relational sentences, he was able to arrive at
a correct conception of space: the elementary fact is not
position of a body but its positional relations relative to
other bodies. He upheld the view on epistemological grounds:
there is no way of determining the absolute position of a
body, but only its positional relations. His campaign in
favor of the relativistic view of space, as against the
absolutistic views of the followers of Newton, had as little
success as his program for logic.
Only after two hundred years were his ideas on both subjects
taken up and carried through: in logic with the theory of
relations (De Morgan 1858; Pierce 1870), in physics with the
theory of relativity (anticipatory ideas in Mach 1883;
Einstein 1905).'
R. Carnap
The Old and the New Logic (1930)
In A.J. Ayer (ed) Logical Positivism (1959)
Throughout these volumes, the case is made that, for PROBE to be used
as an effective system, it will require users to analyse and manage
inmate behaviour exclusively according to an inmate's class
membership, which in turn only makes sense relative to other classes.
The monadic predicate calculus (the calculus of classes), it should be
understood:
'.. consists in characterizing the predicates by their
extension instead of according to their content. To each
predicate corresponds a certain "class" of objects,
consisting of all objects for which the predicate holds. The
case of a class containing no object is of course not
excluded here. Classes are now to be taken as the entities
dealt with by the calculus, which in this interpretation will
be called the calculus of classes.
D. Hilbert & W. Ackermann (1950)
The Principles of Mathematical Logic p.46
As stated above, a list of individuals which can occupy the positions
of an n-place, or n-ary, or degree n predicate, is known as an ordered
n-tuple (n-membered sequence), and this is ultimately what we are
concerned with as behaviour scientists. Date (1992), who along with
E.F. Codd is a major spokesman for relational theory, had this to say
about predicates:
'It is convenient to assume that the predicates "=", ">", " r "
etc, are builtin (i.e they are part of the formal system we
are defining) and that the expressions using them can be
written in the conventional manner, but of course users
should be able to define their own additional predicates as
well. Indeed, that is the whole point, as we will quickly
see: The fact is, in database terms, a user-defined predicate
is nothing more nor less than a user-defined relation.'
...
'The suppliers relation S, for example, can be regarded as a
predicate with four arguments (S#, SNAME, STATUS, and CITY).
Furthermore the expressions S(S1, Smith,20,London) and
S(S6,Green,45,Rome) represent "instances" or invocations of
that predicate that evaluate to true and false respectively.'
C. J. Date (1992)
Logic Based Database Systems: A Tutorial Part II p.378
Relational Database Writings 1989-1991
The import of this statement marks an important step on the route to
widescale practise of logical and actuarial behaviour management
rather than ad hoc clinicalism which as we have seen in Volume 1, can
only be less precise instances of the former, acceptance of this may
be limited solely by the fact that it is all so relatively new:
'Research on the relationship between database theory and
logic goes back at least to the late 1970s, if not earlier.
However, the principal stimulus for the recent considerable
expansion of interest in the subject seems to have been the
publication in 1984 of a landmark paper by Raymond Reiter,
"Towards a Logical Reconstruction of Relational Database
Theory," which appeared in a book entitled On Conceptual
Modelling: Perspectives from Artificial Intelligence,
Databases, and Programming Languages (eds. Brodie,
Mylopoulos, and Schmidt; Spinger-Verlag, 1984). In that
paper, Reiter characterised the traditional perception of
database systems as model theoretic - by means of which he
meant, speaking very loosely, that:
(a) The database is seen as a set of explicit (i.e. base)
relations, each containing a set of explicit tuples, and
(b) Executing a query can be regarded as evaluating some
specified formula (ie truth-valued expression) over those
explicit relations and tuples.
Reiter then went on to argue that an alternative proof-
theoretic view was possible, and indeed preferable in certain
respects. In that alternative view - again speaking very
loosely - the database is seen as a set of axioms ("ground"
axioms, corresponding to tuples in base relations, plus
certain "deductive" axioms, to be discussed), and executing a
query is regarded as proving that some specified formula is a
logical consequence of those axioms - in other words, proving
that it is a theorem....Consider the following query
(expressed in relational calculus)....
SPX
WHERE SPX.QTY > 250
Here SPX is a tuple variable ranging over the shipments
relation SP. In the traditional (i.e. model-theoretic)
approach, we examine the shipment (SPX) tuples one by one,
evaluating the formula "SPX.QTY > 250" for each one in turn;
the query result then consists of just those shipment tuples
for which the formula evaluates to true. In the proof
theoretic approach, by contrast, we consider the shipment
tuples (plus certain other items) as axioms of a certain
"logical theory"; we then apply theorem-proving techniques to
determine for which possible values of the variable SPX the
formula "SPX.QTY > 250" is a logical consequence of those
axioms within that theory. The query result then consists of
just those particular values of SPX.'
ibid p.267-368
Although there is a degree of confusion in terminology in the area,
Date (1992) suggests that a Deductive Database Management System is:
'a database that supports the proof-theoretic view of a
database, and in particular is capable of deducing additional
facts from the "extensional database" (i.e. the base
relations) by applying specified deductive axioms or rules of
inference to those facts. The deductive axioms, together,
together with the integrity constraints (discussed below),
form what is sometimes called the "intensional database"
(IDB), and the extensional database and the intensional
database together constitute what is usually called the
deductive database (not a very good term, since it is the
DBMS, not the database, that carries out the deductions).
As just indicated, the deductive axioms form one part of the
intensional database. The other part consists of additional
axioms that represent integrity constraints (i.e. rules whose
primary purpose is to constrain updates, though actually such
rules can also be used in the deduction process to generate
new facts)....it now becomes more important than ever that
the extensional database not violate any of the declared
integrity constraints! - because a database that does violate
any such constraints represents (in logical terms) an
inconsistent set of axioms, and it is well known that
absolutely any statement whatsoever can be proved to be
"true" from such a starting point (in other words,
contradictions can be derived. For exactly the same reason,
it is also important that the stated set of integrity
constraints be consistent.'
ibid p.394-5
One might profitably read the above with the failure of Leibniz's Law
within intensional contexts clearly in mind. Similarly, neophyte PQL
programmers soon find that the reason why most of what they want to
achieve fails to materialize is due to errors in their programming,
which invariably come down to them not specifying step by step the
logical and procedural steps of their query. Here again, the actual
user, rather than the casual reader will appreciate the didactic force
of the imperative "stay out of your head, and look at the screen". The
experienced user should appreciate that the keyboard and screen
comprise a very effective system of 'virtual' reality, which is
improved by a mouse.
One of the main advantages of a formal database system is that as
updates are made to the overall data structure, cross referencing
maintains database integrity constraints by only making updates
according to well established update rules. We have seen at length,
the problems which results from failure of substitutivity within
intensional contexts - namely, that deductive inference is not
possible. Within PROBE, deductively driven updates are currently quite
minimal, restricted essentially to PQL 'retrieval updates' which cross
update inmate cell location and prison location across relations 3 and
11. Where further updates are possible, implementation beyond
providing quality control reports has been refrained from in the
interests of maintaining a degree of user input to maintaining overall
system integrity.
Returning to the terminology of relational technology, where a
predicate is a two-place predicate, it is an ordered 2-tuple, or
ordered pair. A tuple is a row, and a relation is a set of predicates
comprising a record type (sometimes called a table). In almost all
instances, whether a retrieval generates a simple list of inmates, or
a multivariate statistical analysis (with post-processing using SPSS
for multiple or logistic regression for example), we are practically
interested in value distributions (Kerlinger and Pedhazur 1973).
Carnap (1959) summarised the situation as follows (although it should
be appreciated that Quine's austere, wholly extensionalist system
developed in Word and Object (1960) was largely a critique of the
intensionalism which remained within Carnap's "Meaning and Necessity"
program):
Intensions and Extensions of the Chief Types of Expressions
Expression Intension Extension
Sentence Proposition Truth-value
Individual constant Individual concept Individual
One-place predicate Property Class of individuals
n-place predicate (n>1) n-place relation Class of ordered n-tuples of
individuals
Functor Function Value-distribution
Carnap (1958)
Introduction to Symbolic Logic and its Applications
In an annex to a short paper entitled 'What is a Relation' Date (1992)
put the situation as follows:
'In the body of this paper, I gave the mathematician's view
of a relation as "An n-ary relation is a set of ordered n-
tuples." In this appendix, I would like to mention an
alternative view very briefly - namely, the logician's view.
In logic, an n-ary relation is simply that which is
designated by an n-place predicate in what is called the
first order predicate calculus. For example, the expression
">(A,b) is a 2-place predicate that designates the "greater
than" relation, and "SP(S#,P#,QTY)" is a three-place
predicate that designates the "shipments" relation in the
usual suppliers and parts database. In general, an n-place
predicate can be thought of as a truth-valued function with n
arguments; a given tuple appears in the corresponding
relation if and only if the function evaluates to true for
the argument values represented by that tuple.
..
When we talk about the foundations of the relational model,
we usually talk in terms of sets and set theory - a
mathematical foundation, in fact. But the forgoing indicates
that it is at least equally possible to talk in terms of a
foundation in logic - specifically, in the first order
predicate calculus - instead. And this alternative perception
does have certain arguments in its favor....some people would
argue that the true foundation of the relational model is
really the first order predicate calculus, not set theory,
and moreover that there is no real need to invoke set-
orientated ideas at all in developing and discussing the
model.'
C. J. Date (1992)
What is a Relation? A Logician's View
Relational Database Writings 1989-1991 p.54-5
Whilst initially unfamiliar, this logical notation, basic to the
predicate or functional calculus, provides an invaluable framework
when designing and managing data base management system's structure,
when planning analyses and programming automated reports. It is
certainly easier to deal with in the author's view than the more
commonly encountered set theoretic terminology, and renders the links
with work in theoretical logic (e.g. Quine 1960, 1992) much easier.
All database systems must be reduced to 'normal form' in the interests
of being able to analyse the modelled domain at its most fundamental
levels. Through Quine's critique of analyticity (1951, 1960), coupled
with the axiomatic nature of Leibniz's Law the language of science
(Quine 1954) has little choice but to dismiss intensional notions such
as 'sense' (Frege 1883), or 'individual concept' (attribute, property,
meaning, content etc; Carnap 1947; Church 1951). Intensional contexts
are indeterminate, and thereby unable to occupy positions of bound
variables (Quine 1943;1956) in any form of scientific analysis
(computer or otherwise).
In 1994, we simply do not know how to use formal logic (Information
Technology) to quantify reliably into intensional contexts (such as
the propositional attitudes), and attempts to do so using techniques
such as Repertory Grids (the 'Fragmentation Corollary' aside) and
Factor Analysis may prove to be creative rather than analytical as a
consequence. Less formally, we do not know how to reason within such
contexts without falling into rhetoric and sophistry. Until we are
shown otherwise, extensional systems render us incapable of analysing
inmates by anything other than the classes which they fall into. We
can do no more than use quantification theory to extensionally
identify the functional relations which exist between such classes,
and manage behaviour according to such functions.
Compound predicates, or n-ary relations e.g. Governor's reports can be
created such as 'Rule_Paragraph', 'Date_of_Infraction',
'Time_of_Infraction', 'Location_in_Prison' and a unique
'Inmate_Case_Identifier' (the constant, or when quantified, a variable
x). Each predicate returns one, and only one value, and together they
comprise a vector which can be analysed like the values of any simple
or atomic predicate. In this way, it is possible, using relational
technology, to define the arity of relations or predicates using the
logical connectives within a fourth generation retrieval language and
thereby expand or restrict relations or predicates to certain times,
dates, places, or to inmates with certain classes of index offence,
ages, or whatever the algorithm written, actually 'satisfies' (Tarski
1931) through the tuples meeting the specified value criteria of the
well-formed formula (wff). That is, an instance (or instantiation) of
a clause is obtained by applying a substitution to the clause, and a
substitution is an assignment of terms to variables (Kowalski 1979).
An example to illustrate the above should clarify the terminology and
illustrate the potential of working within this framework, given our
understanding of Leibniz's Law.
We will take record three of PROBE, Behavior at The Current Prison
(CURPRIS). There are (34 Records in all, several one-many (eg. reports
movements, segregation periods, attainment assessments).
Key
'Variable' 'Variable Label'
01 a NATNUM NATIONAL NUMBER
02 b PRESCAT PRESENT SECURITY CATEGORY
a 03 c EDRCPRIS EDR or NPD CURRENT PRISON
r 04 d PRISON CURRENT ESTABLISHMENT
g 05 e DOR DATE OF RECEPTION
u 06 f WINGINST CURRENT WING
m 07 g TPPSYC PSYCHIATRIC DIAGNOSIS AT CURRENT PRISON
e 08 h TPDRUGS EVIDENCE OF DRUGS THIS PRISON
n 09 i ELIST PLACED ON E LIST THIS PRISON
t 10 j NEWHOST HOSTAGE TAKER AT THIS PRISON
11 k TPR43OR RULE 43(OR) SEGREGATIONS THIS PRISON
p 12 l TPR43GO RULE 43(GOAD) SEGREGATIONS THIS PRISON
l 13 m TPC1074 CI1074/3790 TRANSFER FROM THIS PRISON
a 14 n TPSTVIO (PROVEN) STAFF ASSAULTS THIS PRISON
c 15 o TPINVIO (PROVEN) INMATE ASSAULTS THIS PRISON
e 16 p TPADJ (PROVEN) ADJUDICATIONS THIS PRISON
17 q PSYMON3 PSYMON vs F1150 FLAG(3)
18 r DATMOD03 MODIFIED
Relation Name = Curpris
Argument Positions (arity) = 18
As an 18-ary relation:
A R G U M E N T P O S I T I O N S
1 1 1
1 2 3 4 5 6 7 8 9 0 7 8
T Curpris(113386,2,01011700,LLC,05041991,A,0,0,0,0,..... ,0 10041991)
U Curpris(119085,1,01011700,LLC,14111991,Z,0,0,0,0,..... ,0 01061993)
P Curpris(122004,2,01011700,LLC,14101988,B,1,0,0,0,..... ,0 30011989)
L Curpris(132016,1,01111988,LLC,01021979,E,0,0,0,0,..... ,1 01051988)
E Curpris(132687,1,01011700,LLC,30101989,S,0,0,0,0,..... ,0 29031990)
S Curpris(133616,2,01011700,LLC,11051982,F,0,0,0,0,..... ,0 01061993)
Or as a series of binary predicates:
01 Natnum(113386,Curpris)
02 Natnum(119085,Curpris)
P 03 Natnum(122004,Curpris)
R 04 Natnum(132016,Curpris)
E 05 Natnum(132687,Curpris)
D 06 Natnum(133616,Curpris)
I 07 Prescat(113386,2)
C 08 Prescat(119085,1)
A 09 Prescat(122004,2)
T 10 Prescat(132016,1)
E 11 Prescat(132687,1)
S 12 Prescat(133616,2)
13 Etc., etc.
14 Etc., etc.
Queries can then be expressed in 'clausal form' as:
Answer(x)
Answer(x) Inmate(x, Curpris) AND Prescat(x,1)
or
Answer(x)
Answer(x) Curpris(x,y,z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o)
AND
Curpris(x,1,z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o)
Here, the value '1' is substituted for the variable b in order to list
all inmates with a value of 1 for Present Security Category (Prescat).
This presentation should make it graphically clear why some query
languages are given the name 'Query By Example'. The same format is
followed of course when instantiating queries with predicates drawn
from other relations such as Person, Utadata, Curpris, Reports and so
on. As covered at length in Volume 1 and the early parts of this
volume, the fundamental value of relational, deductive technology,
lies in the failure of effective substitutivity of identicals, 'salva
veritate', within intensional contexts. The failure of Leibniz's Law
within epistemic and other intensional contexts renders anything and
everything inferable given the violation of the law of contradiction,
or failure of truth-functionality within such contexts.
Comprehensive relational modelling and extensional deductive analysis
within a domain, or universe of discourse comprises a science of that
domain. The application of the theorems derived from analysis back
into the domain, comprises a technology. There can be nothing
controversial about this claim once the logical basis of relational
theory and scientific method are clearly understood in conjunction and
the significance of the failure of Leibnitz Law within intensional
contexts is fully appreciated.
At the end of Volume 1, and certainly within Volume 2, we used
functional notation rather than the language of relations and
predicates, so before leaving the subject, we show how functional
notation expresses predicates or relations. Recall that in his
discovery of the Predicate Calculus (his 'Begriffsschrift') in 1879,
Frege wrote that his discovery of the quantifiers was in large part a
consequence of rejecting the old Predicate-Argument notation, and
selecting instead an extended concept of the mathematicians notion of
function-argument, at the same time, we will deal with the important
issue of equality or identity.
We can express Times(x,y,z)
as x * y = z
or Father(x,y)
as x = father(y)
Relational calculus query language uses function symbols and equality:
prescat(x) = y
in place of Prescat(x,y)
winginst(x) = y
in place of Winginst(x,y)
The following is taken from Kowalski (1979), and effectively brings us
full circle to the leitmotif of these volumes, beginning with the
quote at the beginning of Volume 1: the identity of indiscernibles and
the failure of Leibniz's Law within intensional contexts.
'Equality is necessary whenever an individual has more than
one name. For example:
Jove = Jupiter .
It is also necessary, even in the relational notation, to
express that one argument of a relation is a function of the
others. For example:
x = y Father(x,z) , Father(y,z)
To show that a set of clauses S containing the equality
symbol is inconsistent, the set of clauses needs to contain
the following axioms characterising the equality relation,
for every function symbol f and every predicate symbol P
occurring in S, (including the equality symbol).
E1 x = x
E2 P(x 1 ,.....,x m ) P(y 1 ,......,y m ), x 1 =y 1 , ..., x m =y m
E3 f(x 1 ,.....,x m ) = f(y 1 ,......,y m ) x 1 =y 1 , ..., x m =y m
for example, to demonstrate that the assumptions
J1 Jekyl = Hyde
J2 father(John) = Hyde
J3 Member(father(John), birthday club)
imply the conclusion
member(Jekyl, birthday club)
it is necessary to deny the conclusion
J4 Member(Jekyl, birthday club)
and add the appropriate axioms for the equality relation:
J5 x = x
J6 Member(x 1 ,x 2 ) Member(y 1 ,y 2 ), x 1 =y 1 ,x 2 =y 2
J7 x 1 = x 2 y 1 = y 2 , x 1 = y 1 , x 2 = y 2
J8 father(x) = father(y) x = y
The following set of clauses J1-8 is inconsistent because J1-3 are
"obviously" inconsistent with the instances
Hyde = Hyde
birthday club = birthday club
Member(Jekyl, birthday club) Member(father(John), birthday club),
Jekyl = father(John),
birthday club = birthday club
Jekyl = father(John) Hyde = Hyde, Jekyl = Hyde, father(John) = Hyde
of J5-7. Clause 8 in this example does not contribute to the inconsistency.
R. Kowalski (1979)
Representation in Clausal Form: Equality
Logic for Problem Solving
In managing and designing and developing the PROBE system, special
care has been taken to ensure that these extensional, ie truth-
functional principles are followed and that referential integrity
constraints or rules on data entry are built in to optimize quality
control. Training has emphasised the pitfalls of clinical judgement
(Volume 1) as evidence of the failure of quantification within
intensional contexts. At times this has been extremely difficult,
since many users still regard databases as 'nothing more than' a
research data storage medium. This can only stem from a poor
conception of the technology behind record (table) design, the power
of 'normal form' or 'clausal form' as an artificial language, and a
very limited practical use of the such systems, e.g. the production of
simple lists rather than full relational analyses. This functional
specification is designed to suggest how the PROBE system might be
used in support of an applied behaviour science and technology, which
in turn supports effective inmate management, not, it must be said, as
an all purpose MIS. Any failure to fully appreciate these points will
inevitably lead to great financial investments with very little in the
way of productive returns. Without a sound appreciation of logic, such
systems simply will not be used effectively. This is a simple lesson
from research in descriptive (folk) psychology (Volume 1).
For those who are sceptical about the value of checklists for
instance, it is important perhaps to point out that the prison rules
can be listed as 21 paragraphs under Rule 47, ie as a series of
observation statements. An inmate will always be charged under one, or
another paragraph of the Rule (each as a separate event or offence).
The paragraphs serve as a set of declarative statements (32 binary
predicates or a 32-ary relation if the circumstances such as date and
time, place etc. are included in the tuple). The Rule 47 system
effectively operate as a behaviour checklist, or criterion referencing
system. Where no offences have occurred it is as if null entries were
entered for each inmate, date, time and place - something which is
made graphically clear when actual offences are plotted against time.
Construed from the perspective of relational theory, this removes in
one move, any objections to 'box ticking' as a means of assessment,
since it can readily be seen that all inmate management must be based
on such predicate or relational systems, albeit sometimes of quite
high arity, and therefore for memory capacity constraints, quite a
bewildering i.e. impossible task for working memory as outlined in
Volume 1 and elsewhere (Miller 1956; Attneave 1959; Cherniak 1986,
Stich 1990).
Based on this conception of a Data Base Management System, PROBE's
second phase of development work between 1991 and 1994 enabled the
system to map entire prison regimes using the relational concepts
outlined above (and as illustrated in Volume 2). A system of Sentence
Management was designed whereby staff are able to continuously define
(and up to a point, dynamically refine) the regime functions they are
responsible for supervising, be these elements of wing routines or the
requirements (performance criteria) of specific inmate activities such
as education courses, periods in prison industries, special programmes
etc. Within the PROBE Sentence Management system, staff are required
to define declarative statements (predicates/regime propositional
functions/relations) or 'Attainment Criteria' which can be assessed as
being true or false of an inmate, at specific stages of programmes, on
specified dates. Just as the truth or falsehood (guilt or innocence)
of a prison rules infraction is ascertained by an expert on the prison
rules (a Governor), so too, the level of attainment an inmate has
attained is ascertained by, ideally, an accredited, expert supervisor.
This system allowed us to expand the arity of the relations available
within the PROBE relational Data Base Management System almost
infinitely without having to make physical changes to the system's
data dictionary (the schema - Volume 5). Such a criterion referencing
system can develop flexibly, with individuals being profiled with
reference to such criteria at any stage of their prison career.
Together, therefore, the predicates/relations/functions and truth
values within PROBE serve as a Knowledge Base for the production of
comprehensive inmate career profiles which are descriptive,
declarative reports of inmate behaviour relative to fixed reference
criteria. Such extensional reports have clear reference criteria and
are produced by algorithms written using the 4GL (PQL) provided within
the DBMS. The skilled work within such a system lies in the writing of
retrievals.
Furthermore, such retrievals can be written to incorporate parameters
of the population from which the inmate is drawn, such parameters
thereby serving as reference classes. PROBE routinely provides
profiles which provide information at both the individual (Section
3.2) and group (Section 3.3) levels. As the technical work is
primarily on the design and use of PQL algorithms in the management of
inmate's as a function of the classes they fall into and the
characteristics of those classes (e.g. age group and report rate),
PROBE is basically an actuarial system (Dawes, Faust and Meehl 1989,
1993), as well as an application of Artificial Intelligence research.
Risk assessment in all areas of inmate management becomes largely a
matter of ascertaining what classes an individual belongs to, and the
characteristics of such classes. Providing that all concerned
appreciate that individual assessment must always, albeit often
implicitly, be assessment relative to some class or another, and that
class membership is a dynamic function of ongoing behaviour, it
becomes clear that the PROBE technology amounts essentially to no more
than an MIS to support effective inmate management based on actuarial
rather than clinical judgment.
As outlined above in the context of quantification, Vickers (1988) and
Lukasiewicz (1909) have generalized the Fregian concept of truth
function:
'The truth value of an indefinite proposition is "...the
ratio between the number of values of the variables for which
the proposition yields true judgements and the total number
of values of the variables" (p.17). The relative
(conditional) truth value of indefinite propositions is the
quotient of the truth value of their conjunction and that of
the antecedent. Lukasiewicz then argues that these truth
values provide an adequate account of probability, free from
many of the difficulties that plague subjectivistic and
empirical views.'
J. M. Vickers (1988)
Chance and Structure:
An Essay on the Logical Foundations of Probability p.149
Statistical technology is covered little in these volumes since most
readers will have already undertaken the course which complements
these volumes. However, for the sake of what follows it is important
that the reader appreciates that we are, at least in part, following
Vickers (1988) in his treatment of Fregian quantification:
'The major motivating principle of probability quantifiers is
the development of probability within pure or general logic
to the extent that this is possible. The great difficulty of
precisely defining general logic can perhaps be avoided by
agreeing that however it is defined, the semantics of first-
order logic as developed by Frege and Tarski fall quite
within its confines. Then, as the above remarks suggest, the
question is just to what extent such notions as "the
proportion of objects falling under a concept" or "the
proportion of assignments satisfying a formula" can be given
a meaning in general logic.'
J. M. Vickers (1988)
Chance & Structure: An Essay on the Logical Foundations of
Probability
Probability quantifiers:principles and semantics p.153
David Longley
FRAGMENTS OF BEHAVIOUR:
EXTRACT 11: FROM 'A System Specification for PROfiling BEhaviour'
Full text is available at:
http://www.uni-hamburg.de/~kriminol/TS/tskr.htm
'Now when I turned to the question... I first had to
determine how far one could go in arithmetic through
inferences alone....So that nothing intuitive could enter
unnoticed, everything had to depend on keeping the chain of
inference free of gaps.'
G. Frege (1879)
Begriffsschrift p.x
Because the following has caused some ripples within my own
profession I have split it into several pieces in order to lighten
its distribution and increase the liklihood of stimulating comment
and criticism from those who specialise more in one area than another.
Some of the issues will be more familiar to philosophers, others
statisticians, others still, applied psychologists etc. An early
version was presented at the Spring 1993 meeting of the Division of
Criminological and Legal Psychology of the British Psychological
Society.
For anyone wishing to read all of the extracts, the following lists
the newsgroups which each part was posted to. I am looking for as many
profess ional comments as possible via newsgroup or e-mail. Full text
as a version 5.1 Wordperfect file, setup to print to a Brother HL8V is
available if you wish.
comp.ai.philosophy Extract 4: 25.04.95
sci.cognitive Extract 3: 25.04.95 Extract 5: 25.04.95
sci.philosophy.tech Extract 1: 25.04.95
sci.psychology Extract 2: 25.04.95
sci.stat.edu Extract 6: 25.04.95 Extract 7: 25.04.95
sci.stat.edu Extract 8: 27.04.95
alt.prisons Extract 9: 27.04.95
sci.stat.edu Extract 10:05.05.95
This ref: Extract 11: sci.stat.edu 10.05.95
'When taught arithmetic in junior school we all learnt to add
and to multiply two numbers. We were not merely taught that
any two numbers have a sum and a product - we were given
methods or rules for finding sums and products. Such methods
or rules are examples of algorithms or effective procedures.
Their implementation requires no ingenuity or even
intelligence beyond that needed to obey the teacher's
instructions.
More generally, an algorithm or effective procedure is a
mechanical rule, or automatic method, or programme for
performing some mathematical operation.'
N.J. Cutland (1980)
Computability: An Introduction to recursive function theory
Ch 1:Algorithms or effective procedures
'We think of a science as comprising those truths which are
expressible in terms of 'and', 'not', quantifiers, variables,
and certain predicates appropriate to the science in
question....To specify a science, within the described mold,
we still have to say what the predicates are to be, and what
the domain of objects is to be over which the variables of
quantification range.'
W.V.O. Quine (1954)
The Scope and Language of Science
The Ways of Paradox and other essays p.242
'Ultimately the objects referred to in a theory are to be
accounted not as the things named by the singular terms, but
as the values of the variables of quantification.'
W.V.O. Quine (1953,1961)
Reference and Modality
From a Logical Point of View p.144-145
'Beginning with a single sense of belief...let us think of
this at first as a relation between the believer and a
certain intension, named by the 'that-clause. Intensions are
creatures of darkness, and I shall rejoice with the reader
when they are exorcised...
......we can clap on a hard and fast rule against quantifying
into propositional-attitude idioms..'
W.V.O. Quine (1956)
Quantifiers and Propositional Attitudes
The Ways of Paradox and other essays p.188-189
PREFACE
This is Volume 3 of the PROBE System Specification, and is structured
as follows. The document comprises 3 sections which functionally
describe the system via routine illustrative examples. Section 1
provides a functional overview of the system, Section 2 covers the
basic technology of PROfiling BEhaviour, ie monitoring, and Section 3
covers the technology of PROgramming BEhaviour, ie Sentence Management
and Planning. Retrievals, system control files and other programs are
referred to at the foot of each sub-section, but are not listed or
annotated. This should provide the reader with a sound, and detailed
understanding of how the system works without the distraction of
technical, algorithmic listings (which dominate Volume 4). PROBE is
designed to support the professional work of behaviour scientists
within establishments and headquarters. It does this through the
provision of distributional data which is the sine qua non for the
practice of behaviour science rather than folk psychology. The latter
is characterised by the use of intensional heuristics. These tend to
predominate in review boards, interviews and standard reports. PROBE,
on the other hand, especially when running Sentence Management,
provides the basic infrastructure recommended by the 1984 CRC
Committee to support an effective (computational) approach to
management of the Long Term Prison System (only historical accident
accounts for it being so restricted).
As a project, PROBE is a research programme, as defined by Lakatos
(1978). As an official project, PROBE is a development in inmate
monitoring arising from the recommendations of the 1984 CRC. However,
as a personal project, it has some of its academic roots in some early
work of the author on Husserlian Phenomenology (Methodological
Solipsism) as the appropriate framework for pure psychology ('Mapping
Intentionality within the Conceptual Nervous System' - BSc thesis
1979), followed by an MRC research studentship into the physical,
rather than conceptual, nervous system and neophobia in the control of
behaviour (National Institute for Medical Research 1979-1983). That
work focused on the role of brain opiate peptides and monoamine
transmitters in the mediation of behaviour in response to novelty (the
sine qua non for learning), and conversely, familiarity (similarity)
and habit formation. Here, as there, the notions of subjectivity and
objectivity find no place. The logical devices of extension and
intension suffice. This volume has been written primarily for staff
interested in furthering the development of the PROBE project in an
applied context. Throughout the document, it should be understood that
in contrasting 'the psychologist', with 'the behaviour scientist', no
disrespect is intended to any practising field psychologist working
for the Prison Service. The contrast is used as a device to highlight
the widely held conviction that the concerns of folk psychology
(propositional attitude psychology) and those of applied behaviour
science are fundamentally and radically different. One is the converse
of the other in fact (Churchland 1989). It is argued throughout these
volumes that the latter discipline requires distributional data to
make any professional contribution, which amounts to providing
accurate reports on inmates and populations of inmates, and that all
such reports must be de dicto compilations of recorded facts. The work
of the former, on the other hand, is literally creative and artistic,
not truth-functional, as is illustrated by what we tend to do when we
claim to 'report' that which others say. Practitioners of psychology
in this sense, lay or professional, make judgments on the basis of
translations or interpretations of what is said or meant
(distributional data being inaccessible to them for one reason or
another). Hopefully, all of these issues will become clearer as each
volume is read.
TWO PERSPECTIVES ON THE PROBE PROJECT
'133. Today the dispersal system in particular needs support,
and we are clear that this means looking at the long-term
system as a whole. There will inevitably be control problems
if long-term prisoners are held in a system that gives
inconsistent messages about the course of their sentences or
the consequences of their actions, and if prison managers'
only recourse in the face of disruption is to switch
prisoners between normal location and the segregation unit,
and between one prison and another. We are sure that both
elements of this situation need to be turned around. The
long-term system should run in accordance with an
intelligible scheme; and this should feature a deliberately
varied pattern of facilities to give management the
flexibility it needs.
134. We are consequently proposing a strategy of two
complementary sets of initiatives. To improve the basic
structure we recommend central control of all long-term
allocations and arrangements for each sentence to begin with
a full period of assessment and sentence planning. This
approach becomes really meaningful only if prisoners are
given individual programmes of activities and are involved in
regular reviews and that is exactly what we should like to
see develop. The level of management and co-ordination that
will be required from the system to deliver such programmes
is, we believe, needed in any event, as is the more rigorous
review of the categorisation system that we propose.
135. The matching line of development that we recommend would
be designed to cater for those prisoners whose behaviour does
not respond to the inbuilt incentives of a better structured
system. The general view that was put to us was in favour of
specialised units, out of the main-stream, for this purpose,
and we see no realistic alternative to that approach. For
some kinds of mentally disturbed prisoner a revitalised
Parkhurst C Wing and a developed Grendon regime would have
much to offer. For other kinds of inmate who constantly
threaten control we shall have to develop a few small units
of a new kind, and we strongly recommend that this should be
done as a positive, developmental initiative, with outside
academics participating in the planning and evaluation, and
with as much openness as possible about the whole project.'
CRC REPORT (1984): Chapter 7 SUMMARY p.40-41
'There was once a chap who wanted to know the meaning of
life, so he walked a thousand miles and climbed to the high
mountaintop where the wise guru lived. "Will you tell me the
meaning of life?" he asked. "Certainly," replied the guru,
"but if you want to understand my answer, you must first
master recursive function theory and mathematical logic."
"You're kidding."
"No, really."
"Well then....skip it."
"Suit yourself."
Daniel Dennett (1982): Dennett and His Critics (1992) Ed. B.
Dahlbom
SECTION 1 THE PROBE DATABASE
1.1 OVERVIEW OF SYSTEM DEVELOPMENT & MANAGEMENT 1985 - 1994
A major thesis running through this document, perhaps the major thesis
is that the fundamental conditions required for valid scientific or
rational inference (existential and universal quantification) do not
exist within intensional, or psychological contexts, and that
effective rational inferences, therefore, are not psychological
processes. The basis for this conclusion lies in work within
mathematical logic (Quine 1956, 1960), and empirical research within
Cognitive Psychology (Slovic, Tversky and Kahneman 1982; Dawes, Faust
and Meehl 1989, 1993). Psychology, narrowly defined, may be said to be
the study of that large (possibly infinite) set of contexts where
extensional reasoning breaks down and a range of heuristics are
resorted to instead (Tversky and Kahneman 1973). The application of
normative principles of reasoning, ie the predicate calculus in
applied settings comprises sets of professional skills defined by the
domain over which those skills are applied (medicine, accountancy,
law, civil engineering etc.). In the case of the PROBE system, the
domain is that of inmate behaviour with reference to the requirements
of prison regimes, and the appropriate class of skills applied are
those of the behaviour scientist or knowledge engineer. His or her
task is to identify functional relations between classes of behaviour
which can then be used to effectively, and objectively manage
behaviour on the basis of those relations.
>From one point of view, PROBE is the beginning of a professional
response to the growing empirical evidence in support of the
modular(ity) and encapsulated nature of human judgment (Fodor 1983).
Evidence suggests that whilst we may be good at classification in
situations where we are trained to make such classifications, we are,
nonetheless, not so good at naturally analysing the relations between
those classes we classify by (Dawes, Faust and Meehl 1989). It is
important that our classes are in fact natural classes, or kinds
(Quine 1969). Research in all aspects of behaviour has shown, as
decisively as research work can show, that we don't generally make the
right connections between classes most of the time. Instead, our
judgements are situation or context specific, probably because that is
the way that our brains are structured in the interests of fault
tolerance (cf. modularity, encapsulation and the recent resurgence of
'connectionism' in the cognitive and neurosciences, Volume 1). Where
we are able to make the right connections, the argument is that we do
so through the use of learned algorithmic principles or rules, which
comprise the deductive principles of scientific method. This being the
case, we may as well turn to the technology which we have created to
do this so effectively for us, and eschew intuitive judgment.
'We suggest that there is no reason not to use available
statistical techniques to maximize the predictability of
models, when in fact models have been shown to be superior to
clinical judgment. The research has been focused primarily on
demonstrating, or even questioning, this superiority, without
a simultaneous consideration of how best to take advantage of
it. Although others (e.g. Kleinmuntz, 1990) have urged that
people combine their heads with their models in predication,
we urge that people use their heads to improve their models.'
R. M. Dawes, D. Faust & P. E. Meehl (1993):
Statistical Prediction versus Clinical Prediction:Improving
What Works :
A Handbook for Data Analysis in the Behaviour Sciences
All models are artificial, and since the domain we are modelling is
judgment, PROBE is, strictly speaking, an application of Artificial
Intelligence rather than psychology. Stored relations comprise our
professional knowledge base, and the query language's well formed
formulae allow us to make deductive inferences within that knowledge
base - a point now even recognised by the popular press:
'..the standard academic view on databases is that they can
be specified as a set of first order sentences....Almost all
approaches to query evaluation treat queries as first order
formulae.'
Personal Computer World April 1993 p.450
>From another point of view, a basic rationale justifying the
development and maintenance of the PROBE system should surely be that
effective (computational) inmate management must be based on the same
principles which accounted for their being convicted and given a
custodial sentence in the first place, namely recorded behaviourial
evidence, and rational processing of such evidence by explicit rules
(the law). In the case of the PROBE system, this relies on trained
staff recording their observations (encapsulated and context specific
though they may be) and then subjecting those observations to logical
and statistical (ie actuarial) analysis (Dawes, Faust and Meehl 1989).
The fundamental task is one of professionally describing behaviour
without 'going beyond the information given' (Bruner 1957,1973). Such
work, it is argued, requires the skill of behaviour scientists for
reasons which should become clear below (and in Volume 1).
In the introduction to the most influential piece of work in logic
since the development of Aristotelian logic, Frege (1879) introduced
his Begriffsschrift as follows:
'Now when I turned to the question... I first had to
determine how far one could go in arithmetic through
inferences alone....So that nothing intuitive could enter
unnoticed, everything had to depend on keeping the chain of
inference free of gaps.'
G. Frege (1879)
Begriffsschrift p.x
So a major objective of the PROBE project is to use computerised,
elementary logic (the propositional and predicate calculus), to
collate and deductively (extensionally) analyse inmate behaviour with
as little inductive (intensional) 'gap filling' inference as possible.
'Frege saw that the general, neutral concept of a function
must be made the principal one in his proposed system for
symbolically representing the forms of "pure thought". The
way in which a function can be defined, or represented, by
giving an expression (as in the above examples) for its
result as a computable or constructible combination of its
arguments, is known as abstraction; and Frege's great insight
was to see that the activity of "pure thought" he wanted to
represent consisted of acts of abstraction of functions from
expressions, interwoven with acts of application of functions
to arguments, formulated as acts of evaluation of
expressions. The interplay between abstraction, application
and evaluation is the whole story of the thought that Frege
wanted to analyze, explain, and represent.'
...
These functions and entities are the logical ones: truth,
falsehood, negation, conjunction, disjunction, universal and
existential generalisation, and exemplification.
....
Once this formalism is understood, the reader can then easily
entertain, and follow the development of a proposition that
has entranced students of logic for centuries: that deductive
reasoning can be mechanised - literally, performed by a
machine - just as many of the routine tasks of numerical
computation can be and have been. It was not Frege's main
motivation to help make the mechanization of deductive
reasoning a practical possibility. He was very much aware,
however, of the attempts of earlier thinkers such as Hobbes
and Leibniz to argue that this could and must be done, and he
well knew that his own work was an indispensable step.'
J A Robinson (1979)
Logic, Form & Function:
The Mechanization of Deductive Reasoning
A convicted, long term prisoner's time in custody will usually include
movements between several prisons, probably one a year on average,
during which time he may come into conflict with the requirements of
the regime, sometimes extensively. The majority of inmates do not,
they complete their sentences without serious incident. However, a
small minority, perhaps no more than 1% do not co-operate, and these
comprise the system's 'control problems'. Most inmates are relatively
well behaved, and as a consequence, their time in custody will be
relatively uneventful. They will spend their time in several prison
activities, averaging little more than a couple of months in each, and
little more than 4 hours a day (Section 2). They will progress from
high to low secure conditions throughout their sentence, many going on
Home Leave towards the end of their sentence and being granted early
release on parole.
PROBE (PROfiling BEhaviour) was developed in 1985-7 as an
operationalisation of research into the identification of control
problems in the English Long Term prison system, and was launched in
April 1988 to aid the identification of control problem inmates, and
to provide field staff with an information system to support the
maintenance of control within their own establishments within the
terms outlined by the Control Review Committee in 1984. Prior to the
development of the system, a single line of data (80 characters of
data on each inmate), which included their surname and number, was
returned to Headquarters each month from field psychology units,
reflecting Sentence characteristics and behaviour up to arrival at
their current prison. That monitoring work was undertaken by HQ
psychologists in the wake of the Hull riot in 1977. These small, 80
byte data files were analysed using a bureau service, and descriptive
statistics were generated each month. Basic statistical analyses would
cost up to 30UKP per run, with more complex analyses, such as Factor
Analysis, costs in the mid 1980s would be as high as 300UKP. With
computing costs this high, a budget of UKP70,000 a year was not
extravagant in 1986. In 1994 it is difficult to convey just how much
skill and effort was required to submit a job to an IBM or CDC
mainframe using punched cards, an arcane operating system, and a 300
baud teletype terminal. Today, the required processing power and
software can be undertaken on a Personal Computer - the skills, the
fundamental personal skills required, however, have not alas,
developed apace.
Routine reports were made to the Dispersal Prison Support Group, which
comprised the Dispersal Prison Governors, various headquarters section
staff and was chaired by the Deputy Director General. Field staff were
also required to return discharge information each month. With these
returns, Headquarters psychologists were able to provide some
indication of the movements within the Dispersal estate.
With the design and introduction of PROBE, and the emergence of
powerful desk top personal computers in the latter quarter of the
1980s, field psychologists acquired the facilities of a full, research
scientist orientated relational database (SIR), which hitherto had
costs up to UKP32K to run on a VAX, the supporting statistics package
SPSS which had been so expensive to run on a mainframe, along with
powerful graphics and report writing software which only became
available in the late 1980s. This technology, it was argued, would
enable field psychologists to provide a comprehensive service in
behaviour profiling and potentially, an actuarial based service to
Governors in inmate management.
Whilst the pre-1986 system of control monitoring was limited in scope
by hardware and the aforementioned very high costs of software and
analysis services in the 1970s and early 1980s, with the introduction
of the PROBE system, the constraints on what could be provided became
largely dependent on the time and extent to which field staff's job
descriptions allowed them to work with the provided systems as a means
of deriving distributional data (population parameters) and individual
inmate profiles. The success of this, in turn, depended on staff
training and adequate dispersion of the results of research and
development work within the infrastructure of the PROBE system. From
the earliest days of the PROBE system, an electronic network (the
PROBE network - Section 5.7.1) was set up to allow the automatic
nightly transfer of database updates to central copies of the database
in Headquarters. At the same time, this technology was used to
distribute material bearing on the project throughout the
participating network. The central databases were made available by
high speed, 9600 baud 6dB low loss, dial up lines so that when an
inmate was received into a PROBE prison, field staff could download
that inmate's data, and have it semi-automatically added to their
database (Section 5.7.2).
The earliest piece of development work generated individual inmate
reports which listed their movements, governor's reports, segregation
periods, along with descriptive statistics showing the intervals
between reports, and how these change as an inmate moves from prison
to prison. These reports (Section 2.1), which were supplemented with
graphics of reports plotted against time into custody, became known as
'PROBE profiles'. This was a direct application of the Experimental
Analysis of Behaviour as developed by B.F. Skinner, ie the analysis of
relative frequencies of behaviour depicted in cumulative records. A
quick glance at a graphical profile of an inmate's reports and
movements plotted against time clearly show whether an inmate's report
rate is accelerating, decelerating or constant, and whether it might
be related to his pattern of movements.
To facilitate the work of the Special Unit Selection Committee (which
considers Governor's referral of candidates for the Special Units and
oversees their stay in units when selected), inmates meeting a set of
criteria would automatically have profiles generated on them each
Sunday. This is done within SUSC Section within Headquarters, and
simultaneously at each field site. Lists of likely SUSC candidates
along with their profiles were then available for staff on Monday
mornings (Section 2.2). This feature was operational by late 1989, and
was used almost on a daily basis by SUSC/CRC staff sharing the systems
in the Adult Offender Psychology Unit. In 1991 SUSC Section acquired
their own system.
In 1989, weekly analyses (Section 2.3) of each prison were programmed
to run centrally each weekend, the data being made available for field
staff to download from the central system, PROBE HOST, each Monday
morning. These population measures allowed ready comparison between
the prisons on measures such as the proportion of the population which
was category A, age distribution, number of reports up to arrival,
breakdown of the type of inmates being received by index offence and
other classification categories. Most significantly, the population of
each prison was broken down by wing, mean scores for a number of
control indices being provided at this level.
The building of the system, ie the entry of data, occupied most of
1988 and continued into late 1989. Whilst field staff worked on
building their databases, ensuring that a full career history of
reports, movements and segregation periods existed for each inmate,
the small PROBE unit at Headquarters focused on building quality
control routines (Section 1.14), monitoring the development of the
databases, and writing algorithms to automate as much of the
management of the system as possible. The rationale here was that the
more that was automated, the more time would be available for research
and development work, both in the field and at HQ. This in turn, it
was reasoned, would enable the necessary system outputs to be produced
to justify system maintenance by field, and HQ staff. To minimize
interruption of field work, HQ maintenance was restricted to periods
outside the standard working hours of field staff (Section 2.5).
Throughout late 1989 and 1990 considerable investment was made in the
development of a Graphic User Interface (GUI) for the spatial mapping
of measures of behaviour by wing and cell location (Section 2.6).
Initially through ad hoc interactive analysis, and later through
programmed nightly analyses of databases, routines were written to
enable control measures to be displayed on screen as 'hot spots' on
prison wings, identifying groups of inmates according to any category:
high rates of reports, prior escape history, and so on. Spatial
proximity and similarity in behaviour profiles would easily be
demonstrated using this graphic technology. Later development
improvements led to the coding of key variables in monochrome together
with different symbols which allowed maps to be automatically
incorporated into reports as vector graphics.
The above technology required field staff to maintain a record of
changes in cell locations, since the spatial mapping system's basic
relational unit was an inmate, date, and ordnance survey grid
reference coordinate of a cell. Through maintaining changes in cell
location, the potential arose to reconstruct behaviourial maps of the
prison population at selected dates back in time. The data also held
out the potential of improving retrospective profiles of the
population, which was possible at whole establishment level in 1990
using the reception and departure dates of the movement records. With
the recording of cell location (along with landing and wing), the
potential to reconstruct the population at wing level became possible,
a facility which is of considerable potential given that institutional
unrest tends to emerge at wing, rather than whole establishment level.
Throughout 1990 work was also undertaken on the development of
Sentence Planning policy in conjunction with a small Steering Group.
This was a recommendation of the 1984 Control Review Committee,
deferred pending analysis into how this recommendation might be put
into practice. Work throughout 1990 focused on whether Category A
inmates could be included in the circular instruction scheduled to
introduce sentence planning that year for all inmates serving 10 years
or more with 5 years or more to their EDR. Field Psychologists had
also been working in 1990 on the prototyping of Optical Mark Reader
based behaviour checklists which we hoped would provide additional
information to that, rather restrictively provided, by governors
adjudications on disciplinary infractions. The PROBE Wing checklist,
similar in design to one which we had used in the 1985/6 work on the
identification of control problems, was designed to be Optical Mark
Machine readable to ease data entry. The proposal was that all inmates
would be assessed relative to the items on the checklist each month,
and that the resulting data could be used to enhance our profiles. The
checklist was run at HMP Parkhurst between 1990 and 1992.
In the context of development work on Sentence Planning, the PROBE
data base and network were used to compare the movement patterns of
Category A inmates with Category B inmates in order to ascertain
whether the constraints on/frequency of Category A movements would
make Sentence Planning impracticable for this group. In a report
submitted to the Steering Group in autumn 1990, we concluded that
population turnover was universally quite high, averaging around 12 to
14 months, and that this would mean that Category A inmates were
constrained the same way as category Bs. We concluded, on the basis of
empirical analysis of movement data, that any viable approach to
Sentence Planning would have to be based on a system of continuous
assessment of behaviour with respect to the demands of activities and
routines, and that such material should then be drawn upon regularly
as reference material for any planning at both the individual and
population levels.
Accordingly, most of the development work on the PROBE system between
1991 and 1994 focused on the development and piloting of a behaviour
assessment system which would, from a systems analytic view, make
Sentence Planning viable (Section 4). The primary recommendation of
the 1984 Control Review Committee was that better control within the
Long Term Prison system would be achieved through establishing
individual inmate programme based Sentence Planning. Throughout 1991
and 1992 we developed a relational system called Sentence Management
(Section 3), which provided field staff with a technology for defining
attainment areas and criteria within all elements of their regime and
also a means of recording individual inmates' levels of attainment
with respect to those criteria. The system was designed to be run on a
monthly basis. This, in conjunction with a record of morning and
afternoon attendance allowed us to elaborate our profiles of behaviour
to provide detailed behaviourial records of attainment for individuals
which could be aggregated for wing analysis, or provided to the Head
of Inmate Activities for analysis of attainment by specific activities
(Section 3). As all behaviour is assessed by expert supervisors
according to criteria generated by them, the system was considered to
be an ideal substrate for Sentence Planning, and a major contribution
towards improving control within the Long Term estate. Identified low
levels of attainment could be used as the basis for F2054 Sentence
Planning target negotiation and setting. To facilitate this, the F2054
Sentence Planning material was incorporated into PROBE during 1992 and
1993 so that field staff could use Sentence Planning data in
conjunction with Sentence Management data. Pilot projects were set up
and run in 1993.
Refinements in retrospective profiling of behaviour led to the
generation of longitudinal graphs of changes in key control measures
by month for sub-establishments. These trend analyses clearly reflect
changes in the function of establishments over time, providing an
ideal means of profiling differential regimes, as shown in Section 2.
Whilst the weekly analyses of wings readily identify patterns such as
the concentration on one wing of a class of inmates with high control
indices (Section 2), the graphic profiles show how establishments and
sub-establishments change over a long period, and therefore provide
feedback on the efficacy of local tactical management and strategic
planning.
Such analyses objectively illustrate how the Long Term system is best
conceived as a system of wings or sub-establishments rather than
prisons. HMP Wakefield for example, although technically a dispersal
prison, has had a consistently low control index level for the past
four years, whilst HMP Garth, a non-dispersal, shows a profile
indistinguishable from several of the other dispersals such as Long
Lartin, Frankland and Whitemoor. The establishment of two or three
wings as a VPU (Vulnerable Prisoner Unit) or Lifer Unit render control
indices at the overall establishment level relatively uninformative
compared to analyses at sub-establishment, and ideally, wing level. In
1994, this is certainly true of HMP Albany for instance, which,
although no longer a dispersal prison, has more difficult inmates on
its non VPU wings than several other dispersal prisons have on their
wings (Section 1.2). Candidates for special units are also likely to
be referred from Category B Training prisons such as Swaleside, Garth
and Dartmoor. All of this can be used in support of the thesis that it
is a mistake to base control classification on intensional labelling
of prisons, it must be on the basis of extensional behaviour measures.
In 1994 the view from that of systems manager is consistent with the
views and recommendation expressed by the CRC committee in 1984,
namely that the Long Term prisons exist as a dynamic estate.
Of the 9 prisons above, 6 are dispersals in 1994, 3 have ceased being
dispersals in the past two years and two have become dispersals. At
the time of writing, two of the above have been considered for re-
designation as Category B Training, and two other Category Bs have
been considered as potential Dispersals. Given that it can take up to
2 years to build a PROBE system, and certainly more than this to train
staff to use it effectively, it seems only logical to argue that in
the interests of system continuity, data entry efficiency, and staff
training and cover that the future of the PROBE system, as a system
for monitoring and contributing towards the maintenance of control
must lie in its expansion to cover the remaining category B training
prisons: Dartmoor, Swaleside, Blundeston, Coldingley,
Grendon/Springhill, Kingston and Nottingham, and ideally the category
C estate also. It is hoped that the first two mentioned Category B
Training prisons will start building PROBE in 1994, and that the force
of the above argument will result in the others eventually joining the
system. The U.S. Federal Bureau of Prisons National Institute of
Corrections' (NIC) control reclassification system and table of
control of indices overleaf (TABLE 1) show the distribution of NIC
control scores and report rate by establishment and wing. These
figures are used operationally by several establishments to monitor
inmate allocation at this level on a weekly basis. A data file,
provided along with the overall statistics allows individual inmates
to be listed within the wings. The data is presented here in support
of the argument that the Long Term Estate is a collection of sub-
establishments, each with their different regimes.
System development in recent years has capitalised on the Artificial
Intelligence potential of the relational system which is fundamental
to PROBE's design. Through an analysis of aggregate data held within
the system it is now possible to build actuarial models to support
decision making in all areas of inmate Sentence Management. In 1993
this was illustrated by the development of an actuarial model to
support decision making in the area of Home Leave. Outcome measures of
the granting of home leave can be taken as one argument of a function,
and literally hundreds of other measures on inmates were drawn, or
constructed from PROBE to comprise other arguments which could then
be weighted to provide a prediction, or likelihood of home leave
failure. With the accumulation of measures of attainment with respect
to the demands of activities and routines, along with individual
attendance records, it is hoped that we can provide historical records
of behaviour change whilst inmates are in custody, thereby allowing
inmate sentence management to be based on records of positive
achievement, ie acquisition of new modes of behaviour and their
demonstrable relations to other outcomes (e.g. apposite allocation to
programmes, likelihood to reconvict, likelihood to escape, abscond,
find gainful employment on release etc).
1.2 DIFFERENTIAL REGIMES AS A FUNCTION OF BEHAVIOUR
Based on the original work on identifying control problems in 1985-7,
the following NIC scale has been used as a control index since the
inception of PROBE in 1986.
NATIONAL INSTITUTE OF CORRECTIONS RECLASSIFICATION CUSTODY RATING SCALE
(Slightly modified, Longley 1985)
1. HISTORY OF INSTITUTIONAL VIOLENCE:
(Most serious offence within last five years to be coded).
None. 0
Assault not involving use of a weapon or resulting in serious injury. 3
Assault involving a weapon and, or resulting in serious injury. 7
Did above assault occur within last six months?
Yes 3
No 0
2. SEVERITY OF CURRENT OFFENCE:
(Score the most severe of current offences.)
Non-violent offences. 0
Assaults (Police, Common). 1
G.B.H., A.O.B.H. 2
Robbery, Wounding, Rape, Terrorism. 3
Murder, Homicide. 4
3. PRIOR ASSAULTIVE CONVICTION HISTORY:
(Score the most severe in inmate's history.)
None. 0
Assaults (Police, Common). 1
G.B.H., A.O.B.H. 2
Robbery, Wounding, Rape, Terrorism. 3
Murder, Homicide. 4
4. ESCAPE HISTORY:
(Rate last three years of incarceration).
No escapes or attempts. -3
Escape or attempt from minimum custody, no actual or threatened
violence:
Over a year ago. -1
Within the last year. 1
Escape or attempt from secure conditions or an escape with actual
or threatened violence:
Over a year ago. 5
Within the last year. 7
SUB TOTAL SCORE _______
5. NUMBER OF DISCIPLINARY REPORTS:
None in last 13-18 months. -5
None in last 7-12 months. -3
None in last 6 months. -1
1 in last 6 months. 0
2 or more in last 6 months. 4
6. MOST SEVERE DISCIPLINARY REPORT RECEIVED (last 18 months):
None 0
Insubordination,GOAD, other non-violent reports. 1
Cell-smashing, Barricading, fighting, possession of weapon. 2
Assaults on staff or inmates. 5
Mutiny, Riot, Gross Personal Violence. 7
7. PRIOR CONVICTIONS:
None. 0
1 2
2 or more. 4
TOTAL SCORE _______
In the 1985 - 86 work on identifying control problems this is how those
nominated as control problems compared to other inmates:
Group All Sources Governors Only
No. NIC Score No. NIC Score
Mean S.E Mean S.E.
Either occasion 203 12.5 0.60 135 13.5 0.73
Both occasions 63 14.8 1.07 41 14.2 1.40
Only first time 93 11.2 0.86 47 13.1 1.25
Only second time 47 11.9 1.22 47 13.2 1.18
Non-problem sample 208 5.4 0.46 208 5.4 0.46
It was upon the basis of what this (somewhat contradictory) data
that a committment to build an actuarially based system was made.
Whilst the control problem inmates clearly differed from from
a matched control group (matched on Sentence, Sentence date etc),
the consistency of identifying WHO was a control problem was not
very consistent from trawl one to trawl two. Clinical judgement
was not a criterion one could reliably base identification of
control problems upon. One required formal, Data Base Management.
David Longley
FRAGMENTS OF BEHAVIOUR 8
Full text is available at:
http://www.uni-hamburg.de/~kriminol/TS/tskr.htm
Here's the reference list to the volume which the posting was an
extract from (7 extracts in all have been posted under the title
'Fragments of Behaviour' 1 - 7.
The article by Dawes, Faust and Meehl was a summary of the state of
the art after reviewing over 100 studies, so the one you refer to may
have been one they refer to, although it isn't one I particularly
recall.
There was a response to Dawes, Faust and Meehl by Kleinmuntz (1990)
with a reply from the above authors. Kleinmuntz has presented the case
for sometimes 'using the head'. Dawes, Faust and Meehl article in
SCIENCE don't agree there's much evidence at all. Kleinmuntz also
published a review article in Psychological Bulletin at about the same
time. When you stand back and think about the whole issue, it comes
down to science vs. folk-psychology!.
In this country, there is an excellent Open University course which is
broadcast on TV (usually at an unearthly hour). The programmes (and
course) is 'Professional Judgement' D300, and is supported by a text
of readings by Dowie & Elstein (1988) 'Professional Judgment: A Reader
in Clinical Decision Making'.
Please see the quote at the end, and beware.....there are very
powerful vested interests at stake in this area. I would very much
like to be able to author a multi-media work on this whole subject of
'extensional vs. intensional judgement', and am toying with the idea
of getting the equipment to do so myself, though finding a suitable
publisher would be a far better idea.
REFERENCES:
A. On The Nature of Deductive Inference & Algorithms
1.Abraham F D A Visual Introduction to Dynamical Systems Theory for
Psychology Aerial Press 1990
2.Church A A note on the Entscheidungproblem J. Symb. Log. 1 (1936)
40-41
3.Cherniak C. Minimal Rationality MIT Press. Bradford Books 1986
4.Codd E F A relational model of data for large shared data banks
Comm ACM 13, 1970, 377-387
5.Frege G. Begriffsschrift (1879) In Heijenhoort (Ed) From Frege to
Godel: A Source Book in Mathematical Logic Harvard University Press
1966
6.Gardarin G & Valduriez P Relational Databases and Knowledge Bases
Addison Wesley 1989
7.Gentzen G Investigations into logical deduction. In M. E. Szabo
(Ed. & Trans.) The Collected Papers of Gerhard Gentzen Amsterdam:
North-Holland 1969
8.Gray P Logic, Algebra and Databases Ellis Horwood Limited 1984
9.Genesereth M R & Nilsson N J Logical Foundations of Artificial
Intelligence Morgan Kaufmann Publishers Inc. 1988
10.Hilbert D & Ackermann W. Principles of Mathematical Logic Chelsea
Publishing Company 1950
11.Hodges W LOGIC: An Introduction to Elementary Logic Penguin Books,
London 1991
12.Johnson-Laird P N Human and Computer Reasoning. Trends in
Neurosciences; 1985 Feb Vol 8(2) 54-57
13.Johnson-Laird P N & Byrne R M Precis of Deduction Behavioral and
Brain Sciences; 1993 Jun Vol 16(2) 323-380
14.Kleene S C Introduction to Metamathematics Amsterdam:North-Holland
1952
15.Kneale K & Kneale M The Development of Logic Cambridge University
Press 1962
16.Post E L Finite combinatory process - Formulation I. J. Symb.
Log. 1 (1936) 103-105
17.Prawitz D Gentzen's Analysis of First-Order Proofs in R. I. G.
Hughes (ed) A Philosophical Companion to First-Order Logic Hackett
Publishing Co. 1993
18.Rips L J Cognitive Processes in Propositional Reasoning Psych.
Rev. 1990,90,1,38-71
19.Robinson J A Logic: Form and Function, the Mechanisation of
Deductive Reasoning Edinburgh: Edinburgh University Press 1979
20.Shinghal R Formal Concepts in Artificial Intelligence:
Fundamentals Chapman & Hall Computing, London 1992
21.Tennant N W Natural Logic Edinburgh University Press 1990
22.Turing A M On Computable numbers, with an application to the
Entscheidungsproblem P. Lond. Math. Soc. (2) 42 (1936-7) 230-265
23.Wos L, Overbeek R, Ewing L & Boyle J Automated Reasoning:
Introduction and Applications McGraw-Hill, London, 1993
B. On The Nature of Inductive Inference & Heuristics
1. Methodology
24.Andrews D A, Zinger I, Hoge R D, Bonta J, Gendreau P & Cullen F T
Does Correctional Treatment Work? Criminology 28,3 1990
25.Andrews D A, Zinger I, Hoge R D, Bonta J, Gendreau P & Cullen F T
A Human Science Approach or More Punishments and Pessimism: A
Rejoinder to Lab and Whitehead Criminology, 28,3 1990 419-429
26.Bakan D The Test of Significance in Psychological Research
Psychological Bulletin,1966,66,6,423-437
27.Bolles R C The Difference Between Statistical Hypotheses and
Scientific Hypotheses Psychological Reports,1962,11,639-645
28.Cohen J Things I Have Learned (So Far) American Psychologist
December 1990, pp 1304-1312
29.Cohen J A Power Primer Quantitative Methods in Psychology:
Psychological Bulletin 1992,112,1,155-159
30.Dar R Another Look at Meehl, Lakatos, and the Scientific Practices
of Psychologists American Psychologist,1987,February
31.Guttman L What is Not What in Statistics. The Statistician, Vol 26
No 2, 1977 p. 81-107
32.Guttman L The Illogic of Statistical Inference for Cumulative
Science. Applied Stochastic Models and Data Analysis Vol 1, 3-10, 1985
33.Lykken D T Statistical Significance in Psychological Research
Psychological Bulletin 1968,70,3,151-159
34.McDougall C, Barnett R M, Ashurst B and Willis B Cognitive Control
of Anger in McGurk B J, Thornton D M, and Williams M (eds) Applying
Psychology to Imprisonment, HMSO 1987
35.Martinson R What Works ? - Questions and Answers about Prison
Reform, The Public Interest 35,22-54 1974
36.Martinson R California Research at the Crossroads Crime &
Delinquency, April 1976, 63-73
37.Meehl P E Theory Testing in Psychology and Physics: A
Methodological Paradox. P 111-112. Philosophy of Science, June 1967
38.Meehl P E Theoretical Risks and Tabular Asterisks: Sir Karl and
Sir Ronald and The Slow Progress of Soft Psychology. J Consulting and
Clinical Psychology 1978,45,4,p806-34
39.Meehl P E What Social Scientists Don't Understand - in Metatheory
in Social Science Eds D. W. Fiske & R. A. Shweder The University of
Chicargo Press, London 1986
40.Porporino F, Fabiano L and Robinson Focusing on Successful
Reintegration: Cognitive Skills Training for Offenders submitted for
publication to the Scandinavian Criminal Law Review July 1991
41.Rozeboom W M The Fallacy of The Null Hypothesis Significance Test
Psychological Bulletin 1960, 57,5,416-428
42.Wainer H Estimating Coefficients in Linear Models: It Don't Make
No Nevermind Psychological Bulletin, 1976, 63,2 213-217
43.Wainer H On the Sensitivity of Regression and Regressors
Psychological Bulletin 85,2, 267-273
2. Inductive Reasoning as Heuristics
44.Agnoli F & Krantz D. H. Suppressing Natural Heuristics by Formal
Instruction: The Case of the Conjunction Fallacy Cognitive Psychology
21, 515-550, 1989
45.Cooke R M Experts In Uncertainty Opinion and Subjective
Probability in Science Oxford University Press 1991
46.Derthick M Mundane Reasoning by Settling on a Plausible Model
Artificial Intelligence 46,1990,107-157
47.Eddy D M Probabilistic Reasoning in Clinical Medicine: Problems
and Opportunities In Kahneman, Tversky and Solvic (Eds) Judgment Under
Uncertainty: Heuristics and Biases Cambridge University Press 1982
48.Fong G T, Lurigio A J & Stalans L J Improving Probation Decisions
Through Statistical Training Criminal Justice and
Behavior,17,3,1990,370-388
49.Fong G T & Nisbett R E Immediate and delayed transfer of training
effects in Statistical reasoning. Journal of Experimental Psychology
General; 1991,120(1) 34-45
50.Fotheringhame J Transfer of training: A field investigation of
youth training. Journal of Occupational Psychology 1984 Sep Vol 57(3)
239-248
51.Fotheringhame J Transfer of training: A field study of some
training methods. Journal of Occupational Psychology 1986 Mar Vol
59(1) 59-71
52.Gardner H The Mind's New Science: A History of the Cognitive
Revolution Basica Books 1987
53.Gigerenzer G & Murray D J Cognition as Intuitive Statistics
Hillsdale, NJ: Erlbaum, 1987
54.Gigerenzer G, Swijtink Z, Porter T, Datson L, Beatty J & Kruger L
The Empire of Chance Cambridge University Press, 1989
55.Gigerenzer G The Superego, the Ego, and the Id in Statistical
Reasoning Ch. 11 A Handbook for Data Analysis in the Behaviour
Sciences Methodological Issues: Eds G. Keren & C Lewis Lawrence
Erlbaum Associates 1993
56.Gladstone R Teaching for transfer versus formal discipline
American-Psychologist; 1989 Aug Vol 44(8) 1159
57.Gluck M A & Bower G. H. From conditioning to category learning: An
adaptive network model. Journal of Experimental Psychology General
(1988) Sep Vol 117(3) 227-247
58.Gluck M A & Bower G H Component and pattern information in
adaptive networks. Journal of Experimental Psychology General; (1990)
Mar Vol 119 (1) 105-9
59.Hecht-Nielsen R NEUROCOMPUTING Addison Wesley 1990
60.Holland J H, Holyoak K J, Nisbett R E & Thagard P R Induction:
Processes of Inference, Learning, and Discovery Bradford Books:MIT
Press 1986
61.Johnson-Laird P N THE COMPUTER AND THE MIND: An Introduction to
Cognitve Science Fontana 1988
62.Johnson-Laird P N & Byrne R M Deduction Lawrence Erlbaum
Associates 1991
63.Kagan J The meanings of personality predicates American
Psychologist, 1988 Aug Vol 43(8) 614-620
64.Kohonen T Self-Organisation and Associative Memory Springer-
Verlag 1988
65.Kosko B Neural Networks and Fuzzy Systems: A Dynamical Systems
Approach to Machine Intelligence Prentice-Hall 1992
66.Kruger L, Gigerenzer G & Morgan M S The Probabilistic Revolution
Vol 1,2 Bradford Books 1987
67.Lehman D R & & Nisbett R E A Longitudinal Study of the Effects of
Undergraduate Training on Reasoning. Developmental Psychology,1990,26,
6,952-960
68.Myers C Core skills and transfer in the youth training schemes: A
field study of trainee motor mechanics. Journal of Organizational
Behavior 1992 Nov Vol 13(6) 625-632
69.Minsky M L & Papert S A Perceptrons: An Introduction to
Computational Geometry MIT Press 1990
70.Nisbett R E & Wilson T D Telling more than we can know: Verbal
reports on mental processes Psychological-Review; 1977 Mar Vol 84(3)
231-259
71.Nisbett R E & Ross L Human Inference: Strategies and Shortcomings
of Social Judgment Century Psychology Series, Prentice-Hall (1980)
72.Nisbett R E & Krantz D H The Use of Statistical Heuristics in
Everyday Inductive Reasoning Psychological Review, 1983, 90, 4, 339-
363
73.Nisbett R E, Fong G T, Lehman D R & Cheng P W Teaching Reasoning
Science v238, 1987 pp.625-631
74.Ploger D & Wilson M Statistical reasoning: What is the role of
inferential rule training? Comment on Fong and Nisbett. Journal of
Experimental Psychology General; 1991 Jun Vol 120(2) 213-214
75.Popper K R The Logic of Scientific Discovery Routledge, Kegan
Paul 1959
76.Popper K R Truth, Rationality, and the Growth of Knowledge Ch. 10,
p 217-8 Conjectures and Refutations RKP London 1965
77.Reeves L M & Weisberg R W Abstract versus concrete information as
the basis for transfer in problem solving: Comment on Fong and Nisbett
(1991). Journal of Experimental Psychology General; 1993 Mar Vol
122(1) 125-128
78.Rescorla R A & Wagner A R A Theory of Classical Conditioning:
variations in the effectiveness of reinforcement and Nonreinforcement.
In Classical Conditioning II: Current Theory and Research (Black &
Prokasy) pp. 64-99. Appleton Century Crofts 1971.
79.Rescorla R A Pavlovian Conditioning: It's Not What You Think It
Is. American Psychologist, March 1988.
80.Ross L & Nisbett R E The Person and The Situation: Perspectives of
Social Psychology McGraw Hill 1991
81.Rummelhart D E & McClelland J L Parallel Distributed Processing:
Explorations in the Microstructure of Cognition Vol 1: Foundations MIT
Press 1986
82.Savage L The Foundations of Statistics John Wiley & Sons 1954
83.Shafir E & Tversky A Thinking Through Uncertainty:
Nonconsequential Reasoning and Choice Cognitive Psychology 24,449-474,
1992
84.Smith E E, Langston C & Nisbett R E The case for rules in
reasoning. Cognitive Science; 1992 Jan-Mar Vol 16(1) 1-40
85.Stich S The Fragmentation of Reason Bradford Books 1990
86.Sutherland S IRRATIONALITY: The Enemy Within Constable: London 1992
87.Tversky A & Kahneman D Extensional Versus Intuitive Reasoning: The
Conjunction Fallacy in Probability Judgment Psychological Review
v90(4) 1983
88.Wason W C Reasoning in New Horizons in Psychology, Penguin Books
1966
89.Wason W C & Johnson-Laird P Psychology of Reasoning
London:Batsford 1972
C. On Clinical vs. Actuarial Judgment
90.Arkes H R & Hammond K R Judgment and Decision Making: An
interdisciplinary reader Cambridge University Press 1986
91.Dawes R.M The Robust beauty of improper linear models in decision
making American Psychologist, 1979 34,571-582
92.Dawes R M Rational Choice in an Uncertain World Orlando: Harcourt,
Brace, Jovanovich 1988
93.Dawes R M, Faust D & Meehl P E Clinical Versus Actuarial Judgement
Science v243, pp 1668-1674 1989
94.Elstein A S Clinical judgment: Psychological research and medical
practice. Science; 1976 Nov Vol 194(4266) 696-700
95.Einhorn H J & Hogarth R M Behavioral decision theory: Processes of
judgment and choice Annual Review of Psychology (1981), 32, 53-88
96.Faust D Data integration in legal evaluations: Can clinicians
deliver on their premises? Behavioral Sciences and the Law; 1989 Fal
Vol 7(4) 469-483
97.Gigerenzer G How to Make Cognitive Illusions Disappear: Beyond
"Heuristics and Biases" in European Review of Social Psychology,
Volume 2 eds W Stroebe & M Hewstone 1991, Ch 4 pp. 83-115
98.Goldberg L R Simple models or simple processes? Some research on
clinical judgments American Psychologist,1968,23(7) p.483-496
99.Kahneman D, Slovic P & Tversky A Judgment Under Uncertainty:
Heuristics and Biases Cambridge University Press 1982
100.Kyllonen P C & Christal R E Reasoning Ability Is (Little More
Than) Working-Memory Capacity?! Intelligence 14, 389-433 1990
101.Lundberg G A Case Studies vs. Statistical Methods - An Issue
Based on Misunderstanding. Sociometry v4 pp379-83 1941
102.Meehl P E Clinical vs. Statistical Prediction: A Theoretical
Analysis and a Review of the Evidence University of Minnesota Press,
Minneapolis. 1954
103.Meehl P E When Shall We Use Our Heads Instead of the Formula?
PSYCHODIAGNOSIS: Collected Papers 1971
104.Meehl P E Causes and effects of my disturbing little book J
Person. Assess. 50,370-5,1986
105.Oskamp S Overconfidence in case-study judgments J. Consult.
Psychol. (1965), 29, 261-265
106.Sarbin T R Clinical Psychology - Art or Science? Psychometrica
v6 pp391-400 (1941)
D. On the contrast Between the Extensional and Intensional Analysis
107.Church A Intensional Isomorphism and Identity of Belief in Salmon
N & Soames S (eds) Propositions and Attitudes Oxford University Press
1980
108.Churchland P M A Neurocomputational Perspective The Nature of
Mind and The Structure of Science Bradford Books 1989
109.Dahlbom B Dennett and His Critics Blackwell, Oxford 1993
110.Deakin J F W & Longley D Naloxone Enhances Neophobia British
Journal of Pharmacology, April 1981
111.Devitt M. Meanings just ain't in the head In Meaning and Method:
Essays in Honor of Hilary Putnam Ed G. Boolos Cambridge University
Press 1990
112.Dretske F I The Intentionality of Cognitive States Midwest Studies
in Philosophy 5,281-294 1980
113.Elgin C Z Facts That Don't Matter In Meaning and Method: Essays
in Honor of Hilary Putnam Ed G. Boolos Cambridge University Press 1990
114.Eysenck H J & Eysenck S introduction to: Using Personality to
Individualize Instruction - J A Wakefield JR Edits, San Diego, 1978
115.Fodor J A Methodological Solipsism Considered as a Research
Strategy for Cognitive Psychology Behavioral-and-Brain-Sciences; 1980
Mar Vol 3(1) 63-109
116.Frege G Function and Concept in Geach P and Black M (eds)
Translations from the Philosophical Writings of Gottlob Frege 3rd
edition : Basil Blackwell Oxford 1980
117.Frege G On Concept and Object in Geach P and Black M (eds)
Translations from the Philosophical Writings of Gottlob Frege 3rd
edition : Basil Blackwell Oxford 1980
118.Frege G On Sense and Meaning in Geach P and Black M (eds)
Translations from the Philosophical Writings of Gottlob Frege 3rd
edition : Basil Blackwell Oxford 1980
119.Frege G What is a Function? in Geach P and Black M (eds)
Translations from the Philosophical Writings of Gottlob Frege 3rd
edition : Basil Blackwell Oxford 1980
120.Kripke S A A Puzzle About Belief in Salmon N & Soames S (eds)
Propositions and Attitudes Oxford University Press 1980
121.Longley D The Interaction of Brain Monoamines and Neuropeptides
In the Control of Operant Behaviour. Unsubmitted PhD Thesis: National
Institute for Medical Research London/Institute of Neurology
University of London 1983
122.Nelson R J Naming and Reference Routledge, London 1992
123.Putnam H The Meaning of Meaning In Mind, Language and Reality:
Philosophical Papers Vol 2 Cambridge University Press 1975
124.Putnam H Representation and Reality Bradford Books 1988
125.Quine W V O Quantifiers and Propositional Attitudes (1956) In
The Ways of Paradox and Other Essays Harvard University Press 1966,
1972
126.Quine W V O The Scope and Language of Science (1954) The Ways of
Paradox and Other Essays Harvard University Press 1966, 1972
127.Quine W V O Word and Object MIT Press 1960
128.Quine W V O What Is It All About ? American Scholar, (1980)
50,43-54
129.Quine W V O The Pursuit of Truth Harvard University Press
1990,1992
130.Ramsey W, Stich S & Garon J Connectionism, eliminativism, an the
future of Folk Psychology in Greenwood J D (Ed) The Future of Folk
Psychology Cambridge University Press 1991
131.Ryle G The Concept of Mind Penguin 1949
132.Schnaitter R Knowledge as Action: The Epistemology of Radical
Behaviorism in B.F. Skinner Consensus and Controversy Eds. S. Modgil
& C. Modgil Falmer Press 1987
133.Skinner B F The Operational Analysis of Psychological Terms
Psychological Review, (1945) 45, 270-77
134.Skinner B F Beyond Freedom and Dignity New York, Knopf 1971
135Skinner B F About Behaviourism New York, Knopf 1974
136.Stich S From Folk Psychology to Cognitive Science: The Case
Against Belief Bradford Books 1983
137.Teasdale J D & Russell L M Differential effects of induced mood
on the recall of positive, negative and neutral words. British Journal
of Clinical Psychology,1983 Sep Vol 22(3) 163-171
Footnote:
Extract from an Open University Third Level Course:
Professional Judgment and Decision Making:
'There is no controversy in social science that shows such a large
body of qualitatively diverse studies coming out so uniformly in the
same direction as this one. When you are pushing 90 investigations,
predicting everything from the outcome of football games to the
diagnosis of liver disease and when you can hardly come up with a half
dozen studies showing even a weak tendency in favour of the clinician,
it is time to draw a practical conclusion, whatever theoretical
differences may still be disputed.'
Meehl 1986, pp373-4
COURSE TEXT:
JACK: Meehl's study set off, or at least much inflamed, the
'statistical versus clinical judgment' controversy, which has rumbled
on ever since, though it's somewhat less fashionable than it was.
PENELOPE: Why?
JACK: Cynically, because the human judges didn't like the results and
made sure that they or their authors didn't get the funding,
circulation or promotion they deserved. Closed shops (as most
professions are to some extent) are not likely to vote for what they
see as de-skilling, and alternative approaches that showed more
respect for the human judge became fashionable and fund worthy
(especially the expert systems we shall meet in the session after
next). Uncynically, the methodological problems in policy-capturing
research are real: it IS difficult to establish the external validity
of the results.'
Page 63 Volume 1 Introductory Text 2
And finally:
'Kelley's (1973) 'covariation principle', which is the
most fundamental assumption of contemporary attribution
theory and of that theory's characterization of people
as generally adequate intuitive scientists, is
essentially an assertion that the layperson can
recognize and make appropriate inferential use of
covariation between events. Common sense also suggests
that the ability to detect covariation would seem
necessary for understanding, predicting and controlling
social experience. The assessment of covariation between
early symptoms and later manifestations of problems, of
covariation between particular behavioural strategies
and subsequent environmental outcomes, and of
covariation between potential causes and observed
effects seems critical to people's success in responding
adaptively to the opportunities and dilemmas of social
life. Indeed, one might well be tempted to regard
harmonious social interchange and the general
effectiveness of personal functioning as EVIDENCE of
people's capacity to recognize covariation between
events.
Most research that has dealt with people's abilities to
recognize and estimate covariation has not been
flattering to the layperson's abilities. Even Peterson
and Beach (1967), in their generally positive evaluation
of 'man as an intuitive statistician' were not very
optimistic about people's capacity to appreciate
relationships between variables. In this chapter we
first review evidence of these shortcomings and then
attempt to reconcile the apparent contradiction between
peoples' failures in the laboratory and their successes
in meeting the demands of everyday social judgement and
interaction.
Judging Covariation from Fourfold Contingency Table
Most of the research available at the time of the
Peterson and Beach review was on people's ability to
estimate association correctly from fourfold, presence-
absence tables of the type presented below, in which the
task is simply to determine whether symptom X is
associated with disease A.
DISEASE A
Present Absent
Present 20 10
SYMPTOM X
Absent 80 40
This task would seem superficially to be the least
demanding covariation-detection problem that one could
pose. The data are dichotomous rather than continuous.
There are no problems of prior data collection,
estimation, or recall; there are no prior, potentially
misleading notions of the relationship; and the data are
conveniently arrayed in summary form that should promote
accurate assessments of covariation. Nevertheless, the
evidence (for example, Smedslund 1963; Ward and Jenkins
1965) shows that people generally perform such tasks
quite poorly.
Almost exclusive reliance upon the 'present/present'
cells seems to be a particularly common failing. Many
subjects say that symptom X is associated with disease A
simply because many of the people with the disease do in
fact have the symptom. Other subjects pay attention only
to two cells. Some of these will conclude that the
relationship is positive because more people who have
the disease have the symptom than do people who do not
have the disease. Others conclude that the relationship
is negative because more people with the disease do not
have symptom A than have it.
Without formal statistical training, very few people
intuitively understand that no judgment of association
can be made legitimately without simultaneously
considering ALL FOUR cells. The appropriate method
compares the ratio of the two cells in the 'present'
column to that of the two cells in the 'absent' column.
One might be tempted to dismiss this research as simply
a demonstration that lay people cannot 'read'
contingency tables and that the errors and biases shown
are artifacts of the unusual format of the judgmental
task. The incapacity, however, resembles shortcomings
that have been observed in circumstances that do not
require 'table reading'. In chapter 3 we reviewed the
literature on the ability of people (and animals) to
learn from negative or null instances. It should be
recalled that learning is greatly retarded or prevented
altogether when the instances are conceptually negative
('blue things are NOT gleeps'). The finding that
subjects are preoccupied with the present/present cell
in contingency tables is reminiscent of people's
inability to learn from negative instances.'
R. Nisbett and L. Ross (1980)
Ch.5 Assessment of Covariation p.90-92
Not only does this sit well with Popperian falsificationism and the
Quine-Duhem thesis (Quine 1951) as the LOGIC of scientific discovery,
but in eschewing intuitive strategies, in not going beyond deduction
(not 'going beyond the data given'), a co-operative use of technology
can in the end only pay dividends in the quest to more effectively
manage the Prison Service:
'Humans did not "make it to the moon" (or unravel the
mysteries of the double helix or deduce the existence of
quarks) by trusting the availability and
representativeness heuristics or by relying on the
vagaries of informal data collection and interpretation.
On the contrary, these triumphs were achieved by the use
of formal research methodology and normative principles
of scientific inference. Furthermore, as Dawes (1976)
pointed out, no single person could have solved all the
problems involved in such necessarily collective efforts
as space exploration. Getting to the moon was a joint
project, if not of 'idiots savants', at least of savants
whose individual areas of expertise were extremely
limited - one savant who knew a great deal about the
propellant properties of solid fuels but little about
the guidance capabilities of small computers, another
savant who knew a great deal about the guidance
capabilities of small computers but virtually nothing
about gravitational effects on moving objects, and so
forth. Finally, those savants included people who
believed that redheads are hot-tempered, who bought
their last car on the cocktail-party advice of an
acquaintance's brother-in-law, and whose mastery of the
formal rules of scientific inference did not notably
spare them from the social conflicts and personal
disappointments experienced by their fellow humans. The
very impressive results of organised intellectual
endeavour, in short, provide no basis for contradicting
our generalizations about human inferential
shortcomings. Those accomplishments are collective, at
least in the sense that we all stand on the shoulders of
those who have gone before; and most of them have been
achieved by using normative principles of inference
often conspicuously absent from everyday life. Most
importantly, there is no logical contradiction between
the assertion that people can be very impressively
intelligent on some occasions or in some domains and the
assertion that they can make howling inferential errors
on other occasions or in other domains.'
R. Nisbett and L. Ross (1980)
Human Inference: Strategies and Shortcomings of Social
Judgment
My general conclusion is that *many* psychologists have in gfact
misread what their discipline has all been about since the 1960s.
As an ampirical discipline, and in contrast to the technology of
AI, it is a catalogue of the failings of a system (*human*
information processing) optimised for fault tolerance
biologically, but minimally rational without the support of the
ediface of scientific method.
David Longley
FRAGMENTS OF BEHAVIOUR 10 - Extract from:
'A System Specification for PROfiling BEhaviour'
Full text is available at:
http://www.uni-hamburg.de/~kriminol/TS/tskr.htm
Whilst the following is written with prison inmates in mind, the
same principles and system are being advocated for education &
training programmes more generally. Whilst some of the material
within this extract bears on this thread, it is posted in the
hope that it will elicit wider evaluation and discussion -
hopefully, what emerges from these fragments is an empirical
conclusion, not a particular ideaology.
BEHAVIOUR MODIFICATION: SENTENCE MANAGEMENT & PLANS
'No predictions made about a single case in clinical work are
ever certain, but are always probable. The notion of
probability is inherently a frequency notion, hence
statements about the probability of a given event are
statements about frequencies, although they may not seem to
be so. Frequencies refer to the occurrence of events in a
class; therefore all predictions; even those that from their
appearance seem to be predictions about individual concrete
events or persons, have actually an implicit reference to a
class....it is only if we have a reference class to which the
event in question can be ordered that the possibility of
determining or estimating a relative frequency exists.....
the clinician, if he is doing anything that is empirically
meaningful, is doing a second-rate job of actuarial
prediction. There is fundamentally no logical difference
between the clinical or case-study method and the actuarial
method. The only difference is on two quantitative continua,
namely that the actuarial method is #more explicit# and #more
precise#.'
P. E. Meehl (1954)
Clinical versus Statistical Prediction
A Theoretical Analysis and a Review of the Evidence
This section outlines the second phase of PROBE's technology, that of
PROgramming BEhaviour. Monitoring behaviour is one essential function
of PROBE, and the major developments to date having been outlined in
Section 2. Effective *control* of behaviour on the other hand requires
staff and inmates to make use of that information in the interests of
programming or shaping behaviour in a pro-social (non-delinquent)
direction. This is what the Sentence Management and Planning system,
covered in this section is designed to provide. Further technical
details can be found in *Volumes 1 & 2* of this system specification.
If there is to be any change in an inmate's behaviour after release,
there will need to be a change in behaviour from the time he was
convicted, either through acquisition of new behaviours or simple
maturation (as in the age-report rate function). In ascertaining the
characteristic behaviour of classes, it is not that we make
predictions of future behaviour, but that we describe behaviour
characteristic of classes. This is clearly seen in discriminant
analysis and regression in general. We analyse the relationship
between one class and others, and, providing that an individual can be
allocated to one class or another, we can say, as a consequence of his
class membership, what other characteristics are likely to be the case
as a function of that class membership. Temporality, i.e. pre-diction
has nothing to do with it.
Any system which provides a record of skill acquisition during
sentence must therefore be an asset in the long term management of
inmates towards this objective. However, research in education and
training, perhaps the most practical areas of application of Learning
Theory, clearly endorse the conclusions drawn in *Volume 1* on the
context specificity of the intensional. Some of the most influential
models of cognitive processing in the early to mid 1970s took context
as critical for encoding and recall of memory (Tulving and Thompson
1972). Generalisation Theory, ie that area of research which looks at
transfer-of-training has almost unequivocally concluded that learning
is context specific. Empirical research supports the logical
conclusion that skill acquisition does not readily transfer from one
task to another. This is another illustration of the failure of
substitutivity in psychological contexts. In fact, upon detailed
analysis, many of the attractive notions of intensionalism, so
characteristic of cognitivism, may reveal themselves to be vacuous on
closer analysis:
'Generalizability theory (Cronbach, Gleser, Nada & Rajaratnam
1972; see also, Brennan, 1983; Shavelson, Webb, & Rowley,
1989) provides a natural framework for investigating the
degree to which performance assessment results can be
generalised. At a minimum, information is needed on the
magnitude of variability due to raters and to the sampling of
tasks. Experience with performance assessments in other
contexts such as the military (e.g. Shavelson, Mayberry, Li &
Webb, 1990) or medical licensure testing (e.g. Swanson,
Norcini, & Grosso, 1987) suggests that there is likely
substantial variability due to task. Similarly,
generalizability studies of direct writing assessments that
manipulate tasks also indicate that the variance component
for the sampling of tasks tends to be greater than for the
sampling of raters (Breland, Camp, Jones, Morris, & Rock,
1987; Hieronymous & Hoover 1986).
Shavelson, Baxter & Pine (1990) recently investigated the
generalizability of performance across different hands-on
performance tasks such as experiments to determine the
absorbency of paper towels and experiments to discover the
reactions of sowbugs to light and dark and to wet and dry
conditions. Consistent with the results of other contexts,
Shavelson et al. found that performance was highly task
dependent. The limited generalizability from task to task is
consistent with research in learning and cognition that
emphasizes the situation and context-specific nature of
thinking (Greeno, 1989).'
R. L. Linn, E. L. Baker & S. B. Dunbar (1991)
Complex, Performance-Based Assessment:
Expectations and Validation Criteria
Educational Researcher, vol 20, 8, pp15-21
Intensionalists, holding that what happens inside the head matters, ie
that intension determines extension, appeal to our common, folk
psychological intuitions to support arguments for the merits of
abstract cognitive skills. However, such strategies are not justified
on the basis of educational research (see also *Volume 1*):
'Critics of standardized tests are quick to argue that such
instruments place too much emphasis on factual knowledge and
on the application of procedures to solve well-structured
decontextualized problems (see e.g. Frederiksen 1984). Pleas
for higher order thinking skills are plentiful. One of the
promises of performance-based assessments is that they will
place greater emphasis on problem solving, comprehension,
critical thinking, reasoning, and metacognitive processes.
These are worthwhile goals, but they will require that
criteria for judging all forms of assessment include
attention to the processes that students are required to
exercise.
It should not simply be assumed, for example, that a hands-on
scientific task encourages the development of problem solving
skills, reasoning ability, or more sophisticated mental
models of the scientific phenomenon. Nor should it be assumed
that apparently more complex, open-ended mathematics problems
will require the use of more complex cognitive processes by
students. The report of the National Academy of Education's
Committee that reviewed the Alexander-James (1987) study
group report on the Nation's Report Card (National Academy of
Education, 1987) provided the following important caution in
that regard:
It is all too easy to think of higher-order skills
as involving only difficult subject matter as, for
example, learning calculus. Yet one can memorize
the formulas for derivatives just as easily as
those for computing areas of various geometric
shapes, while remaining equally confused about the
overall goals of both activities.
(p.54)
The construction of an open-ended proof of a
theorem in geometry can be a cognitively complex
task or simply the display of a memorized sequence
of responses to a particular problem, depending on
the novelty of the task and the prior experience of
the learner. Judgments regarding the cognitive
complexity of an assessment need to start with an
analysis of the task; they also need to take into
account student familiarity with the problems and
the ways in which students attempt to solve them.'
ibid p. 19
As covered at length in Section 1.3, skills do not seem to generalise
well. Dretske (1980) put the issue as follows:
'If I know that the train is moving and you know that its
wheels are turning, it does not follow that I know what you
know just because the train never moves without its wheels
turning. More generally, if all (and only) Fs are G, one can
nonetheless know that something is F without knowing that it
is G. Extensionally equivalent expressions, when applied to
the same object, do not (necessarily) express the same
cognitive content. Furthermore, if Tom is my uncle, one can
not infer (with a possible exception to be mentioned later)
that if S knows that Tom is getting married, he thereby knows
that my uncle is getting married. The content of a cognitive
state, and hence the cognitive state itself, depends (for its
identity) on something beyond the extension or reference of
the terms we use to express the content. I shall say,
therefore, that a description of a cognitive state, is non-
extensional.'
F. I. Dretske (1980)
The Intentionality of Cognitive States
Midwest Studies in Philosophy 5,281-294
As noted above, this is corroborated by transfer of training research:
'Common descriptions of skills are not, it is concluded, an
adequate basis for predicting transfer. Results support J.
Fotheringhame's finding that core skills do not automatically
transfer from one context to another.'
C. Myers
Core skills and transfer in the youth training schemes:
A field study of trainee motor mechanics.
Journal of Organizational Behavior;1992 Nov Vol13(6) 625-632
'G. T. Fong and R. E. Nisbett (1993) claimed that human
problem solvers use abstract principles to accomplish
transfer to novel problems, based on findings that Ss were
able to apply the law of large numbers to problems from a
different domain from that in which they had been trained.
However, the abstract-rules position cannot account for
results from other studies of analogical transfer that
indicate that the content or domain of a problem is important
both for retrieving previously learned analogs (e.g., K. J.
Holyoak and K. Koh, 1987; M. Keane, 1985, 1987; B. H. Ross,
1989) and for mapping base analogs onto target problems
(Ross, 1989). It also cannot account for Fong and Nisbett's
own findings that different-domain but not same-domain
transfer was impaired after a 2-wk delay. It is proposed that
the content of problems is more important in problem solving
than supposed by Fong and Nisbett.'
L. M. Reeves & R. W. Weisberg
Abstract versus concrete information as the basis for
transfer in problem solving: Comment on Fong and Nisbett (1991).
Journal of Experimental Psychology General; 1993 Mar Vol
122(1) 125-128
'Content', recall, is a cognate of 'intension' or 'meaning'. A major
argument for the system of Sentence Management is that if we wish to
expand the range of an individuals' skills (behaviours), we can do no
better than to adopt *effective* (ie algorithmic) practices to guide
placements of inmates into activities based on actuarial models of
useful relations which exists between skills, both positive and
negative. We are unlikely to identify these other than through
empirical analyses. These should identify where such skills will be
naturally acquired and practised. As discussed at length in Section 1
and in Volume 1, there is now overwhelming evidence that behaviour is
context specific. Given that conclusion, which is supported by social
role expectations (see any review of Attribution Theory), we are well
advised to focus all attempts at behaviour engineering via inmate
programmes and activities with this fully understood. Furthermore,
within the PROBE project at least, we have no alternative but to
eschew psychological ie intensional (cognitive) processes because
(Section 1.3), as we have seen, valid inference is logically
impossible in principle within such contexts.
The work on Sentence Planning and Management represents work on the
second phase of PROBE's development between 1990 and 1994. The work on
Sentence Planning is a direct development of the original CRC
recommendations, and comprises record 33 and 34 of the PROBE system.
Sentence Management, comprising records 30,31 and 32 is designed as an
essential substrate, or support structure, for Sentence Planning.
3.1 SENTENCE MANAGEMENT
'I wish I had said that', said Oscar Wilde in applauding one
of Whistler's witticisms, Whistler, who took a dim view of
Wilde's originality, retorted, 'You will, Oscar; you will.
This tale reminds us that an expression like 'Whistler said
that' may on occasion serve as a grammatically complete
sentence. Here we have, I suggest, the key to a correct
analysis of indirect discourse, an analysis that opens a lead
to an analysis of psychological sentences generally
(sentences about propositional attitudes, so-called), and
even, though this looks beyond anything to be discussed in
the present paper, a clue to what distinguishes psychological
concepts from others.'
D. Davidson (1969)
On Saying That p.93
'Finding right words of my own to communicate another's
saying is a problem of translation. The words I use in the
particular case may be viewed as products of my total theory
(however vague and subject to correction) of what the
originating speaker means by anything he says: such a theory
is indistinguishable from a characterization of a truth
predicate, with his language as object language and mine as
metalanguage. The crucial point is that there will be equally
acceptable alternative theories which differ in assigning
clearly non-synonymous sentences of mine as translations of
his same utterance. This is Quine's thesis of the
indeterminacy of translation.'
ibid. p.100
'Much of what is called for is to mechanize as far as
possible what we now do by art when we put ordinary English
into one or another canonical notation. The point is not that
canonical notation is better than the rough original idiom,
but rather that if we know what idiom the canonical notation
is for, we have as good a theory for the idiom as for its
kept companion.'
D. Davidson (1967)
Truth and Meaning
Sentence Management is a behaviour assessment system, and comprises
the proactive, behaviour modification component of the PROBE system.
Sentence Management is based on a simple 5 step cycle:
The system is designed to support full recording of inmate behaviour
and, based on co-operation with the demands of the routines and
activities, allow staff to negotiate and contract behaviour targets
based on their level of behaviour and known empirical relations which
hold between classes of behaviour.
The details of this system are covered in Fragments of Behaviour 9 in
alt.prisons, & at greater length in Volume 2 of the full PROBE system
specification (Longley 1994).