Pattern Recognition Mechanisms and St. Thomas' Theory of Abstraction - article ; n°69 ; vol.61, pg 24-43


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Revue Philosophique de Louvain - Année 1963 - Volume 61 - Numéro 69 - Pages 24-43
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Joseph Bobik
Kenneth M. Sayre
Pattern Recognition Mechanisms and St. Thomas' Theory of
In: Revue Philosophique de Louvain. Troisième série, Tome 61, N°69, 1963. pp. 24-43.
Citer ce document / Cite this document :
Bobik Joseph, M. Sayre Kenneth. Pattern Recognition Mechanisms and St. Thomas' Theory of Abstraction. In: Revue
Philosophique de Louvain. Troisième série, Tome 61, N°69, 1963. pp. 24-43. Recognition Mechanisms
St. Thomas9 Theory of Abstraction
I. Whereas once the study of the mental faculties of man be
longed exclusively to philosophy, recent insights into these faculties
have come mostly from psychology, physiology, and now increas
ingly from computer technology. The deceptively simple puzzle,
« Can computers think ? », has become a popular topic among com
mentators on our technological age. And the apprehension many
people feel that the answer to this question might be affirmative is
heightened by reports of chess playing machines, computers which
compose music, and programs which enable to make
strategic military decisions.
A facet of computer technology which is less spectacular than
these, but which perhaps is more portentous in its promise to aid
our understanding of the human mind, is the use of computers to
recognize elementary numeral and letter patterns. In order to be
recognizable by a computer, these patterns must be inscribed within
a standard format ; but it is not necessary that they be identical in
shape or size. Computer programs have been shown capable of
singling out, as a basis for recognition, characteristics which are
essential to these patterns, and of ignoring other characteristics, like
fuzzy or wavy lines, which are merely incidental. Thus a computer,
when properly instructed, seems capable of an activity which in
humans would be called 'abstraction*.
Although technical literature on pattern recognition by comp
uters is still mostly exploratory, the philosophic undercurrents
already are stirring. It is beginning to appear that one of the oldest Pattern Recognition Mechanisms 25
problems in our philosophic tradition, that regarding the nature of
abstraction, may soon be overcome by a technology still in its in
fancy. For presumably we would consider the problem of abstraction
solved if well understood mechanical means could be provided for
duplicating all human functions which normally go under the name
of abstraction. If the problem could be solved in this way, philo
sophers would have occasion for gratitude and relief. But as matters
stand, there is good reason to believe that some human abstractive
functions cannot be performed by any techniques currently contemp
lated by computer technologists. If this is the case, and if philo
sophers have within their repertoire the ability to express clearly
why it is the case, technologists on the other hand might have
occasion for gratitude to philosophy.
The aim of this paper is to illuminate important differences be
tween human and mechanical recognition with reference to remarks
on abstraction found within the writings of St. Thomas Aquinas.
There will be no attempt to defend these remarks as the basis of an
entirely correct, or of a uniquely correct, theory of the mental act of
abstraction. It will be enough for present purposes to show that
Thomas' remarks, when expressed in current terminology, proSt.
vide for an intelligible description of aspects of human abstractive
behavior which cannot be duplicated in the present state of the
computer art.
Part II describes in non-technical language how computers
function in mechanical pattern recognition systems. Part III provides
Thomas' a brief statement of St. theory of abstraction, and discusses
three types of abstraction which are distinguished in the Summa
Theologiae and in his commentary on the De Anima. Part IV illus
trates these several types of abstraction with examples from ordi
nary cases of human recognition, and argues that not all of these
abstractive capabilities of the human recognizer can be duplicated
by purely mechanical mean*.
2. Our contemporary electronic computers descend directly
from the « difference engines » of the English mathematician Charles
Babbage, and indirectly from calculating mechanisms built by Pascal
and Leibniz. In Babbage's engine, as well as in its modern counter-
Collège D. Mercier
Place du Cardinal Mercier. 14
B- 1348 Louvain-la-Npuve 26 Joseph Bobik and Kenneth M. Sayre
part the desk calculator, numbers are represented within the machine
by the orientation of one or several mechanical components. Cal
culations in such a machine are achieved by altering the positions of
physically interconnected parts. The operating speed and informa
tion-handling capacity of such a machine, consequently, are gover
ned by the constraints of an efficient mechanical connection of a
large number of different physical components.
The technological advance which made computer technology in
its contemporary form possible was the replacement of mechanically
operated components by electronically operated storage tubes and
switching devices. It then became possible to represent numbers
and other items of information by the momentary electronic states
of series of vacuum tubes. Since vacuum tube states can be altered
very rapidly, the speed of these computers was increased by several
orders of magnitude. Whereas the best performance expected of
Babbage's machines was one addition of large numbers a second,
electronic computers of a decade ago could perform one addition
in approximately four microseconds, and contemporary computers
employing solid state storage and switching devices (transistors and
electromagnetic cores) instead of vacuum tubes can operate several
times faster than that. The information-handling capacity of these
later machines also was greatly increased, since greater speed of
operation enabled the processing of a greater amount of information
in a given period of time. Further increases in information-handling
capacity were achieved with the replacement of vacuum tubes by
solid state components. The amount of heat energy dissipated by a
solid state component is considerably less than that by
a vacuum tube, and consequently more transistors than tubes can
be packed into the enclosed space of the computer. As a result of
these technical improvements, contemporary computers no larger
than Babbage's engines can perform calculations with thousands of
items of information at speeds hundreds of thousands of times faster
than that of the earlier machines. It is this capacity for speed which
makes it possible for electronic computers to perform in a way
which leads us to think of them as exhibiting mind-like behavior.
Since the representation of information within a calculating
machine is in terms of discrete states of its components, the user
of the machine must communicate with it through a special lan
guage. The language of the desk calculator is one of the cogs and
levers. Information is presented to the by pushing buttons Pattern Recognition Mechanism» 27
which alter its internal state, and instructions for processing this i
nformation are entered by moving levers or other buttons. Informat
ion and instructions must be presented to the electronic computer in
the machine language of electronic states, and such data usually is
passed through intermediary devices which translate form the lan
guage of the human user to the machine language.
This requirement that communication with computers be in a
language which is translatable in terms of discrete electronic states
imposes restrictions upon the range of uses to which computers
fruitfully can be applied. In general, computers are capable of per
forming only those tasks which can be specified in complete detail
by the human programmer in the machine language. Any operation
of a computer which is not governed by its instructions is a mistake.
And since in general the machine's instructions are provided by the
programmer, the range of fruitful applications of the machine is
determined by human ingenuity.
There is a sense, however, in which today's high-speed comp
uters can be made to do more than we know how explicitly to
instruct them to do, and hence can be made to exhibit a sort of
originality. This originality does not involve operating without in
structions, but rather results from the computer's ability to provide
its own instructions for operating in situations not anticipated by its
programmer. Since the most promising techniques of pattern recog
nition rely upon this self-programming ability of the computer, it
will be helpful to illustrate this ability with some hypothetical
Consider first the routine case of the computer assigned the
task of summarizing a set of numerical data. The form of the sum
mary is to depend upon the distribution of the data. If the distr
ibution is flat, the median is to be calculated, and if skewed, the
mode is to summarize the data. The computer first arranges the
data in a convenient order and determines its distribution. It then
selects the appropriate method for further processing, and calcu
lates the result required by this method of processing. Although
in this case the programmer cannot anticipate the unique charact
eristics of the set of data the computer is to process, he has antic
ipated each type of distribution which the computer is likely to
encounter and has instructed it in detail how to respond to each
type. There is no call in this example for the computer to provide
part of its own instruction. 28 Joseph Bobik and Kenneth M. Sayre
Consider next the case of a large city with severe traffic prob
lems which turns to a computer for assistance in determining the
optimal rate of change of its traffic lights in especially congested
locations. Each traffic light is geared to the computer in a way which
allows the machine complete control over the times the light shows
green, yellow, and red. Devices are set up in the streets between
these lights to inform the computer of the rate of traffic flow in any
street at any given time. The computer then is instructed to deter
mine the combination of rates of changes of the various traffic lights
which result in the least over-all delay in traffic during times of day
in which traffic normally is heaviest. Since it would be fruitless for
the programmers of the computer to attempt to anticipate all contin
gencies of traffic that the machine might encounter at various time
of the day, the particular combinations of rates of changes which
the computer will consider must be determined by the machine
itself. The computer begins by providing a fixed rate of change for
all traffic lights concerned, and determines the over-all rate of traffic
flow under these conditions. Then it begins to experiment by varying
the rates of key traffic lights randomly, and checking in detail the
changes in traffic flow which result from these variations. Soon cer
tain combinations of rates are found to result in appreciably im
proved traffic flow. These combinations are noted by the computer,
and given preference to other in its further experi
mentation. By recording and continually re-examining the traffic
conditions which result from each combination it tries, and by con
tinually altering its processing routines to increase the probability
that favorable combinations occur more frequently than unfavorable
combinations, the computer soon evolves a set of normal working
instructions which enables it to control traffic during peak periods
in a near optimal fashion.
In the second example, the computer is given a specific task
to perform, and a specific criterion by which to judge its progress
towards the completion of the task. But because of the complexity
of the task, it is not instructed specifically how to proceed in accomp
lishing it. Instead it is given general instructions to try various pos
sible solutions in random order, and then to begin to bias its ope
rations for selecting alternative solutions in the direction of solutions
which upon test appear more fruitful. A successful result of this pro
cedure would be a set of operating instructions evolved by the Pattern Recognition Mechanisms 29
machine through trial and error which could not have been antic
ipated in any detail by its human programmer.
As a final case, conceive a group of speculators who engage a
computer to predict stock market fluctuations. At first they attempt
to provide the computer with data which they think should be rele
vant to its predictions, data such as rates of change of major commod
ities during typical market conditions in the past, buyer activity
during recent weeks, states of health of key executives, and similar
matters. But the computer's results with these data are not encour
aging. Finally they hit upon the idea of letting the computer select
its own data on which to base its predictions. The is to
follow its own promptings, not only in selecting the data to be
considered, but also in determining what form the data is to take
for processing. By giving the machine complete freedom in selecting
and organizing its data, the speculators hope it will originate a set
of categories for describing and processing market information which
could not have been anticipated by human means alone.
To understand the burden placed upon this computer, recall
that all information presented to it must ultimately be expressed in
terms of series of electronic charges. Different items of information
are represented by different formations of these series, and to each
unique item there must correspond a unique serial formation. Since
many different items of information are supplied to a computer in
typical use, the programmer supplying the information must share
with the machine a set of explicit conventions regarding how much
data in a given series of charges is relevant to a particular item of
information, and regarding the order in time in which various sorts
of information will be presented. If the convention is to present
numerical data first, and then instructions for processing the data,
and if these items of information are presented in reverse order due
to some mistake of the programmer, the resulting series of charges
in the computer will have no significance. In the absence of con
ventions of this sort, or in case of violations of the conventions, the
computer fails to organize the discrete electronic charges in its
storage components in a way which enables them to have any signi
ficance as part of an information-laden pattern. By refraining from
specifying the form in which information is to be presented to their
computer, and by requiring that it impose order on its data without
preliminary instructions of human origin, the speculators have assu
red themselves of results devoid of intelligible content. Computers 30 Joseph Bobik and Kenneth M. Sayre
at their present state of development cannot provide their own cate
gories for information processing, and there is no good reason to
prognosticate that machines of the future will be more talented in
this respect.
These examples are useful as illustrations of the capabilities and
limitations of the pattern recognition techniques discussed below.
3. In speaking of either human or mechanical recognition, the
term * recognition ' is typically used in a way which involves refer
ence to a recognizer, to a recognized object, and to a class of which
the object is recognized as a member. To say that M (whether man
or machine) recognizes x will be understood in the present context
to mean that there is a class of objects {containing one or more
members) of which x is a member, and that M correctly identifies x
as a member of that class. Use of the term 'recognition' in this
fashion does not prejudge the question whether machines should be
said to perform cognitive functions, since there is no requirement
that the identification of x involve a uniquely mental process. It will
be argued below that, although machines indeed are capable of r
ecognizing patterns in a proper sense of that word, there are pro
cesses involved in typical instances of human recognition which can
not be duplicated mechanically.
In recognition of the inscription 'A*, that class of which the
symbol would be identified as a member is the class of all inscrip
tions which symbolize the first letter of the alphabet. Speaking care
fully, we should not say that the letter A is recognized, but rather
that an inscription, or perhaps an instance, of the letter A is recog
nized. An inscription is identifiable as a member of its class with
reference to the characteristics by virtue of which it is a member of
'invariant' will be used to dethat class and no other. The term
signate that characteristic which distinguishes a given class of indi
viduals from all other classes, and the possession of which qualifies
an individual for membership in that class. Any characteristic of an
actual inscription, for example 'A', is an invariant of some class of
individuals. The characteristic of being black, in this instance, is an
invariant of the class of all black objects, of which that inscription is
a member. But no one color property is the invariant of the class of
inscriptions of the letter A, since members of that class can be
inscribed in any conceivable color. The fundamental problem of
preparing a computer to recognize inscriptions of the letter A is Pattern Recognition Mechanisms 31
to find what characteristics serve as invariants of the class of inscrip
tions of that letter.
Attemps by technologists to provide invariants for the mechan
ical recognition of patterns generally are of three sorts : in order
of increasing sophistication, (1) the template method, (2) the property
list method, and (3) the self-programming method. In the brief dis
cussion of each of these methods which follows, no attempt will be
made to cite all important work in the area (1).
The template method is illustrated by a relatively simple system
in which a computer takes its input from a photo-electric scanner.
The scanner is capable of reacting differently to light and to dark
spots on a sheet exposed to it, and is connected with the computer
in such a way that a unique location in the computer's storage
section corresponds to each small area on the sheet which the scan
ner can discriminate. The reaction of the scanner to a dark area is
to deposit an unambiguous « plus » charge in the computer at the
corresponding location, the reaction to a light area is to deposit an
unambiguous « minus ». As the scanner covers the series of light
and dark spots on the sheet before it, the pattern of those spots is
transferred to the computer in terms of « plus » and a minus »
To prepare the computer-scanner system to recognize an in
scription, say of the letter A, the programmer presents a standard
inscription to the scanner, which in turn translates the inscription
into computer language and passes it into the computer's storage
section. This standard inscription serves as a « template » against
which inscriptions subsequently presented to the scanner can be
compared. If the series of « pluses » and « minuses » received from
a subsequent inscription corresponds item for item with the series
of « pluses » and « minuses » of the standard figure, that inscription
is identified by the computer as being of the same configuration as
the standard. In such a case, the computer would have recognized
the inscription as being one of the letter A. If a series of charges
from an inscription corresponded in very few items with the stan
dard, the computer would determine that the inscription was not
(1) A comprehensive bibliography of literature through I960 pertaining to
pattern recognition and related areas in the general field of artificial intelligence
has been published by M. MlNSKY in Institute of Radio Engineer» Transaction*
on Human Factor» in Electronic», 1961. 32 Joseph Bobik and Kenneth M. Sayre
of the letter A. Generally, of course, neither of these extremes
would occur, since even carefully formed inscriptions would differ
in some details from any one inscription taken as standard. Hence
the programmer must decide what degree of correspondence with
the standard is sufficient for recognition of an inscription as an A.
This technique would work well in cases where the inscriptions
to be recognized are generally similar in regard to size, shape, and
orientation. The major shortcomings of this technique would be its
inapplicability in recognition of patterns in contexts other than a
printed page, and its dependency upon mere shape of an inscription
as a basis for recognition. In cases of patterns in which successful
recognition involves invariants more subtle than actual shape, it is
better to describe invariant features of the pattern than to represent
them by standard inscriptions stored within the computer.
In applying the property list method, any feature or combi
nation of features of a pattern which can be described in computer
language can be taken as an invariant feature of that pattern. One
basic property of several letters which can be exploited by this
method is closure. An O is a closed figure, while a C is not. Any set
of invariants which did not include closure probably would be inad
equate to distinguish between an inscription of an O and an in
scription of a C. Another important property is concavity. An
scription of Z is concave to the right below and to the left above,
while an inscription of N, similar in other respects including orien
tation, is concave up to the right and down to the left (2>.
The property list method allows more versatility in the choice of
invariants than the template method. But this poses its own prob
lems. Since any consistent combination of features might serve as
an invariant, and since most patterns of even moderate complexity
possess many features, the number of combinations a programmer
would have to examine to determine the most successful invariant
might be excessive. It would be a relatively minor problem to pro
vide a list of features to serve as the basis of a program to recognize
well-formed letters in bold face type. But when the programmer's
goal is to provide a set of invariants which enable the computer to
perform as well as humans perform in recognizing poorly-formed
<*> S. H. UNCER reports a pattern recognition syttem involving 32 feature»,
including closure and concavity, in « Pattern Detection and Recognition », Pro
ceeding* of the InttittOe of Radio Engineer*, Vol. 47, Oct. 1959.