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Kenneth R. Conklin, "The Integration of the Disciplines," EDUCATIONAL THEORY, XVI, 3 (July, 1966), pp. 225-238.
Reprinted from EDUCATIONAL THEORY, Vol. XVI, No. 3, July, 1966
THE INTEGRATION OF THE DISCIPLINES
BY KENNETH R. CONKLIN
Introduction
IN PREPARING STUDENTS FOR THE ACTIVITY CALLED LIVING, THOSE WHO DEVELOP THE CURRICULA FOR THE SCHOOLS RECOGNIZE THAT DIFFERENT ASPECTS OF LIFE MAY BE DEALT WITH IN RELATIVELY SEPARATE COURSES OF INSTRUCTION. Thus
the schools teach courses in mathematics and science, language, art, music, drama,
and automobile driving. Two broad types of schooling seem to be present in most
curricula: science and humanities. These two types of courses correspond to two
kinds of life activity: technological manipulation of the material world, and value-oriented
axiological aspects of life where action is directed according to notions of
what is good or beautitul or ethical. Some subjects, for example the content of
courses in the "social sciences," include both scientific and axiological aspects;
thus, in studying history we ask what happened and why (science), and whether
that which happened was good or how we ought to behave today in view of what
happened in the past (axiology).
Some educators believe that the subject area divisions are quite artificial. On
this view, life is a unified activity which requires simultaneous or inter-related
action in both the scientific and axiological spheres. The disciplines or school
subjects are studies of limited aspects of life. Educators who hold this view
advocate the integration of the disciplines. By this they mean that the school
subjects should be taught in such a way as to convey to the student the cross-relevance
and cross-fertilization of the subjects he studies. The integration of the
disciplines involves curriculum planning and teaching methods designed to make
clear the unification in life (or the possibility of such unification) of the limited
aspects of life studied in school subjects.
If the integrated teaching of the subject areas is possible, there must in fact
be an integration of these subject areas -- if the scientific and axiological subjects
in the curriculum are capable of being taught in a way which integrates them into
a meaningful unified approach to life, it must in fact be true that science and
axiology share common structures, methods, or objects of inquiry.
The purpose of this paper is to explore whether there are in fact any such
integrating factors which are common to both science and axiology. I shall try
to show that metaphl'sical inquiry provides such a unifying bond. Since those
who study axiological subjects usually offer less resistance to metaphysics than do
the scientists (indeed, some philosophers build value theories openly and directly
based on metaphysical foundations), I shall concentrate in this paper on studying
the relationship between science and metaphysics.
---------
KENNETH R. CONKLIN is a teaching assistant in the Department of History and Philosophy of Edacation, University of Illinois, Urbana, where he is doing research for his Ph.D. thesis on the properties of relevance between philosophy and education.
[end page 225 / start page 226]
The distinction between science and metaphysics is simply this -- science is
the study of empirical observations; metaphysics is the inquiry into the ultimate
nature of Reality, including the study of how such inquiry is to be conducted
properly. This distinction will be clarified throughout the paper, particularly in
section one.
I hope to show that, although science and metaphysics sometimes consciously
exclude each other from consideration, they are in fact close relatives engaged in a
family squabble. Metaphysics is essential in science, in ways which will be made
clear. Finally, I shall claim that metaphysics is a bridge between science and
axiology. The existence of this bond means that the integration of the disciplines
is possible, and the study of the bond may help us understand and teach the
disciplines in an integrated manner, thereby providing a unified world view.
The first two sections of this paper are devoted to a discussion of the nature
of scientific knowledge and method. Sections three and four describe the nature
of mathematics and its role in science. Because science deals with empirical
observations while mathematics is the a priori study of logical symbolism, we
might expect that science and mathematics have radically different structures
and methods -- yet, we shall see that there is a remarkable unity and harmony
between these two disciplines. The purposes of the first four sections of this
paper are two-fold: (1) to study the nature of science and mathematics in order
to discover how metaphysics is related to these disciplines; (2) to perform an actual
integration of these two disciplines in order to demonstrate what is meant by
"the integration of the disciplines" and in order to suggest a method for performing
integrations between disciplines generally. Section five draws upon the previous
four sections to comment specifically upon the relationship between metaphysics
and science; in addition, some hints are given which indicate possible directions
toward the integration of science and axiology on a metaphysical basis.
It would seem appropriate to interject a brief explanation concerning the
footnotes in this paper. The issues dealt with in this paper have been debated
for centuries by hundreds of authors, and I know no fair way of representing all
the pro and con writers adequately; furthermore, I am not an expert on the history
of the philosophy of science, nor do I claim exhaustive knowledge of the positions
which have been taken or who has taken them. The views presented are my own;
some points have undoubtedly been made by others without my knowledge, and
other points have been consciously borrowed. The footnotes are intended to give
credit in those instances where I have borrowed directly from the work of someone
else.
I. The Nature of Scientific Knowledge
Scientific "knowledge" consists entirely of two kinds of objects: (l) facts,
(2) theory-like constructs based upon facts.
(l) As Eddington has indicated,/1 the empirical basis of science consists of
pointer readings -- nothing more. These pointer readings are quantified reports
of empirical experience -- they are measurements which describe the inter-relationship
between an event in the physical world and a device which records or measures
that event.
-------
1. Arthur S. Eddington, The Nature of the Physical World, Chapter 12.
[end page 226 / start page 227]
A closer examination of the character of pointer readings will disclose the
source of the division between science and metaphysics. The interaction between
a measuring device and the rest of the physical world is simply a fact of nature, in
the same way as a collision between two billiard balls is a fact of nature. The
distinction between measuring devices and ordinary billiard balls is to be found in
the special uses we make of measuring devices. The difference is that human
beings design measuring devices in such a way that the position of a pointer can
be interpreted as indicating the truth of a human description of the world. Thus,
we observe opposite the tip of an arrow a number on a scale, and conclude that
the weight of an object is ten grams. The arrow and the scale over which it passes
are connected with other physical objects in such a way that we claim that the
position of the arrowhead on the scale tells us the weight of objects placed on top
of our measuring device.
As mentioned before, the interaction between objects and measuring devices
is a simple fact of nature. However, our conclusions based on the pointer readings
are not facts of nature -- they are human interpretations. Saying that (l) we see
an arrow pointing to ten, differs remarkably from saying that (2) the weight of
some object is ten grams. Both statements are subject to error; however, the
first statement is a report of a sense perception while the second statement claims
to represent a true condition of the real world. Without haggling over the meanings
of "true" and "real," the difference should be clear.
The objects dealt with by science are the reports of pointer readings; thus,
science deals with statements of the first type. Statements of the second type are
typically made by scientists, but if pushed to an explanation of what they mean,
the scientists still resort to statements of the first type. Thus arises a sharp
distinction between science and metaphysics -- the statements of science are
reports of pointer readings, while the statements of metaphysics are claims about
truth and reality in the objective world. Some philosophers of science make the
division complete by relegating theories about the "true" nature of the "real"
world to metaphysics, using the term "metaphysical speculation" to label the
ideas thereby excommunicated from scientific deliberation.
Such philosophers of science defend this excommunication in a most reasonable
way. A typical defense might run something like this:
"What do you mean when you say that scientists do not make true statements about
reality? Scientists investigate what happens, and they take special care to be sure
their reports are both accurate and objective. Anyone can check the validity of scientific
statements by performing appropriate experiments; thus, science, like democracy,
is open to all who care to participate. Furthermore, scientists are careful to
talk about facts, as you have indicated, and the facts are there for everyone to see."
To which we reply:
"Certainly the licts are there for all to see. But in seeing the facts we see them
only as we are able to see them, and we interpret them only as we are able to understand
them. Our interpretations of the facts may very well differ from the truth.
The essential point is that human nature may impose certain limitations upon our
ability to understand the facts, which limitations may invariably distort our view of
reality. On what basis do you claim both that there are no such limitations and that
science actually does report the 'true' facts of the 'real' world?"
[end page 227 / start page 228]
To which they reply:
"Your discussion about absolute limitations to human powers of interpretation is
pointless. (1) If there were such limitations on knowledge they would, by their very
nature, remain forever unknown to us; hence, it is pointless to ask about what we can
never know. (2) If there is a Reality beyond human knowability, why worry about
it? If such Reality affects our knowledge in ways we can know, then we shall know
these influences; if not, then such Reality will never give us cause for concern. (3)
Your claims cannot be publicly tested -- nobody can ever know whether they are true or
false, by their very definition. Hence, your claims are dishonest. (4) Science reports
and measures facts. Your claims, if true, do not report the kind of facts amenable to
the methods of science. Hence, science cannot concern itself with your claims -- your
claims are metaphysical speculations."
To which we reply:
"Thank you for clarifying our case. As you have shown, science is limited to pointer
readings and their interpretations. Nothing else can be studied by science, and discussions
about topics beyond the reach of pointer readings and their empirically testable
interpretations are excommunicated as metaphysical speculation."
We shall return to these considerations later. For the present we shall
merely observe that the nature of scientific knowledge, as outlined so far, gives us
cause to worry about the narrowness of the scientific view of the world. We shall
see later that this narrowness may hold back the progress of science. What is
more important for the purposes of this paper, we shall observe that this narrowness,
if maintained, may actually eliminate any possibility of integrating the disciplines
into a unified world view acceptable to all the disciplines.
(2) It will be recalled from the opening sentence of this section that, in addition
to dealing with facts, science deals with theory-like constructs based upon facts.
Aside from simple interpretations of the pointer readings (such as the interpretation
that an object weighs ten grams), scientists build theory-like constructs, which are
attempts to classify the facts of science. These constructs are man-made edifices
whose purpose is to provide frameworks of simplification and generalizations so
that the facts may be better understood in the context of their inter-relationships.
Laws and explanations are nothing more than classifications of facts into
generalized statements which are ultimately reducible to assertions of the form
"x is y." Thus, a law is a statement such as "all apples, when released, fall to
the ground." Given the observation that some particular apple has fallen to
the ground, we desire an explanation. In this case, the explanation is the conjunction
of two statements: (1) "all apples, when released, fall to the ground";
(2) "this is an apple which was released." The logical conclusion, "this apple fell
to the ground," is the observation whose explanation is the conjunction of general
law (1) and initial condition or observation of fact (2).
I do not wish to engage in the disputes among philosophers of science concerning
the exact nature of laws and explanations. My point is simply this: all
theory-like constructs are classifications of facts, and all such constructs provide
logical or verbal frameworks in which statements representing observed facts are
listed as logical deductions.
[end page 228 / start page 229]
Clearly, theory-like consructs are different in character from reports of pointer
readings. It will be noted that laws and explanations, discussed so far, classify
reports of events which occurred in the past. With some fairness it may be said
that laws and explanations are man's attempts to understand what happened.
If man desires to control the future he will be interested in making predictions.
Without becoming involved in nasty disputes, we may say, again with some fairness,
that predictions are statements to the effect that the laws and explanations,
established on evidence from the past, apply to the future. We shall recall the
character of laws, explanations, and predictions in a subsequent section of this
paper.
This section is entitled "The Nature of Scientific Knowledge," and it yet
remains to identify what it is that science calls knowledge. When used in the
strong sense, we say that knowledge entails truth (in the sense of correspondence
to reality), belief, certainty, and good evidence. Thus, when we say in the strong
sense that person X knows that proposition p holds, we mean all of these: (1) p is
true, (2) X believes that p is true, (3) X is certain that p is true (there can be no
doubt in X's mind), (4) X's belief is based on good evidence.
The discussion about pointer readings and metaphysics shows that in science
no claim can be made to truth -- at least, no claim can be made that we know for
certain that our statements are true. The history of science shows that our concepts
about the world have radically changed, and hence we remain uncertain
about our present concepts since the advance of science may yet produce further
change. The lack of certainty in scientific statements is further illustrated by the
belief of some philosophers of science that the method of science involves universal
doubt -- Popper, for example, believes that scientific statements to be scientific
must be testable and that we must always continue to doubt and test;/2 Bartley's
comprehensively critical rationalism/3 formalizes the method of universal doubt by
establishing universal criticism as the operational definition of rationalist identity.
Thus, truth and certainty are to be eliminated from the definition of scientific
knowledge. We are left with belief and good evidence -- hence, the claim that
scientific knowledge is warranted belief. The only thing standing between scientific
knowledge and knowledge in the weak sense of ordinary usage is therefore the
strength of the evidence supporting scientific assertions.
To summarize the results of this section: Scientific knowledge consists in
pointer readings which are classified into categories called laws and explanations.
All laws and explanations resemble definitions in their formal character: they may
also be regarded as testable predictions. Science calls its facts knowledge in the
sense that scientific statements represent belief which is founded upon good
evidence.
II. The Nature of Scientific Method
Science advances by beginning with ordinary common-sense observations;
the means of observation are refined to promote accuracy and the observations are
-------
2. Karl R. Popper, The Logic oJ Scientifc Discovery, Chapters I and 4.
3. William Warren Bartley III, The Retreat to Commitment, Chapter 5.
[end page 229 / start page 230]
interpreted formally into laws and explanations. These laws and explanations
are then regarded as predictions which provide hypotheses, and the hypotheses are
used to stimulate our search for data and to provide criteria for selecting relevant
data from out of the mass of sense perception. The process outlined here is
circular -- no evidence is gathered and called evidence until our search is oriented
by a hypothesis, and no hypotheses are long entertained unless they are suggested
and supported by observations. Our hypotheses, taken all together, are the nets in which we catch our experiences.
Science makes progress by the successive improvement of hypotheses through
the conjecture-refutation process -- we strengthen hypotheses by eliminating their
untenable aspects through suitable modifications in the light of experience, and
we sometimes reject hypotheses or hypothesis systems (theories) entire.
In general, no hypothesis stands or falls alone. Networks of inter-related
hypotheses are all involved every time an experiment is performed, and we must
decide on other than empirical bases how the network is to be reorganized in the
light of experience. Consider the following conversation in this respect:
P: (lying still on the ground): "I am dead."
Q: "You are not dead, and I shall prove this to you."
P: "Please do, for I should like to be alive."
Q: "Do you agree that dead people do not bleed?"
P: "I agree."
Q.: "I have a knife and shall cut your arm off. If you bleed, that will prove
you are not dead."
P: "Go ahead with the experiment."
Q: (after cutting off P's arm): "It is done. Your arm has been severed
and you do bleed. Therefore, you are not dead."
P: "I agree that my arm has been severed and I do bleed. But I do not
accept your conclusion that I am not dead. Rather, the experiment
proves": (here P chooses one of these alternatives)
(a) "Some dead people do bleed -- I was mistaken in accepting your
generalization."
(b) "That blood you saw came from somewhere else."
(c) "Our logic is ali fouled up."
There may be other alternatives which would enable P to maintain with
consistency that he is dead. Perhaps (a) is the most reasonable alternative because
it does not at all strain the limits of possibility. The important thing to see from
this example is that a network of hypotheses is involved in the experiment, and we
must choose on other than experimental grounds which hypotheses in the network
will be maintained and which will be called experimentally falsified. No recourse
is had to the results of other experirnents designed to test specific hypotheses in
the network, because any given experiment always has the character of this one
in that any experiment calls into play whole networks of hypotheses. Ultimately
our restructuring of the network involves a criterion or a choice which is not itself
the sole directed result of experiment. This situation will be recalled subsequently
when we discuss more directly the relationship between science and metaphysics.
The dialogue presented here will also be further analyzed in section four.
[end page 230 / start page 231]
To summarize the results of this section: By whatever means they are arrived
at, the hypotheses of science orient our search for new data and remain standing
or fall according to our interpretation of experiments which we believe test the
hypotheses. No single hypothesis ever bears the full brunt of experimentation -- rather,
networks of hvpotheses are involved in every experiment and we choose,
on other than stricdy empirical grounds, how the network will be reorganized with
respect to truth and falsity in the light of experimental evidence.
I I I . The Structure of Mathematics
Sections three and four are concerned with the structure of mathematics and
its uses in science. Hence, it would seem appropriate to justify the inclusion of
such topics in a paper on the integration of the disciplines. I hope to show that,
although mathematics and science seem to be radically different in outward
appearance and method, these subject areas show remarkable similarities. It is
certainly no secret that scientists make extensive use of mathematics; indeed,
many people speak about "math and science" in the same breath, as though these
two subjects were really only one. We shall soon observe that mathematics is
quite different from science -- and yet, we shall see that science and mathematics
fit together like hand and glove (which, incidentally, are quite unlike each other).
The purposes of sections three and four are two-fold: (1) to explore how two quite
different subject areas are in fact integrated, and thereby to get a glimpse at an
actual integration of disciplines; (2) to further clarify certain aspects of our earlier
discussion concerning the nature of scientific method.
If facts are the materials of the sciences, theorems are the materials of mathematics.
In discussing the nature of mathematics, we must distinguish carefully
between the way mathematicians go about their work and the refined structure
which they seek to produce. A mathematician may very well be inspired by
practical applications or problems in the sciences -- the "logic" of mathematical
discovery must surely include guesswork, insight, and practical motivation.
The ultimate aim of the mathematician, however, is the statement and proof
of theorems. Every theorem in mathematics is reducible to if-then form, where
the "if" includes the axioms and rules of inference adopted in the formal mathematical
system being employed, and the "then" is the final conclusion actually
stated in the theorem. Ultimately, the terms employed in stating a valid theorem
can be reduced to primitive, undefined symbols in such a fashion that the lengthy
string of undefined syrnbols constituting the "if" clause is identical to the string
constituting the "then" clause.
Very few mathematicians have ever gone to the full extreme of establishing
an alphabet of undefined symbols, listing rules for combining these symbols into
"meaningful" strings, stating axioms in terms of these strings, and proving
theorems by reducing them to strings of acceptable form./4 Nevertheless, proofs
-----------
4. Russell and Whitehead provide such a formal system for arithmetic in Principia Mathematica.
Kurt Goedel has proved by means of formal logic that arithmetic is essentially incomplete and that its
consistency cannot be internally demonstrated. Loosely speaking, "arithmetic is consistent" is the
only statement proved by Goedel to be formally undecidable; hence, his proof does not affect the general
validity of formalistic methods for proving theorems.
[end page 231 / start page 232]
of theorems are usually regarded as outlines presenting the major transformations
which must be made in order to achieve validity, and behind every theorem and
proof stands the formal deductive structure described here. In short, every
theorem of mathematics is formally equivalent to the definitional tautology
"x is x"; the value of a theorem consists in the validity which it accords to representing
mathematical statements in forms which are more convenient or more
immediately applicable.
IV. Mathematics In Science
Bertrand Russell once said that mathematics is the subject in which we never
know what we are talking about nor whether what we are saying is true. The
discussion of the last section should clarify his meaning. Mathematics deals in
the transformation of symbols from one form into another, and is formally reducible
to statements of the form "x=x." As such, mathematics has a formai structure
which is independent of experience. Science, however, is concerned with "is"
statements which report facts in the forrn "x is y." How is it, then, that something
as empty as mathematics is such a valuable tool to the scientist? How is it
possible for two such opposite endeavors to fructify each other? Perhaps our
answers to these questions will point the way to the integration of the disciplines.
We recall that scientific reports of observations take the form "x is y," while
laws, explanations, and predictions are logical structures which enable us to deduce
observational statements of the form "x is y" from statements which classify
collections of previous observations. We also recall that mathematics is composed
of theorems which are ultimately reducible to tautological definitions of the form
"x=x"; however, the tautology is usually concealed in the form "if A . . then B."
A and B may not be obviously related, but the logical system in which the theorem
is proved enables us to reduce A and B to the same string of symbols, although the
complete reduction is seldom carried out.
(1) Both mathematics and science therefore reduce to the logical structure of
systems of definitions. Science says x is y, and thus classifies. Mathematics
says x is x, expressed differently, and shuffles our way of saying x. Thus, mathematics
and science reduce to logical structures. (2) At the level of actual usage,
science reports empirical observations and mathematics exhibits a priori statements
of if...then form, called theorems -- the a priori staternents of mathematics
are neither true nor false but are logically valid, while the empirical observations
of science are represented as statements about fact which are called true.
The ultimate formal character of mathematics and science will be discussed first,
followed by a discussion about their nature at the level of actual usage.
(1) In their ultimate formal characters, it is clear that both mathematics and
science involve the use of logic -- both draw upon the same notions of what is
logical. Evidence is seen for this in the fact that the mathematical framework
applies to science, so that we must be using common logical structures in both
areas. Notice, for example, that we demand consistency in mathematics (among
the hypotheses or axioms of the system) and in science (among the laws or explanations
or hypotheses which constitute a theory). Whatever this "consistency" is,
it seems that the notion is common to both mathematics and science and that the
notion comes from sources broader than either subiect area.
[end page 232 / start page 233]
(2) At the level of ordinary usage, it appears that mathematics provides
theorems of the form "if B then C," while science provides statements of the
form "B is true" or "B has been observed." The conjunction of the statement
"if B then C" with the statement "B is true" yields the conclusion "C is true."
Therein lies the harmony between science and mathematics -- the statement "C
is true" is a mathematical deduction which can be interpreted as a statement of
fact to be tested by science. Thus, mathematics provides a formal deductive
structure which science fills with facts. Science chooses which deductive structure
it wishes to adopt, and when and whether the axioms of that structure are
satisfied in their factual interpretations./5 Mathematics provides pre-fabricated
deductive systems into which science inserts statements about observations and
extracts statements about other observations which may or may not have been
made.
The common structure and mutual interaction of science and mathematics
are seen even more clearly when we realize that science accepts re-transmission
of falsity from conclusions to hypotheses through the mathematical structure. In
the example above, given the theorem "if B then C," and given the scientific
observation "C is false," science accepts the falsity of statement B, based upon
this mathematical property of if...then relations: if the conclusion of a valid
deduction is false, then the premise is false. Notice that this re-transmission of
falsity requires both that the deductive argument is valid and that the conclusion
is in fact false. Granted both of these conditions, we may safely declare that
falsity has been established for the premise.
Given an axiomatic system A and a theorem of the form "if B then C," and
given the hypothesis or generalization "B is true" we require the truth of the fact-statement
"C is true." The statement that C is true may be considered as a
prediction, or deductive elaboration based on the statement "B is true." The
truth of C is to be tested by scientific observation. If we now fail to confirm the
truth of C but instead observe that C is false, one of the following conclusions is
drawn: (1) B is false in point of fact (this would be re-transmission of falsity); (2)
We were mistaken about C and indeed C is true -- we must search more diligently;
(3) A does not apply to this physical situation.
Notice that any one of these three alternatives is equally as consistent with
observation as any other. I do not know how scientists actually choose among
these alternatives in practice, but it should be clear that pointer readings and
empirical observations alone cannot be a sufficient basis for decision. Probably
(1) is the most frequent choice -- it corresponds to experimental refutation or falsification
of a hypothesis. (2) is perhaps almost as frequently chosen as (1), and
corresponds to the claim that we must repeat our experiment because we are calling
the results themselves into question. (3) corresponds to the claim that the
logical or mathematical assumptions or axioms underlying our reasoning processes
are not appropriate for the situation at hand. Alternative (3) is seldom used, but
occasionally occurs: witness the dispute over whether Euclidean geometry or one
of the non-Euclidean geometries is appropriate for scientific use (Newton chose
Euclid and Einstein chose Riemann).
--------
6. Henri Poincare, Science and Hypothesis, Chapter 3.
[end page 233 / start page 234]
In this scheme, A is the system of mathematical or logical axioms, including
rules of deduction and criteria for meaningfulness of strings of symbols. B may
represent a hypothesis (which is to be tested by testing one of its consequences),
a law, an explanation, or a prediction. C is usually a statement of fact concerning
a particular situation. The reader will do well at this point to compare alternatives
(1), (2), and (3) in this example with alternatives (a), (b), and (c) available
to the "dead" man in the example discussed in the section on the nature o[
scientific method. In that example we were concerned only with scientific statements;
in the present example we are discussing a system in which mathematics
and science are mixed. However, even in "purely scientific" problems the logical
structure of our reasoning processes plays the role of a system of axioms.
We note here that if the hypothesis B of the present example is equated with
the generalization "dead men do not bleed" in the earlier example, we have a
perfect correspondence between the alternatives of the two examples, such that
(a) corresponds to (1), (b) corresponds to (2), and (c) corresponds to (3). However,
if the hypothesis under test in the earlier example is the statement "P is
dead," then to make the same correspondence between alternatives we must
revise alternative (a) as follows: (a) "P is not dead, but alive"; (b) and (c) remain
as before. Thus, to maintain that he is dead, P claims that the generalization
"dead men do not bleed" was the hypothesis being tested, or else escapes by
accepting alternative (b) or (c). If Q wishes to win the argument, he denies
(b) and (c) and maintains the truth of the generalization while claiming that
the hypothesis being tested is the statement "P is dead."
It is hoped that by studying these examples the reader will discover that,
indeed, networks of hypotheses are involved in every experiment, and we choose
on other than experimental grounds how the network is to be reorganized with
respect to truth and falsity in the light of experimental evidence. In this section
we have also seen how science uses the deductive framework supplied by
mathematics.
V. Metaphysics is Essential in Science and Integrates Science and Axiology
Finally we have arrived at the point where we may reap the harvest from
the crops cultivated in the earlier sections of this paper. In this section we shall
discover how and why metaphysical considerations form an essential part of science,
whether or not scientists are aware of such considerations. We shall also discover
the ways in which metaphysical inquiry can play a major role in stimulating the
advance of science. Finally, we shall notice a few of the problems which metaphysics
must help us solve if we are to be successful in integrating science and
axiology.
We have defined metaphysics as the study of the true nature of Reality,
including the study of how such a study may best proceed. In section one we
observed that scientific knowledge consists in pointer readings which are classified
into categories called laws and explanations, and that science calls its facts knowledge
in the sense that scientific statements represent belief which is founded
upon good evidence. The discussion reported there between the scientist and the
metaphysician should indicate clearly the difference between their points of view.
[end page 234 / start page 235]
(1) Scientists are motivated to their work in the belief that they will discover
regularities of nature which will enable them to understand and control nature.
Thus, scientists are interested in discovering the truth about the way things are.
However, for the sake of objectivity or precision or communicable meaningfulness,
they confine their activities to observations of pointer readings and statements
which classify these observations. They exclude as "unscientific" those
"metaphysical speculations" which question the basis for scientific claims to
truth or which attempt to discover whether there is a Reality which underlies and
causes the phenomena observed by science but which is itself not capable of being
studied through observations of pointer readings.
(2) Metaphysicians are motivated to their work in the belief that they will discover
the true nature of Reality, or how we should go about making such discoveries.
However, for the sake of generality or universal validity, they refuse
to admit the claim that pointer readings are true indicators of Reality; and, even
if they would agree that pointer readings are true indicators of Reality, they
would claim that much more is needed besides pointer readings in order to justify
that pointer readings are true indicators of Reality. To discover the true nature
of Reality we cannot rely on pointer readings alone, and perhaps not at all.
It should be clear from this brief discussion that science and metaphysics are
at war because each denies the validity of the other's approach or method of inquiry.
Science refuses to discuss anything that cannot be studied through pointer
readings, and metaphysics refuses to accept scientific claims as accurate when
they are based solely on pointer readings. It should also be clear that science
and metaphysics both share the same goal -- the discovery and understanding of
Reality.
In section two we discussed the nature of scientific method. The point made
in that section was that science proceeds by generating and testing hypotheses.
Although the source of the hypotheses may be of interest, the crucial part of
scientific method is the testing of hypotheses by performing empirical observations,
We then discovered that no single hypothesis ever bears the full brunt of
experimentation -- rather, networks of hypotheses are involved in every experiment
and we choose, on other than strictly empirical grounds, how the network
is to be reorganized with respect to truth and falsity in the light of experimental
evidence. The discussion between the dead man and the butcher gave an illustration
of how one network of hypotheses could be reorganized in several different
ways in the light of one experiment.
The results of sections two and four provide grounds for questioning the
adequacy of pointer readings as indicators of Reality. Not only are scientific
constructs based on pointer readings subject to human limitations on ability to construct -- there is also serious doubt about the source of authority employed
by a scientist who claims that experiment X demonstrates that proposition Y
has been falsified or corroborated. The generalized example in section four, and
the specific example in section two, show that something other than publicly verifiable
empirical data is involved in the process whereby scientists make claims
concerning the interpretations of their experiments.
It therefore appears that an essential part of scientific research should be
the study of how networks of hypotheses are to be reorganized with respect to
[end page 235 / start page 236]
truth and falsity in the light of experience. Such inquiry would be metaphysical
in the sense that it goes beyond the range of empirical verifiability or falsifiability;
such inquiry requires that decisions be made concerning what kind of logic is
most appropriate to the interaction between experiments and their associated
networks of hypotheses. Since networks of hypotheses are also involved in non-scientific
subjects like axiology, the study of network logic seems to involve all
the disciplines, and the attempt to build generalized network logics could pronmote
the integration of the disciplines at the theoretical level. It should be clear that
metaphysical inquiry into the nature of Reality is essential if we are to build
"correct" network Iogics or choose among several proposed logics which may all
equally well fit all the various disciplines.
In studying the structures of mathematics and science, we observed that a
vague notion of consistency is common to both. (1) A mathematical system is
not considered valid unless its axioms are mutually consistent. Consistency of
axioms usually is taken to mean that at most one of any pair of statement- and-contradictory-
statement can be deduced from a consistent set of axioms. Thus
we say a system of axioms is inconsistent if it is possible to derive or prove both a
statement and its contradiction in ways labeled valid by the system. The circularity
among "valid" "consistent" "contradictory" "proof" and "derivation"
should be obvious here, and our vagueness concerning the notion of mathematical
consistency remains unclarified. (2) Scientific systems or theories are not considered
valid if it is possible to account for both the occurrence of a fact and the
non-occurrence of a fact under the same conditions in theory. Thus we say a
theory is "refuted by the facts" in case the theory predicts or explains the opposite
of what is observed, and we do not seriously consider theories which are shown
to be compatible with any eventuality.
Whatever this "consistency" is, it certainly includes the notion that statements
p and not-p are not both simultaneously admissible. Perhaps it would
be the very definition of madness to question the unquestioned assumption that
no theoretical construct or axiornatic system can be "correct" unless it is at least
consistent. Yet, without a rational defense of the consistency criterion for acceptability,
we cannot claim that our theories are rational. To my knowledge
there is no clear formulation of the consistency criterion and there is no rational
defense of the criterion which does not assume the criterion to begin with. Perhaps
the criterion is too narrow, so that we exclude valuable theories. It appears
that metaphysical inquiry is needed here.
An important by-product of section four is the observation that science and
mathematics fit together in much the same way as hand and glove --mathematics
provides a formal deductive structure which science fills with facts. This integration
between science and mathematics exists in spite of their outward difference
in appearance. Mathematics is a subject which is not concerned with experience
and which cannot be studied bv means of pointer readings; science is concerned
entirely with pointer readings and constructs which classify them.
By making a study of two disciplines which are obviously connected in actual
practice, we have explored how it is that they are integrated in their theoretical
foundations. In a similar manner it is to be hoped that other disciplines which
are inter-connected in actual practice can be integrated through theoretical study.
[end page 236 / start page 237]
Discovering the integration of disciplines which are clearly related may help us
learn how to integrate those disciplines which are less clearly related. The integration
of science and axiology will require vast effort, and could be helped along
the way by smaller-scale integrations within each general area.
Thus far in this section, we have clarified and elaborated the issues raised
in earlier sections concerning the relationship between science and metaphysics.
The following problems have been proposed as examples of how metaphysical
inquiry can contribute directly to the advance of science, and is necessary for the
theoretical foundation of science: (1) What is the logic of hypothesis networks and
their interaction with experiments? (2) What is the meaning of "consistency"
and is consistency appropriate as a necessary condition of mathematical and scientific
acceptability?
In the eventual integration of the scientific and axiological areas, both of
these problems will have to be expanded: (1) what must be the character of universal
network logics applicable to all the disciplines? How can we construct
universal network logics consistent with the network logics of all the various
disciplines and broad enough to "include" them all? (2) What will an expanded
notion of "consistency" look like? How can we obtain a generalized notion of
consistency which is consistent with and includes all the notions of consistency
in mathematics, science, ethics, aesthetics, etc.? (3) In addition to these two
problems, we must face the determinism-indeterminism issue and resolve it in a
way satisfactory to all the disciplines. Thus, science assumes by its very methods
the universal applicability of cause-effect (the Uncertainty Principle says only
that we cannot measure the cause-effect relationship with complete accuracy -- this
strengthens the demand for metaphysical explanation), while axiology and
especially moral theory assume the freedom of man's action from total external
constralnt.
No doubt, other problems exist in any attempt at theoretical integration of
the disciplines. Certainly the above three problems will be involved in the integration
of science and axiology. By way of concluding remarks, I shall offer the
following four points:
(1) Whether or not scientists realize the inter-relationship between science
and metaphysics, the two areas of inquiry are closely connected. Science can
make progress without paying attention to metaphysics, but does so at the risk
of building on hollow foundations which someday might crumble under the weight
of the scientific edifice. Furthermore, the technological usefulness and practical
fruitfulness of science may continue to provide civilization with increasingly better
means of living, but science without metaphysics will suffer from shallowness of
understanding and appreciation of the universe.
(2) Metaphysical inquiry provides a rich source of speculation concerning the
nature of Reality, and such speculation may lead to insight or beliefs which will
provide new scientific theories. In science it is not particularly important where
a theory comes from -- the important thing is whether a theory stands up to test.
Whether or not well-corroborated scientific theories correspond to Reality, they
do provide technological advance, and metaphysics can have no cause for complaint
if science uses metaphysical speculation to generate scientific theories.
[end page 237 / start page 238]
Elevating scientific theory to the status of metaphysical description of Reality is
beyond the capacity of scientific method, but metaphysical speculation may produce
insight leading to valuable scientific theory. Thus, 200 years ago the theory
that matter is composed of atoms, or the theory that matter is some kind of dense
energy, would have been called metaphysical.
The simple mechanical models we use to explain to children the complex
scientific theories about the structure of matter or the nature of the space-time
warp are illustrative of the aid to understanding and further inquiry which metaphysics
can supply. Certainly these models do not in any sense represent Reality
nor are they scientifically accurate, but they do supply a temporary means of
understanding the first approximation to scientific truth while continuing the
process of gaining a better refinement. The use of temporary shelters along the
wilderness trail to the mansion on top of the hill characterizes both childhood
learning and scientific progress.
(3) If a fisherman uses a net with a mesh-width of three inches, he may con-clude
that there are no minnows in the sea./6 Even if his net cannot be refined to
a smaller mesh-width due to the nature of the building materials, he will profit
by making the observation that indeed his net is limited by its very nature to
catching fish longer than three inches. For with this knowledge he will not claim
there are no small fish. Rather, he will recognize the limitations of his net and
seek other ways of accounting for the mysterious "fact" that three-inch fish come
into existence three inches long, without having grown through smaller sizes first.
His "meta-net" theories may even enable him to learn to build fish-hatcheries and
thereby avoid the capriciousness of nature. Thus science, by learning its limitations,
may learn to make use of other means of obtaining progress in areas of
interest to science.
However, if the net has no inherent limitations on the size of the mesh-width,
a knowledge of the fact that the mesh-width is three inches and that this limits
the kind of catch the fisherman can make will encourage the fisherman to refine
his net. By studying the possible limitations on human knowledge, the processes
used by the mind in organizing experience, and the nature of scientific method in
comparison with the methods of other disciplines and the reality revealed by other
disciplines, the scientist may learn how to improve his reasoning processes and his
technology of discovery.
(4) The Reality which is "out there" is the ultimate source of all that we
observe and all that we experience. In studying that Reality, by whatever
means, we are studying the ultimate subject matter which science aims to produce.
Such study is simultaneously' the study of what is possible, what is necessary, and
what range of choice is available to man. Hence, metaphysical inquiry is the
ultimate goal and subject matter of both scientific studies and studies of value
(such as ethics and aesthetics ). Therefore, metaphysical inquiry provides a
unifying bond between science and axiology. Knowledge that this bond exists
means that the integration of the disciplines is possible, and study of the bond
may help us understand and teach the disciplines in an integrated manner, thereby
providing a unified world view.
---------
6. The metaphor of the fish net was suggested by Arthur S. Eddington, The Philosophy of Physical Science, Chapter 2.
[end of article]
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