1. Empirical meanings require ordinary language and mathematics for their expression.
2. Science is concerned with matters of fact.3. Knowledge in science is of the actual world.4. Scientific knowledge is factual.5. To know a science is to be able to formulate valid
general descriptions of matters of fact.6. The scientific enterprise is aimed at the discovery
of truth.7. Science is characterized by descriptions that are
essentially abstract.8. Physical science provides descriptions of the world
as experienced through the activity of physical measurement.
9. Measurements are capable of yielding universal agreement.
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156 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
10. The ideal of knowledge in physical science is the expression of its propositions in mathematical form.
11. Physical measurement provides the data that are the basis of knowledge in physical science.
156 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
12. The student completely misunderstands science if he thinks that observations somehow speak for themselves.
13. The investigator cannot learn anything by taking measurements at random.
14. In science the observations follow from the gener-alizations; the generalizations do not (as com-monly assumed) follow from the observations.
15. Principles, generalizations, and laws are not di-rectly inferred from the data of observation.
16. Observations do not test the truth or falsity of hy-potheses, but rather their scope and limitations.
17. “Facts” usually refer to particular data of observa-tion.
18. “Hypotheses” are generalizations in need of test-ing by further observations.
19. “Principles” are fundamental ways of representing physical processes.
20. “Generalizations” are hypotheses whose scope of application has been well tested.
21. “Laws” usually refer to generalizations that have been firmly established and precisely formulated.
22. “Theories” are conceptual structures that provide explanations for laws.
23. A “model” is any kind of pattern or structure that provides a satisfactory basis for theory construc-tion.
24. A “map” is a formal representation of an area.25. A theory or model provides an abstract pattern.26. Any particular model or theory is not to be ac-
counted true or false in the guidance of observa-tion and experimentation.
27. The ultimate goal of science is theoretical under-standing.
28. There is no routine or foolproof system of hypothe-sis formation.
29. In empirical science the deductions must finally be checked against sense observations.
PHYSICAL SCIENCE 157
30. All empirical propositions are provisional, tempo-rary holding good only within the limits established by prior tests and always subject to revision in the light of new evidence.
31. All physical sciences deal with patterns of matter (or energy) in motion under the influence of forces of interaction.
32. Scientific inquiry is aimed at bringing some order and intelligibility out of what appears to be a mis-cellaneous and unrelated profusion of phenomena.
33. A law reveals a pattern common to many particu-lar happenings.
34. Theories bring many apparently diverse events within a single conceptual scheme.
35. The search for principles, generalizations, laws, and theories is aimed at discovering similarities among different things and constancies among changing things.
36. The essence of physical science is the discovery and formulation of general patterns among quanti-ties derived from the process of physical measure-ment.
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158 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
The essence of symbolisms is formal expressive pat-terns created for purposes of communication. Empirical meanings require ordinary language and mathematics for their expression. However, the formalisms used do not constitute empirical knowledge itself. Science, or systematic empirical inquiry, is concerned with matters of fact, not with symbolic conventions. Knowledge in language is of formal properties and relations within a symbolic design. Knowledge in science is of the actual world. It is of the world as it appears to be in sense ex-perience and as it is inferred to be on the basis of this experience. In short, while language knowledge is purely formal, scientific knowledge is factual.
CONTRASTING SYMBOLICS AND EMPIRICS
The contrast between symbolics and empirics can further be stated as that between symbolic prescription and factual description. To know a language is to be skillful in the use of the rules prescribed for discourse within the particular language community. To know a science is to be able to formulate valid general descrip-tions of matters of fact.
Because language is prescriptive, knowledge of it does not yield truth, but only the power of intelligible expression. On the other hand, the scientific enterprise is aimed at the discovery of truth. Conventions are never true or false; they are only more or less conve-nient or appropriate to specified purposes. The forms of descriptions in science are likewise more or less conve-nient, but what is asserted is either true or false (or probable).
SCIENCE IS CHARACTERIZED BY DESCRIPTIONS
Science is characterized by descriptions that are essentially abstract. It does not deal with the actual world in the fullness of its qualitative meanings. Rather, certain carefully defined aspects of the experienced world are selected as the basis for scientific descrip-
PHYSICAL SCIENCE 159
tions. Different sciences deal with different aspects of the experienced world, using different schemes of ab-straction. In the present chapter we shall deal with those aspects of the world that are the subject matter of physical science.
PHYSICAL SCIENCE PROVIDES DESCRIPTIONS OF THE WORLD
Physical science provides descriptions of the world as experienced through the activity of physical mea-surement. By “physical measurement” is meant the quantitative assessment of material objects by refer-ence to agreed upon standards of mass, length, and time. The world described in physical science is the world revealed through measurements made by stan-dard balances, rulers, and clocks, or equivalent instru-ments. Anything whatever is an appropriate object of physical description, including stars, rocks, liquids, gases, plants, animals, and people. The only require-ment is that the things described be accessible to phys-ical measurement.
Because of the severe limitations imposed by the requirements of physical measurement, it is clear that physical science provides only a limited description of the experienced world. It affords only knowledge of cer-tain selected aspects of things. It does not express the whole truth about the world. Physical science deals with the world as apprehended or inferred from certain nar-rowly specified classes of sense experience, namely, the reading of scales on instruments that directly or in-directly measure mass, length, and time.
THE PROCESS OF PHYSICAL MEASUREMENT
There are two reasons for using the process of physical measurement. The first is that such measure-ments are capable of yielding universal agreement. The reading of measuring instruments is in principle the most simple and certain of operations. It requires only the ability to perceive the position of a pointer on a scale. Being exactly defined and demanding only the
160 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
most elemental sensory capacities, physical measure-ments yield data on which agreement by all observers is possible, subject only to errors of measurement that can be progressively reduced by refinement of instru-ments and repeated observations.
The second value of physical measurement is the opportunity it affords for mathematical formulation. Physical science is completely quantitative. it takes no account of qualities of things that are not expressible in numbers. For example, colors as directly perceived qualities have no place in physical science. Colors enter only in the form of measurable wavelengths of light, that are expressible numerically. This quantification of the data of physical observation makes available to the scientist the rich resources of the field of mathematics, facilitating the process of inference and providing pow-erful and precise formulations of scientific ideas. The ideal of knowledge in physical science is the expression of its propositions in mathematical form.
GENERALIZATIONS, LAWS, AND THEORIES
Physical measurement provides the data that are the basis of knowledge in physical science. The mea-surements are in themselves of no scientific value. They yield scientific knowledge only when they are used to establish generalizations, laws, and theories. The goal of scientific investigation is not the accumula-tion of particular observations, but the formulation and testing of general laws. To understand the methods of scientific inquiry, it is necessary to be clear as to how generalizations are obtained from the data of observa-tion. The process is essentially indirect. Generalizations are not directly derived from the particulars of observa-tion by a chain of logical inference. It is truer to say that generalization comes first, as an imaginative construc-tion, and that the data of observation are then used to validate the generalization. In teaching science the im-portance of this priority can hardly be exaggerated. The student completely misunderstands science if he thinks
PHYSICAL SCIENCE 161
that observations somehow speak for themselves, yielding laws and theories by some straightforward process of reasoning from the data of sense to the gen-eral propositions of science.
The priority of generalization to observation is even more thoroughgoing than just indicated, for obser-vation itself is guided by reference to what is to be es-tablished. The investigator cannot learn anything by taking measurements at random. He must carefully ar-range his observations and experiments with the aim of verifying some generalization he already has in mind. Therefore, in science the observations follow from the generalizations; the generalizations do not (as com-monly assumed) follow from the observations.
Generalizations introduced in scientific investiga-tion are called “hypotheses,” From the hypothesis, a plan of experiment and observation is laid out. If the hypothesis is true, it is argued, then such and such ob-servations could be made and such and such measures obtained. When the indicated measurements are taken, the hypothesis is either confirmed or not confirmed. If the observations do not check with what is expected from the hypothesis, the hypothesis is not necessarily rejected. What may be required is a restriction of the conditions within which the hypothesis holds.
For example, from the hypothesis that the formula relating distances to time for freely falling bodies is s = 1/2gt2 one can predict a series of measurable length and time correspondences that can be checked against actual observation. If observations do not agree with predictions, the hypothesis is not at once rejected. It may be argued instead that the formula holds true, but only on the condition that there is no air friction. The validity of this condition may be checked by further ex-periments using evacuated vessels.
ILLUSTRATION OF METHOD IN PHYSICAL SCIENCE
162 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
Stephen Toulmin in The Philosophy of Science: An Introduction1 provides an illuminating illustration of method in physical science by a discussion of optical phenomena. Geometrical optics is based on the princi-ple of the rectilinear propagation of light. What is the logical status of this principle, that light travels in straight lines? The principle is not the consequence of any direct observation. Rather, it is a deliberately cho-sen way of representing optical phenomena, and it is justified by the fact that expected results, such as the casting of shadows of specified positions and dimen-sions, are actually observed. When in other experi-ments the principle appears not to hold, as, for exam-ple, in the passage of light from one medium to another of different density, the principle is not simply rejected. Instead, it is accepted as applying under the limiting conditions of homogeneity in the medium of transmis-sion, and for this refracted light a new principle may be adopted, taking account of the change in direction that occurs on passage to a new medium (quantitatively ex-pressed in Snell’s law).
The phenomenon of refraction requires for its ex-planation new principles, from physical optics, in which light is regarded as a series of wave fronts. This is an-other way of representing light, justified by agreements of predictions with observations in experiments with re-fraction as well as other phenomena, such as diffraction and interference.
The wave principle also proves to have limitations. The wave representation turns out to be incapable of explaining certain other phenomena, notably those of photoelectricity. Here a new representation is intro-duced to the effect that light is made up of photons, or discrete packages of energy. The photon principle per-mits further quantitative predictions that can be tested by a variety of experiments and observations.
1 Harper & Row, Publishers, Incorporated, New York, 1960.
PHYSICAL SCIENCE 163
ESSENTIAL POINTS TO REMEMBER
The essential points to be established are these: first, that principles, generalizations, and laws are not directly inferred from the data of observation, and sec-ond, that observations do not test the truth or falsity of hypotheses, but rather their scope and limitations.
FACTS, HYPOTHESES, PRINCIPLES,GENERALIZATIONS, LAWS, AND THEORIES
While no sharp lines can be drawn between facts, hypotheses, principles, generalizations, laws, and theo-ries, the distinctions implied by these different terms are useful. “Facts” usually refer to particular data of ob-servation. As we have seen, the determination of which facts are relevant and the methods of formulating ob-servations and experiments depend on the prior con-struction of hypotheses. “Hypotheses” are generaliza-tions in need of testing by further observations. “Princi-ples” are fundamental ways of representing physical processes, suggesting further consequences to be tested by experiments and observations. “Generaliza-tions” are hypotheses whose scope of application has been well tested. “Laws” usually refer to generaliza-tions that have been firmly established and precisely formulated. “Theories” are conceptual structures that provide explanations for laws.
AN EXAMPLE
For example, the study of the behavior of gases yields certain observable facts about pressure, volume, and temperature. Experiments can be performed to test the hypothesis that under constant temperature, when the pressure of a given mass of gas is increased, its vol-ume will decrease. This hypothesis, when confirmed by experiment, becomes a valid generalization. When quantitatively expressed by the mathematical relation PV = constant, it qualifies as a law (Boyle’s law). The principle implicit in this investigation is that gases may be treated as homogeneous compressible substances
164 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
with such measurable properties as pressure, volume, and temperature (each specified by experimental oper-ations). The explanation for Boyle’s law (and others, in-cluding Gay-Lussac’s law and Charles’ law) is provided by a theory (the kinetic theory of gases), according to which a gas is regarded as a collection of perfectly elas-tic molecules in random motion.
THE USE OF MODELS IN FORMULATING
THEORIES IN SCIENCE
In the formulation of theories in science, use is made of models. A “Model” is any kind of pattern or structure that provides a satisfactory basis for theory construction. For example, the kinetic theory of gases makes use of the model of mechanical interaction of colliding hard bodies, even though gas molecules them-selves are not regarded as actually being such entities. The model is useful because when gas molecules are treated as if they were colliding elastic bodies, the re-sulting predictions are largely verified by experiments. Similarly, the Bohr model of the atom, in which the electrons are represented as miniature planets revolv-ing in elliptical orbits around a nuclear sun, is not re-garded as literally true, but only as a useful representa-tion for atomic theory, giving a basis for explaining (among other things) the observed frequencies of light revealed in spectrum analysis.
Not all models are mechanical or pictorial, as in the two cases cited above. More common are mathe-matical models—formal symbolic patterns that fit the data of observation reasonably well. For example, a set of partial differential equations provides the model in the Schrodinger theory of the atom, producing predic-tions as good as or better than those of the Bohr model, and with more predictive power, flexibility, and ele-gance.
MODELS AND THEORIES CONSTRUCTED
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Models and the theories constructed from them may perhaps best be understood after the analogy of maps. A “map” is a formal representation of an area, chosen for the purpose of directing travel in that region. Its usefulness derives from the fact that the relation-ships among the elements on the map are congruent with the relationships between places and things in the area mapped. A theory or model (whether visual or mathematical) provides an abstract pattern whose structure in relevant respects is congruent with the structure of the physical world, as demonstrated by the agreement between observations and predictions made from the theory or model.
MODELS AND THEORIES
It should be added that, as in the case of princi-ples, generalizations, and laws, any particular model or theory is not so much to be accounted true or false as more or less successful in the guidance of observation and experimentation. Models and theories are mainly judged as to scope of application and degree of rele-vance to the physical systems studied.
THE ULTIMATE GOAL OF SCIENCE ISTHEORETICAL UNDERSTANDING
We return again to the point that the ultimate goal of science is theoretical understanding. Individual facts are not in themselves important scientifically. Individual facts are significant only as they contribute to general-izations, laws, and finally to theories that explain all the lower levels in the hierarchy of scientific propositions. It is in this theoretical manner that physical science is concerned with descriptions of the metrical features of material things. The descriptions sought are not of par-ticular things, but of regular patterns of change in the measurable aspects of material bodies.
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THE CREATIVE IMAGINATION ACTIVELY PROJECTS POSSIBILITIES NO FOOLPROOF SYSTEM OF HYPOTHESIS
FORMATION
In the above discussion of scientific methods the primacy of the general and theoretical has been stressed, but no indication has really been given as to the basis for selecting the hypotheses, principles, and models to be tested experimentally. For the most part the choice is made by noting similarities between new phenomena and more familiar ones and adapting to the new situation conceptual schemes that have previously proved successful. There is no routine or foolproof sys-tem for hypothesis formation. The construction of fruit-ful conceptual patterns to be tested by observation is essentially a work of the creative imagination. The cre-ative imagination actively projects possibilities and re-flectively sifts them by well-informed thought-experi-ments before undertaking any actual physical tests.
METHODS OF THEORETICAL SCIENCE
The methods of theoretical science are remarkably similar to those of mathematics in that imaginative con-struction of conceptual schemes with deductive elabo-ration occurs in both fields. The one decisive difference is that in empirical science the deductions must finally be checked against sense observations. In mathematics the only requirement is internal consistency within any given theory. In empirical science the chain of proposi-tions must also be consistent with the results of actual physical measurements.
Because future observations might at any time fail to agree with predictions made on the basis of earlier verified hypotheses, no generalization, law, or theory in science may be regarded as finally and fully proved, no matter how accurate previous predictions have been. All empirical propositions are provisional, temporary holding good only within the limits established by prior tests and always subject to revision in the light of new evidence.
PHYSICAL SCIENCE 167
A great amount of physical scienceis based on measurement.
Precise calculation depends onprecise data collection. People
remember the stories about theastronauts skipping off of the
atmosphere if their angle of entry was just a few degrees off.
As a general rule, precessionrequires patience.
How accurate can a lesson be if a teacher cannot get a
child to sit still long enough to do an experiment?
168 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
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PHYSICAL SCIENCE 169
Much of the above synopsis of methods in scien-tific investigation applies to all branches of science and not only to physical science. The high degree of preci-sion and quantification possible in the physical sciences makes them the ideal toward which the other sciences aim. Nevertheless, there are representative ideas that belong specifically to physical science. These will be considered in the remainder of this chapter.
REPRESENTATIVE IDEAS BELONGING TO PHYSICAL SCIENCE
The basic concepts of physical science derive from the definition of physical measurement by means of rulers, clocks, and balances, or their equivalents. All physical sciences deal with patterns of matter (or en-ergy) in motion under the influence of forces of interac-tion. Rulers measure space intervals and therefore ma-terial configurations. Clocks measure time intervals, which, in conjunction with spatial measurements, yield information about motion. Balances measure the forces of interaction that effect changes in motion.
ParticlesThe fundamental model for analyzing any event in
the physical world is that of particles moving in fields of force, the fields being themselves determined by the character and configuration of the interacting particles. The material world is built up in a hierarchy of succes-sively complex configurations, beginning with certain elementary particles, including electrons, neutrons, and protons, and more than two dozen other particles that play important roles in establishing stable patterns of interaction. The strongest interactions occur within the most intimate material configurations, the atomic nu-clei. The weakest known interactions between elemen-tary particles are those of gravity. Intermediate in strength are the interactions in electromagnetic fields and in the process of nuclear decay.
Atoms
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The elementary particles are organized into more or less stable energy distributions called “atoms,” each consisting of a nucleus of given mass and charge sur-rounded by one or more layers of orbiting electrons. The structural patterns of the various kinds of atoms are the basis for understanding the physical and chemi-cal properties of all material bodies whatsoever. Each distinct atomic pattern belongs to one element (e.g., hydrogen, sodium, carbon), and these elements may be arranged in cycles according to the Periodic Table of the Elements, certain physical and chemical similarities among elements belonging to the same cycle being ex-plainable by their corresponding patterns of orbital electrons.
MoleculesAtoms interact to form still more complex struc-
tures called “molecules,” the combination possibilities of that depend upon the patterns of interaction be-tween the electron systems of the constituent ele-ments. The study of these structures and processes be-longs to the field of chemistry.
Solid State PhysicsThe study of the modes of atomic and molecular
patterning occurring in crystals and metals is usually designated as the field of solid state physics. More ran-dom types of particle distributions are studied in the theory of liquid flow (hydrodynamics) and in the theory of gases. The statistical analysis of random molecular motions is the key to all the phenomena connected with heat and forms the substance of thermodynamics.
Electromagnetic TheoryElectromagnetic Theory deals with particles bear-
ing electric charges and with the fields of force result-ing from these charges and their movements. Within this theory are comprehended not only the phenomena of electricity and magnetism in their ordinary sense,
PHYSICAL SCIENCE 171
but also those of light and of radio waves, infrared rays,
X rays, gamma rays, and cosmic rays. In modern physics it has further been shown the field theory of these various forms of electromagnetic radiation must be complemented by a particle theory, since the energy in such fields is not continuous, but “quantized,” i.e., comes in discrete units or packets (quanta). Specifi-cally, the particle-field model is appropriate not only to the domains of atomic and molecular interactions, but also to the study of energy distributions themselves. This is to be expected in view of the know equivalence of mass and energy.
Celestial MechanicsGravitational interactions that become important
with large aggregations of matter, are most thoroughly analyzed in the study of celestial mechanics. In this study planets, stars, and satellites at great distances from one another can be treated as interacting particles in gravitational fields of force, using models similar to those applicable to the motion of charged particles in electromagnetic fields.
The same fundamental ideas apply in every other branch of physical science. For example, Geology is concerned with the structures and transformations of the material aggregates forming the crust of the earth. This study requires the use of the same conceptual tools as in physics and chemistry for the analysis of the hierarchies of material configurations, movements, and forces that effect changes.
THE SEARCH FOR PRINCIPLES, GENERALIZATIONS,LAWS, AND THEORIES
Order and IntelligibilityIn the most general terms, scientific inquiry is
aimed at bringing some order and intelligibility out of what appears to be a miscellaneous and unrelated pro-
172 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
fusion of phenomena. A principle is a way of ordering sense perceptions according to some rational scheme. A law reveals a pattern common to many particular happenings. Theories bring many apparently diverse events within a single conceptual scheme. The search for principles, generalizations, laws, and theories is aimed at discovering similarities among different things and constancies among changing things. For example, the general gas equation, PV = RT, shows that when a given body of gas undergoes changes due to heating or cooling, expansion or contraction, increase or decrease of pressure, something remains constant, namely, the quantity PV/T.
Laws of MotionEvery law expresses relationships that remain in-
variant despite changes in variable factors. Laws of mo-tion are constant patterns that changing things exhibit. Therefore, while the planets move around the sun, con-stantly changing their positions and velocities, Kepler’s laws of planetary motion express the fact that certain relations among these changing factors remain un-changed. The theory of relativity, beginning with the premise that physical measurements are definable only in relation to arbitrarily designated frames of reference, culminates in the formulation of laws that are invariant under changes in frames of reference and in the discov-ery of an important metric invariant, specifically, the speed of light in a vacuum.
Constancy Amid ChangeThe idea of constancy amid change is particularly
well illustrated in the various laws (or principles) of con-servation in physical science. For example, according to the law of conservation of energy, in any closed or iso-lated system, while energy may change from one form to another (e.g., from energy of position to kinetic en-ergy to heat energy), the total amount of energy in the system remains unchanged. Similarly, according to the
PHYSICAL SCIENCE 173
law of conservation of mass, when a given body of ma-terial undergoes physical and chemical transformations, the total mass of the material remains unchanged. While it is now known that this principle does not hold except for closed systems and with the understanding that mass and energy are interchangeable, it is still of great value in scientific investigation, as in the study of chemical reactions. These and other conservation prin-ciples, including the conservation of momentum and the conservation of parity—a discovery in nuclear physics—are powerful concepts for exploring unchang-ing properties and relations of changing things, specifi-cally contributing to the rational ordering of physical phenomena.
Much of physical science dealswith how things work and why
they work that way.Teachers want students
to gain understanding of theworld around them.
Scientific inquiry is aimed atbringing order and intelligibility
to the light of the student.How important is it for
teachers to follow through inteaching the student how to use
174 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
that knowledge?
PHYSICAL SCIENCE 175
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176 PART TWO: FUNDAMENTAL PATTERNS OF MEANING
THE ESSENCE OF PHYSICAL SCIENCE
IS DISCOVERY AND FORMULATION
In summary, the essence of physical science is the discovery and formulation of general patterns among quantities derived from the process of physical mea-surement. These patterns express constancies that hold, within specified limits and under stated condi-tions, throughout the changes occurring in the interac-tion of material entities within given fields of force.
WAYS OF KNOWING
1. Why are symbolisms important for purposes of communications?
2. Why is systematic empirical inquiry concerned with matter of fact and not with symbolic conven-tions?
3. Why is knowledge in science concerned with the real world?
4. Why is language knowledge considered purely formal?
5. Why is scientific knowledge considered purely factual?
6. What does it mean to know a science?7. Why is language considered prescriptive?8. Why is science aimed at discovering the truth?9. Why is science characterized by descriptions
that are essentially abstract?10. Why is measurement critically important to
physical science?11. What are some severe limitations imposed on
physical science because of physical measure-ment?
12. What are two reasons for applying the process of physical measurement on physical science?
13. When do physical measurements have scientific value?
14. How does one understand the methods of scien-tific investigation?
PHYSICAL SCIENCE 177
15. Why is it necessary to be clear as to how gener-alizations are obtained from the data of observa-tion?
16. Why can’t the investigator learn by taking mea-surements at random?
17. What are generalizations called that are intro-duced in scientific investigation?
18. Can you provide an imaginative illustration of method in physical science?
19. What essential points in physical science should be established relative to principles, generaliza-tions, and laws?
20. Why is the use of models helpful in formulating theories in science?
21. What is the ultimate goal of science?22. Are there any routines or foolproof systems of
hypothesis formulation?23. How should the creative imagination of a person
be implemented in hypothesis formulation?24. What are the methods of theoretical science?25. Why is it said that all empirical propositions are
provisional or temporary?26. From what devices do basic concepts of physi-
cal science derive their physical measurements?27. What is the fundamental model for analyzing
any event in he physical world?28. In the most general terms, what is the purpose
of scientific inquiry?29. What is the essence of physical Science?
