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PHILOSOPHY OF SCIENCE
The Link Between Science and Philosophy
By Philipp Frank
Dover Publications, Inc.Copyright © 2004 Dover Publications, Inc.
All rights reserved.
The Chain That Links Science With Philosophy
1. Facts and Concepts
In his poem "Sonnet to Science," Edgar Allan Poe indicts science as follows:
Science! true daughter of Old Time thou art
Who alterest all things with thy peering eyes.
Why preyest thou thus upon the poet's heart,
Vulture, whose wings are dull realities?
Hast thou not dragged Diana from her car?
And driven Hamadryad from her wood?
The modern scientist will hardly agree that his science consists of "dull realities." The more we study science, the more we shall notice that science is neither "dull," nor that it speaks of "realities." The "car of Diana" is much nearer to the "dull realities" of our everyday life than the symbols by which modern science describes the orbits of the celestial bodies. "Goddesses" and "nymphs" look much more like people we meet in our everyday life than the electromagnetic field, the energy or the entropy that populates the "unseen universe," which, according to modern science, accounts for the "dull realities" of our direct sense observation.
When we speak of science, we always speak on two levels of discourse or abstraction. The first of these is the level of everyday common-sense experience; e.g., we observe some dark spot moving with respect to some other dark spots. This is the level of direct observation; laboratory reports deal with these simple facts of experience. One could analyze these simple experiences from the psychological point of view, but we shall not do that here; we shall take it for granted that we all share these experiences. By this, we do not mean to imply that these simple experiences cannot be discussed in a more profound way, but simply that this discussion does not belong to the philosophy of science. The second level to which we have referred is that of the general principles of science. This is completely different from the level of common-sense experience. The latter can be shared by all; the former employs language very far from that of everyday experience. Science consists essentially of these general principles. A collection of mere statements about dancing spots is not science. The central problem in the philosophy of science is how we get from common-sense statements to general scientific principles. As we have said, these common-sense experiences and statements are understood and accepted by all. This basis of acceptance is well characterised in the lines of the great American poet, Walt Whitman:
Logic and sermons never convince,
The damp of the night drives deeper into my soul,
Only what proves itself to every man and woman is so,
Only what nobody denies is so.
Statements of this type are: "In this room stands a round table. Now this table is removed from this room into the adjacent room." Or: "On this scale the pointer coincides with a mark between two and three; now the position of the pointer changes and it covers a mark between three and four." A general agreement is certainly possible about statements of this type. We do not claim that such statements describe a "higher reality" than other statements; nor do we pretend that the world described is the "real" world. We make such statements the basis of all science only because there can be achieved a general agreement among men of average education whether, in a specific case, such statements are "true" or not. We may refer to discourse consisting of such statements as common- sense discourse, or everyday discourse. It "is so," to Walt Whitman, because it "proves itself to every man and woman."
But the situation is completely different if we consider general statements formulated in abstract terms like the "Law of Inertia," or the "Conservation of Energy." Whether we call them principles or premises or hypotheses or generalizations, one thing is certain: We cannot achieve about them a general understanding of the kind we can achieve about common-sense statements. Therefore, naturally, the question arises: Why do we accept some general scientific statements and not others? What are the causes of our acceptance of these general statements? This is partly a psychological and sociological problem. The general statements of physical science are not simply empirical facts. The fact is that people advance and accept these general principles: This fact, however, belongs not to physics but to, say, psychology or anthropology. Thus we see that even the philosophy of physical science is not exhausted by physics itself. In physics, we learn some of the reasons why these general principles are accepted, but by no means all of them. The philosophy of science is part of the science of man, and indeed, we shall not understand it unless we know something of the other sciences of man, such as psychology, sociology, etc. All the reasons for the acceptance of the general principles of science belong to the philosophy of science. What is actually the relationship between common-sense experience and these general principles? Is mere common-sense experience sufficient? Are the general statements of science uniquely determined, or can the same set of common-sense experiences give rise to different general statements? If the latter, how can we choose one of these general statements rather than another? How do we get from the one—common-sense experience—to the other—the general statements of science? This is the central problem of the philosophy of science.
We might describe here, in a preliminary and perfunctory way, what the relationship between science and philosophy is. If we speak in the ordinary way of a chain that connects common-sense experience with the general statements of science, at the end of this chain, as the statements become more and more general, we may place philosophy. We shall see that the more one goes into generalities, the less uniquely are the latter determined by direct observations, and the less certain they are. For the moment we shall not go further into the distinction between science and philosophy. We shall discuss this later.
2. Patterns of Description
By collecting and recording a large stock of common-sense experience in a certain field, we may produce long lists of pointer readings or descriptions of dancing colored spots. But by mere recording, accurate and comprehensive as it may be, we do not obtain the slightest hint as to how to formulate a theory or hypothesis from which we may derive in a practical way the results of our recording. If we simply set as the problem the finding of an hypothesis which would be in fair agreement with our records, it does not seem possible for us to obtain an unambiguous result. As early as 1891, C. S. Peirce wrote:
If hypotheses are to be tried haphazard, or simply because they will suit certain phenomena, it will occupy the mathematical physicists of the world say half a century on the average to bring each theory to the test, and since the number of possible theories may go up into the trillion, only one of which can be true, we have little prospect of making further solid additions to the subject in our time.
If we make an attempt to set up a theory or hypothesis on the basis of recorded observations, we soon notice that without any theory we do not even know what we should observe. Chance observations usually do not lend themselves to any generalization. It is perhaps instructive at this point to peruse a passage from Auguste Comte's Course of Positive Philosophy. Comte has been regarded as the father of a school of thought known as "Positivism." According to an opinion frequently held by philosophers, he and his school have extolled the value of observations and minimized, or even rejected, the formation of theories by creative imagination. However, he writes:
If, on the one hand, every positive theory must necessarily be based on observations, it is equally sensible, on the other hand, that in order to carry out observations our minds need some theory. If, in contemplating the phenomena, we did not attach them to some principles, it would not be possible to combine these isolated observations and to draw from them any conclusions. Moreover, we would not even be able to fix them in our minds. Ordinarily these facts would remain unnoticed beneath our eyes.
Hence, the human mind is, from its origin, squeezed between the necessity to form real theories and the equally urgent necessity to create some theory in order to carry out sensible observations. Our minds would find themselves locked within a vicious circle, if there were not, fortunately, a natural way out through the spontaneous development of theological concepts.
The theological concepts are very near to common-sense experience. They interpret the creation of the world by the gods as analogous to the making of a watch by a watchmaker. We shall see later that this kind of analogy has been the basis of all metaphysical interpretations of science. At this point, we must be distinctly aware of the fact that a mere recording of observations provides us with nothing but "dancing spots," and that "science" does not begin unless we proceed from these common-sense experiences to simple patterns of description, which we call theories. The relationship between direct observations and the concepts that we use in "scientific description" are the main topics with which any philosophy of science is concerned.
Let us take a relatively simple example, where this relationship is rather direct. Let us imagine that we launch a body into the air—say, a remnant of cigarette paper—what does it do? If we do this many times—a hundred, a thousand, hundreds of thousands of times—we shall find simply that the motion is different every time. The accumulation of all these observations is obviously no science. And this is not the way that the physicist works, unless it is in a field that is very little advanced, about which he knows almost nothing. If we study physics, we learn some rules—for uniform motion, for accelerated motion, for combinations of uniform and accelerated motions. These are schemes of description. We must invent them before we can check them, but how are we to invent these schemes? The human imagination enters here. We try to imagine some simple scheme. But what is simple? We must try out all such different imagined schemes to see if the actual motion of our falling paper is approximately described by any one of them. In textbooks of physics one finds the statement that these schemes are "idealized motion." This is a very misleading expression; it refers to a metaphysical doctrine which maintains that for every empirical object there is a corresponding idea of it. The result of "idealization" is entirely arbitrary. By the word "idealizing" you say nothing except that you compare some empirical object with some "idea" that you have invented. There is the question of the purpose of your making this invention or "idealization": for example, for some problems it would be more useful to idealize the ordinary atmosphere as a very thick medium, for others as empty space.
Now let us return to the question of the falling cigarette paper. In the mechanics of today, we compare every motion with a scheme that is the motion of a mass point in empty space. We consider two types of motion as the components of the motion of a launched body, a uniformly accelerated motion downward and a uniform motion horizontally. The first of these we call gravitational motion and the second inertial motion. From this scheme we can derive many useful things, but not everything. This analysis is approximately correct for thin air but not so much for a medium of high viscosity. We need the invention of another scheme if we want to compute the effect of a dense or viscous medium.
The pattern by which we describe motion in thin air is a motion of constant "acceleration." The concept of acceleration is very remote from the dancing spots of our direct observations. If the position of the moving body is described mathematically by an arbitrary function of time, the acceleration is described by the computation of "second derivatives with respect to time" in the sense of differential calculus. To observe the equivalent of a "second derivative" in the domain of common-sense experience would mean to carry out a very great number of extremely delicate pointer readings; we must not forget that the "second derivative" is defined as the limit of an infinite set of values.
We can, therefore, say that the experimental scientist does not observe at all the quantities that occur in the patterns of scientific description, in the laws of science. Suzanne Langer in her book Philosophy in a New Key, writes:
The men in the laboratory ... cannot be said to observe the actual objects of their curiosity at all.... The sense data on which the propositions of modern science rest are, for the most part, little photographic spots and blurs, or inky curved lines on paper.... What is directly observable is only a sign of the "physical fact"; it requires interpretation to yield scientific propositions.
3. Understanding by Analogy
We shall, for the time being, consider motion only in very thin air. Is the human mind then satisfied if it knows this scheme of constant acceleration? No, it asks why does it accelerate downward and go with uniform motion horizontally? If you want to explain this to a schoolboy (and in a sense we are all schoolboys of the world), you say that it accelerates downward under the influence of the attraction of the earth. But if you think a little, you realize that this is no explanation at all. What is attraction? In medieval times, explanations were always anthropomorphic, and consisted of a comparison with human actions. It was believed that heavy objects wanted to get as close as possible to the center of the earth. The closer they approached, the more jubilant they became and the faster they went. Although more sophisticated today, we still use the concept of attraction. If we record the positions of the falling cigarette paper, we act on the level of everyday experience. But we try to "understand" the general law of its motion by comparing it directly with attraction, which is a psychological phenomenon of our everyday life. We are not satisfied to introduce everyday experience solely by direct observations of the falling body.
It is harder to explain the uniform motion of the body. We say that it is caused by inertia; we all know what this means because we know from everyday experience that we are inert. Inertia means sluggishness, the lack of a desire to move. For example, there must be some external inducement to get up in the morning—some class that must be attended, or the expectation of a good breakfast. The law of inertia seems very plausible to us on the basis of this comparison. We only wonder why it took so many thousands of years for man to discover it. However, this method of explanation by introducing the experience of our own sluggishness is quite arbitrary. Things are not so simple as they seem.
If we are in bed in a train, we cannot determine simply from our own sluggishness whether without effort we will stay in bed or be thrown out. If the train stops or changes its speed, our "sluggishness" does not help us to stay at rest in bed. What really happens is that "without effort" we keep our velocity with respect to some physical masses. In the example of the train this mass is our earth. But from the example of the Foucault pendulum or the deviation of launched projectiles by the rotation of the earth, we can see that the earth is only a substitute for some larger mass with respect to which we keep our velocity; for instance, the mass of our galaxy. And we shall see later that even this is not completely correct. In any case, the analogy of the everyday experience of sluggishness predicts the observable effects of motion only in a very vague way, which is useful only under very special circumstances. What really matters in physical science is the abstract scheme: Every velocity will remain constant with respect to some specific mass which constitutes what we call an inertial system. Comparison with the phenomena of everyday life will not show any inconsistency with this scheme. Sluggishness has only as vague an analogy to inertia as attraction has to gravitation.
If we find a simple scheme for a group of phenomena—e. g., constant acceleration for a body falling in thin air—we are apt to think as follows: "The motion with precisely constant acceleration is an idealization of the actual fall of a body in thin air." The word "idealization" hints that we omit the accidental deviations of the actual motion, and retain only the "essential part of the motion," the uniformly accelerated motion. To the scientist, the term "essential" means "pertinent to reaching the intended goal." As far as our example is concerned, it means "pertinent to the simplest and most practical description of a fall in thin air."
Excerpted from PHILOSOPHY OF SCIENCE by Philipp Frank. Copyright © 2004 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
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Table of Contents
|Introduction. Of What Use Is the Philosophy of Science?||xi|
|1||The Rift Between Science and Philosophy||xi|
|2||The Missing Link Between Science and the Humanities||xii|
|3||Science as the Balance of Mind||xiii|
|4||Is the Scientist a "Learned Ignoramus"?||xv|
|5||Technological and Philosophical Interest in Science||xvi|
|6||Obsolete Philosophies in the Writings of Scientists||xix|
|7||Information or "Understanding"?||xxi|
|8||Footnotes for the Introduction||xxi|
|Chapter 1||The Chain That Links Science With Philosophy||1|
|1||Facts and Concepts||1|
|2||Patterns of Description||4|
|3||Understanding by Analogy||7|
|4||Aristotle's Scheme of Natural Science||9|
|5||From "Confused Aggregates" to "Intelligible Principles"||10|
|6||"Science" and "Philosophy" as Two Ends of One Chain||12|
|7||The "Scientific" and the "Philosophical" Criteria of Truth||15|
|8||The Practical Use of "Philosophic Truth"||17|
|Chapter 2||The Rupture of the Chain||21|
|1||How the Rupture Occurred||21|
|2||Organismic and Mechanistic Philosophy||23|
|3||How Science in the Modern Sense Was Born||25|
|4||Science as a Fragment of Philosophy||28|
|5||How "Science" Can Become "Philosophy"||32|
|6||Speculative Science and Metaphysics||36|
|7||The Belief in Intelligible Principles||38|
|9||Science, Common Sense, and Philosophy||44|
|Chapter 3||Geometry: An Example of a Science||48|
|1||Geometry as the Ideal of Philosophy||48|
|2||"Intelligible Principles" and "Observable Facts" in Geometry||51|
|3||Descartes, Mill, and Kant||54|
|4||"Axioms" and "Theorems"||57|
|5||The Euclidean Axiom of Parallels||60|
|7||"Validity" of Propositions in Geometry||69|
|8||"Formalization" of the Axioms||72|
|9||Formalization of "Congruence"||75|
|10||Operational Definitions in Geometry||79|
|11||The Twentieth-Century Conception of Geometry||82|
|Chapter 4||The Laws of Motion||90|
|1||Before Galileo and Newton||90|
|2||The Ancient Laws of Motion Were "Organismic"||93|
|3||The Universe as an Organism||96|
|4||The Copernican System and the "Organismic" Laws of Motion||100|
|5||Newton's Laws of Motion||104|
|6||The Operational Definition of "Force"||108|
|7||The Operational Definition of "Mass"||111|
|8||Remnants of Organismic Physics in Newtonian Mechanics||116|
|Chapter 5||Motion, Light, and Relativity||122|
|1||Aristotle, St. Augustine, and Einstein||122|
|2||"Relativity" in Newtonian Mechanics||124|
|3||Newton's Relativity and Optical Phenomena||126|
|4||The Electromagnetic World Picture||130|
|5||The Principles of Einstein's Theory||133|
|6||The "Theory of Relativity" Is a Physical Hypothesis||136|
|7||Relativity of Space and Time||140|
|8||The "Disappearance" and the "Creation" of Matter||144|
|Chapter 6||Four-dimensional and Non-Euclidean Geometry||149|
|1||The Limitations of Euclidean Geometry||149|
|2||Relativity of Acceleration and Rotation||151|
|3||Curvature of Space||155|
|4||Is the World "Really Four-Dimensional?"||158|
|Chapter 7||Metaphysical Interpretations of Relativistic Physics||163|
|1||Metaphysical Interpretations of "Inertia,"||163|
|2||The "Indestructibility of Matter" as a Metaphysical Interpretation||169|
|3||Metaphysical "Implications" of the Theory of Relativity||172|
|4||In What Sense Does the Theory of Relativity Refute Materialism?||181|
|5||Is the Theory of Relativity Dogmatic?||186|
|Chapter 8||Motion of Atomic Objects||189|
|1||Newton Was No Newtonian||189|
|2||The "Crucial Experiment" Versus the Corpuscular Theory of Light||193|
|3||A Second "Crucial Experiment,"||197|
|4||The Laws of Motion for Light Quanta||200|
|5||The Laws of Motion for Very Small Material Particles||203|
|Chapter 9||The New Language of the Atomic World||207|
|1||Heisenberg's Uncertainty Relation||207|
|2||Bohr's Principle of Complementarity||212|
|3||"Position and Momentum of a Particle" Has No Operational Meaning||216|
|4||Facts, Words, and Atoms||219|
|5||Phenomena and Interphenomena||223|
|6||The Variety of Formulations in Atomic Physics||228|
|Chapter 10||Metaphysical Interpretations of the Atomic World||232|
|1||The "Spiritual Element" in Atomic Physics||232|
|2||Popular Interpretations of Atomic Physics||238|
|3||Science and Metaphysics in the Principle of "Indeterminacy,"||242|
|4||Physics and "Free Will,"||249|
|Chapter 11||Causal Laws||260|
|1||The Meaning of "Predetermination,"||260|
|2||LaPlace, Newton, and the Omniscient Intelligence||263|
|3||The Mathematical Form of a Causal Law||266|
|4||Relevant and Irrelevant Variables||268|
|5||Causal Laws in Field Theory||271|
|6||"Gaps" in Causal Laws||274|
|Chapter 12||The Principle of Causality||278|
|1||Discussion of How to Formulate the General Principle of Causality||278|
|2||Causality as a Recurrence of Sequences||282|
|3||Causality as the Existence of Laws||286|
|4||Causal Law and Statistical Law||290|
|Chapter 13||The Science of Science||297|
|1||The Place of Induction in Ancient and Modern Science||297|
|2||Induction, General Laws, and Single Facts||301|
|3||Induction by New Concepts||304|
|4||Concepts and Operational Definitions||311|
|5||Induction by Intuition and Induction by Enumeration||316|
|Chapter 14||The Validation of Theories||323|
|1||Induction and Statistical Probability||323|
|2||Statistical and Logical Probability||327|
|3||Which Theory of Probability Is Valid?||336|
|Chapter 15||Theories of High Generality||342|
|1||The Role of Causality in Twentieth-Century Science||342|
|2||The "Scientific" Criteria for the Acceptance of Theories||348|
|3||The Role of "Extrascientific" Reasons||354|