[00:00:02] DR. ASCHENBRENNER:
Ladies and gentlemen, for many years, the University of California has honored the memory of the founder of its Department of Philosophy, George Holmes Howison, by presenting a contemporary and leading member of the teaching profession in philosophy. You will have seen in the program distributed for this lecture the many distinguished names of philosophers who have spoken in Berkeley as Howison Lecturers. There’s never enough time in introductions of this sort to do justice either to the past or to the present.
It will have to suffice to say that just as in the case of the United States of America, one discovers that this is actually one of the oldest, if not the oldest, continuing government in the world, so the University of California is no longer a young institution. It is, in fact, exactly as old as Cornell University. And since graduate instruction began in America, everywhere about the same time, the Department of Philosophy, which began under Howison about 1889, is almost as old as any such department in the country.
One could speak at greater length about Howison, but it is even more necessary that I speak of the lecturer of this evening, Professor Ernest Nagel. To many people of my age, Mr. Nagel will always be the Ernest Nagel who, with Morris Cohen, first introduced us to the wonderful world of modern logic through their Introduction to Logic and Scientific Method, which appeared in 1934. Mr. Nagel is perhaps the first Howison lecturer born in the twentieth century.
Singular distinction. He studied at the College of the City of New York and took his doctorate at Columbia in nineteen thirty-one. He has since then taught at Columbia, where in nineteen fifty-five he became John Dewey Professor of Philosophy.
Um, earlier this year, many of you heard him speak here honoring the centenary of John Dewey’s birth. Mr. Nagel is the author of many articles and reviews in various branches of philosophy. I have, in fact, on my desk a bibliography of one hundred and twenty-five such items.
To be brief, in order that, uh, we may proceed at once
(coughs)
to hear Mr. Nagel, I mention only the following further facts about him. He’s the author, among much else, of Sovereign Reason, a book published in 1954, Logic Without Metaphysics in 1957. He was the editor of the Journal of Symbolic Logic from 1934 to 1945, of the Journal of Philosophy from 1940 to 1956, and since 1956 of the Philosophy of Science Journal.
He’s at present a fellow at the Center for Advanced Study in the Behavioral Sciences at Palo Alto. This year has given us the pleasure of getting to know him better. You will find him, as we have, one of the most interesting and capable of philosophers now at work.
I regret that our chairman is, uh, away from Berkeley on university business and is un-unable to attend and to present Mr. Nagel. However, it is with great pleasure that I present him to you, and he will speak to you on the topic, \”The Cognitive Status of Theories.\” Mr. Nagel.
(applause)
[00:04:24] ERNEST NAGEL:
Thank you very much, Dr. Aschenbrenner. It’s a very great privilege for me to speak here on this lecture foundation, which has so many distinguished predecessors, uh. Uh, it’s a great honor to be included am-
among them. In his, uh, boldly far-ranging and seminal book, Adventures of Ideas, Whitehead id-identified four major philosophical doctrines that have emerged in the age-old debate over the fundamental character of the relations asserted by laws of nature to hold between the allegedly ultimate constituents of nature. He examined with unrivaled skill the metaphysical assumptions implicit in those doctrines, and he also sketched with imaginative sympathy their influential careers in the history of science as well as in other areas of human concern.
These doctrines, Whitehead found, are the expressions of antagonistic schools of thought, each producing grave reasons for its own distinctive claims, though paying little heed to the opposing considerations advanced by its rivals. He observed, however, that, and I quote, “There is no greater hindrance to the progress of thought than an attitude of irritated party spirit.” Urbanity, the urbanity of Plato, and if we may trust his dialogues, the urbanity of Athenian society were part of the intellectual genius of those times.
Tempered by such urbanity, Whitehead sought to locate the exact point of divergence between these warring schools in order to indicate the measure of conciliation of which they are capable, and to incorporate what is undeniably sound in each of them into his own systematic views concerning the ultimate presuppositions of all laws of nature. The present paper also deals with the laws of nature, but my problem is a logical or methodological one in a broad sense, rather than the metaphysical one Whitehead discussed. Although the question I propose to examine is not unrelated to his, and is, in my opinion, an essential preliminary to the one that he considered.
My question concerns the cognitive status of so-called laws of nature. On this question, as on the issue Whitehead discussed, there has been a similarly long and inconclusive debate in which conflicting positions have been taken. And it is my intent, as it was Whitehead’s, to assess the merits of warring schools on a question that seems to me of great importance.
I would be dissembling were I to claim that Whitehead’s metaphysical concerns are mine, or that I have found his metaphysical analyses illuminating on the subject of the present paper. I would nevertheless like to believe that my own attempt to adjudicate between antagonistic schools of philosophy reflects some gleams of the urbanity and the ironic temper which no reader of Whitehead can fail to recognize as shining qualities of his thought. The issues raised by the familiar controversy over the cognitive status of universal statements in general, and of laws of nature in particular, are enormously complex.
They involve not only highly technical problems of logic and questions of s-scientific fact, but also large philosophical considerations about the nature of meaning and knowledge. Limitations of time alone make it impossible for me in the present paper to deal with more than a small fraction of the relevant issues. And I will therefore restrict myself to consideration of two major positions that have been taken on the question whether, and if so, in what sense, theories in the physical sciences, as distinct from what are commonly designated as experimental laws, may be significantly construed as either true or false.
In the present context, I will use the locution theory for a body of assumptions such as the Newtonian theory of mechanics and gravitation, or the kinetic theory of gases. And the expression experimental law for statements such as Galileo’s law for freely falling bodies, or the Boyle-Charles law for gases. I do not believe that a sharp line of demarcation can be drawn between theories and experimental laws.
Nevertheless, I think the labels cover important differences, although I lacked the time to argue the point adequately. I can only suggest briefly two such differences. In the first place, the systematic explanation that can be achieved with the help of theories are unmistakably more comprehensive than those which experimental laws make possible.
In the second place, unlike experimental laws, theories employ ideas such as the idea of instantaneous velocity, the idea of a molecule, that are generally defined only implicitly by the fundamental postulates of the theory, so that in consequence, rules of correspondence must be introduced to associate some of the theoretical ideas, though not necessarily or usually all of them, with overt experimental procedures. Three major positions seem to have been taken on the question whether theories can be significantly said to be either true or false. According to the first and historically oldest view, a theory is literally either true or false, even if no theory is known to be one or the other, and can be established as only probable at best.
It is in consequence just as significant to ask whether the kinetic theory of matter is true as it is to ask a similar question about a statement concerning some individual happening, such as the statement, “Krakatau was destroyed by a volcanic eruption in eighteen eighty-three.”” A corollary often drawn from this account is that when a theory is well supported by empirical evidence, the objects ostensibly postulated by the theory, for example, as atoms in the case of some atomic theory, must be held to possess a physical reality, at least on par with the physical reality commonly ascribed to familiar objects such as sticks and stones. A second and historically youngest standpoint on the cognitive status of theories maintains that theories are primarily logical instruments for organizing our experience and for systematically ordering experimental laws. Accordingly, although some theories may be more effective tools than our other theories for attaining these ends, theories are not statements and belong to a different category of linguistic expression than do statements.
For theories function as rules or principles in accordance with which empirical materials are analyzed or inferences are drawn, rather than as premises from which factual conclusions are deduced. And they cannot therefore be usefully characterized as either true or false, or even as probably true or probably false. The third view on the cognitive status of theories is a halfway position between the first two.
According to it, a theory is a compendious but elliptic formulation of relations of dependence between observable events and properties. A theory cannot therefore be properly characterized as either true or false when it is taken at its face value or literally. It can be so characterized, however, insofar as it is translatable into statements about matters of observation.
Proponents of this view usually maintain in consequence that insofar as an atomic theory can be significantly said to be true, theoretical terms like atom are simply a shorthand notation for a complex of observable traits and events and do not signif-signify some observationally inaccessible physical reality. Although this third standpoint has enjoyed a wide following during various periods of intellectual history, it is nowhere near the center of current philosophical interest. Partly for this reason, partly because in my judgment, its substance is at best only an unrealizable program of analysis, but largely for lack of time, I will say nothing further about it here.
The second standpoint, which for the sake of brevity I shall call the instrumentalist view of the status of scientific theory, has been given a variety of formulations. However, despite important differences between some of these versions, the merits of the position do not derive from any particular formulation. The strength of the position lies in its concern with the actual function of theories in scientific inquiries and in its ability, as a consequence of this concern, to outflank a number of difficulties that embarrass alternatives to it.
The central claim of the instrumentalist view is that a theory is neither a summary description nor a generalized statement of relations between observable data. On the contrary, the theories have to be a rule or a principle for analyzing and symbolically representing certain materials of gross experience, and at the same time, an instrument in a technique for inferring observation statements from other such statements.
(coughs)
For example, the theory that a gas is a system of rapidly moving molecules is not a description of anything that has been or can be observed. The theory is rather a rule which prescribes a way of symbolically representing, for certain purposes, such matters as the observable pressure and temperature of a gas. And the theory shows, among other things, how when certain empirical data about a gas is supplied and incorporated into that representation, we can calculate the quantity of heat required for raising the temperature of the gas by some designated number of degrees.
That is, we can calculate the specific heats of a gas. The molecular theory of gases is thus neither logically implied by, nor according to some proponents of the instrumentalist view, does it logically imply any statements about matters of observation. The raison d’être of the theory is to serve as a rule or guide for making logical transitions from one set of experimental data to another set.
More generally, a theory functions as a leading principle or inference ticket, in accordance with which conclusions about observable facts may be drawn from given factual premises, not as a premise from which such conclusions are obtained. Several consequences follow directly from this account. The view that a theory is a convenient shorthand for a class of observation statements, whether finite or infinite in number, and the correlative claim that a theory must be translatable into the language of observation, are both irrelevant and misleading approaches to understanding the role of theories.
The value of a theory for the conduct of inquiry would not be enhanced if perchance it could be shown to be logically equivalent to some class of observation statements. And failure to establish such an equivalence for any of the theories of physics does not diminish their importance as instruments for analyzing the materials of experience with a view to solving concrete experimental problems and systematically relating experimental laws. It is common, if not normal, for a theory to be formulated in terms of ideal concepts, such as the geometrical one of straight line and circle, or the more specifically physical ones of instantaneous velocity, perfect vacuum, infinitely slow expansion, perfect elasticity, and the like.
Although such ideal or limiting notions may be suggested by empirical subject matter, for the most part, they are not descriptive of anything experimentally observable. Indeed, in the case of some of them, it seems quite impossible that when they are understood in a literal sense, they could be used to characterize any existing thing. For example, we can attribute a velocity to a physical body during a finite non-vanishing interval of time.
But instantaneous velocity is defined as the limit of the ratios of, of the distance and time as the time interval diminishes towards zero In consequence, it is difficult to see how the numerical value of this limit could possibly be the measure of any actual velocity. There is nevertheless a rationale for using such limiting concepts in constructing a theory. With their help, a theory may lend itself to a relatively simple formulation, simple enough at any rate, to render it amenable to treatment by available methods of mathematical analysis.
To be sure, standards of simplicity are vague. They’re controlled in part by intellectual fashions and the general climate of opinion, and they vary with improvements in mathematical techniques. But in any event, considerations of simplicity undoubtedly enters into the formulation of theories.
Despite the fact that a theory may employ simplifying concepts, it will in general be preferred to another theory using more realistic notions, if the former answers to the purpose of a given inquiry and can be handled more conveniently than the latter. On the other hand, the use of such limiting concepts in the formulation of a theory presents difficulties to the view that factual truth or falsity can be significantly predicated of the theory. For a factual statement is normally said to be true if it formulates some indicated relation, either between existing things and events in the omnipotent, um, um, omnitemporal sense of exist, or between properties of existing things and events.
However, if a theory formulates relations between properties that ostensibly do not or cannot characterize existing things, it is not clear in what sense the theory can be said to be factually true or false. Analogous difficulties for this view are raised by the circumstance that, in general, a theory contains terms for which no rules of correspondence are given.
(clears throat)
Whether or not an interpretation is provided for the theory on the basis of some model. In consequence, no experimental notions are associated with such terms, so that in effect, those terms have the status of variables. However, though such terms enter into expressions having the grammatical form of expressions,
(clears throat)
many of these expressions are in fact not statements at all, but only statement forms. For example, in the molecular theory of gases, there is no correspondence rule for the expression of the velocity of a molecule, though there is such a rule for the expression, the average value of the velocities of all the molecules. Similarly, the expression, the psi function in quantum mechanics, is employed in the Schrödinger equation for characterizing the state of an electron.
There is, in effect, a correspondence rule for the product of the psi and its conjugate, but no, but no such rule for the psi function itself. On the face of it, therefore, theories containing such terms are statement forms and cannot be said to be true or false. These and similar difficulties do not arise for the instrumentalist view of theories.
Since on this view, the pertinent question about theories is not whether they are true or false, but whether they are effective techniques for representing and inferring experimental phenomena. The fact that theories contain expressions which describe or designate nothing in actual existence, or which are not associated with experimental notions, is indeed taken as confirmation for the claim that theories must be construed in terms of their intermediary instrumental function in inquiry, rather than in terms of their adequacy as objective descriptive accounts of some subject matter. From the perspective of this standpoint, it is not a flaw in the molecular theory of gases, for example, that it employs limiting concepts such as the notions of point particle, instantaneous velocity, and perfect elasticity.
For the task of the theory is not to give a faithful portrayal of what transpires within a gas, but to provide a method for analyzing and symbolizing certain properties of the gas, so that when information is available about some of these properties in concrete experimental situations, the theory makes it possible to infer information having a required degree of precision about other properties. Similarly, it is not a source of embarrassment to the instrumentalist position that in inquiries into the thermal properties of a gas. We use a theory which analyzes a gas as an aggregation of discrete particles.
Although when we study acoustic phenomena in connection with gases, we employ a theory that represents the gas as a continuous medium. Construed as statements that are either true or false, the two theories are on the face of it mutually incompatible. But construed as techniques or leading principles of inference, the theories are simply different, though complementary instruments, each of which is an effective intellectual tool for dealing with a special range of questions.
In any event, physicists show no noticeable compunction in using one theory for dealing with one class of problems and an apparently discordant theory for handling another class. They employ the inclusive wave theory of light, according to which optical phenomena are represented in terms of periodic wave motion when dealing with questions of diffraction polarization, but they continue to use the relatively simpler theory of geometrical optics, according to which light is analyzed as a rectilinear propagation when handling problems in reflection and refraction. They introduce considerations based on the theory of relativity in applying quantum mechanics to the analysis of the fine structure of spectral lines.
They ignore such considerations when quantum theory is exploited for analyzing the nature of chemical bonds. Such examples can be multiplied. And if they prove nothing else, they show at least that the literal truth of theories is not the object of primary concern when theories are used in experimental inquiry.
It does not follow, however, that on the instrumentalist view, theories are fictions, except in a quite innocent sense that theories are human creations. For, in a pejorative sense of the word, to say that a theory is a fiction is to claim that the theory is not true to the facts. And this is not a claim which is consistent with the instrumentalist position that truth and falsity are inappropriate characterizations for theories.
It is indeed possible to maintain, consistently with that position, that many of the models in terms of which theories have been interpreted are fictions, in some cases even explicitly introduced as, as fictions, as were some of Lord Kelvin’s mathematical models of the ether. In maintaining this much, one is merely asserting either that there simply is no empirical evidence satisfying some assumed criterion for the physical reality of those models, or that in terms of this criterion, the available evidence is negative. On the other hand, it is also consistent with the instrumentalist view to recognize that some theories are superior to others, because one theory serves as an effective leading principle for a more inclusive range of inquiries than does another, or because one theory supplies a method of analysis and representation that makes possible more precise and more detailed inferences than does the other.
However, a theory is an effective tool only if things and events are actually so related that the conclusions of the theory enables us to infer from a given ex-experimental from given experimental data are generally in good agreement with further matters of observed fact. As in the case of other instruments, the effectiveness of a theory as an instrument or its superiority to some other theory is thus contingent on objective features of a subject matter and depends on something other than personal whim or preference. But it is time for noting some limitations in the instrumentalist position.
Proponents of this view often seem to believe that if the instrumental role of theories is once established, theories are thereby shown to be improper subjects for the characterization true and false. There is, however, no necessary incompatibility between saying that a theory is true and also maintaining that a theory performs important functions in inquiry. Few will deny that statements such as the distance between New York and Washington is, is approximately two hundred and twenty-five miles may be true and yet play valuable roles in the plans of men.
Indeed, most statements that by common consent can be significantly affirmed as true and false, true or false, can also be studied for the use that is made of them. In brief, it does not follow that theories cannot be regarded as genuine statements and cannot therefore be investigated for their truth or falsity merely because theories have indispensable functions in inquiry. Moreover, those who characterize theories as leading principles, as rules in accordance with which inferences are drawn, rather than as premises from which conclusions are derived, often overlook the contextual nature of this distinction.
It is today common knowledge that an inference such as the familiar one which proceeds from the premise, “All men are mortal, and the Duke of Wellington is a man,” to the conclusion, “The Duke of Wellington is mortal,” makes tacit use of the purely logical rule of inference or leading principle known as the principle of the syllogism. This leading principle is not a premise in the inference, and the conclusion is drawn not from it, but in accordance with it.
(cough)
The principle is, moreover, a formal one, since it refers only to the form of statements irrespective of what subject matter terms they may contain. However, it is now also generally recognized that an argument sanctioned by a formal rule of inference can be reconstructed so that the same conclusion can be obtained from a set of the original from a subset of the original premises in accordance with the material leading principle that compensates for the premise which has been dropped. On the other hand, this procedure can in general be used in reverse, so that a material leading principle for an argument can be dropped and replaced by a corresponding pr-premise.
For example, the conclusion, “This piece of copper Y will expand,” can be inferred from the premise, “This piece of copper Y will be heated,” in accordance with the material leading principle, which runs as follows: A statement of the form, “X will expand,” is derivable from a statement of the form, “X is copper and will be heated.” But the same conclusion can be obtained without this leading principle if we add the statement, “All copper expands,” to the original premise. It is clearly a matter of convenience in which of these alternative ways an argument is constructed.
Accordingly, though the distinction between premise and rule of inference is both sound and important, a given statement may function as a premise in one context, but may in effect be used as a leading principle in another context, and vice versa. The point illus-illustrated by these simple examples obviously holds for the more complex arguments in which theories play a fundamental role. There’s little doubt, for example, that in many cases, the wave theory of light is used or can be construed as a leading principle or technique for inferring ste- statements about experimentally identifiable data from other such data.
Nor is it disputable that this way of viewing the theory brings out a role it plays in inquiry that might otherwise be overlooked, or that this perspective on theories is a salutary antidote to dogmatic affirmations that some particular theory is the final truth about the ultimate nature of things. It nevertheless does not follow that theories do not or cannot also serve as premises in scientific explanations and predictions as bona fide as statements occurring– uh, concerning which it therefore seems quite proper to raise questions of truth and falsity. In point of fact, theories are usually presented and used as premises rather than as leading principles in scientific treatises, as well as in papers reporting the outcome of theoretical or experimental research.
Some of the most eminent scientists, both living and dead, certainly have viewed theories as statements about the constitution and structure of a given subject matter. And they have conducted their investigations on the assumption that the theory is pro– uh, is, is a projected map of some domain of nature, rather than a set of principles of mapping. Much experimental research is undoubtedly inspired by a desire to ascertain whether or not various hypothetical entities and processes postulated by a theory, for example, neutrons, mesons, neutrinos, current atomic physics, do indeed occur in circumstances and relations stated by the theory.
But research which is ostensibly directed to testing a theory proceeds on the prima facie assumption that the theory is affirming some things and denying others. In short, neither logic nor the facts of scientific practice, nor the frequently explicit testimony of practicing scientists supports the dictum that there is no valid alternative to construing theories simply as techniques of inference. Moreover, as has already been suggested, questions can be raised about a theory when it is regarded as a leading principle that are substantially the same as those which arise from the theories used as a premise.
For whether or not a material leading principle happens to be a theory, the principle is dependable only if the conclusions inferred from true premises in accordance with the principle are in agreement with facts of observation to some stipulated degree. In consequence, there’s on the whole only a verbal difference between asking whether a theory is satisfactory as a technique of inference and asking whether a theory is true as a premise. One final comment on the instrumentalist view must be made.
It has already been briefly noted that proponents of this view supply no uniform account of the various scientific objects, such as electrons or light waves, which are ostensibly postulated by microscopic theories. But the further point can also be made that it is far from clear how, on the instrumentalist view, such scientific objects can be said to be physically existing things. For if a theory is just a leading principle, a technique for drawing inferences based upon a method of representing phenomena.
Terms like electron and light wave presumably function only as conceptual links in rules of representation and inference. On the face of it, therefore, the meaning of such terms is exhausted by the roles they play in guiding inquiries and in ordering the materials of observation. And in this perspective, the supposition that such terms might refer to physically existing things and processes that are not phenomena in a strict sense seems to be excluded.
Proponents of the instrumentalist view have indeed sometimes flatly contradicted themselves on this issue. Thus, while maintaining that the atomic theory of matter is simply an inference ticket, some writers have nevertheless seriously discussed the question whether atoms exist, and they have even argued that the evidence is sufficient to show that atoms really do exist. Others have explicitly asserted that atoms and other scientific objects are generalized statements of relations between sets of changes and cannot be individually existing things.
But they have also declared that atoms are in motion and possess a mass. But since what it is to be an atom is specified by a given atomic theory, to assert the physical existence of atoms or to maintain that atoms have a mass is to accept the theory, not simply as a technique of inference, but as a true statement. Such glaring inconsistencies suggest that those who are guilty of them are not entirely prepared to exclude as improper questions of truth and falsity concerning theories.
In any event, it is clearly not inconsistent to admit the logical propriety of such questions and also to recognize the important instrumental functions of theories. Are theories then really statements of which truth and falsity are meaningfully predica-predicable despite the difficulties that have been noted in this view? Enough has already been s-said to suggest that whether the question is answered affirmatively or negatively, the answer given may not be the exclusively reasonable one.
Indeed, those who differ in their answers to it frequently disagree neither on matters falling into the province of experimental inquiry, nor on points of formal logic, nor on the facts of scientific procedure. What often divides them are in part loyalties to different intellectual traditions, in part, inarbitrable preferences concerning the ap-appropriate way of accommodating our language to the generally admitted facts. It is a matter of historical record that while many distinguished figures in both science and philosophy have adopted as uniquely adequate the characterization of theories as true or false statements, a no less distinguished group of other scientists and philosophers have made a similar claim for the description of theories as instruments of inquiry.
However, a defender of either view not only can cite eminent authority to support his position. With a little dialectical ingenuity, he can usually remove the sting from apparently grave objections to his position. In consequence, the already long controversy as to which of the two is the proper way of construing theories can be prolonged indefinitely.
The obvious moral to be drawn from such a debate is that once both positions are so stated that each can meet the prima facie difficulties it faces, the question as to which of them is the correct position has only terminological interest. Let me therefore consider the chief obstacles to each of the two views under discussion, beginning with those confronting the realist conception of theories as true or false statements.
There is in the first place the purely formal difficulty that a theory is not a statement, but only a statement form. For as already noted, if some terms of a theory are not associated with any correspondence rules, those terms are in effect variables, and in consequence, the theory does not satisfy the grammatical requirements for statements. However, this difficulty can be met by a formal device, quite familiar and first explicitly proposed by Frank Ramsey.
The device consists simply in introducing existential quantifiers as prefixes to statement forms. Thus, the expression, “If a human being has the trait P, then that person has blue eyes,” is a statement form. But by adding the prefix, there is a trait P, we can obtain from it a statement, there is a trait P such that if a human being has P, then that person has blue eyes.
Similarly, suppose that although the terms mass and acceleration are associated with the following expressions with correspondence rules, the term force is not. The expression, if a body undergoes changes in motion, then the product of the mass and acceleration of the body is equal to the force F acting on it, is then a statement form from which we can obtain the statement, if a body undergoes changes in motion, then there is a measurable property F, such that the product of the mass and acceleration of the body is equal to F. Accordingly, since by using the Ramsey device, the observational consequences that can be derived from the theory are not altered, that device suffices for outflanking the formal difficulty on the discussion. In the second place, there’s the objection previously mentioned that theories are commonly formulated in terms of limiting concepts, which characterize nothing actually in existence, so that at any rate, non-vacuous factual truth cannot be claimed for such theories.
This objection can be turned in a number of ways. A familiar gambit is to challenge the contention that limiting concepts do not apply to existing things. To be sure, we cannot, for example, ascertain by overt measurement the value of an instantaneous velocity or the magnitude of some length whose theoretical value is stipulated to be equal to the square root of two.
But unless accessibility to overt measurement, or more generally to observation, is made the criterion of physical existence, so it is sometimes said, this does not show that bodies cannot have instantaneous velocities or lengths with real number magnitudes. On the contrary, if a theory postulating such values is supported by competent evidence, then according to the rejoinder under discussion, there is good reason to maintain that these limiting concepts do designate certain phases of things and processes. Since in testing a theory, we test the totality of assumptions it makes, so the rejoinder continues: If a theory is regarded as well-established on the available evidence, all of its component assumptions must also be so re-regarded.
Accordingly, unless we introduce quite arbitrary distinctions, we cannot pick and choose between the component assumptions, counting some as descriptions of what exists and others as not. There’s another way in which the objection under discussion is sometimes countered. The rejoinder then consists in admitting that limiting concepts are simplifying devices and that a theory employing them does not in general assert anything for which literal truth can reasonably be claimed.
Nevertheless, existing things possess traits that are often either indistinguishable from the ideal traits men-mentioned in a theory or differ from such ideal traits by a negligible factor. In consequence, on this rejoinder to the objection, a theory is said to be true in the sense that the discrepancy between what a theory asserts and what even ultra-find– ultra-refined observation can discover is small enough to be counted as arising from experimental error. A third type of difficulty for the realistic view of theories is created by the fact already noted that apparently incompatible theories are sometimes employed for the same subject matter.
Thus, a liquid cannot be both a system of discrete particles and also a continuous medium. Though theories dealing with the properties of liquids adopt one assumption in some cases and the so– uh, and the opposing assumption in other problems. The usual reply to this objection consists of two parts.
One of them is essentially a repetition of the rejoinder mentioned in pre– in, in the preceding paragraph. “A theory may be employed in a given area of inquiry,” even though it is apparently incompatible with some other theory that is also used, because the former is more simple than the latter, and because for the problems under discussion, the more complex theory does not yield conclusions in better agreement with the facts than are the conclusions of the simpler theory. Accordingly, the simpler theory can be regarded as, in a sense, a special case of the more complex one rather than as contrary of the, of the latter.
The second part of the reply is that though incompatible theories may be used for a time, their use is but a temporary makeshift to be abandoned as soon as an internally consistent theory is developed more comprehensive than either of the previous ones. Thus, although there were serious discrepancies between the atomic theories employed at the turn of the present century to account for many of, many facts of physics and chemistry respectively, these conflicting theories have been replaced by a single theory of atomic structure currently used in both of these sciences. Indeed, inconsistencies between theories, each of which is nevertheless useful in some limited domain of inquiry, are often a powerful incentive for the construction of a more inclusive but consistent theoretical structure.
Accordingly, a proponent of the realistic view of theories can escape any embarrassment for his position from the circumstance that incompatible theories are sometimes employed in a science by insisting on the corrigible character of every theory and by refusing to claim final truth for any theory. He can freely admit that even a false theory may be quite useful for handling many problems. And he can join this admission with a claim that the succession of theories in some branch of science is a series of progressively better approximations to the unattainable but valid ideal of a limiting and finally true theory.
Finally, there’s the objection currently raised against the position under discussion stemming from the difficulties encountered in interpreting quantum mechanics in terms of some familiar model. For example, there are theoretical as well as experimental ob– considerations which have led physicists to ascribe to electrons and to other entities postulated by quantum theory, apparently incompatible, and, in any case, puzzling characteristics. Thus, electrons are construed to have features which make it appropriate to think of electrons as a system of waves.
On the other hand, electrons also have traits which lead us to think of them as particles, each having a spatial location and a velocity, though no determinate position and velocity can in principle be assigned simultaneously to any of them. Many physicists have therefore concluded that quantum theory cannot be viewed, cannot be viewed as a statement about an objectively existing domain of things and processes, as a map that outlines even approximately the microscopic constitution of matter. On the contrary, the theory must be regarded simply as a conceptual schema or a policy for guiding and coordinating experiments.
The rejoinder to this objection follows a familiar pattern. The fact that a visualizable model embodying the laws of classical physics cannot be given for quantum theory, so runs the reply, is not an adequate ground for denying that the theory does formulate the structural properties of subatomic processes. It is doubtless desirable to have a satisfactory model for the theory.
But the type of model that is regarded as satisfactory at any given time is a function of the prevailing intellectual climate. Even though current models for quantum theory may strike us as strange and even as unintelligible, there are no compelling reasons for assuming that the strangeness will not wear away with increased familiarity, or that a more satisfactory interpretation for the theory will not be eventually found. Moreover, the alleged unintelligibility of the present model stems in large measure from a failure to note that words like wave and particle used in describing it are being employed in an analogical manner.
It is only in a Pickwickian sense that an electron is a particle in the customary meaning of the word, just as it is in a stretched sense that the square root of minus one is a number, in the sense in which the cardinal integer three is a number. An electron is said to be a particle, or alternatively a wave, because some of the properties ascribed to electrons are analogous to certain properties associated with classical particles, or alternatively with familiar water waves, even if the analogy fails for other properties. When the language of particles and waves is understood in terms of the way these words are actually used in the context of quantum mechanics, so it has been contented, not even the appearance of contradiction arises in the quantum theoretical characterizations of electrons.
But in any event, the basic issue is not whether a particular sub-substantive model of subatomic processes is satisfactory. The basic issue is whether the relations between elementary constituents of physical objects and processes are more adequately stated by the mathematical formalism of quantum mechanics than by any other formal model available at present. On this issue, there’s no disagreement among competent students that the answer is affirmative.
This sample of objections to the realistic view of theories as true or false statements suffices to show that the view has dialectical resources for maintaining itself in the face of severe criticism. Undoubtedly, the rejoinders to these criticisms can be met with counter-rejoinders, though none to which defenders of the position under attack cannot offer at least a prima facie suitable reply. It will therefore not be profitable to continue this phase of the discussion any further.
Let me turn instead to some of the criticisms of the instrumentalist position. Two main difficulties have been noted in the instrumentalist position as usually formulated. The first of them is that much experimental research is directed to finding evidence for or against a theory, an undertaking which is apparently pointless if a theory is not a genuine statement, but simply the formulation of a policy or rule of procedure.
However, this objection can be readily made innocuous, for it is sufficient to reply that a theory can indeed be tested by searching for evidence which will either confirm or refute it, But only in a sense that confirmatory or disconfirmatory evidence is sought for observational conclusions drawn from observational premises in accordance with a theory. As has already been argued, the sole issue raised by this way of putting the matter concerns the relative convenience of employing material rather than purely formal leading principles in reconstructing deductive inferences. The second and more serious difficulty is that a consistently held instrumentalist view apparently precludes its adherents from, from admitting the physical reality or physical existence of any scientific objects ostensibly postulated by a theory.
For if a theory employing such terms as atom or electron is just a leading principle, it is incongruous to ask whether there really are atoms. And it is then acutely puzzling to say, as some physicists do say, that because of the experimental evidence now pointing to the atom, and I quote, “We are as convinced of its physical existence as of our hands and feet.” However, the force of this objection is unclear because of the notorious ambiguity, if not obscurity, of the expression physical reality or physical existence.
In any event, writers using these phrases do not in general understand them in the same sense. It will therefore be useful to consider some of the different criteria that are commonly employed, whether explicitly or tacitly, when physical reality is either affirmed or denied of scientific objects such as electrons, atoms, electric fields, and the like. Perhaps the most familiar requirement for anything to be physically real is that the thing or event can be publicly, be publicly perceived when suitable conditions for its observation are realized.
In terms of this criterion, sticks, stones, flashes of lightning, the smells of cooking, and the like can be said to exist physically, but not the pains a man feels when he turns an ankle, nor the pink elephants a drunkard may experience in his delirium. However, n-neither are most scientific objects, if any, physically real in this sense. Thus, although illuminated surfaces are physically real on this criterion, light waves are not.
And although the condensations of water vap-vapor in a Wilson cloud chamber to form visible tracks are real, the alpha particles, which according to current physical theory produces those tracks, are not. Certainly it is not in in on this interpretation of physically real that we are as convinced of the physical reality of atoms as we are of our hands and feet. On the other hand, even if some hypothetical scientific objects were physically real in this sense, for example, if perchance the genes postulated by current biological theory of heredity could be made visible, the role in science of the theoretical notions in terms of which such objects are specified would not be altered.
It is, of course, quite possible that could we perceive molecules, many questions still outstanding about them would be answered, so that molecular theory would receive an improved formulation. Nevertheless, molecular theory would still continue to formulate the traits of molecules in relational terms, that is, in terms of relations of molecules to other molecules and to other things, not in terms of any of their qualities that may be directly apprehended Through our sense organs. For the raison d’être of molecular theory is not to supply information about the sensory qualities of molecules, but to enable us to understand and perhaps predict the occurrence of events and the relations of their independence in terms of pervasive structural patterns into which they enter.
Accordingly, in this sense of the phrase, the physical reality of theoretical entities is of little import for science. A second widely accepted criterion of physical reality is close to being the polar opposite of the first, and has already been mentioned in passing. According to it, every non-logical term of an assumed law, whether experimental or theoretical, designates something that is physically real, provided that the law is well-supported by empirical evidence and is generally accepted by by the scientific community as likely to be true.
On this criterion, therefore, not only is the physical reality ascribed to such experimentally identifi- and identifiable items as the kinetic energy of a bullet, the strains in a body subjected to stresses, the viscosity of a liquid or the electrical resistance of a wire, but also to theoretical objects like light waves, atoms, neutrinos, and waves of probability. Anyone who employs this criterion will accordingly hold many objects postulated by some accepted theory to be physically existing things, even before any empirical evidence confirming detailed specified assumptions about those objects is available. This seems to have been the criterion adopted by many contemporary physicists who believed in the physical existence of antiprotons as postulated by quantum theory, although definite experimental evidence for them was lacking until recently.
On the other hand, those who employ this criterion will deny physical reality to a scientific object once held to be physically real, such as the phlogiston substance postulated by the phlogiston theory of combustion, when the theory postulating that object is abandoned as unsatisfactory, unless indeed a different but acceptable theory postulates a closely analogous object. A third criterion of physical reality sometimes employed is that a term designating anything physically real must enter into more than one experimental law. This requirement can obviously be strengthened by demanding that there must be a considerable number of such experimental laws.
The rationale for this requirement is to characterize only such things as physically real, which can be identified in ways other than and independently of the procedures used to define those things. For example, the magnitude of the gravitational force of the Earth on a body appears as the constant g in Galileo’s law for freely falling bodies. If this were the only law in which G occurred, then on this criterion, the term gravitational force would not designate a physical reality.
However, the constant G enters into a number of other experimental laws, such as the law for the period of the simple pendulum. Accordingly, physical reality can be ascribed to the gravitational force of the Earth. On the other hand, the situation appears to be different in the case of the notion of electric field.
We can determine the strength of an electric field in a region by introducing into that region a test body with known mass and electric charge and measuring the force upon that body. The field strength is then defined as the ratio of the force to the charge on the body. And it’s an experimental law that, under specified conditions, this ratio had the same constant value for any test body of relatively small dimensions.
It seems, however, at least according to one analysis, that though in this way the term electric force enters into an experimental law, this is the only experimental law in which the term does occur. If this is so, then according to the present cri- uh, criterion, physical reality cannot be ascribed to electric fields. The application of this criterion to scientific objects postulated by microscopic theories involves some complications, since theoretical terms do not occur in statements of experimental law.
It would take me too far afield to unravel these complications in any detail. For my present purposes, it will suffice to construe the cri-the criterion for the physical reality of theor-theoretical entities as requiring, first, that a theoretical term ostensibly referring to such an entity must be associated with some experimental concept by a rule of correspondence. And secondly, that the experimental concept must enter into at least two logically independent experimental laws which can be derived from the theory.
For example, in the kinetic theory of gases, theoretical expressions such as the mass of a molecule, the mean kinetic energy of molecules, the number of molecules and the like are associated with experimental concepts such as the mass of a gas, the temperature of a gas, the ratio of the product of the pressure and volume of the gas to its temperature, and so on. These latter terms occur in several experimental laws, such as Boyle-Charles law, Dalton’s law of partial pressures, or the law that at given temperature and pressure, the difference of the two specific heats per unit volume is the same for all gases. All laws which are derivable from a theory.
It is worth noting that on this criterion of physical existence, not every entity postulated by a theory will in general be said to exist, even if the theory as a whole is well confirmed by experiment and is accepted as likely to be true. Thus, some physicists were once doubtful about the physical existence of neutrinos, initially postulated to preserve the conservation of energy principle in quantum theory. And it is possible that this doubt was based on the fact that the term neutrino did not conform to the requirements set by this criterion.
Similarly, when Planck first introduced the theoretical notion of discrete quanta of energy in order to account successfully for the distribution of energy in the spectrum of black body radiation, physicists, including Planck himself, were doubtful of the existence of such quanta. The situation was altered in this respect when the notion of energy quanta was associated with the constant h that appeared not only in Planck’s radiation law, but also in other experimental laws concerning the photoelectric effect, the line spectra of the elements, specific heats of solids, and so on, all of which were derived from theories containing the quantum hypothesis as one component assumption. One final criterion of physical reality is worth noting, according to which the real is that which is invariant under some stipulated set of transformations, changes, projections, or perspectives.
An elementary geometrical example will illustrate the general idea underlying this criterion. Imagine a circle painted on a sheet of glass and a small source of light at some distance perpendicularly above the center of the circle. The circle will then be projected as a shadow cast on a screen parallel to the glass, and this shadow will also be a circle.
Suppose, however, that the glass is rotated, where the axis of rotation passes through the glass sheet and is parallel to the screen, while the source of light and the screen remain in their initial positions. The shadows on the screen will then no longer be circles. They will first assume the form of ellipses and eventually take the form of parabolas.
Under this projection, neither the shape nor the perimeter nor the area of the circle on the glass will, will be preserved in the circle’s shadow. These are not invariant properties of the circle on the projection. Nevertheless, there are some properties of the circle which are invariant under such projection.
For example, if a straight line is painted on the glass to intersect the circle, the shadow of the line will always intersect the shadow of the circle in two points. If the present criterion were applied to this example, we would have to say that neither the shape, nor the perimeter, nor the area of the figure on the glass is a physical reality, but that only properties of the figure invariant of the projection, such as the one mentioned, are physically real. It will be evident that on this criterion, different sorts of things can be characterized as physical realities according to which set of transformations is specified for this purpose.
Thus, some writers have denied physical reality to immediate sensory qualities, since these vary with physical, physiological, and even psychological conditions. The title to such reality has been reserved by these thinkers for the so-called primary qualities of things, whose interrelations are independent of physiological and psychological changes and are formulated by the laws of physics. Similarly, the numerical value of the velocity of a body is not invariant when the motion of a body is referred to different frames of reference, so that on this criterion, relative velocity is not a physical reality.
Many writers on the theory of relativity have in fact maintained that spatial distance and temporal duration as conceived in pre-rel-relativity physics are not physically real, since they’re not invariant for all phys– all systems moving with respect to each other with constant relative velocities. Physical reality, according to these writers, must be ascribed only to those features of things that are formulated by the invariant laws of relativity physics, such as the relativistic kinetic energy of a body or its relativistic ma-momentum. In an analogous manner, physical reality has been attributed to theoretical entities like atoms, electrons, mesons, probability waves, and the like, because they, too, satisfy some indicated condition of invariance.
This brief list of criteria does not exhaust the senses of real or exist that can be distinguished in discussions about the reality of scientific objects. It is long enough, however, to indicate that a proponent of the instrumentalist view of theories cannot give an unambiguous answer to the am– to the ambiguous question whether it is congruous with his position to accept the physical reality of such things as atoms and electrons. But the list is also long enough to suggest that there are at least some senses of the expressions physically real and physically exist in which an ironically-minded instrumentalist can acknowledge the physical reality or existence of many theoretical entities.
More specifically, if the third o-of the the above criteria is adopted for specifying the sense of physically real, it is quite patent that the instrumentalist view is entirely compatible with the claim that atoms, say, are indeed physically real. In point of fact, many instrumentalists themselves urge such a claim. For to make it is to assert that there are a number of well-established experimental laws related in a certain manner to one another and to other laws by way of a given atomic theory.
In short, to assert that in this sense atoms exist is to claim that available empirical evidence is sufficient to establish the adequacy of the theory as a leading principle for an extensive domain of inquiry. What has has already been noted, this is in effect only verbally different from saying that the theory is so well confirmed by the evidence that the theory can be tentatively accepted as true. Proponents of the instrumentalist position may, of course, reserve judgment whether other theoretical entities postulated by the theory really do exist, since the requirements for their physical reality as set by the criterion adopted may not be clearly satisfied.
But on such particular issues, proponents of the view that theories are true or false statements may have similar hesitations. It is therefore difficult to escape the conclusion that when the two apparently opposing views on the cognitive status of theories are each stated with some circumspection, each can assimilate into its formulations not only the facts concerning the primary subject matter explored by experimental inquiry, but also all the relevant facts concerning the logic and procedure of science. In brief, the opposition between these views is then a conflict over preferred modes of speech.
And so I’d like to conclude with repeating the quotation from Whitehead: “There is no greater hindrance to the progress of thought than an attitude of irritated party-spirit.” Urbanity, the urbanity of Plato, and if we may trust his Dialogues, the urbanity of Athenian society, were part of the intellectual genius of those times. Thank you very much.
(applause and cheering)