LOGIC AND SCIENCE

Epistemology and Science

Epistemologists can begin the task of analyzing knowledge from a variety of viewpoints. At a very abstract level, an epistemologist may attempt to prove the mere possibility of knowledge in an effort to confront skepticism.

To see more clearly what is at stake in the approach of epistemology through examples, we can turn to Plato. Plato appropriately chose mathematical examples as his paradigms of knowledge, and then sought to find the limits of the human knowledge that could be construed as similar in nature to the mathematical knowledge that he started with. There is no reason why human knowledge should be uniformly sub­ject to the same philosophical analysis, but Plato proceeded as though an analysis of knowledge should be the same for all types of knowl­edge, and most philosophers have followed him in this.

The philosophy of science is heir to the tradition of epistemology based on examples. Philosophers of science have assumed that at least some examples of scientific knowledge are genuine examples of hu­man knowledge, and that the way to proceed is to analyze the impli­cations of these examples for the total range of human knowledge. This much will not be contested here as a reasonable procedure. Other aspects of the legacy are more troubling. If Plato was correct that mathematical knowledge once gained could not be refuted, is scien­tific knowledge to be measured against the same standard? There is the awkward fact that much of what scientists believe at any point is later found to be modified or abandoned, although the assumption that scientific knowledge continuously progresses gives hope that there is an accumulating core of scientific experimental fact that will explain this as progress.

Considered at a point in time, a scientist will be acquainted with certain supposed facts and theories, and may intend to work with these materials in order to extend scientific knowledge. An episte­mology should discuss the procedure of obtaining and extending knowledge. For this purpose, the concept of rationality plays a central role in philosophical epistemology.

For all of the initial plausibility of this variant of rationality, it has some serious problems. An important consequence of this concept of rationality, even when it is fully spelled out in some particular variant, is that it is not sufficiently clear to entail the actions of a rational scientist in many of the situations that arise in scientific practice. The irritating and apparently insurmountable results of undecidability and incompleteness of modern logic suggest that interesting bases for sci­entific practice may not be provably consistent, and logic can press for revision only after the actual crime of inconsistency has been ob­served. There are in addition to these matters many problems with no known mathematical or logical solution. A salesperson with a list of towns to visit who wishes to visit each town once only on a pro­jected sales trip, and is subject to various other constraints, cannot in general reason to an optimal route, but must proceed by instinct, or trial and error.¹ In addition to all of these problems, the consequences of much of the work that has been done on inductive inference sug­gest that logic cannot coerce toward a single possibility the direction in which projection from a basis to anticipated future data should take place.² None of these problems begins to deal with empirical uncer­tainty in the data, or other difficulties with the supposition that a good basis for scientific practice can be provided, but they are sufficient to show why the normative thrust of philosophies of science based on rationality is blunted by confrontation with actual scientific practice.

Similar objections stand in the path of any attempt to utilize game theoretic rationality as definitive of sound scientific practice. Where the value of a set of alternative actions can be expressed in terms of utilities, and a probability measure for the likelihood of obtaining these values on the given actions is available, rationality seems to compel the view that that end should be sought promising the highest ex­pected utility on these measures, or one of those ends with the high­est expected utility if there are more than one. This view relaxes the concept of philosophical rationality, since different probability meas­ures can be defended by different scientists, leading to the conclusion that alternative strategies on some basis may be equally reasonable. Hope then arises that the formal philosophy of science might be brought into closer conformity with the observed practice of science through a cooperative game theoretic analysis. But problems again mount as the details are considered. Game theory is of great value and can lead to deep explanatory insights when utilities and their attainment are related in a clear way, as in many standard gambling situations. In science, as Levi and others have shown, to apply game theoretic anal­yses requires some notion of epistemic utilities and risks that are dif­ficult to quantify as probabilities.³ Where there are difficulties in quantification, as Newcomb’s puzzle indicates, pairs of seemingly ob­vious maximal strategies may come into conflict even when the quan­tification is not at issue.⁴ Perhaps game theoretic analyses of scientific behavior will be insightful in limited cases, where the possible out­come of a range of experiments is pretty well settled by past experi­ence, or where a group of scientists share a sufficient range of opinion to make the probabilities and properties of outcomes of various op­tions a matter of agreement. Even in such cases, however, game the­oretic analyses would reveal similarities between scientific practice and other game strategies, and although such similarities might be illuminating of the actions of scientists in certain situations, they could not by themselves give an insight into the distinctive nature of sci­entific knowledge, one of the presumed objects of philosophical anal­ysis.

All of these attempted analyses of rationality have in common the Cartesian assumption that the isolated scientist dealing with a basis for scientific practice by means of reason is the appropriate basic framework for understanding the nature and scope of scientific knowl­edge.⁵ Philosophers may slide into this assumption by taking philo­sophical reflection as a model for scientific thought, or by thinking in terms of Cartesian epistemology. Its consequence, however, is a con­ception of scientific activity in which scientists are viewed as a group of individuals all more or less trying to do the same thing, with vari­ance explained by the fact that some of them do it faster, or do it better, than the rest. On the Cartesian assumption that the individual scientist is the appropriate locus of philosophical reflection into the nature and scope of scientific practice, the only significance of having groups of scientists involved in scientific practice can be that the prac­tice is speeded up, accelerating the rate of scientific progress. This is implicit in Popper’s metaphor that the community of scientists can be compared to masons working on a cathedral.⁶ Here the masons are conceived of as more or less interchangeable in function, and the consequence of more or fewer masons seems simply that a greater or lesser number of stones will be laid in a fixed period of time. It is the first intention of this text to challenge this natural philosophical start­ing point. Our considerations in later chapters will lead us to argue that the social structure of science requires for maximal advance of knowledge that the rational scientist react not only to the known the­ories and evidence but also to what other scientists are doing, and can do, in connection with possible research topics. Because of this, philosophical epistemologies that attempt to isolate scientific ration­ality by using merely the theory and data available to a scientist at a time, and logical functions over this basis, cannot achieve a satisfac­tory epistemology for science.

In line with prevalent philosophical practice, we have taken a basis for an analysis of scientific practice to be a personal belief structure containing facts and theoretical conjectures. Refining this conception of a basis, we can note that various philosophers have taken differing positions on the kind of facts that such a basis should contain, and on the nature of permitted theoretical conjectures over such a basis. It is also possible for philosophers to conceive of the faculty of reason used to test and enlarge the basis in different ways. The resulting complexity of possible positions is enormous, but we shall make a first division of epistemologies constructed on personal belief structures into two traditions, the empiricist and rationalist traditions.

Both the rationalist and empiricist traditions depend on a presup­position that a single person, isolated from his or her fellows, could in principle encounter the real world and reason about it in terms of ideas. Empiricists emphasize the reliability of careful sense experi­ence as the foundation and evaluation of scientific knowledge. Empir­icism as a philosophy of science has attempted to analyze scientific knowledge as the logical organization and augmentation of scientific observations. An empiricist who believes that the relevant logical or­ganization is capable of expression within modern symbolic logic is usually a positivist as well. By contrast, one could define rationalism as the view that knowledge about the world is the development of what, in some sense, we already know in the form of clear, distinct, and mutually consistent ideas present to our consciousness. Ration­alists emphasize the power of reasoned theorizing in science, and make theoretical coherence the foundation of scientific knowledge and the valuator of scientific data.

Empiricists tend not to find necessary connections between sense experiences. One experience might always be imagined as followed by almost any other experience so far as the logical analysis of expe­rience is concerned. Logic has no empirical content, but merely al­lows sense experiences to be organized in a useful way. Such organi­zation can never lead to a substantive extension of what has been observed except in the form of a hypothesis or conjecture. For ration­alists, the fixed connections between ideas that are discovered by rea­son may be discovered in the world that is accessible to experience, but only after the connections have been thought. These connections can be recognized in the world, but they cannot be first noticed in the confusion of experience. The precise relationships of ideas are never precisely equivalent to the loose and indeterminate relation­ships of data.

Empiricism and rationalism have been discussed as philosophical temptations to ground scientific knowledge, and by extension all of human knowledge, in either experience or ideas. Scientists have been subject to the same conflicting temptations. Many scientists, notably Newton and many later Newtonians, have wanted the arbiter of sci­ence to be experience, and have held that mathematics and theorizing cannot discover knowledge, although theory may anticipate knowl­edge where it manages to accurately mirror empirical data. Empiri­cism is the natural ally of all experimentalists who feel that scientific knowledge can only properly advance on the basis of careful, repeated experimental results. For these scientists, some mathematical systems will be helpful in organizing data and expressing conjectures, but such systems could not be provably insightful into reality apart from their shaping in experience. Experience has to perform the separation be­tween what is useful and what is not useful. Other scientists have seen experience as a snare, partly because of errors of perception and measurement, and have seen experience as little more than a check on whether the precise assumptions of theory point in the right di­rection. For these scientists, reality must have the precision and beauty of a mathematical development if it is to be understood, and hence mathematical system must be the primary instrument for insight into natural process. Only mathematical systems can transcend the limi­tations of human perception.⁷ Rationalism is the natural ally of all scientists who see theorizing as the primary motor of scientific ad­vance. Scientists have generally spent little time on the philosophical articulation of these themes, but it should not be imagined that the incapacities and problems of empiricism and rationalism are totally isolated from tendencies in the practice of scientists.

Empiricism and rationalism, however, have joint difficulties that cannot be traced to the clash between their intuitions about the rel­ative importance of theory and data. Neither empiricism nor ration­alism can satisfactorily explain sufficiently rapid theoretical changes in the sciences. Both have historically seen the object of knowledge as unaffected by the process of acquiring knowledge. After the knower studies the object of knowledge, it remains unaffected, and the knower changes primarily by adding information about the object to the stock of his scientific basis. These epistemologies would be quite servicea­ble if the world were stable, and if the main features of the world could be read by human sense organs and human reason. There is a sense in which these epistemologies were defensible before the ac­celerated growth of modern science and the confusion of data pro­duced by modern scientific instruments. If the properties of the world as revealed in experiment change sufficiently rapidly, then the rela­tively static traditional epistemologies will not prove adequate to sci­ence, since the fit between language and data on which they depend will be constantly disrupted by newer data produced by a rapidly changing instrumentarium. It will be argued here that the features of the world revealed to experiment cannot be philosophically proven to be revealing of the world’s real properties, but that experiment pro­duces a text of data that must be interpreted, and whose augmenta­tion may not seem initially consistent. The complexity of the world revealed by modern science, as well as the failure of epistemological independence between knower and known (and between theory and data), seems to point inevitably toward a newer epistemology if the structure of science is to be captured at a satisfactory level of philo­sophical analysis.

The case against rationalism and empiricism need not rest on any claim that they are prima facie inadequate to current scientific theo­rizing based on intuitions about the dynamics of scientific progress. In order to motivate serious consideration of the more dynamic epis­temology to be presented in this book, it will be argued that both empiricism and rationalism suffer serious internal difficulties. Neither the idea that knowledge can be grounded in clear and distinct ideas nor the idea that knowledge about the world can be developed as properly organized clear sense perception can result in a self-consis­tent epistemological position, that is, a position that can legitimate its own view of scientific knowledge. This is the root problem with these traditions and their informal allies in scientific practice, although the consequences only prove devastating where data development is ex­tremely rapid. Rationalists are unable to establish that knowledge read from clear and distinct ideas is knowledge about the same world stud­ied in modern scientific experimentation without assuming the legit­imacy of at least some sense experiences, that is, without accepting some minimal empiricist assumptions. Empiricists are unable to es­tablish that knowledge about the world exceeding the knowledge rep­resented by past sense experience can be obtained by logical means without assuming the legitimacy of at least some intuitive idea about how the world is structured, that is, without accepting some minimal rationalist assumption. Neither epistemology, therefore, can be sat­isfactorily closed in terms of its own assumptions.

Both rationalism and empiricism, as well as their scientific allies, are partly correct in their insights. At times, scientific advance is pow­ered primarily by theorizing or by experimenting, and on such occa­sions the relevant epistemological position is completely serviceable in practice. When a scientific language suitably reflects the facts of experimentation over a period of time, either rationalism or empiri­cism may seem correct and defensible. Both make assumptions that are sometimes reasonable in a scientific context, and this helps to explain why variations of these classic positions tend to recur in writ­ing about the epistemology of science, and why particular scientists can see their work as consistent with one view or the other. In at­tacking each as a partial or incomplete account, we also need to pre­serve the important moment of insight that accounts for its longevity. Then after this comparison, it will prove possible to expose the ap­parent clash between them as mistaken, and to find a more dynamic perspective within which the advantages of both can be preserved.

The Closure of Rationalism

It has seemed so obvious to so many philosophers that modern sci­entific knowledge is grounded in the close observation of nature rep­resented in experimental results that some form of empiricism under­lies many contemporary works on the philosophy of science. The implicit challenge to the tradition of rationalism in connection with modem science is to show how one can, by contrast, read reliable knowledge from one’s ideas. Since our ideas are frequently contradictory or un­clear, rationalism must restrict the ideas from which reliable knowl­edge about reality can be read to carefully prepared candidates for a theoretical system. Turning to an example of how ideas can apparently augment knowledge, we can consider the transitivity of the relation longer than. Clearly, if one suitable object is longer than a second, and the second longer than a third, we feel sure without further meas­urement that the first is longer than the third. Suitability here rules out change in length, and includes a clear significance for the direc­tion of length. Experimenting on objects to determine whether this relation is transitive seems pointless, and the transitivity is conse­quently not merely a contingent conjecture. Such a principle is nei­ther formally provable nor logically valid, and yet it is not supported merely by fact.⁸ Some philosophers have said that such a principle is true because of the meanings of the terms involved. Should this be so, the unobservability of meanings seems to force the view that this principle is a paradigmatic case of rationalistic knowledge.

Another example will indicate how useful scientific information about the world seems to flow from a principle based on ideas plus thought experiment. We will call this the Brake Principle. The Brake Princi­ple can be formulated as follows: Two bodies moving in parallel paths at different velocities will, if then rigidly coupled, not be able to move in coupled form at a velocity greater than the faster of the two veloc­ities before coupling. To put this in quite informal terms, a slower body will typically act as a brake on a faster body to which it is rigidly coupled, and can certainly not speed it up. Two horses or two humans coupled together cannot presumably run more quickly coupled to­gether than the faster of them can run alone. Thus, thought may convince us that the Brake Principle may be used legitimately in physical reasoning. Suppose we now consider the rate of free fall of bodies in the earth’s gravitational field, once a significant unsolved problem in physics. Let us consider a batch of objects, all of the same size and weight, manufactured so that two, three, or more of these objects can be rigidly fastened together. We can imagine, for exam­ple, that the objects are threaded metal cylinders that can be screwed together in arbitrary combinations. Suppose each single cylinder weighs one pound. We can imagine dropping simultaneously two objects, one of them a single cylinder and the other three cylinders screwed to­gether. There are three possibilities. The three-pound object can fall faster than the one-pound object, slower, or at the same rate of speed. The Brake Principle is sufficient to rule out two of these possibilities, leaving us with a significant fact about the world.

Suppose, for example, that the three-pound weight falls faster be­cause heavier bodies fall faster. If we couple the two objects together to get a four-pound object, it should fall faster then the three-pound weight by this line of reasoning; but it can’t fall faster according to the Brake Principle, since the four-pound weight is the rigid coupling of the one-pound and three-pound cylinders. This contradiction elim­inates one option. A similar line of reasoning is sufficient to find a contradiction between the assumption that heavier bodies fall more slowly than lighter bodies and the Brake Principle. But if all bodies fall freely at the same rate of speed, no contradiction appears.⁹ These results hold when such factors as air resistance are considered, and discounted, so that free fall in the gravitational field is made as precise as one wishes conceptually. The Brake Principle in conjunction with this thought experiment seems to entail that all bodies freely falling in the earth’s gravitational field must fall at the same rate of speed, a physically significant fact. The necessity involved follows from the contradiction entailed by any deviation from this point of view.

No actual experiment has been performed to arrive at this conclu­sion, and once this line of reasoning has been discovered, an experi­ment may seem superfluous save as a crude check that no major error in thinking had occurred. Many readers will suspect that the straight­forward attack on this problem is to drop pairs of objects from a height. From a rationalist point of view, however, observation cannot deter­mine whether objects are dropped simultaneously, or whether they hit the ground at the same time. An observation could determine that the objects hit more than a second apart, but observation can’t deter­mine whether two objects hit simultaneously or a thousandth of a second apart, a difference that may be crucial to theory. It is assumed here that naked eye observation is the relevant means of determina­tion. Experiment can show that we are not wildly wrong, but can it find the truth about nature? Many hypotheses are always logically compatible with experimental observation. Only reasoning based on correct ideas can seem to penetrate this confusion and locate scientific truth.

We hope this example is sufficient to show the often unrecognized power of reason. The ideal rationalist, as gentleman, is prepared to wait for these moments of convincing insight, no matter how fruitless a temporary search for results. Rationalists will not spread mere ru­mors about nature, a lady. Empiricists, who are prepared to violate nature through experiment, can force their advances on her, but she will not necessarily tell them the truth. It is undeniable that there is a rationalist component in much of science, and in nearly all theoriz­ing. Many areas of science have received extensive and persuasive rationalist organization, with experiment merely seeming to corrobo­rate a structure of ideas that can literally stand on its own. And the­ories about ideal gases, frictionless surfaces, perfect competition, and so on, seem to tell us something about the world even though no experiments can be performed directly on these objects. The world of scientific theorizing is a world of precise intellectual constructs. Rationalism must locate enough such structures to provide a suitable account of contemporary science and of the dynamics of scientific progress, but it falls short.

Where language has been sufficiently often used successfully in in­teracting with the world, and perhaps even modified to produce this success, the ideas it can express may seem to reveal the precise struc­ture of the world. But by examining ideas alone, even clear and dis­tinct ideas, we can discern no relationship between these and the empirical world open to sense experience that philosophically legiti­mizes rationalist knowledge as knowledge about this world. One can­not postulate a correspondence of some kind, because insofar as one cannot get away from ideas to examine the world directly, one cannot externally examine a relationship between an idea and its referent in the world. Such a relationship transcends rationalist knowledge, since within rationalism the only relationships are those between ideas. Much of scientific knowledge, of course, can be seen as a set of relationships between theoretical ideas and conceptualized data, but this still omits any legitimation that the conceptualized data are reflective of the ac­tual world. Perhaps a more promising direction is to believe that ev­olutionary adaptation or God’s benevolence has resulted in a corre­spondence between ideas and the relevant objects in the world. The attempt to reach beyond the circle of ideas to a correspondence with the world through God’s benevolence, such as the attempt in Des­cartes’ Meditations, has never resulted in an argument demonstrating more than the possibility that such connections could exist. Any ev­olutionary argument has similar problems, and also has problems with the rate of possible theoretical development. Perhaps ideas have evolved so as to correspond with important features of the world, but changes in the world, or in the world of data, could leave such ideas without purchase. Indeed, in this respect, the difference between changes in the world and changes in the data that we use to describe the world is moot. What is required is a method of forcing ideas to develop so as to accomodate empirical evidence in such a fashion that new dis­coveries can be reasonably anticipated. This strategy cannot be ac­commodated within traditional rationalism, since an empirical input is required as a guide, no matter how uncertain, for the direction in which ideas must be developed. A self-consistent rationalism comes close to the vacuous assertion that empirical knowledge can be read from ideas whose structure suitably mirrors the structure of the world, without telling us how such ideas can be recognized and acquired.

Both phenomenology and Platonistic philosophies remain viable in spite of this critique, since they do not purport to give us knowledge about the empirical world, but about at least some of our mental acts and about ideal mathematical objects, respectively. This is perhaps why they are still viable forms of rationalism in special subject matter domains. Although not subject to an internal critique, these forms of rationalism may be subject to external critique. As is well known Hus­serl was never able to extend phenomenology to an account of societal interaction between human beings, and modern forms of phenome­nological sociology seem to be heir to this original difficulty.¹⁰ In this sense, pure phenomenology is insufficient to explore the entire hu­man world. Platonistic philosophies of mathematics would be open to a charge of superfluousness if philosophies of mathematics could be worked out to account for the mathematical knowledge we need for science and other endeavors that do not need to postulate independ­ently existing mathematical ideas. Perhaps the necessity of mathe­matical truth can be captured in the rules of constructivist proof, or in some notion of reflected social structure, but the debates over these questions are anything but settled. In view of the fact that pure logical structures do not seem adequate to the development of mathematics, some version of nonempiricist mathematical truth still seems an at­tractive possibility, and at this point it is impossible to rule out. What we can say here is that modem rationalism avoids entanglement with dialectical problems through restriction of its claims to truth to the relatively settled underpinnings of everyday judgment or to mathe­matical truth.

As has been noted, there is a pressure in rationalist thought toward comprehensive system, with the idea that a sufficiently vast, consis­tent, and coherent account of the world would have to be true. In such a program, revision to bring about consistency might cause any part of the system to require repair. In this view, specific ideas need only be generally related to empirical reality, since the ultimate fit of system and reality could only be assured when the system was suffi­ciently complex. Rationalism thus has some difficulty in accepting the structure of the sciences, which according to the scientific division of labor allow for small domains of fact to be closed off and definitively settled from the perspective of theory.

The rationalist tradition has observed correctly that one can read knowledge from ideas, including ideas that have been expressed in linguistic systems. But knowledge about the world, scientific knowl­edge, can only be read from ideas or language that happen to fit the world or isolated domains of fact within the world. Then the fact that the fit exists need not be kept constantly in mind, and the role of past experience in developing such a fit can be forgotten. As our Cartesian example shows, our everyday language fits the world fairly well as the result of a long history of its adaptation to human observations and human interests. The fact that we experience objects of stable size that we can easily reidentify in much of everyday life forms part of the essential background in which the transitivity of tallness seems essentially correct. Similarly common experiences with moving ob­jects of normal dimension and speed are part of the background of the plausibility of the Brake Principle. A great deal of knowledge about the world has already been coded by an evolutionary process into our vocabulary and the way in which we use language. Early scientists required little more than this everyday language to describe the world and to speculate about it, and experimentation did not al­ways need to play a big role in scientific advance. It was possible then to be optimistic about the completion of a rationalisitc program and the development of a language that could completely and accurately describe the world. Crushing problems for traditional comprehensive rationalism arose with the rapid advance of modern science. The data obtained from many new scientific instruments, especially in the nat­ural sciences, are not naturally dealt with in many cases in existing languages, and they may seem alien to expectations based on past experience and present languages. Scientists have had to develop their own languages to describe such data and to pursue theoretical devel­opment. But in this process the basic insight of rationalism is not lost. Languages are sought that will fit data so closely that information can be read from proper linguistic expression without further experimen­tation, and the history of science shows that such languages have been repeatedly developed.

Chemical symbolism provides a good example. Using it, a chemist can anticipate the success of chemical experiments, which therefore need not actually be performed, as well as the impossibility of hypo­thetical compounds, whose synthesis therefore need not be at­tempted. The symbolism of chemistry was originally used to mark the proportions of reagents involved in certain experiments, but it came to fit chemical structure so closely in certain data domains that chem­ists could take it to represent the actual structure of the molecules whose study constitutes their science.

There undoubtedly is a strain of rationalism in science. Scientists seek to develop languages like that of chemical symbolism to facilitate the growth of science. Languages with sufficient fit to the available data and to potential experience make a suitable instrument for guid­ing scientific advance. The development of such languages cannot be explained save partly in terms of language that is already understood, language that has earned trust in terms of its wide consonance with the structure and process of the experienced world. The failure of rationalism in the context of modem science is its failure to explain how language and the world can be brought into consonance when the experimental interaction with the world is producing data that break the confines of existent expression. Rationalism must assume that existent expression is adequate. We need to understand the role of scientific inquiry in forming legitimate semantics and syntax for scientific languages. Rationalism is correct that the existence of these languages is crucial for science, but it had precious little to say about the process by which adequate languages can be formed.

The Closure of Empiricism

We will consider the empiricist tradition primarily in the modern form most frequently encountered in the study of science, that of positivism and consequential positions. This form of empiricism pre­sents the issues that concern us directly, since even if it be conceded that positivism is self-consistent, its failure to provide a complete grounding of scientific knowledge solely in experience will show con­vincingly that empiricism cannot yield an adequate account of science. Positivism is a form of empiricism that arose after the development of modern science explicitly to explain its epistemology. The failure of positivism is partly the failure of one form of scientific self-under­standing.

The first positivists in the 1920s were concerned to argue that sci­ence could be sharply distinguished from theology, common sense, and even logic and mathematics. In this way they hoped to show that science was sharply superior as a means of acquiring empirical knowl­edge. In order to draw a boundary around science to highlight its unique status, early positivists construed science as resting on para- digmatically clear, carefully prepared observation and experiment, and they tended consequently to downplay the role of imagination in theo­rizing. Creative theorizing, wherever it occurred in science, had to be subject to definite and vigorous control through scientific obser­vation. In this way theorizing in science could be distinguished from theorizing in other areas of human interest. Although logic and math­ematics were construed as having no substantive content, they were useful in organizing scientific knowledge and in legitimating infer­ences from accepted observation statements and sets of such state­ments.

Positivists were anxious to sweep away theology, aesthetics, and so on, as intellectual rubbish, and to restrict knowledge to scientific knowledge. There is in this approach a kernel of the booster, and positivists often sounded like pitchmen even if the results of science they were interested in were real enough. Some positivists were anx­ious to draw the line around science so as to include sociology as a science, while others thought that perhaps only physics, chemistry, and biology belonged clearly to the sciences. We will not concern ourselves with the details, but with the shape of the common struc­ture of science admitted by the positivists. As we have already noted, this structure was designed to show that science represents the most certain knowledge available to human beings, logic and mathematics being regarded as auxiliaries without content, and a form of knowl­edge that might be indefinitely expanded through controlled experi­ment and research.

The general features of science, as understood by the positivists, were roughly the following. First, science is a clearly demarcated body of knowledge that is the only worthwhile object of philosophical con­templation. The clear line of demarcation between science and non­science is roughly (or even exactly) equivalent to the boundary be­tween sense and non-sense, or rationality and irrationality. Second, science is the only hope for the future of mankind, the only instru­mentality for successfully solving the problems facing the human pop­ulation, and as such deserves the support of philosophers. Third, sci­ence has a tripartite structure consisting of logic and mathematics, which provide the language within which scientific results are for­mulated; an experientially given basis, the factual content of science; and at least some theories and hypotheses, which could provide ra­tional expectations about the future given the experiential basis. Fourth, the future of science is optimistic. Since the experiential basis can be indefinitely expanded through controlled experiment, enough infor­mation could, in principle, always be accumulated to provide the an­swer to any intelligible questions. Fifth, there is a potential division of labor between scientists and philosophers. Scientists are constantly expanding the experiential basis and proposing theories, but philoso­phers have the expertise to decompose and analyze the relationship between the basis and theories proposed in order to determine what part of the basis any given theory can be said to explain, and which theories are best supported or confirmed by the experiential basis. Even if a general characterization of explanation and confirmation is possible, the precise values of the relationships of explanation and confirmation linking the basis with available theories will require up­dating as the experiential part of the basis expands, and philosophers can find here a constant source of service in support of the progress achieved by their scientific colleagues.

The major internal tension in positivism is caused by a combination of the first and third characteristics cited above. According to the first characteristic, storytelling (including metaphysical stories) is to be banned from science as not sufficiently grounded in the experiential basis of science, but the problem is to include scientific theories along the lines suggested in the third characteristic, some of which are pretty wild, imaginative extrapolations from accepted data, while ruling out nonscientific storytelling as having no cognitive purchase. The famous rejection of metaphysics was required if positivists were to feel that they knew exactly what was being discussed among scientists so that they could map out the appropriate logical relationships. It seems dubious whether scientific theorizing can be accomodated within such a conservative outlook. No one has ever found an analytically precise way to include scientific theories and hypotheses within science, ex­cluding other forms of storytelling and fitting scientific intuition about the extent of proper theorizing.¹¹ Positivism has provided a restrictive account of theorizing in science because of one attempt to restrict the meaning of theories to some close logical tie with the data in any basis. Some positivists have simply accepted the consequences of their analysis as binding on science, and they have drawn the conclu­sion that our normal intuitions about the role of theories and hy­potheses in science are quite extravagant, if not incorrect.¹² While this illustrates one of the charms of philosophy, we shall pursue here a path designed to protect the intuition that the use of theory and the importance of constantly developing new theories are essential com­ponents of scientific progress.

This brief summary of positivism must inevitably brush aside some subtleties that have been at the center of positivism’s own justifica­tions for the relationship of philosophy and science that positivism wishes to defend. In the logical analysis of science, positivism brings to bear on scientific practice a normative logical yardstick that can evaluate practice in terms of logical rigor, an evaluation that must ultimately complicate any crudely defined border between philoso­phers and scientists. This normative purchase, of which positivism can rightly be proud, is leached away in any philosophy of science that makes total scientific practice the sole standard of scientific rationality. Many positivists also drew on a distinction between the context of justification and the context of discovery, arguing that their logical methods could be realized only in the context of justification, that is, after sufficiently sharp statements of theory and data were available for logical models to come into play. In the heuristics of theory pro­posal, however, scientists were free to draw on any sources, no matter how irrational they might seem. Thinking of a theory and then stating it for other scientists and confirming it were regarded as two quite distinct steps. The process of discovering new theories was conflated with an unanalyzable, and possibly irrational, sequence of acts. The process of confirmation, on the other hand, was subject to a rational and public corpus of rules for proceeding with the analysis of the degree of support of the theory by empirical evidence. In view of the fact that the distinction itself seems implausible and difficult to main­tain, but requires extensive and subtle development if it is to be as­sessed, and the fact that a position will be developed here that par­tially analyzes theory development against the control of data domains, we shall proceed here with an evaluation based solely on positivism’s analysis of the logical structure of the context of justification, which by its own admission is positivism’s major contribution to the under­standing of science.

We can now turn directly to the internal question of the failure of closure of positivism. It is an astonishing fact that no comprehensive and adequate account of the relationships of explanation and confir­mation between the experiential basis and the layer of theory in the positivistic account of the structure of science has ever been provided, even though such relationships are frequently cited in empiricist prac­tice. Neither the concept of explanation nor that of confirmation can be closed according to empiricism for reasons to be developed shortly; and to accomodate the observed features of scientific practice, both must be taken to involve at least some assumptions that cannot be justified solely in terms of the experiential basis and logical consid­erations. The logic assumed historically by the positivists to be the logic of science, roughly the first-order predicate calculus, seems in­adequate to capture these important concepts in terms of the data basis. More recently, intensional, modal, many-valued, and other lands of logical systems have been utilized in an attack on this problem, so far without success.¹³ This diversity, of course, threatens the concep­tual unity attempted by positivism, but we cannot rule out that some exciting developments may be in store. The appropriate relationships may one day be established at the level of data domain and theory to be developed here, but the extent of the problems with a purely empiricistic set of relationships can be developed in the context of positivism.

It seems clear that acceptable scientific theories in a basis at any time must explain at least some of the facts in the experiential basis by permitting deduction of statements representing these facts from other parts of the basis. Positivists originally took the position that deductive scientific explanation of this kind (with suitable restrictions) was the sole requisite kind of scientific explanation, but controversy has arisen on this point. The statistical inferences encountered in many branches of contemporary science may have to be explicated in terms of a distinct notion of statistical explanation if there is to be a compre­hensive philosophical account of scientific explanation.¹⁴ There may, therefore, be at least two relevant notions of explanation associated with at least some bases. The original models of deductive explanation were also restricted somewhat by inability to specify formally what constituted legitimate scientific theories, laws, and hypotheses. Be­cause of this, no one could say which explanations or apparent expla­nations actually contained scientific laws, theories, or hypotheses. An explanation could be defined as a syntactic or logical relationship in­volving putative theories (or laws or hypotheses) and experimental statements, but a semantics could not be worked out that would elim­inate only accidentally true generalizations. Empiricism thus wavered between providing an analysis of explanations and explanation sketches, the latter having only the syntax of proper explanation.¹⁵ All of these problems can be waived, including the precise distinction between laws, hypotheses, and theories, since the problem of closure will arise for deductive explanation even if we assume that all of these niceties have been satisfactorily resolved.

The most widely defended model of deductive scientific explanation is due primarily to Hempel.¹⁶ In this model the deductive inference that is an explanation has two premises and a conclusion. One premise must be a theory, or conjunction of theories that is used as a theory in the relevant explanatory deduction. The second premise, usually found in practice, expresses some known facts or boundary conditions that are necessary to utilize the theoretical premise in a particular case. A satisfactory scientific explanation is then a deduction of the statement to be explained from this pair of premises.

Although scientific explanations may, at least on some occasions, fit the model, and although scientists would be embarrassed to discover that some explained statement did not follow logically from suggested theory and certain background facts, it is quite clear that the Hempel model in its full generality does not capture the intuitive structure of sound scientific deductive explanation. An argument having the struc­ture of a Hempelian explanation may simply not capture any intuitive relationship of relevance between its premises and conclusion of the kind that scientists would expect. This has been shown rigorously by Eberle, Kaplan, and Montague.¹⁷ Thus the full deductive model does not seem to capture the intuitive relationship of relevance between an explaining theory and a factual statement that is to be explained in the general case. The upshot of this result is that the relatively clear Hempelian model has had to be replaced by a group of explanatory models, each member of which offers a restricted model of explana­tion that can be regarded at best as a sufficient condition for scientific explanation if the relevant semantical properties are satisfied.¹⁸ It is absurd in this situation that some philosophers should proceed on the assumption that the empiricist notion of scientific explanation is a sat­isfactorily clear concept.

We have seen that the Hempelian model is too loose, that is, that it lets in at least some intuitive nonexplanations, and hence requires restriction, but it is also too stringent. Many, if not all, of the expla­nations accepted by working scientists in the course of normal scien­tific activity fail to be Hempelian explanations. The basic reason for this is that while scientists want what they explain to follow from what they already know and from the theoretical apparatus they believe to be true in the straightforward sense that the premises of an explana­tion couldn’t all be true while the explained statement was false, they are concerned with this relation only in the space of scientifically plau­sible worlds, and not in the space of all logically possible worlds. The difference is important. If a critic can describe a scientifically plausible world in which an explanation’s premises are true and the explained statement false, any scientist will recognize the need to attempt repair of the putative explanation. On the other hand, the fact that one can describe a logically possible world in which the premises of an expla­nation are true and the explained statement false need not have an impact on scientific practice. The set of logical possibilities is much wider than the set of scientific possibilities, and some logical possibil­ities will be scientific implausibilities.

Let us imagine an anthropologist interested in demography who suspects a migration to have occurred between village A and village B during a certain period, where the villages are part of an extensive archaeological exploration.¹⁹ She is concerned first to prove that a migration did take place, and then to speculate on the reasons for the migration. Perhaps the demographic data, derived from archaeologi­cal findings, show the two villages to have been relatively isolated, and the villages surrounding them to have remained stable in popu­lation during the period in question. We will also assume that the demographic data indicate that the suspected migration occurred so rapidly that the shift in population from A to B could not have been the result of a natural population decline in the one village and a natural population rise in the other. While we re imagining the facts, let us grant data so extensive that any reasonable anthropologist would concede that a migration took place on the strength of the evidence. But while the fact of the migration may seem the only reasonable interpretation of the data, it is not the only logical interpretation. There is no theory that will derive the statement of the migration in a Hempelian explanation from the data, and there cannot be. In the total space of logical possibilities there are such possibilities as a spaceship’s picking up some or all of the population at village A, re­programming it, and somehow returning it to the wrong village. We can assume here that this occurred without a trace in the relevant history. Anthropologists simply do not normally consider the possi­bility of intervention by space visitors, which would enormously com­plicate their work, but our imagined data could not rule it out. Of course, if evidence for intervention by space visitors became ac­cepted, anthropologists might evaluate the migration data in the wider perspective. This example is sufficient to indicate how good inferences made within the constraints of discipline plausibility may be invalid for the logician, who cannot recognize these constraints.

Scientific explanation is actually highly dependent on context, for the set of relevant possibilities to be considered at any point in time is determined by the then current state of scientific knowledge and the associated space of scientific plausibility. It would not be helpful to science to demand that logical rigor be met, since the necessary excluding clauses would make for inelegant and implausible scientific explanations, and they would have to be altered in the event of sci­entific progress anyway. Beyond the common-sense agreement that explanation should be deductive within the appropriate space of pos­sibilities, the allegedly greater rigor and uniformity of logical tests is a complicating factor in the pragmatics of explanation that does not seem to have a clear compensating advantage for scientific practice. Scientists will frequently have a relatively precise agreement on the competing possibilities because of extensive discussion and negotia­tion, but while this may lead to more uniform patterns of inference than are encountered outside of science, it will leave logical rigor unaffected. Invalid arguments are invalid arguments, consensual agreement or not. Philosophical accounts of scientific explanation would prove more illuminating if philosophers were to study these local con­textual constraints, rather than pursuing the path of promoting an excessively idealized logical paradigm with no hope of advantage for scientific practice. But to concede this point is to modify considerably the idea that general methodological remarks can be insightful in all areas of scientific research.

Let us turn to the complementary notion of support or confirma­tion. Initially the notion may seem equally as central as that of expla­nation, perhaps because scientists do discuss the evidence in favor of various theories. We can imagine that two different theories are both useful in explaining the same range of data, or roughly the same range of data, even though they can be shown to diverge on anticipated data. It is legitimate to ask which theory should be pursued, and which theory ought to be accepted for the time being in the pursuit of practical goals. If we could say that one theory was more likely to be true than the other, then we would have a reason to prefer this one for such purposes. At the same time, one might be skeptical, cautious, and rationalistic, and refuse to speak of one as more likely true than the other. In this case one could wait until the data differ­entiated the rival theories, and adopt an agnostic position regarding their merits in the interval.

One version of this policy is the critical rationalist stance of Popper, and it can’t be faulted logically.²⁰ On Popper’s view, one considers only falsifiable theories in science, and one must reject them only if they are falsified by the data. For practical purposes, one might adopt the most highly corroborated theory in a stable data environment for development, or for practical purposes, but the fact that the data en­vironment might change radically and unexpectedly rules out reliance on any inductive inferences to a most likely true theory or hypothesis. Anticipating later discussion to a certain extent, we can notice at this point why confirmation is so problematic on epistemological grounds. Two scientists may be forced to agree after examination of the facts that some theory explains some range of data, even if one of them doesn’t find the theory otherwise promising. Now suppose that two scientists are forced to agree after examination of the facts that one of two theories is better supported by the current data. It can hardly follow that it is irrational to pursue development of the weaker theory on suspected future evidence, and it may be helpful in locating the best theory if the two scientists divide up their labor, each working on the development of one (but not both) of the theories in a coop­erative rivalry, or at least a rivalry constrained by certain norms. Be­cause of the possible advantages of such a division of labor, it is not clear what consequences a precise empiricist theory of confirmation might have for scientific purposes.

The failure of closure of empiricism is quite clear with respect to inductive inferences to a most likely true theory or to a theory with maximal confirmation. No matter how confirmation is construed, as long as it measures in some sense the intuitive notion of support, this observation will remain correct. This will be illustrated here by an example that will exhibit the primary reason for this failure.²¹ In our example, we will attempt to learn something about a coin by tossing it and observing the outcome of the tosses. This example will stand for the general problem of learning from experience. Suppose we have previously manufactured two identically appearing coins, one of which has a probability of one in two of coming up heads when tossed by a mechanism designed to randomize outcome, and one of which has a probability of three in four of coming up heads when tossed by the same mechanism. The latter coin is said to be biased toward heads. We are attempting to learn which of the two coins we have by tossing it. Without going into mathematical details, we expect the sequence of heads and tails to have a higher probability of matching the se­quence predicted by the true hypothesis than by the false hypothesis. If we toss the coin one thousand times, and we obtain approximately three in four heads or one in two heads on the tosses, we are pretty sure which coin we have. Statistical induction proceeds on such in­tuitive bases, even though the mathematical theory can be used to compute precise probabilities and to settle intuitively obscure alter­natives. We know in theory that we can never be certain about any such inference. In the case of the coin, logically all of the tosses could show heads no matter which hypothesis was true. In spite of this fact, we have little trouble reaching seemingly settled convictions on the basis of statistical reasoning in clear circumstances, and we can easily develop the formalism that seems to express this situation.

Let’s look at what we have to assume in order to legitimate our inferences from experience in the case of the coin. If we set down all of the possible specific sequences of 1,000 tosses before we start ex­perimenting, it may seem tempting to suppose that in regarding all of them as equally likely, we are not making any empirical guess about the actual nature of the world, but are simply expressing the logical situation. Now suppose we have tossed the coin 999 times and have 749 heads among these tosses. Intuition says that the coin is the biased coin in this situation, and that heads is therefore more likely than tails on the next toss. But we have no mechanism for changing our original assumption, which is that heads and tails are equally likely on any particular toss, hence on the last toss of the coin. The original as­sumption thus turns out not to be neutral at all. It does not provide a logical space within which we can make discoveries. It actually leg­islates that the coin is fair, after which we can’t discover from expe­rience that the coin is biased. No matter what we have obtained on our 999 tosses, either heads or tails remains equally likely on the next toss.

We can try another assumption. The old assumption was that there is no connection between what we observed and what we hadn’t ob­served, that they were independent. Let us assume in a simple way that what we haven’t observed is likely to be similar to what we have observed. This is not to refute Hume, but to assume that he is wrong. We will assume, not that each specific sequence of 1,000 tosses is equally likely before we start, but that we are as likely to get any fixed number of heads in 1,000 tosses as any other. This assumption has an interesting consequence. There is only one specific way of getting 1,000 heads or of getting 1,000 tails. There are more specific ways of getting 999 heads or tails, and this number continues to rise until we look at the specific sequences for getting 500 heads or 500 tails.²² If we assume that all of the ways of getting a fixed number of heads are equally likely, and that we are as likely to get any fixed number of heads as any other, our expectation before experiment has a different structure. Of two specific sequences that have 500 or more heads in them, and that differ in that one of them has a greater num­ber of heads in it, that one is more likely that has more heads, because it comes from a smaller set of original possibilities, which have to divide up equally the equal probability of getting a fixed number of heads.²³ Now suppose we have 999 tosses in which there are 749 heads, and we are anticipating the last toss. It is more likely to be heads than tails, in virtue of this distribution. If we have 999 tosses in which we have 500 heads, the last toss is also more likely to be heads than tails, but there is a difference in the probabilities. The probability of getting a head on the next toss when we have 749 heads is larger than it is when we have 500 heads, since our method of deriving probabilities assigns getting 750 and getting 501 heads the same probability, but the probability of getting 750 heads is divided by fewer ways of achieving this result. Thus, we can apparently learn from experience if we make this assumption concerning the probabil­ities before we start. We can argue that the probability of getting a heads on the last toss is greater if we’ve had 749 heads than if we’ve had 500 heads, quite in conformity with intuition.

In our example, we have seen that we can obtain what seems the intuitively correct result by making some empirically unjustified as­sumptions about the nature of the world. The history of this point is a little more subtle. At first it was thought that the assignment of prior probabilities was a logical measure over a language describing the world. Now since different logical measures result in different prior probability assignments, and hence in different appraisals of the sig­nificance of the coin tossing, we are left with the alternatives that either logic has content or some substantive presuppositions must be made if a logic of confirmation is to produce results in practice. Since the claim that logic has no empirical content was important histori­cally to the positivists, they were forced gradually into the position of conceding that some substantive presuppositions are necessary in or­der to obtain a suitable theory of confirmation. No self-consistent em­piricism employing a notion of confirmation, therefore, seems to be possible.

The nonempiricist assumptions required to augment empiricism can be squeezed into a choice of formal language or into a choice of logics, but they are unavoidable. If a formal language is chosen for expressing scientific statements, it is a selection from a set of possible languages, and any logical distribution of probabilities over its simplest sentences will reflect the substantive aspects of the structure of the particular language chosen. A language that asserts that there are an infinite number of objects and one that does not so assert will lead to different probability measures that will be reflected in different confirmation estimates in at least some cases. But even if a language can be found that achieves only intuitive results, the move to a formal language is a concession to rationalism, since rationalism can be viewed as an attempt to find languages from which correct information about the world can be read in scientific practice.

In the context of everyday inference, scientists make assumptions about the world that affect their notions of evidential support. They are likely to assume that only a few explanatory possibilities exist, and discuss which of these is most likely given the evidence. These ar­guments may be so informal as to defeat the point of formal philo­sophical clarification, partly because the scientists involved see the context of these discussions as constantly altering. For example, the use of statistical inference nearly always assumes that some distribu­tion is present, and then attempts to work out the consequences of that assumption. This is to bypass the philosophical problem of in­duction, rather than to solve it. For example, one may assume that a population is normally distributed in a standard way, and then at­tempt to calculate the value of the mean and the standard deviation of that population on the basis of the empirical evidence. Sampling plus the assumption about the general distribution leads to the de­sired description of the total population. This sort of problem tran­scends empiricism because the assumption about the distribution can­not always be empirically justified, and because the kind of distributions considered will depend on the plausibility space of the local scientific investigation. Scientists are just likely to try what has worked in what they see as similar situations, an attitude that flirts with profligacy for the methodological puritan. We will attempt to show how the intui­tive correctness of this procedure can be rationally grounded once the constrictions of strict empiricism have been laid to one side.

If empiricism cannot be closed, why do so many philosophers re­main committed to empiricist programs, attempting to refine empir­icism rather than looking for alternatives? Such philosophers seem in fact to exhibit the profile of Kuhn’s normal scientists, assuming that the anomalies surrounding explanation and confirmation will be set- tied by other specialists and, hence, allowing themselves speculations that proceed on that assumption.²⁴ Looking further, empiricists typi­cally have an investment in technical and analytical tools that is di­rectly threatened by recognition of the general failure of closure in empiricism. But the construction of axiomatized theories, the analysis of causality, and similar topics would still be of importance even if the pure epistemological stance of empiricism is let go, as we shall see. But there is the underlying point for many philosophers that the aban­donment of the direct empirical anchor would threaten anarchy and relativism for scientific knowledge. This issue is probably crucial. The stakes in abandoning empiricism are so high from this point of view that they are equivalent to the intuition with which empiricism be­gins, the intuition that scientific examples of a certain kind are our best examples of genuine knowledge and must form the starting point of a satisfactory epistemology of science. A satisfactory postempiricism must preserve intuitions about these examples without threatening loss of objectivity.

To amplify this point slightly, suppose that it is conceded that back­ground values and attitudes are coded into paradigms in order to pro­vide scientists working in any area with a basic set of problems and kinds of solutions to these problems, but that these paradigms may undergo sudden and not entirely foreseeable shifts, as in Kuhn’s de­scription of scientific activity.²⁵ In our discussion of explanation, we noted that scientists are often constrained by intuitions about scien­tific plausibility, a view that would mesh nicely with Kuhn’s account. Philosophical empiricism sees this view as threatening the objectivity of science, the conception that science progresses toward truth over time, and it even threatens the optimism for the future of science that is associated with empiricism. The slightest concession to internalized intuitive constraints seems to threaten relativism and even chaos. If the history of sociology of science suggests that scientists are governed by paradigms, the empiricist must see this as a lapse from normative ideals of disinterested experimentation and completely open logical criticism. Clearly the pressures toward remaining inside an empiri­cist’s framework are quite strong for analytic philosophers who wish to retain a privileged conception of sound scientific advance, and the philosophy of science must respect these pressures.

A Dynamic Approach

In the history of science one encounters many cautious experimental­ists who are suspicious of speculative science, and many bold theorists

who are impatient with the repetition of clear experimental achieve­ments. Both sides of the debate can score off recognized folly on the other side and develop a sound defense of their preferred position on the basis of key examples. Could science as a whole advance without bold speculation to point the way? Could science be trusted if it weren’t for the cautious repetition and testing of results? Since the answer to both of these questions is clearly negative, there is some­thing wrong with the attempt to reduce science either to bold theo­rizing or to cautious experiment. Without attempting simply to com­promise between them, both activities will have to play a role in our account of science. If rationalism seems best to support theorizing, and empiricism best to support experimentation, they must both fall short of epistemological adequacy. For philosophers in these tradi­tions, retention of their ideas must ultimately result in a considerable rewriting of scientific history. This seems too high a price to pay for philosophical theory.

Many attempts to avoid standard empiricist philosophies of science have not been able to avoid the conceptual framework of empiricism in accommodating the pressure from scientific history. Feyerabend, for example, has argued that there is no logical structure common to various scientific practices, so that the positivist attempt to find one would put blinders on scientists if they were to follow positivistic suggestions about method.²⁶ Feyerabend likes to consider as repre­sentative scientists figures like Galileo, who clearly violated any con­sistent methodological rules that might have been abstracted from the surrounding practice of his time, and who also violated in practice some standard empiricist notions of scientific rationality. In view of this situation, Feyerabend suggests a whiff of anarchism, and proposes that the concept of methodological rules be abandoned and that sci­entists and philosophers be encouraged to find and pursue as many alternative theories as possible to those now being developed. What seems here to be totally at odds with the standard view—a call to the greatest possible diversity and the scumbling of any clear line of de­marcation between science and nonscience—actually shares many fea­tures with the empiricism it opposes. Each scientist is conceived as a solitary individual confronting amorphous data, free to theorize on his or her own. These scientists will still engage in standard forms of scientific argument and controversy, which Feyerabend expects to be usefully heightened by a more articulate diversity of outlook. Feyer- abend’s view that science (or society) should keep all possible tradi­tions alive is politically naive.²⁷ No social theory is presented in his writings to make it at all clear how a multitude of traditions could appropriately be kept viable and yet in useful communication. Crite­ria and mechanisms for the protection of the weak are not elaborated. Feyerabend’s advice is also historically naive. Some scientists, partly on competitive grounds, always seek alternative accounts to those cur­rently reigning in any area of research. The real problem is to do this at an interesting level. Data frequently rule out all but one or two plausible alternative theories, and the advice to find more is ineffec­tive without hints on how plausible alternatives are to be found. The scientists who don’t pay attention to philosophy—and there are many— are hardly to be liberated by philosophical pronouncements of meth­odological anarchy. With modern big science, there may be economic silliness in proposing that every conceivable alternative tradition should be equally supported and encouraged. Perhaps just what is done is optimal for the rate of growth of science; whether true or not, this is just as unprovable as the advantages of anarchy. Anarchy or dadaism, while perhaps a healthy philosophical antidote to overly restrictive philosophies of science, doesn’t seem to provide an account of science that brings us closer to answering our questions about the superiority of the insights of science into the empirical world, nor does it offer workable advice for improving or justifying scientific practice. Rather, anarchy or dadaism compromises empiricism and rationalism, but in the laziest possible fashion.

Kuhn’s approach, so intensely disliked by empiricists, abandons any cumulative notion of the data to which theory is fitted, and makes data partially the result of observation that is determined by a back­ground of paradigms. Revolutions occur in science, in which these background paradigms change; and after a revolution old data may be completely irrelevant to new paradigms, and thus there is no way to utilize them to evaluate the new theoretical outlook. Old data may simply be forgotten. For empiricism, there is no way to anticipate the content of data gathered by new instruments, and for Kuhn there is no way to anticipate the new theoretical outlook that may come into view when anomalies lead to an older outlook going under. In empir­icism, even sophisticated versions, the data are perfectly consistent, determinate, and fixed at any point in time, at least after methodo­logical laundering, and they determine the value of theories. In ra­tionalism, including the variety offered by Kuhn, there is a fixed and determinate theoretical background that determines the value of data. There is give and take in neither. Popper allows one counterexample to prove a theory false, and Kuhn allows that sufficient anomalies will typically lead to adoption of a new paradigmatic background. What we do not find in either view is a constant accommodation of theory to experiment, or vice versa. Normal science as puzzle solving sug­gests wrongly that the pieces are given in advance, and need only to be correctly manipulated.

At any given time there will be experiments and theories or, as we shall put it more precisely, scientific facts comprising data domains and scientific theories. The significance of both cannot be given at the time when they are both first introduced and considered. What a fact is will depend on the development of theory to give it significance. What a theory is will depend on the development of scientific fact to give it significance. Were the significance of facts given with their discovery, then empiricism would be correct, and theory would be dependent on fact. Were the significance of theories given with their formulations, then rationalism would be correct, and facts could only confirm the theories they were collected to test. Both philosophies assume something in advance of further fact.

Empirical reality is too complex to be more than partially captured in any actual discourse, including human scientific discourse. All suc­cessful theories, as indeed all successful fictions, show us a way the world is without revealing the way that the world is, even partially.²⁸ They are thus false of total reality, while they may be true of some aspect of it. Our discourses describe an aspect of the world, and they describe the world most adequately at the rough level of our dis­courses, the level of human perception, not at the level of the very large or the very small with respect to that level. Rationalism, looking for comprehensive system, and empiricism, which supports typically the unified science hypothesis, share the conviction that empirical reality might in principle be fully described.²⁹

A dynamic approach that transcends traditional empiricism and ra­tionalism should not lapse into an easy relativism incompatible with our intuitions about the objectivity of science. It is not being said that all of an apparently incompatible set of theories can be true of reality; rather it is being said that all theories are (strictly) false of reality. Because of this, neither realism nor instrumentalism fits neatly into the view being developed. Insofar as theories show us a way the world is, a way we can expect to utilize in constructing new experiments, they are realistic. They work because they mirror reality, but their mirroring is always imperfect and can be improved. What can provide the principle of division of subject matter into controllable areas within which progress is a measurable achievement, even if the division is seen to violate philosophical desires for grand theory? Previous views have left the role of scientific experimentation out of account. A the­ory will be proposed to explain a range of data gathered by some fixed instrumental means. As these instruments are refined, so are the data, and theory will have to adjust to such refinement. Empiricism as­sumed that we can learn facts about nature, but instrumental means only produce a data text whose relationship to nature is problematic. A good fit with refined data constitutes success for a theory, and con­tinued success is the clear indicator of progress. The ability to fit refined data constitutes success even where boundaries must be ad­justed or auxiliary hypotheses added, provided that simpler rival the­ories do not materialize. Scientific progress will be measurable only for specific theories against such data domains on this view, and in these domains falsification cannot be sharp because the significance of apparently falsifying data cannot always be known when they are first taken from instruments. Over a period of time, the boundaries of a data domain may settle because of recognition of standard instrumen­tation for that domain. When new data are produced by new kinds of instruments, a new domain may be created for which quite different kinds of theories are needed. This fact will not erase the significance of the theories fitting established domains, thus allowing success of theory to have a permanent place in scientific history. These topics will be developed below.

The view proposed here is that fictions, including scientific theo­ries, are not to be regarded as describing hypothetical worlds, but as describing aspects of a single, very complex reality. Scientific theories are fictions that in many cases anticipate aspects of reality to be ob­served later, but fictions that can be (counterfactually) regarded as true, just like various portraits and novels can be regarded as impor­tant insights into their subject matter. Although it may seem initially outrageous to assimilate novels and scientific theories as both reveal­ing aspects of empirical reality, we can differentiate them. Theories, where they offer empirically valid constructions, are distinguished from other fictions in that the offered constructions satisfy criteria of ex­perimental method and interpret important data text. To avoid a re­lapse into some form of vacuous rationalism, it is necessary to show how we can get outside the circle of theoretical ideas so that experi­mental results can be taken as a check upon and as causing revisions in, the theories and theoretical results that produced them. How is it that theories, if they control observation, do not reach down all the way into the data to make them useless except as confirmation of the theories that produced them?

If theory-laden observation cannot be avoided, we can still make it clear how observation can contradict theory. Unusual observations can be made against a background of everyday theoretical anticipa­tions. Roentgen did not expect to see anything unusual when he de­veloped the famous photographic plate, byt he did. The very fact that language has a loose fit to the world allows such primitive observa­tions of the unanticipated to be described, at least in graphic terms. At first such strange and unanticipated observations may seem diffi­cult to analyze until enough theory is built up to enclose them.³⁰ In many cases, an observation is of no significance until a theoretical anticipation is developed that makes it significant. The bubble of rare gases at the end of experiments designed to filter out the constituents of air was seen as an artifact of an insufficiently completed experiment until the possibility of rare gases was conceived. This is why the title of a first discovery is generally awarded, not to the scientist first to confront a particular phenomenon, but to the scientist first to confront the phenomenon and recognize it (in an anticipatory fashion) for what it is in terms of the current theoretical framework.³¹

Now we can turn to everyday cases of experiments run to test a more or less explicitly formulated theory. First, a theory constrains observation by determining what to look for. When objects of differ­ent weight (properly: mass) were dropped in the seventeenth century to study their rate of fall, the theoretical background took only weight to be relevant to rate of fall, not, for example, color or shape. Objects have too many properties, properly an infinite number, for experi­ment to differentiate them and rule them out as relevant variables. A theory or theoretical concept makes a bold conjecture. It says what is relevant, and what to look for. Because of this, Galileo’s theoretical background determined that he plot weight against rate of fall, and in this sense his observation was theory laden, but it did not determine that his plotting could come out in only one way. As experiments are repeated, they never produce exactly the same data in interesting cases. Thus the data aren’t determined in every detail by prior theory. Only the kind of data to be sought is determined by theoretical ex­pectation. Theory indicates what needs to be attended to in order for an experiment to come out right.³² If it weren’t for theory, we could never be even reasonably sure that we had isolated the right factors to observe, and that we were allowing them to run a significant course for our enlightenment.

Philosophers frequently confront theory and data, and either theory threatens the integrity of data because observation is thought to be theory dependent, or the data are taken to be fixed by observation independently of theory, so that theory must adjust to changing data and cannot evaluate, but merely explain, the data. If the data of sci­ence were typically subjective impressions or observations, then our reading of them would be suspect if our theory of the observations underwent a change. We might suspect that if we were to observe again, we would observe differently. The advantages of a scientific instrument are that it cannot change theories. Instruments embody theories, to be sure, or we wouldn’t have any grasp of the significance of their operation. They can be taken to reveal a way that the world is in interaction with the world, just because their properties remain relatively fixed. Instruments create an invariant relationship between their operations and the world, at least when we abstract from the expertise involved in their correct use. When our theories change, we may conceive of the significance of the instrument and the world with which it is interacting differently, and the datum of an instru­ment reading may change in significance, but the datum can none­theless stay the same, and will typically be expected to do so. An instrument reads 2 when exposed to some phenomenon. After a change in theory, it will continue to show the same reading, even though we may take the reading to be no longer important, or to tell us some­thing other than what we had thought originally.

An interpretation of other sorts of text, such as Biblical materials or Shakespearean drama, deals with a fixed quantity of data represented by a finite amount of text to be interpreted. Clashing interpretations may be irresolvable, since each interpretation sees the text differ­ently, but the text to be interpreted may be finite and fixed unless lost manuscripts are discovered. Such interpretation seems subjective to many, and interpretation itself seems based on insight or feeling, since there is no way to go beyond the given text to resolve disputes or to locate the reality that it describes. In science the situation is different, but not because the data necessarily measure reality, as traditional empiricism has claimed. The total text to be interpreted, the text of data, is not fixed before interpretation. The text of fact is constantly expanding, and can seemingly be endlessly expanded. Thus the clash of interpretations of fact, the clash of theory, is always po­tentially resolvable by expanding the factual text. What may seem objective by comparison to other textual interpretation because of this potential for the resolution of conflict does not require that language be circumvented in direct experience of nature. It is not part of the account offered here that one can step outside of scientific data to determine that they are actually true of the world. The primitive raw data of scientific experience have an unknown relationship to the world and are determined by the history of instrumentation.

The hypothetico-deductive account never produced a true dialec­tical interplay between theory and data. Because of its assumption that data were revelatory of nature, it always made data the test of theory and oversimplified the connection between theory and data. Our aim is to make data text as open to skepticism as theory, and to observe that advances in theory or instrumentation may render data useless or obsolete. Facts will not be traced to the level of individual experience, and they will prove to be as constructed as theory. This will allow us to avoid the simplified notions of explanation, falsifiabil­ity, or confirmation that have rested on simplified notions of scientific fact.

We have now made some progress toward discerning the elements required in a dynamic account of science. The interplay between the­ory and experiment is not simply an interplay between theory and subjective experience, but an interplay between theory and scientific fact, where a scientific fact is the product of an interaction between a scientist and the world as mediated by a scientific instrument in the typical contemporary case. That instruments will function similarly with scientists who hold quite different theoretical outlooks begins to point to a realm of scientific fact that is not dependent on subjective or intersubjective impressions, but much remains to be done. It will be argued that the history of instrumentation provides a unidirectional explanation of progress, in that later, more refined instruments are uniformly preferable to earlier instruments directed toward obtaining data in the same domain, and that this fact is essential to understand­ing the creation of what will be called data domains for scientific the­ory. Above these domains a complex dialetic of scientific fact and theory will hold sway, but the relevant facts will not be the impres­sions of individual scientists of the data in the domains, but publicly negotiated provisional fixed points for scientific argument about the significance of theory. What is left of empiricism is that these facts will play a coercive role in determining the development of theory.