To my regret, there is little recent literature cited, because there is little written on statistics from a philosophical and non-technical point of view. There also is an almost complete absence of formulae, which I do not regret at all; this absence is because simulation in general, and resampling in particular, make formulae unnecessary. The book's goal is large: To present the basic elements of statistical inference without absurdities or inconsistencies, and to resolve on-going controversies about fundamental conceptions. The reader may well disagree with the basic approach, that of the operational definition rather than a structure built on first principles, and the reader may also feel that I skirt the key issues rather than overcome them. But such disagreements are a matter of taste, whereas it should be a matter of ascertainable fact whether the book succeeds in making its main statements clear and mutually consistent, within the book's chosen basic approach. OUT AND MAYBE USE LATER The present volume presents the philosophical ideas at a high level of abstraction for the consideration of professional statisticians and philosophers; also unlike a text, it does not contain a survey of resampling techniques. If anyone buys the book and feels that s/he has not received full money's worth because some of the material is not new to them, please write me for a refund. The writing style in this book is a simple one, born of a desire to make reading as easy as possible. Simplicity has a drawback, however; there is a psychological need for writing to be somewhat difficult, which partly accounts for the effective- ness of including formulaic mathematics in one's writing. (T. S. Eliot wrote somewhere that a poem must be easy enough to under- stand, but hard enough not to be understandable immediately.) I hope that simplicity of style does not mislead the reader into thinking that the ideas are not deep. Indeed, as I urge through- out the book, the fundamental ideas in statistical inference are as deep as any in the intellectual enterprise (excluding those that are apparently deep only because they are fundamentally nonsensical). And I hope that the reader recognizes the novelty in the ideas presented here despite the simplicity of treatment. I say this in part because I want credit for these ideas, but even more so because I want the reader to take them seriously. Only the fundamental and controversial issues in statistics are covered here. Methods such as regression (whose essence is not probabilistic) and path analysis are hardly mentioned here (though see Chapter 00 on the role of regression. Readers interested in how I treat these subjects may consult Simon and Burstein (1985). page 1 statphil sintro Chapter 1 4-1-6900 PART I: GENERAL PHILOSOPHY OF STATISTICAL INFERENCE CHAPTER 0: INTRODUCTION Statistical inference is a set of devices designed to help us comprehend and deal with the world in which we live. This book'S primary aim is to clarify and resolve the confusions at the conceptual base of statistics. Its secondary aim is to provide a theoretical rationale for the use of resampling (Monte Carlo) methods in statistics, and to systematize its practice, illustrate the power of the "new statistics" in clarifying the theory and bettering the practice of statistical inference. Statistical inference seems mysterious to the uninitiated. And situations where knowledge is uncertain seem different in nature from situations where knowledge is clearcut. But in fact there is no clearcut distinction between situations of certainty and uncertainty. Consider the analogy of a two-horse race. In most cases our unaided visual faculties can easily determine the winner; that is, we can usually determine that the probability a given horse won is either zero or one. But some races are so close that our eyes alone are not sufficient to determine which horse won, and observers differ in their judgments; these are situations in which the probability that a given horse won is somewhere between zero and one. In such cases we resort to photography or electronic determination to resolve the "photo finish". Similarly, we call upon statistical inference to help us resolve those situations in science, business, medicine, sports, and other knowledge-creating and knowledge-using arenas in which the data are sufficiently unclear that our unaided intuition does not enable us to agree which data constitute the "winner", or we need to asses the reliability of our best estimate. These are the situations of uncertainty wherein our naked faculties do not suffice. These uncertain cases are only a small proportion of all the situations we encounter, but they can be important. And cases requiring statistical inference are becoming more prominent with each decade, it would seem, if only because of the increasing availability of quantititative evidence. Viewing statistical inference in this way should reduce its mystery, which should be welcome to the layperson. Such demystification may not be considered desirable by some technicians, however, because (they say) this viewpoint - together with the availability of resampling methods - may lead laypersons to take probabilistic statistics into their own hands and hence to lead them into error as they try to do it all themselves. It is often said that statistics is applied probability theory. That is about as true as that engineering is applied calculus, financial and national accounting are applied arithmetic, and art criticism and political science are applied logic. Computing probabilities is the smallest part of statisti- cal inference, and the least difficult part intellectually - even though the development of the formulaic mathematics of probabili- ty and statistics has been a wonderfully challenging and valuable feat during the past four centuries. The analysis of the context of a statistics problem, the proper posing of the question, and the interpretation of the results of the probabilistic calculations are much more difficult and fraught with error than are the probability calculations alone. And unlike the probabilistic calculations, the other aspects of statistical inference cannot be reduced to logical tests of correctness. Rather, inference requires judgment and art, though this is difficult for some scholars to accept. I am not a professional mathematician or academic philosopher. Rather, I write as a person who has been doing empirical statistical work for 35 years, mainly in the field of economics and demography but also in psychology, sociology, business, and library science. I also write as someone who has since the late 1960s been working with, pondering, and teaching the resampling (Monte Carlo) approach to calculating probabilities in statistical inference (including the bootstrap) as a handmaiden to empirical research (see Simon, 1969). This book shares a basic outlook with my previous books about thinking and decision-making, and it overlaps with them. The others are: Basic Research Methods in Social Science (New York: Random House, 1969, third edition, with Paul Burstein], 1985), which is about the scientific research process; Applied Managerial Economics (Englewood Cliffs: Prentice-Hall, 1975), a text on business and other decision-making; Resampling Statistics (Boston: Wadsworth, 1993), a text in the resampling method; and The Science and Art of Thinking Well, which encompasses a wide variety of ways of using one's mind to the advantage of oneself and of others. My Easy Resampling Answers to Fifty Challenging Problems in Probability may also be of interest to readers of this book. This book is not a compendium of resampling methods. For a a wide variety of illustrative methods, one may consult Simon (1969; 1975/1993/1996), Noreen (1989), Manly (1991), and Efron and Tibshirani (1993). SHAKINESS AND CONTROVERSY AT THE FOUNDATIONS OF STATISTICS There is much controversy about the fundamentals of statis- tics. This book aims to show that most (perhaps even all) the controversial issues can be settled by recognizing that all the contending points of view are appropriate in some domains and for certain problems, but not elsewhere. And using the philosophical tool of the operational definition<1>, the apparent incompatibilities of the various points of view about statistics can be resolved, and they can be integrated into a consistent theoretical framework. As eminent Bayesian statistician Leonard Savage noted, the bases of any science are often its least solid elements. "[T]he foundations are the most controversial parts of many, if not all, sciences." And this is especially true of inference. "As for statistics...[its foundations are] as controversial a subject as one could name." (1972, p. 1). As an illustration of these controversies, one of the greatest modern statisticians, Ronald Fisher, refers to the work of two other great moderns as follows: ... It is to be feared, therefore, that the principles of Neyman and Pearson's "Theory of Testing Hypotheses" are liable to mislead those who follow them into much wasted effort and disappointment (1973, p. 92). In turn, another great probabilist has this to say about a key part of Fisher's work: I do not understand the many beautiful words used by Fisher and his followers in support of the likelihood theory. The main argument...does not mean anything to me (von Mises, 1981, p. 158) There is sharp disagreement between Bayesians and non- Bayesians. For example, a Bayesian textbook writer has this to say about non-Bayesian writing: When I first learned a little statistics, I felt confused, and others I spoke to confessed that they had similar feelings. Not because the mathematics was difficult -- most of that was a lot easier than pure mathematics -- but because I found it difficult to follow the logic by which inferences were arrived at from data...the books I looked at were not answering the questions that would naturally occur to a beginner, and that instead they answered some rather recondite questions which no-one was likely to want to ask... But attempts such as those that Lehmann describes to put everything on a firm foundation raised even more questions. (Lee, 1989. p. vii) An inter-disciplinary team (Gigerenzer et. al., 1989) asserted: The idea spread by the textbooks that "statistics" is an uncontroversial, objective instrument for inductive inference is, of course, an illusion. Statistical theories diverge not simply in the third decimal place, but in the very questions they ask. (p. 228) Yet despite the fundamental controversies, most textbooks discuss inference as if there is consensus on the subject within the profession. Gigerenzer et. al. (1989) studied these texts in depth and concluded: ... all of these unresolved controversial issues, con- ceptual ambiguities, and personal insults have been more or less completely suppressed from the textbooks... Although the debate [about significance testing] continues among statisticians, it was silently resolved in the "cookbooks" written in the 1940s to the 1960s, largely by non-statisticians, to teach students in the social sciences the "rules of statistics." Fisher's theory of significance testing, which was historically first, was merged with concepts from the Neyman-Pearson theory and taught as "statistics" per se. We call this compromise the "hybrid theory" of statistical inference...(pp. 106-107) <2> But the standard pastiche that is routinely presented - that which Gigerenzer et. al. call the "hybrid" theory - is simply an illusion. This patchwork would be rejected by all the major intellectual figures whose elements are mixed into it. [I]t goes without saying that neither Fisher nor Neyman and Pearson would have looked with favor on this off- spring of their forced marriage (Gigerenzer et. al., pp. 196-7) Because this book finds that the controversies in the field arise mainly because different schools of thought focus upon different sorts of problems, the book systematically employs the various procedures and their logics for the particular circum- stances for which they were originally designed and fit best. But the book goes further. It shows, I believe, that the different methods are all theoretically compatible with each other. This is quite different from what Gigerenzer et. al. call "ecumenism". That is, the presentation here is not combination of differing intellectual cultures living in peace with each other, but rather an intellectual synthesis. Illusory compromise among basic points of view, with its suppression of discussion of foundational ideas, has had grave effects on understanding and practice. As a consequence, scientific researchers in many fields learned to apply statistical tests in a quasi- mechanical way, without giving adequate attention to what questions these numerical procedures really answer. (Gigerenzer et. al., 1989, pp. 105, 106) This book aspires to resolve the fundamental controversies by dissolving the basic confusions. If one hews closely to an operational-definition view of probability, the apparent contradictions and the grounds of controversy disappear (except with respect to the conventional concept of confidence intervals). And with respect to each particular case (or type of case) that we seek to address, one can lay down a reasonable and perfectly understandable approach. The approach offered here may not be "justifiable" in terms of one or another axiomatic foundation, but it seeks to be pragmatically sound in the sense that it will lead to more reasonable decisions than other ways of looking at the matter. The main tools used in this integration are a) the concept of the operational definition, which obviates all arguments about the appropriate definition of "probability," and also goes a long way toward eliminating conflicts about the proper place of the Bayesian, Fisherian, and Neyman-Pearson points of view; and b) the technique of resampling (Monte Carlo simulation) to remove difficulties connected with the estimation of probabilities once the problem has been delineated. <3> THE INHERENT DIFFICULTY OF STATISTICAL INFERENCE A successful statistical inference is as difficult a feat of the intellect as one commonly meets, in my judgment. This is not because of mathematical difficulties. Rather, it is due to the long chain of reasoning connecting the original question with a sound conclusion; indeed, the mathematical operations involved in estimating probabilities once the problem has been correctly specified can be straightforward, especially when one estimates with the experimental resampling method rather than with formulaic sample-space methods. Indeed, perhaps the greatest benefit of the resampling approach is that it clears away the mathematical difficulties so that the difficult philosophical and procedural issues can be seen clearly, and hence may be tackled head on. Ironically, however, this characteristic of reducing the computational difficulties has also been a drawback of the resampling method; by making the necessary mathematical operations so simple as to be accessible to any clear-thinking layperson, resampling has made the assistance of professional statisticians seem less necessary, which naturally educes resistance by the traditionalists in that profession. To restate the point: The great challenge presented by the ideas of statistics does not stem from the need for a large body of prerequisite knowledge, or for mathematical sophistication and inclination. The challenge stems, rather, from the inherent difficulty of making sense of a complicated situation. Indeed, if any particular situation is not hard to understand, statistical inference is not needed. The difficulty lies in there being a very long sequence of decisions that must be made correctly about such matters as the nature of the correct hypothetical population, the correct sampling procedure, and so on. This essential difficulty will be seen more clearly in Chapters 00 where canonical procedures for confidence intervals and hypothesis tests are set forth. The book assumes that every statistical problem contains at its core a problem in probability estimation. The simplest sort of problem is to state the (absolute) probability that a given model produces results like the set of data in the sample of observations. A second sort of problem, which builds upon the simplest problem, is to state the relative probabilities that two or more models produce results like the observed sample. Once the question has been correctly formulated in a technical form such as this, the actual estimation of probabilities is quite simple. STATISTICS AND ACADEMIC PHILOSOPHY There is a long philosophical tradition of studying how to distinguish truth from falsity, both in logic and in scientific hypotheses. Until this century discussion mostly was limited to yes-no distinctions, rather than the sort of graded assessment of truth and falsity that is more consistent with the notion of probability. And it turned out that as soon as one moves toward a more probabilistic treatment of truth and falsity, the subject becomes much more complex, and much harder to treat in a technical fashion. The result has been that academic philosophy has come very late to dealing with statistics; Kaplan (1964) is a shining exception. <4> And as a working scientist who only later addressed the philosophy of science, Michael Polanyi properly viewed philosophy as the handmaiden of science. (See especially his Personal Knowledge, 1962, a sensible and practical work.) The present book is in especial accord with Polanyi's writings that there is inevitably some non-objective aspect - what Polanyi calls a personal element , and what I usually call judgment - to all scientific statements.<5>Probability itself was largely left to the mathematicians, and statistics to practicing scientists. And when philosophers have made forays into the field, they have usually focused on technical issues which have led them to neglect the crucial non-technical issues.<6> Introduction of probabilistic considerations greatly complicates matters. Consider for example Popper's falsificationist notion; one cannot prove a theory but one can falsify it with a single counterexample. Yet in the practical world of science or craftsmanship or enterprise, a single counterexample experiment or datum almost never is sufficient to kill a theory, because one can never be sure that the experimetn or datum is completely reliable or relevant. On the other hand, it is beyond doubt that the increasing accumulation of confirming evidence increases the propensity of scientists and decision- makers to rely upon a theory in subsequent actions. Everyone who has participated in discussions of theory together with data must recognize how it will be forever impossible to produce formal criteria that can bring together different opinions on what is reasonable to conclude on the matter. It is equally clear that the formal procedures of statistics can help clarify such discussions and often reduce and/or sharpen the differences opinion. The point is that if philosophers are to be helpful in the study of knowledge-getting in a modern world, they will have to temper their value for formal technical analyses, and enter into the messy and less-than-objective give and take of everyday scientific discourse. It is an important fact that most of the useful philosophical treatments of science in the Twentieth Century have come from persons who began as working scientists and later turned to philosophy either part-time or full time; this includes such persons as Michael Polanyi (1962; 1969), John Ziman (1968), and before them Einstein, Bohr, Bridgman, Plank, and Heisenberg, to name a few of that extraordinary generation of physicists in the first half of the century. Morris Raphael Cohen and F. S. C. Northrop were exceptions; both treated probability and scientific inference in a reasonable and practical fashion<7>[fn-s1]. And Abraham Kaplan (1964) deserves favorable notice here, too. NOVELTY, SIMPLICITY, AND CREDIT Though it is difficult for any author to view his or her own work with any objectivity, these are the main elements in the book that I believe are new: 1. Though many philosophers and statisticians have discussed continuity in connection with forecasting, the systematic analysis of the role of continuity and sameness - described in Chapter 2 as the key concept in inference - is a novel treatment of this fundamental concept, I believe, . 2. The chapter on causality (first published in Simon, 1969 and 1970) seems to be the first explicit statement of the first major advance in the subject since David Hume's seminal treat- ment. The analysis presented here, based on an operational- definition approach to the concept, follows pathbreaking pragmatic decision-connected illustrations of this advance in epidemiology (in connection with the 1964 Surgeon General's Report on Smoking and Health), in the study of juvenile delinquency (Hirschi and Selvin, 1964), and probably elsewhere, but none seem to have tackled the concept of causality in its broad generality. This analysis fits hand-in-glove with the other ideas in Part II of the book. 3. The analysis of resampling as a device that does not require the calculations of the size of the sample space and parts of it, described in Chapters 00, seems not to have been suggested before, to my knowledge. 4. The broad idea of using Monte Carlo simulation to handle most everyday problems in statistics is the main novelty for statistical practice that is offered in the book, and the most radical. Dwass in 1957, and Chung and Fraser in 1958, had published the stochastic version of Fisher's exact test, Barnard in 1963 published a Monte Carlo test for runs, and in 1969 I published what has come to be called the bootstrap. But in my view the key innovation is the broader suggestion: considering resampling as the tool of first resort to handle the estimation of probabilities in everyday statistics problems. My early publications of this idea (1969; 1976 with Atkinson and Shevokas) did not succeed in convincing the profession. But the time for these ideas to be adopted may finally to have come in the 1990s, after the work of Efron and others has formalized the mathematical ideas and hence made them acceptable and exciting to mathematical statisticians. 5. An approach to assessing reliability is offered that has much in common with the conventional concept of confidence intervals, but that involves none of the obscurity in interpretation of the conventional concept. 6. It is difficult to believe that the idea is novel, but I have not yet come across in the literature the statement that at the core of every statistics problem is a question about the behavior of a probability model, and the likelihood that that model will produce the observed sample. (The only exceptions are [a] a Neyman-Pearson sort of setup where the question instead asks about the relative likelihoods of two distributions producing the observed sample, and [b] a Fisherian framework where one asks about which distribution among many would be the most likely to produce the observed sample.) All the rest of statistics consists of framing the probabilistic question and interpreting the results. As noted earlier, this book has considerable overlap both with my 1969 book on research methods (third edition, 1985, with Paul Burstein), and with my 1975/1993 text on resampling statistics (and even more so with the second edition to come, which will draw heavily on the present volume). For this overlap I make no apology; these volumes are different vehicles intended to (among other jobs) present a common set of ideas in a variety of contexts<8>[fn]. This book is part of a lifetime evolution of thought on these ideas, and I hope that this practice therefore seems appropriate. IN CONCLUSION The discipline of statistics has long been in a state of controversy about its most fundamental ideas. This book aims to integrate the fundamental ideas in such fashion as to reduce the controversy. I hope the book advances a bit the philosophy and practice of getting knowledge by making it coherent in both senses - making the argument hang together, and making it understandable. FINAL NOTE The spirit of this book is exploration of data. There are no conclusive answers now, nor can we expect there to be, even though many of us desperately want such answers just as Bertram Russell did: I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. (Russell, 1963, p. 54) But there are no firm first principles on which we can confidently base our assumptions, our procedures, or our conclusions. There is no ultimate intellectual justification for scientific work or for the decisions we make. In the following extraordinary passage David Hume summed up this inevitable ambiguity in our view of nature and ourselves, which is in the spirit of the duality of Nils Bohr's concept of quantum physics: This sceptical doubt, both with respect to reason and the senses, is a malady, which can never be radi- cally cur'd, but must return upon us every moment, however we may chace it away, and sometimes may seem entirely free from it. 'Tis impossible upon any system to defend either our understanding or senses; and we but expose them farther when we endeavour to justify them in that manner. As the sceptical doubt arises naturally from a profound and intense reflection on those subjects, it always encreases, the farther we carry our reflections, whether in opposition or con- formity to it. Carelessness and in-attention alone can afford us any remedy. For this reason I rely entirely upon them (1777/1949, pp. 254-5.); So this book is about doing the best that we can, and I hope that it helps us move in that direction. We cannot know perfectly, as Hume tells us, and as Godel and Bohr and Heisenberg and Hayek agree. We do not even know what we are able to know and what we are not able to know. But we need not and should not be dismayed by our inability to satisfy the longing for surety and for unity. As a species we have already been spectacularly successful, and we have in our hands the intellectual tools to learn more and more and hence live better and better. Need we long for more? P. S. The reader may wish to begin with Chapter III-1 if entirely unfamiliar with the resampling method. page 1 statphil sintro Chapter 1 4-1-6900 ENDNOTES **ENDNOTES** <1>: Among statisticians, W. Edwards Deming has been perhaps the most forceful advocate of operational definitions; see his 1986 book, Chapter 9. For a general discussion of the operational (or "working") definition in social science, see Simon and Burstein (3rd edition, 1985). Chapter 00 [scausali] contains further discussion of operational definitions. As I see it, the operational definition is a way to close the system so that one can begin to analyse it analogous to the way that one closes a system by assumption when one wishes to analyse it with respect to the conservation of energy. When it is and is not appropriate to close a system is a decision that requires scientific wisdom. <2>: Gigerenzer et. al. expand on this thesis: The creation of the hybrid can be understood on three levels -- mathematical statisticians, textbook writers, and experimenters. On the first level, there was a tendency to resolve the controversial issues separating the three major schools by distinguishing between theory and application, and by saying that practical-minded people need not be bothered by these mainly theoretical issues (noted in Hogben, 1957). To users of statistics, this seemed perfectly acceptable, since often the same formulae were used and the same numerical results obtained. The great differences in conceptual interpretation were overlooked in the plug- in-and-crank-through use of statistical rules. But, on the second level, writers of textbooks for education, psychology, sociology, and so on, commenced peace negotiations and created a hybrid theory, to which shelves and shelves in research libraries now pay tribute. The hybrid theory combines concepts from the Fisherian and the Neyman-Pearson framework. It is presented anonymously as statistical method, while unresolved controversial issues and alternative approaches to scientific inference are completely ignored. Key concepts from the Neyman-Pearson theory such as power are introduced along with Fisher's significance testing, without mentioning that both parties viewed these ideas as irreconcilable. For instance, checking (without random sampling) thirty books on statistics for psychology, education, and sociology that were readily available, we found that the names of Neyman and E. S. Pearson were not even mentioned in twenty-five of them, although some of their ideas were presented. None even hinted at the existence of controversy, much less spelled out the issues in dispute. The crucial concepts were not identified with their creators -- which is very unusual in fields like psychology, where textbooks list competing theories and the researchers who proposed them for almost every phenomenon discussed. Statistics is treated as abstract truth, the monolithic logic of inductive inference. (pp. 106, 107)***) As an apparently non-controversial body of statistical knowledge, the hybrid theory has survived all attacks since its inception in the 1940s. If only for practical reasons, it has easily defeated ecumenism (Box, 1986), in which one applies the different approaches to the same data, acknowledging that the different approaches are conceptually unlike. It has survived attacks from proponents of the Neyman-Pearson school, and the Bayesians (Edwards, Lindman, and Savage, 1963), and Popperians (Meehl, 1978). Its dominance permits the suppression of the hard questions. What, if any, is the relation between statistical significance and substantial importance within the scientific discipline? To what aspects of the scientific enterprise do the ideas of Fisher, and of Neyman and Pearson, appeal, and how can these be combined? Are the experimental designs developed by statisticians in agriculture and biology really a good model for all experimentation in the social sciences? What is most remarkable is the confidence within each social-science discipline that the standards of scientific demonstration have now been objectively and universally defined. In fact, the standardization of statistical methods becomes much less complete if one looks across disciplines. In econometrics, to take the most striking contrast, experiment is comparatively rare, and the standard statistical tool is regression analysis. It has often been applied by economists with a lack of imagination that matches the psychologists' use of hypothesis testing (McCloskey, 1985). Graduate students within the social and biological sciences have routinely been taught to view their statistical tools as canonical, given by logic and mathematics. The methods of statistical inference could be seen by practitioners uncomfortable with higher mathematics as someone else's concern, the province of statistical specialists. (pp. 109, 110) <3>:This integration is likely to be unwelcome not just because it it is a disagreement with all of the separate schools of thought, but also because contending schools of thought tend to like the existence of controversy, and find its continuation pleasant and profitable. That this is so was one of the less pleasant discoveries of what is now a long period of time doing scholarly work. <4>: An outstanding example of malpractice among philosophers is the much-respected Richard Rorty, who managed to write an entire chapter on social science research without referring to a single actual or even hypothetical study (1982, Chapter 11). [see letters on Rorty to Michael, perhaps others] Another example is an entire small book entitled Philosophy of Social Science by Richard Rudner, wherein the only social scientists mentioned are sociologist Max Weber (who did not do quantitative work), economist Joan Robinson (who probably never touched a piece of data in her life and whose entire economics is now seen as wrongheaded), and three famous anthropologists; no research study or procedure was analysed in any way, and there is much talk of axiomatic systems and sentences such as "The hounds hunted the vixens" (p. 16). I suppose it should not be surprising that philosophers can write so much nonsense about the research process when they confine themselves to such examples as the existence of unicorns, the surety of a human's mortality, and whether all Martians are green. (Indeed, academic philosophers do not aim at being useful, by their own accounts; rather, their discipline is an art form, they often say.) <5>: A thoughtful research methods text may actually be the best instruction in the philosophy of research, though implicit rather than explicit. (When I first worked on my own text, I felt as if I was engaged in a bootlegging operation in epistemology.) <6>: Consider by analogy the running of a restaurant and the cooking of the food. The chef's job is quite technical, and can be specified with recipes and other procedures; this is analogous to the pre-probilistic technical study of logic, and to the approach that philosophers have brought to the study of statistics generally. But the tasks of organizing a restaurant, such as choosing a style of food and a decor, and tasks such as attracting and pleasing a clientele, are much less technical yet at least as important - and the talents and skills are usually in shorter supply - than cooking the food. Under some conditions, the running of a food facility is a technical matter; an army field kitchen is such an example that can be specified in specific objective terms. But to attempt to run civilian restaurants the same way must fail; no army field kitchen can thrive under conditions of consumer choice. Similarly, the context of statistics - choosing problems, designing studies, interpreting the results - cannot be specified formally and handled technically. And this the philosophers have left alone. <7>:Cohen referred to Leibniz, Cournot, and Peirce as "honorable exceptions to the practice of philosophers of giving "scant attention" to the idea of probability (1956, p. 113). <8>:I doubt that anyone wants to know which passages have been published before, and hence I will not distract the reader by putting them in quotation marks or footnoting them (though I do note the chapters that have previously been published as articles). page 2 statphil sintro Chapter 1 4-1-6900