In this introduction we shall array a family of fundamental questions pertaining to probability, especially as it has been judged to bear upon the guidance of life. Applications and uses of probability theory need either to address some or all of these questions, or to tell us why they don’t. The essays assembled in this volume bring integrative perspectives on this family of questions. We asked the authors to describe in their own voices the intellectual histories of their contributions, so (...) as to shed further light upon the philosophical interest of their projects, and their particular integrative approaches, within the broader context we have sketched. The authors’ comments precede the essays. (shrink)

This collection represents the best recent work on the subject and includes essays by Clark Glymour, James H. Fetzer, and Wesley C. Salmon.

What importance does “race” have as a meaningful category in the study of literature and the shaping of critical theory? If we attempt to answer this question by examining the history of Western literature and its criticism, our initial response would probably be “nothing” or, at the very least, “nothing explicitly.” Indeed, until the past decade or so, even the most subtle and sensitive literary critics would most likely have argued that, except for aberrant moments in the history of criticism, (...) race has not been brought to bear upon the study of literature in any apparent way. Since T. S. Eliot, after all, the canonical texts of the Western literary tradition have been defined as a more or less closed set of works that somehow speak to, or respond to, “the human condition” and to each other in formal patterns of repetition and revision. And while most critics acknowledge that judgment is not absolute and indeed reflects historically conditioned presuppositions, certain canonical works do seem to transcend value judgments of the moment, speaking irresistibly to the human condition. The question of the place of texts written by the Other in the proper study of “literature,” “Western literature,” or “comparative literature” has, until recently, remained an unasked question, suspended or silenced by a discourse in which the canonical and the noncanonical stand as the ultimate opposition. In much of the thinking about the proper study of literature in this century, race has been an invisible quantity, a persistent yet implicit presence.This was not always the case, we know. By mid-nineteenth century, “national spirit” and “historical period” had become widely accepted categories within theories of the nature and function of literature which argued that the principal value in a great work of literary art resided in the extent to which these categories were reflected in that work of art Montesquieu’s De l’esprit des lois considered a culture’s formal social institution as the repository of its “guiding spirit,” while Giambattista Vico’s principi di una scienza nuova read literature against a complex pattern of historical cycles. Friedrich and August von Schlegel managed rather deftly to bring “both national spirit and historical period” to bear upon the interpretation of literature, as W. Jackson Bate has shown. But it was Hippolyte-Adolphe Taine who made the implicit explicit by postulating “race, moment, and milieu” as positivistic criteria through which any work could be read and which, by definition, any work reflected. Taine’s History of English Literature was the great foundation upon which subsequent nineteenth-century notions of “national literatures” would be constructed. Henry Louis Gates, Jr. is professor of English, comparative literature, and African studies at Cornell University. He has edited several books and has written Figures in Blood and The Signifying Monkey. (shrink)

Readers of the Analects of Confucius tend to approach the text asking what Confucius believed; what were the views that comprise the 'ism' appended to his name in English? A Reader's Companion to the Confucian Analects suggests a different approach: he basically taught his students not doctrines, but ways for each of them to find meaning and purpose in their lives, and how best to serve their society. Because his students were not alike, his instruction could not be uniform; hence (...) the large number of incompatible readings that have been given to what he said. By providing brief essays, finding lists, background and comparative materials, and historical context, this Companion is not intended as another interpretation of the ancient text, but rather as an aid for contemporary students to develop their own interpretive reading of it, in the hope of thereby aiding them in the search for meaning, purpose, and service in their own lives - as seventy-three generations of Chinese have done. (shrink)

There are two main classes of interpretations of probability. The first are those that rely on a measure of frequency. The other is those that take a logical or subjective view of a unique event, independent of past or future events. The interpretation of probability which is used in the book is then defined as evidential probability, a function based on a set of known statements based on frequency or measure. The properties of probability are then enumerated and explained. Probabilities (...) can also be based on statistical inference. Statistical inferences are statistical properties with high probability based on statistical evidence. (shrink)

Perhaps only Tar Baby is as enigmatic and compelling a figure from Afro-American mythic discourse as is that oxymoron, the Signifying Monkey.3 The ironic reversal of a received racist image of the black as simianlike, the Signifying Monkey—he who dwells at the margins of discourse, ever punning, ever troping, ever embodying the ambiguities of language—is our trope for repetition and revision, indeed, is our trope of chiasmus itself, repeating and simultaneously reversing in one deft, discursive act. If Vico and Burke, (...) or Nietzsche, Paul de Man, and Harold Bloom, are correct in identifying “master tropes,” then we might think of these as the “master’s tropes,” and of signifying as the slave’s trope, the trope of tropes, as Bloom characterizes metalepsis, “a trope-reversing trope, a figure of a figure.” Signifying is a trope that subsumes other rhetorical tropes, including metaphor, metonymy, synecdoche, and irony, and also hyberbole, litotes, and metalepsis. To this list, we could easily add aporia, chiasmus, and catachresis, all of which are used in the ritual of signifying.The black tradition has its own subdivisions of signifying, which we could readily identify with the typology of figures received from classical and medieval rhetoric, as Bloom has done with his “maps of misprision.” In black discourse “signifying” means modes of figuration itself. When one signifies, as Kimberly W. Benston puns, one “tropes-a-dope.” The black rhetorical tropes subsumed under signifying would include “marking,” “loud-talking,” “specifying,” “testifying,” “calling out”, “sounding,” “rapping,” and “playing the dozens.”4 3. On Tar Baby, see Ralph Ellison, “Hidden Man and Complex Fate: A Writer’s Experience in the United States,” Shadow and Act, p. 147, and Toni Morrison, Tar Baby. On the black as quasi-simian, see Jean Bodin, Method for the Easy Comprehension of History, trans. Beatrice Reynolds, p. 105; Aristotle Historia Animalium 606b; Thomas Herbert, Some Years Travels, pp. 16-17; and John Locke, An Essay Concerning Human Understanding, 8th ed., 2 vols., 2:53.4. Geneva Smitherman defines these and other black tropes and then traces their use in several black texts. Smitherman’s work, like that of Claudia Mitchell-Kernan and Abrahams, is especially significant for literary theory. See Smitherman, Talkin and Testifyin: The Language of Black America, pp. 101-66. See also nn. 13 and 14 below. (shrink)

Our decision to bracket “race” was designed to call attention to the fact that “races,” put simply, do not exist, and that to claim that they do, for whatever misguided reason, is to stand on dangerous ground. Fromm understands this all too well, it seems, judging from the satirical tone of his response. Were there not countries in which the belief in racial essences dictates social and political policy, perhaps I would have found Fromm’s essay amusing and our gesture merely (...) one more token of the academic’s tendency to create distinctions which common sense alone renders unnecessary. The joke, rather, is on Fromm: one’s task is most certainly not to remain “permanently quiet”; rather, our task is to utilize language more precisely, to rid ourselves of the dangers of careless usages of problematic terms which are drawn upon to delimit and predetermine the lives and choices of human beings who are not “white.” Fromm’s response only reinforces Todorov’s worry about not bracketing “race” every time it occurs in our texts, because “race” simply does not exist. (shrink)

The distinction between cause and effect has been viewed as crucial to scientific thinking. David Hume dedicates many pages of his “Enquiry” to the argument of causality, and it appears to be of central vitality to our understanding of the world, despite the fact that he can find nothing to the notion. In Hume's prose, one senses both disappointment and heroic resignation. Some philosophers view causality—sometimes even universal causality—as a needed assumption or basic “presupposition” of science. It is sometimes argued (...) that universal causation, or at least its probability, is required for the induction's justification. (shrink)

The majority of the philosophical attention on induction has been connected with universal conventions: “All crows are black,” “All emeralds are green,” “Every creature with kidneys is a creature with a heart,” and others. It has been observed that if it can be shown how and why such conventions can be given rational justification by our restrained observations of the world, the outcome will be simpler. It is felt that it is but a small step from here to quantitative laws (...) and only a little-longer jump to general theories. After achieving an understanding of general theories, we can go back, in a mopping-up approach, to handle such irrelevant trivia as statistical conventions. (shrink)

Probabilistic connections are simple to reproduce counterfactually or hypothetically, since this involves simply adding the required statements to our evidential corpus without worrying about erasing some statements. In the serious uniform causal connections' case, the problem is complicated by the fact that some erasures will almost always have to be made, and that leads to the problems of intention and vagueness. On the other hand, uniform causal connections, considered both counterfactually and hypothetically, are exactly the connections needed to be taken (...) into account in life. Finally, however, some dispositions can be no more than hard facts. (shrink)

Efforts to get scientific knowledge reap valuable knowledge about the world. It is often rewarding simply to know more, but a greater benefit of knowing more is that, knowing the future, one can make sound decisions. There is an easy and unified decision theory that, if only it applied to everything, would solve all the decision problems humans face. It is known as “Bayesian” decision theory because it requires a set of probabilities determined over the world states.

Induction is the inference from a sample to a population, regardless of the possible existence of exceptions. Induction is used in the practice of science and engineering based on knowledge that can be accepted as evidence. There are two bodies of knowledge: evidential corpus, a set of propositions acceptable as evidence in a certain context; and practical corpus, a set of propositions counting as “practically certain” in that context. There are five kinds of induction described: statistical, universal, nomic, theoretical, and (...) instantial. (shrink)

In order for an “ideal” to make relevance, it is not mandatory, certainly, to be able to reach it. It is enough that it is possible to approach it, and even only to a certain extent. To be able to approach the ideal arbitrarily closely is not needed, even “theoretically.” To make sense of the “improvement” we can get in approaching an ideal, the measure of how close the ideal needs to be must be determined. In the thermometer's case, the (...) measure was determined by the bias in the error distribution at different points on the scale. An essentially internal measure was given, a measure related closely to the pertinent kind of measurement. (shrink)

This chapter discusses the philosophy and logic behind the mathematical ideas of first-order logic, metalanguages, arithmetic, and geometry. It familiarizes the reader to these mathematical ideas, which will be used in succeeding chapters. The chapter also contrasts that mathematical or logical theories can utilize these mathematical ideas, while scientific theories will find them inapplicable. First-order logic involves conclusions based on premises which are given to be true with no room for imprecision or vagueness, both of which are crucial to the (...) productive use of scientific language. Metalanguage is contrasted with object language, in which scientific laws are expressed. Both arithmetic and geometry are used with idealized, abstract objects and have a limited physical application. (shrink)

In general, quantities should be interpreted in the same way as random quantities or random variables are interpreted in statistics: namely, as functions from a domain to a special set of objects. The fact that they reflect to some level the structure of a set of mathematical objects makes the range of these functions extraordinary. Measurement, meanwhile, is not a process of “assigning numbers to objects,” but rather of formulating the values of quantity functions given to objects. More briefly, it (...) is giving magnitudes to objects. (shrink)

One problem that has been plaguing for the long term is the problem of choosing the levels of rational corpora. Since what goes into a corpus is what has a probability higher than the index of that corpus, that index has a bearing on what is in a corpus. We have two levels to deal with, since the focus is both with the evidential corpus and with the practical corpus. What principles can be used to select these levels? A practical (...) way to approach this question is through the analysis of full belief or acceptance. Partial belief is distinguished in terms of a propensity to make, or fail to make, bets. (shrink)

The chapter begins by explaining the concepts of quantity and magnitude. It then presents the method of measurement without using magnitude. This method of direct measurement can be achieved through the observation of the transitive relation among objects. A particular set of equivalence classes is selected to serve as a unit of measurement and is assigned magnitude. The concept of measurement error and approximation is then introduced. In some cases, such as temperature, indirect measurement, or measurement in terms of a (...) different quantity, yields less error and proves more accurate and convenient than direct measurement. In general, indirect measurements of different kinds are appropriate at different regions of the scale. (shrink)

Knowledge is distinguished between knowledge about the relations of ideas, like mathematical truths and logic, and knowledge of matters of fact or empirical knowledge of the world, which is derived from “sense experience.” Observational sentences are based on sense experience and can sometimes be judged to be true or false. Thus, the possibility of errors in observational judgment must be allowed. We can acknowledge the existence of observational error in general, and even be unable to specify any particular observation statement (...) that is certain, and yet be able to accept most observation statements on the basis of the corresponding reports and to reject others. (shrink)

This chapter chronicles the complex relationship between philosophy and science throughout history. It illustrates how they have mutually influenced each other in modern times. Philosophy and science are thought to be polar opposites, but they are not as different as they seem to be. Philosophy is considered part of the humanities and not the sciences. However, it can be argued that schools of science branched off from the domain of philosophy. Scientific studies start as or are inspired by philosophical ideas. (...) Mathematics, the very paradigm of a logical and rational discipline that much of science embodies, is a lot like philosophy in that it involves ideas that have no empirical basis and uses logic. (shrink)

In the previous chapter, it was considered in very broad terms what can happen when the ties are cut between observability and certainty. More needs to be proved, however, before the framework developed can be applied to the types of real theories of interest: quantum mechanics, relativity, and other such highbrow creations. Particularly, close observation at the nature of those statements is needed in the corpus of practical certainties that comprise the analytical observational content of the corpus that we get (...) from the sorts of theories accepted. Consideration of choices among distinct theories is needed, if such there be, having the same analytical observational content. (shrink)

Speculation is often opposed with scientific knowledge. Life existence on other planets of the solar system is through “sheer speculation,” while the chemical nature of the other planets' atmospheres is a matter of scientific knowledge. The present chapter does not dispute the distinction but it aims to examine the importance to science of speculation. The most vital role of speculation is that it provides us with scientific theories.

An answer to the fact that it is very complex to find convincing grounds for considering in universal deterministic uniformity has been to suggest that causality is indeed universal: all events are caused—but many, if not all, causal laws are statistical or probabilistic in character. Thus, a law of causality does not spell out what will be the effect of a given cause in a particular case; it just provides a probability of a given effect when the cause is determined. (...) This seems suitable not only in the rarified air of quantum mechanics, but particularly in the swampy territory of human activity: in epidemiology, psychology, economics, and the like. One way of interpreting statistical relationships as causal is through the law of large numbers. (shrink)

It has been manifested over the past few centuries that science provides superbly powerful tools and methods for modifying the natural world. Many people would agree that it has also offered explanation and understanding. But it is still unclear that these tools and methodology can propel us to solve all of the cognitive dilemmas that exist. It has been assumed, for example, that scientific knowledge and religious knowledge are so different that they cannot even clash with one another. But the (...) recent arguments about creation and evolution show that perhaps they can come into conflict after all. (shrink)

Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book (...) will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science. (shrink)

Following discussions by Callicott and Zimmerman, I argue that much of deep ecology’s critique of science is based on an outdated image of natural science. The significance of the quantum revolution for environmental issues does not lie in its alleged intrusion of the subjective consciousness into the physicists’ description of nature. Arguing from the viewpoint of Niels Bohr’s framework of complementarity,I conclude that Bohr’s epistemological lesson teaches that the object of description in physical science must be interaction and that it (...) is now mistaken to imagine that physical science aims to represent nature in terms of properties it possesses apart from interaction. (shrink)

Crawshay-Williams defines the scope of his book as the study of statements "put forward with a sort of claim to general acceptance by the company [to which they are addressed]". Perelman and Olbrechts-Tyteca would certainly agree that only such statements are capable of giving rise to controversy. But this point, and one other that I shall mention shortly, are nearly the only ones on which the two books agree. And there is profound disagreement about how even this point is to (...) be interpreted. Crawshay-Williams is interested only in the extent to which the claim to acceptance can be satisfied. The phrase I have just quoted is his definition of statements that are testable. His book is largely a discussion of the tests that can be used to determine the correctness of such statements. The implication is, of course, that any genuine controversy can, in principle, be adjudicated by applying such tests to the statements over which it arises. Perelman and Olbrechts-Tyteca, on the other hand, are primarily interested in ways of expressing the claim to general acceptance. Their book is mainly a study of the means by which a statement, or a series of them, can be put forward so as to claim general acceptance by the company to which it is addressed. For them, controversy consists in claims and counter-claims. It can thus be decisively settled only when a claim is sufficiently overpowering to silence all counter-claims. But such a result can be accomplished only by force or hypnosis, and these settle controversy not by adjudicating it but by abolishing it. Controversy cannot therefore be adjudicated at all, except in relatively trivial cases. (shrink)

There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should be construed as (...) lower probabilities, etc. Updating probabilities introduces new considerations, and it is shown that the representation of belief as a set of probabilities conflicts in this regard with the updating procedures advocated by Shafer. The attempt to make subjectivistic probability plausible as a doctrine of rational belief by making it more flowery -- i.e., by adding new dimensions -- does not succeed. But, if one is going to represent beliefs by sets of distributions, those sets of distributions might as well be based in statistical knowledge, as they are in epistemological or evidential probability. (shrink)