Experimental observations are often taken in order to assist in making a choice between relevant hypotheses ∼ H and H. The power of observations in this decision is here metrically defined by information-theoretic concepts and Bayes' theorem. The exact (or maximum power) of a new observation to increase or decrease Pr(H) the prior probability that H is true; the power of that observation to modify the total amount of uncertainty involved in the choice between ∼ H and H: the power (...) of a new observation to reduce uncertainty toward the ideal amount, zero; all these powers are systematically shown to be exact metrical functions of Pr(H) and Pr(o/H)/Pr(o)-1 where the numerator is the likelihood of the new observation given H, and the denominator is the "expectedness" of the observation. (shrink)

Experimental observations are often taken in order to assist in making a choice between relevant hypotheses ~H and H. The power of observations in this decision is here metrically defined by information-theoretic concepts and Bayes' theorem. The exact of a new observation to increase or decrease Pr the prior probability that H is true; the power of that observation to modify the total amount of uncertainty involved in the choice between ~H and H: the power of a new observation to (...) reduce uncertainty toward the ideal amount, zero; all these powers are systematically shown to be exact metrical functions ofwhere the numerator is the likelihood of the new observation given H, and the denominator is the “expectedness” of the observation. (shrink)

Since the time, about a century ago, when DeMorgan, Boole and Jevons, inaugurated the study of the logic of numerically definite reasoning, no one has been concerned to establish the validity rules for a very general type of numerically definite inference which is a strong analogue of the classical syllogism. The reader will readily agree that the traditional rules of syllogistic inference cannot even begin to decide whether the following proportionally quantified syllogism is a valid argument: at most 4/7 p (...) are at most 2/3 not-m and at least 3/5 s are precisely 7/8 m, hence, at most 1/3 s are p. Likely reasons, of broad methodological interest, why this readily definable type of formal inference has been neglected will presently be proposed. Among the masters of twentieth century logic, Hilbert and Bernays have, to be sure, meticulously shown how such numerically definite propositions as “at least 7 individuals have the property p” can be expressed in the predicate calculus with the use of the identity relation. They do not, since their concern with such propositions is indirect, proceed to establish a systematic calculus of classes whose “size” or extent is numerically definite. As we shall always notice, traditional logic and even ordinary Boolean algebra prefer to generalize about the laws governing the interrelationship of classes in inference systems without making any hypotheses concerning class “size” or extent except by the classical quantifier “some”, which quantifier admits the measure or extent of a class only in terms of the proposition that a given class contains or does not contain at least one member. Such a restricted admission of the relevance for inference of class size is among the fundamental reasons for the neglect of proportional quantifiers, i.e., quantifiers where numerical value is any rational number r such that 0/100 ≤ r ≤ 100/100. It can, of course, also be pointed out that the traditional syllogism and ordinary Boolean algebra do not i.e. measure, numerically define, the degree of inclusion of one class in another. Inclusion is taken either as total or partial, with no discrimination of the degree of partial inclusion. (shrink)

' What comes through strongly in this book are Weil's power of analysis and criticism, her love of truth and hunger for justice, her commitment to non-violence, ...

For a generation increasingly fragmented by a glut of unassimilable information and unrelated "facts", "Wittgenstein" from The Element Masters of Philosophy series focuses on his groundbreaking perspective of understanding concepts.

Experimental observations are often taken in order to assist in making a choice between relevant hypotheses ∼ H and H. The power of observations in this decision is here metrically defined by information-theoretic concepts and Bayes' theorem. The exact (or maximum power) of a new observation to increase or decrease Pr(H) the prior probability that H is true; the power of that observation to modify the total amount of uncertainty involved in the choice between ∼ H and H: the power (...) of a new observation to reduce uncertainty toward the ideal amount, zero; all these powers are systematically shown to be exact metrical functions of Pr(H) and Pr(o/H)/Pr(o)-1 where the numerator is the likelihood of the new observation given H, and the denominator is the "expectedness" of the observation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:702 JOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER t99 5 appears more as an anomalous figure in the spirit of Kierkegaard than a thinker of the mainstream. For Jaspers, philosophy is a vehicle to provoke a spiritual sense of the wonder of existence rather than an autonomous vocation which strives to recast its questions in increasingly radical ways. Most typically, Jaspers's emphasis on darker aspects of the human (...) predicament--guilt, anxiety, and death as the seminal existential motifs--does not exclude a more positive vision of Existenz as revealed through transcendence. The limits do not provoke a discourse of radical finitude which skirts the edges of presence, but instead indirectly point toward a transcendent mystery, or the "encompassing" (19-2o). If there is an aspect of Jaspers's philosophy that remains inadequately addressed in either volume, it is his preoccupation with the role of tragedy in the post-war era? In light of the premier importance that Hegel, Nietzsche, and Heidegger all grant to tragedy, Jaspers's passionate treatment of this topic in the context of the catastrophe of Western Europe merits far closer attention. Does not the issue of tragedy provide indispensable dues to chart the landscape of twentieth-century thought, and to amplify the differences which prevail in the portrait of politics as displayed by such diverse philosophers as Jaspers and Heidegger, Derrida and Levinas? FRANK SCHALOW DiUard University Norman Malcolm. Wittgenstein: A Religious Point of View? Edited with a response by Peter Winch. Ithaca, New York: Cornell University Press, a994. Pp. xi + 14o. Norman Malcolm at the outset of this, his posthumously published last book, focuses on the question: What did Wittgenstein mean when he said to his friend M. O'C. Drury, "I am not a religious man, but I cannot help seeing every problem from a religious point of view"? It was the right question. But Malcolm then--again on the first page of his book-proceeded to place restrictions on it, which were quite foreign to the spirit of Wittgenstein 's remark and which virtually crippled it. (1) He took Wittgenstein to be speaking of not social, psychological, or presumably even personal problems, but only of philosophical ones. (2) He chose to say that in Wittgenstein's later philosophy "there is not strictly a religious point of view, but something analogous to a religious point of view" (1, Malcolm's emphases). There is no reason to think that Wittgenstein would have accepted either of these restrictions on his remark. Nor does Peter Winch accept them in his forty-page discussion, which follows Malcolm's text in this book. In the upshot Malcolm finds "four analogies between Wittgenstein's conception of the grammar of language and his view of what is paramount in a religious life" (92). In both, he says, Wittgenstein emphasizes "an end to explanation," a sense of an "illness" pervading the human situation, "an inclination to be amazed at the existence of some ' Karl Jaspers, TragedyIs Not Enough, trans. Harald A. T. Reiche, Harry T. Moore, and Karl W. Deutsch (Boston: Beacon Press, 1952), 31-4O,93- io5_ BOOK REVIEWS 703 thing," and "doing, acting [having.] priority over intellectual understanding and reasoning " (92). But are such "analogies" really the crux of the "religious point of view" in terms of which Wittgenstein said that he could "not help seeing every problem"? When we recall that Wittgenstein's later philosophy was a proibund attack upon what he regarded as the idolatry of science, logic, and mathematics (an idolatry of which he himself, in the Tractatt~,, was partly guilty), and that he was also bent on undermining the accompanying subjectivized and privatized view of the human mind, as well as the scientistic reading of religious beliefs and primitive religions, we may be inclined to see his philosophy as clearing the way for the simple noninstitutionalized Tolstoian faith which he himself accepted. Philosophy and religion were on the same track in his mind (and not merely related by "analogies") when he wrote: "All that philosophy can do is to destroy idols. And that means not creating a new one--for instance, as in the 'absence of an idol' " (MS 213, 89). Peter Winch... (shrink)