| 期刊全称 | Belief and Probability | | 影响因子2023 | John M. Vickers | | 视频video | http://file.papertrans.cn/184/183311/183311.mp4 | | 学科分类 | Synthese Library | | 图书封面 |  | | 影响因子 | 1. A WORD ABOUT PRESUPPOSITIONS This book is addressed to philosophers, and not necessarily to those philosophers whose interests and competence are largely mathematical or logical in the formal sense. It deals for the most part with problems in the theory of partial judgment. These problems are naturally formulated in numerical and logical terms, and it is often not easy to formulate them precisely otherwise. Indeed, the involvement of arithmetical and logical concepts seems essential to the philosophies of mind and action at just the point where they become concerned with partial judgment and" belief. I have tried throughout to use no mathematics that is not quite elementary, for the most part no more than ordinary arithmetic and algebra. There is some rudimentary and philosophically important employment of limits, but no use is made of integrals or differentials. Mathematical induction is rarely and inessentially employed in the text, but is more frequent and important in the apP‘endix on set theory and Boolean algebra. • As far as logic is concerned, the book assumes a fair acquaintance with predicate logic and its techniques. The concepts of compactness and maximal consistency | | Pindex | Book 1976 |
| 1 |
Front Matter |
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Abstract
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| 2 |
,Introduction, |
Jaakko Hintikka,Robert S. Cohen,Donald Davidson,Gabriël Nuchelmans,Wesley C. Salmon |
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Abstract
The subject of this monograph is the relation of logic and probability. That is a large subject, and the work does not approach comprehending it. It is rather the attempt to develop a particular point of view about logic and probability, which is, roughly put, that the function of logic in the theory of probability is to specify the equivalence classes of sentences or propositions, such that members of the same class have always the same probability. That is the view, and a lot of the work of the book consists in finding out what the limits of this function are; just how much effect logic can have on probability, and to just what extent probability may be assumed to reach conclusions which are independent of assumptions about the logical relations among its objects.
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| 3 |
,The Natures of Judgment and Belief, |
Jaakko Hintikka,Robert S. Cohen,Donald Davidson,Gabriël Nuchelmans,Wesley C. Salmon |
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Abstract
It is natural and usual in a theory of judgment to distinguish the . of a judgment, what is judged, usually a proposition, from the act of judging. There are theories, most notably Hume’s, in which this is not done. The difficulties which such theories encounter result for the most part from the difficulty they have in allowing the mind to entertain or assume the same proposition which it might also judge. I postpone until succeeding sections the question of how such theories may be modified to meet these problems and turn initially to theories in which the act is distinguished from the content.
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| 4 |
,Partial Belief, |
Jaakko Hintikka,Robert S. Cohen,Donald Davidson,Gabriël Nuchelmans,Wesley C. Salmon |
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Abstract
Hume’s account of partial belief is an extension in a quite natural way of his account of non-partial belief.. Partial belief is a consequence, on his view, of the mind’s capacity to divide its force equally among distinct alternatives. This is most simply applicable to . partial beliefs, of the form ’. will be consequent upon .’. The strength of such a belief will, he says, be ./. just when:
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| 5 |
,Logic and Probability, |
Jaakko Hintikka,Robert S. Cohen,Donald Davidson,Gabriël Nuchelmans,Wesley C. Salmon |
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Abstract
We shall assume that the objects of belief are or correspond to sentences. These sentences should not be thought of as uninterpreted, they are assumed to have determinate meanings. We understand a sentence to be much like what logicians have traditionally referred to as a .; it is the bearer of truth or falsity, the intended object of thought, what is contemplated in an assertoric judgment, the ontent of an assertion, and so on.
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| 6 |
,Coherence and the Sum Condition, |
Jaakko Hintikka,Robert S. Cohen,Donald Davidson,Gabriël Nuchelmans,Wesley C. Salmon |
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Abstract
In Chapter II the attempt to account for belief in terms of willingness to gamble was discussed. That discussion was inconclusive. It seems clear that belief is not reducible to such willingness or disposition, and it also seems clear that in at least some cases willingness to gamble in stakes of utility is at least an important consequence of believing.
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| 7 |
,Probability and Infinity, |
Jaakko Hintikka,Robert S. Cohen,Donald Davidson,Gabriël Nuchelmans,Wesley C. Salmon |
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Abstract
In the preceding chapter the relations between the epistemic concept of probability, as a logic of partial belief, and the measure-theoretic concept of probabilitywere developed for objects — sentences — of finite complexity. The account showed that there are nice relations among (i) probabilities on sets of sentences, (ii) probabilities on the Tarski-Lindenbaum Algebras associated with those sets of sentences, (iii) the transparency of partial belief, and (iv) a condition formulated there, based upon the concept of coherence, called the simple sum condition. That account seems satisfactory as far as it goes, but, leaving aside the question to what extent it can be made less relativistic, that is to say, in what ways appropriate logics . can be more precisely specified, it remains obviously incomplete in one important formal respect: The functions there defined apply only to finitely complex objects, and, in particular, are additive only over finite disjunctions of incompatible sentences, or over finite unions of disjoint sets.
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| 8 |
,Infinity and the Sum Condition, |
Jaakko Hintikka,Robert S. Cohen,Donald Davidson,Gabriël Nuchelmans,Wesley C. Salmon |
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Abstract
In Chapter IV the laws of probability were related to the simple sum condition: If Ω is a denumerable field of sentences, . an absolutely consistent and at least tautological logic, and . . numerical function on Ω, then Ω, . and . satisfy the simple sum condition if and only if for every subset . of Ω.
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| 9 |
Back Matter |
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Abstract
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