This book is meant to be a primer, that is, an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premisses. This is a clear well-written text on the subject of probability logic, suitable for advanced undergraduates (...) or graduates, but also of interest to professional philosophers. There are well-thought-out exercises, and a number of advanced topics treated in appendices, while some are brought up in exercises and some are alluded to only in footnotes. By this means, it is hoped that the reader will at least be made aware of most of the important ramifications of the subject and its tie-ins with current research, and will have some indications concerning recent and relevant literature. (shrink)
The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)
This volume is dedicated to the life and work of Ernest Nagel counted among the influential twentieth-century philosophers of science. Forgotten by the history of philosophy of science community in recent years, this volume introduces Nagel’s philosophy to a new generation of readers and highlights the merits and originality of his works. Best known in the history of philosophy as a major American representative of logical empiricism with some pragmatist and naturalist leanings, Nagel’s interests and activities went beyond these (...) limits. His career was marked with a strong and determined intention of harmonizing the European scientific worldview of logical empiricism and American naturalism/pragmatism. His most famous and systematic treatise on, The Structure of Science, appeared just one year before Thomas Kuhn’s even more renowned, The Structure of Scientific Revolutions. As a reflection of Nagel’s interdisciplinary work, the contributing authors’ articles are connected both historically and systematically. The volume will appeal to students mainly at the graduate level and academic scholars. Since the volume treats historical, philosophical, physical, social and general scientific questions, it will be of interest to historians and philosophers of science, epistemologists, social scientists, and anyone interested in the history of analytic philosophy and twentieth-century intellectual history. (shrink)
This book is less about disjunction than about the English word ‘or’, and it is less for than against formal logicians—more exactly, against those who maintain that formal logic can be applied in certain ways to the evaluation of reasoning formulated in ordinary English. Nevertheless, there are many things to interest such of those persons who are willing to overlook the frequent animadversions directed against their kind in the book, and this review will concentrate on them.
Whereas epistemology is the philosophical theory of knowledge, its nature and scope, metaepistemology takes a step back from particular substantive debates in epistemology in order to inquire into the assumptions and commitments made by those who engage in these debates. This entry will focus on a selection of these assumptions and commitments, including whether there are objective epistemic facts; and how to characterize the subject matter and the methodology of epistemology.
Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...) conclusions must have positive probability when premisses do, and in the last case conclusions must be at least as probable as their least probable premisses. Precise definitions and well known examples are given for each of these properties, characteristic principles are shown to be valid and complete for deriving conclusions of each of these kinds, and simple trivalent truthtable 'tests' are described for determining which properties are possessed by any given inference. Brief comments are made on the application of these results to certain modal inferences such as "Jones may own a car, and if he does he will have a driver's license. Therefore, he may have a driver's license.". (shrink)
No semantic theory is complete without an account of context sensitivity. But there is little agreement over its scope and limits even though everyone invokes intuition about an expression's behavior in context to determine its context sensitivity. Minimalists like Cappelen and Lepore identify a range of tests which isolate clear cases of context sensitive expressions, such as ‘I’, ‘here’, and ‘now’, to the exclusion of all others. Contextualists try to discredit the tests and supplant them with ones friendlier to their (...) positions. In this paper we will explore and evaluate Cappelen and Hawthorne's recent attempts to discredit Cappelen and Lepore's tests and replace them with others. We will argue they have failed to provide sufficient reason to abandon minimalism. If we are right, minimalism about context sensitivity is still viable. (shrink)
Modifications of current theories of ordinal, interval and extensive measurement are presented, which aim to accomodate the empirical fact that perfectly exact measurement is not possible (which is inconsistent with current theories). The modification consists in dropping the assumption that equality (in measure) is observable, but continuing to assume that inequality (greater or lesser) can be observed. The modifications are formulated mathematically, and the central problems of formal measurement theory--the existence and uniqueness of numerical measures consistent with data--are re-examined. Some (...) results also are given on a problem which does not arise in current theories: namely that of determining limits of accuracy attainable on the basis of observations. (shrink)
How do concepts of topology such as that of a boundary apply to the empirical world? Take the example of a chess board, represented here with black squares in black and red squares in white. We see by looking at the board that the squares of any one color have common boundaries only with squares of the opposite color, but each square has corners in common with other squares of the same color, which are points at which their common boundaries (...) intersect. For example, the white square labelled ‘A’ has common boundaries with the black squares that surround it, and common corners with the white squares like square B that are diagonally adjacent to it. (shrink)
Among the “Ernest Nagel Papers 1930–1988” at Columbia University’s Rare Book & Manuscript Library, there is a file at Box 7, entitled “The Philosophy of Science: University of Delaware 1961”. This is the edited text with some editorial comments and polishing.
This chapter provides an overview of the life and philosophy of Ernest Nagel, as well as a summary of the chapters in this volume. Regarding Nagel's philosophy, we focus on his role and activities to stabilize analytic philosophy and make it a profession, his views about the role and nature of history and sociology of science, naturalism, and socially engaged philosophy, and finally his understanding of the relation between science, society, and philosophy.
. Syllogisms like Barbara, “If all S is M and all M is P, then all S is P”, are here analyzed not in terms of the truth of their categorical constituents, “all S is M”, etc., but rather in terms of the corresponding proportions, e.g., of Ss that are Ms. This allows us to consider the inferences’ approximate validity, and whether the fact that most Ss are Ms and most Ms are Ps guarantees that most Ss are Ps. It (...) turns out that no standard syllogism is universally valid in this sense, but special ‘default rules’ govern approximate reasoning of this kind. Special attention is paid to inferences involving existential propositions of the “Some S is M” form, where it is does not make sense to say “Almost some S is M”, but where it is important that in everyday speech, “Some” does not mean “At least one”, but rather “A not insignificant number”. (shrink)