THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

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 the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn.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 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 purpose of this note is to dispute Michael Ayers' claim that "there is no special problem of subjunctive conditionals".

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

Finding a powerful ally in Bertrand Russell, who provided the foreword for this book, Gellner embarked on the project that was to put him on the intellectual ...

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)

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)

Kitcher and Aspray distinguish a mainstream tradition in the philosophy of mathematics concerned with foundationalist epistemology, and a ‘maverick’ or naturalistic tradition, originating with Lakatos. My claim is that if the consequences of Lakatos's contribution are fully worked out, no less than a radical reconceptualization of the philosophy of mathematics is necessitated, including history, methodology and a fallibilist epistemology as central to the field. In the paper an interpretation of Lakatos's philosophy of mathematics is offered, followed by some critical discussion, (...) and an extension to a social constructivist position (which might well have been unacceptable to Lakatos). (shrink)

This volume of essays deals with the problem of relativism, in particular cultural relativism. If our society knows better than other societies, how do we know that it knows better? There is a profound irony in the fact that this self-doubt has become most acute in the one civilisation that has persuaded the rest of the world to emulate it. The claim to cognitive superiority is often restricted, of course, to the limited sphere of natural science and technology; and that (...) immediately raises the second main theme of this volume - the differences between the human and natural sciences. These essays reach towards a new style and mode of enquiry - a mixture of philosophy, history and anthropology - that promises to prove more revealing and fruitful. (shrink)

This volume of essays deals with the problem of relativism, in particular cultural relativism. If our society knows better than other societies, how do we know that it knows better? There is a profound irony in the fact that this self-doubt has become most acute in the one civilisation that has persuaded the rest of the world to emulate it. The claim to cognitive superiority is often restricted, of course, to the limited sphere of natural science and technology; and that (...) immediately raises the second main theme of this volume - the differences between the human and natural sciences. These essays reach towards a new style and mode of enquiry - a mixture of philosophy, history and anthropology - that promises to prove more revealing and fruitful. (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)

Heralded as "the crowning work of a great career," Logic: The Theory of Inquiry was widely reviewed. To Evander Bradley McGilvary, the work assured Dewey "a place among the world's great logicians." William Gruen thought "No treatise on logic ever written has had as direct and vital an impact on social life as Dewey's will have." Paul Weiss called it "the source and inspiration of a new and powerful movement." Irwin Edman said of it, "Most philosophers write postscripts; Dewey has (...) made a program. His Logic is a new charter for liberal intelligence." Ernest Nagel called the Logic an impressive work. Its unique virtue is to bring fresh illumination to its subject by stressing the roles logical principles and concepts have in achieving the objectives of scientific inquiry.". (shrink)

Grice's arguments that ordinary language indicative conditionals are logically equivalent to material conditionals are criticized. It is agreed that 'indirectness conditions' going beyond the material conditional can "sometimes" be detached' from ordinary language conditionals, but it is argued that this is not always possible. An example in which a speaker who knows that some mushrooms are non-poisonous tells a hearer "if you eat those mushrooms you will be poisoned", causing the hearer not to eat the mushrooms, is discussed, and it (...) is argued that this utterance should be regarded as factually unsatisfactory', and therefore, by Grice's own standards, false. (shrink)

Applying first-order logic to derive the consequences of laws that are only approximately true of empirical phenomena involves idealization of a kind that is akin to applying arithmetic to calculate the area of a rectangular surface from approximate measures of the lengths of its sides. Errors in the data, in the exactness of the lengths in one case and in the exactness of the laws in the other, are in some measure transmitted to the consequences deduced from them, and the (...) aim of a theory of idealization is to describe this process. The present paper makes a start on this in the case of applied first-order logic, and relates it to Plato's picture of a world or model of 'appearances' in which laws are only approximately true, but which to some extent resembles an ideal world or model in which they are exactly true. (shrink)

. 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)

The essays in this volume gather together Gellner's thinking on the connection between philosophy and life and they approach the topic from a number of directions: philosophy of morals, history of ideas, a discussion of individuals including R. G. Collingwood, Noam Chomsky, Piaget and Eysenck and discussions on the setting of philosophy in the general culture of England and America.