It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more (...) intuitive diagnoses of the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)

This paper focuses on abduction as explicit or readily formulatable inference to possible explanatory hypotheses--as contrasted with inference to conceptual innovations or abductive logic as a cycle of hypotheses, deduction of consequences and inductive testing. Inference to an explanation is often a matter of projection or extrapolation of elements of accepted theory for the solution of outstanding problems in particular domains of inquiry. I say "projections or extrapolation" of accepted theory, but I mean to point to something (...) broader and suggest how elements of accepted theory constrain emergent models and plausible inferences to explanations--in a quasi-rationalist fashion. I draw on illustrations from quantum gravity below just because there is so little direct evidence available in the field. It is in such cases that Peirce's discussions of abductive inference provide the most plausible support for the idea of a logic of abduction--as inference to readily formulatable explanatory hypotheses. The possible need for conceptual innovation points to the limits on the possibility of a logic of abduction of a more rationalistic character--selecting uniquely superior explanations. Abduction conceived as a repeated cycle of inquiry also points to limits on our expectations for an abductive logic. My chief point is that the character of inference to an explanation, viewed below as embedded within arguments from analogy, is so little compelling, as a matter of logical form alone, that there will always be a pluralism of plausible alternatives among untested hypotheses and inferences to them--calling for some comparative evaluation. This point leads on to some consideration of the virtues of hypotheses--as a description of the range of this pluralism. (shrink)

Many necessitarians about cause and law (Armstrong 1983; Mumford 2004; Bird 2007) have argued that Humeans are unable to justify their inductive inferences, as Humean laws are nothing but the sum of their instances. In this paper I argue against these necessitarian claims. I show that Armstrong is committed to the explanatory value of Humean laws (in the form of universally quantified statements), and that contra Armstrong, brute regularities often do have genuine explanatory value. I finish with a Humean (...) attempt at a probabilistic justification of induction, but this fails due to its assumption that the proportionality syllogism is justified. Although this attempt fails, I nonetheless show that the Humean is at least as justified in reasoning inductively as Armstrong. (shrink)

One of Weatherson's main goals is to drive home a methodological point: We shouldn't be looking for deductive arguments for or against relativism – we should instead be evaluating inductive arguments designed to show that either relativism or some alternative offers the best explanation of some data. Our focus in Chapter Two on diagnostics for shared content allegedly encourages the search for deductive arguments and so does more harm than good. We have no methodological slogan of our own to (...) offer. Part of what we were trying to do was to clearly articulate what the relevant issues even are. Often relativism is characterized in a way that is offhand and sloppy. The relativist, we are told, accepts 'disquotational truth' for various kinds of claims but denies that they are 'true simpliciter'. What exactly is going on here? Do the relevant distinctions even make sense? Before engaging in various abductive manoevers we need to get much clearer about what it is that we are trying to argue for and against. That said we are perfectly happy with the kind of inductive enterprise that Weatherson sketches. For our part, we were fully aware (and indeed explicit) that the 'agreement' diagnostic does not ‘deductively’ settle all of the relevant disputes. A significant part of Chapter Four is dedicated to something in the vicinity of Weatherson's project. Note, indeed, that our diagnostics are even stated using the ideology of 'providing evidence' – hardly the basis for a straightforwardly deductive argument for or against relativism. Finally, though, we should point out that we are not hostile to deductive arguments against relativism. A philosopher's evidence is theory-laden and in part owes itself to epistemic powers that his or her opponents may not acknowledge. In short, their evidence may not always have the hallmarks of 'evidence neutrality' --- evidence that their opponents would recognize as such. We are perfectly open to there being compelling deductive arguments against relativism from such evidence.. (shrink)

The ability to make inductive inferences is important because without it, generalization of knowledge to new circumstances would be impossible. One context in which such inductive skills are likely to have been important over evolutionary time is encounters with animals. Previous research suggests that children take into account at least two kinds of relationships between animals when making inductive inferences about them: descent relationships, and design relationships. Because descent and design relationships are sometimes orthogonal, making correct inferences (...) about particular traits sometimes requires overlooking one kind of relationship in favor of the other. In this study, I used a base-to-target induction task to examine the use of two inference rules in 5 to 12 year old Shuar children from the Amazon region of Ecuador. The descent rule uses taxonomic relationships when the function of the trait being judged is ambiguous or unknown, and the design rule privileges ecological relationships over taxonomic relationships when the function of the trait is relevant to the ecological category in question. The results show that Shuar children do employ both of these rules, and are able to switch between them for different kinds of traits, as the descent/design mode hypothesis predicts. Children in both the younger age group and the older age group were able to use these rules, but the older children showed a slightly different pattern due to the use of specific acquired knowledge about some of the taxa. (shrink)

In this book I have tried to develop an analysis of the concept of an empirical law, an analysis that differs in many ways from the alternative analyse's found in contemporary literature dealing with the subject. 1 am referring especially to two well-known views, viz. the regularity and necessity views, which have given rise to many interesting papers and books within the philosophy of science. In developing my own views, it very soon became clear to me that the mere restatement (...) of these alternative views, followed by a discussion of their defects and an explanation of my own view, would not suffice to show what 1 regard as basically unsound in these views. If we seriously consider the well-known difficulties facing the regularity view, we have to consider the possibility that the time has arrived to stop our attempts to solve, by means of patch-work additions, the fundamental problem of empirical laws within the traditional context of logical positivist doctrines. I have tried to find a solution which is based on a different philosophical context, the main incentive being that the discouraging results of the customary attempts to solve the problem might have been the outcome of the fundamental philosophical setting within which the problem had been formulated and within which everyone looked for a solution. The problem of empirical laws is not a problem existing by its own rights - it is shaped by an underlying point of view or theoretical framework. For this reason I have started with a brief sketch of the logical positivist context. However, I want to stress the fact that my intention was not to offer an historical exposition, but an exposition which becomes meaningful when related to the subsequent arguments concerning empirical laws. The notion of direct or theory-free observation has been taken as the fundamental characteristic of the logical positivist point of view. This view has been further characterised by means of five theses, among which is the thesis that observational terms are isolated or theory-independent units of extensional meaning. These terms are then supposed to be the starting-points of meaning and the end-points of confirmation, and these very characteristics mark the privileged position such terms have in a logical positivist philosophy. The post-positivist view, on the other hand, is characterised by the opposing notion of theory-loaded observation. This notion leads to other conclusions which radically oppose some of the theses of logical positivism. The notion of theory- loaded observation itself, although often clearly stated, has not yet been systematically elucidated, and I have made an attempt to do this in ch. I after my sketch of the logical positivist context. This seemed to me to be necessary in order to make my post-positivist point of view as clear as possible, before tackling the problem of empirical law itself. I have paid special attention to the lawlikeness of concepts and their confirmation and falsification. These epistemological issues are followed by a separate examination of Goodman's riddle in ch. II, because it lies somewhere between the lawlikeness of concepts and the lawlikeness of laws. If Goodman's riddle is taken as a serious problem, as I think it should, it is primarily a problem of concept or theory formation and not a problem of induction. In ch. III the regularity view has been examined and the well-known difficulties related to such a view are considered, assuming the knowledge gained in ch. I. This has led to some interesting results, especially in connection with the analysis of counterfactuals and the confirmation of 'normal' singular conditionals, to which I return in the last chapter. Three different views of the necessity view are briefly stated and investigated in ch. IV. RESCHER'S view is, I think, close to mine, which has been developed in ch. V. However, there are fundamental epistemological differences between our views. In the last chapter I have given my own analysis of the concept of an empirical law, which should not be taken as a synthesis of a regularity and a necessity view, but as opposed to both. It is, as far as particulars may count, the result of an analysis of the concepts 'regularity' and 'necessity'. I have tried to argue that the greatest shortcoming of the regularity view lies in the fact that the proponents of such a view have not been really concerned with the concept of 'regularity' itself. They usually take this concept to be intuitively clear enough to serve as basis for their analysis. Their attacks upon the necessity view are based on the reproach that 'necessity' is a very obscure concept, and that it should, therefore, be avoided in the philosophy of science. We could, however, reproach them in a similar way, since the concept of 'regularity' is anything but clear. One may say that an empirical law formulates a 'regularity in nature', but we can only do justice to the function a law has in science, if we are ready to view this regularity as a necessary connection, which does not exist in an observer-independent reality, but in a theoretically co-constituted empirical world. This investigation does not pretend to answer all questions concerning empirical laws. It should, therefore, not be regarded as complete, but neither should the arguments and suggestions be regarded as completely free from ambiguity. Much remains to be done in order to offer a generally acceptable theory and better understanding. (shrink)

This remarkably clear and comprehensive account of empirical knowledge will be valuable to all students of epistemology and philosophy. The author begins from an explanationist analysis of knowing—a belief counts as knowledge if, and only if, its truth enters into the best explanation for its being held. Defending common sense and scientific realism within the explanationist framework, Alan Goldman provides a new foundational approach to justification. The view that emerges is broadly empiricist, counteracting the recently dominant trend that rejects that (...) framework entirely. Topics treated include the Gettier problem, the nature of explanation and inductive inference, the justification of foundations for knowledge in terms of inference to the best explanation, the possibility of realist interpretations of contemporary science, reference, and the relations between empirical psychology and epistemology. Professor Goldman defends the need for a foundational theory of justification and presents a version that refutes standard criticisms of that doctrine. His defense of realism takes into account contemporary advances in semantics and philosophy of science. It attempts to clarify the kinds of skeptical argument the philosopher must take seriously, without succumbing to them. While recent epistemology has tended to dismiss the traditional foundational approach, it has not provided a suitable alternative. Goldman breaks new ground by adapting that approach within his explanationist, inductive theory. (shrink)

Papers collected in this volume were originally presented at a symposium held at the University of Pennsylvania in December, 1968 and revised in the light of discussion at the symposium for publication. The contributors hold different views about the role played by induction in theories of knowledge and rational belief but many of the papers are conciliatory, reflecting no doubt a good deal of helpful communication at the symposium. For example, Frederic Schick's clearly written and informative lead article considers subjectivist, (...) empiricist, and pragmatist theories of rational belief, arguing that they are compatible theories relevant to different types of issues. Marshall Swain follows with an article which presents a general framework within which rules of rational acceptance can be constructed. An exchange between Isaac Levi and Richard Jeffrey shows that advocates of theories of acceptance and theories of partial belief may be defending complementary and not mutually exclusive theories. In the remaining three essays Henry Kyburg Jr., Gilbert Harman, and Keith Lehrer defend their own distinctive views about the nature of inductive inference and rational belief. Kyburg traces difficulties in some theories to the acceptance of the principle of conjunction which he rejects. Harman and Lehrer both see the relation of inductive inference to explanation as crucial to understanding the former and they develop theories along different lines which make use of this relation. A long and useful bibliography was prepared for the symposium by Ralph L. Slaght and revised for publication in the volume.--R. H. K. (shrink)

The solution is that there can be no justification of induction, "the rule we use to make inferences about unknown events from a sample of data drawn from experience." A principle may be justified either by validation or by vindication; Hume's argument showed conclusively that no validation of induction is possible, but left open the possibility of a vindication. Reichenbach explored this possibility within the framework of a frequency theory of probability. Katz now explores Reichenbach's treatment in detail, finding (...) that it ultimately fails to produce either a "preferability vindication" or an "expediency vindication." Katz then argues that it is in principle impossible ever to modify Reichenbach's account in a way which would allow such vindication-for the inductive rule or, in fact, any convergent rule whatever, whether on a "frequency" or a "degree of confirmation" interpretation of probability. But if no vindication is possible, then no justification of any kind is possible, providing we have correctly reduced the problem; so the problem of induction has received its solution. This in no way calls for skepticism or conventionalism concerning empirical knowledge; we can certainly criticize various inductive procedures and show that one canon is better than another. We can "convince those who are in agreement about basic standards but are interested in more precise versions and their proper application to particular cases"; these are quite different issues from the general "problem of induction." A boldly-outlined argument, drawing upon a good deal of complex material, and handled very skillfully.--B. H. (shrink)

_Probability: A Philosophical Introduction_ introduces and explains the principal concepts and applications of probability. It is intended for philosophers and others who want to understand probability as we all apply it in our working and everyday lives. The book is not a course in mathematical probability, of which it uses only the simplest results, and avoids all needless technicality. The role of probability in modern theories of knowledge, inference, induction, causation, laws of nature, action and decision-making makes an understanding of (...) it especially important to philosophers and students of philosophy, to whom this book will be invaluable both as a textbook and a work of reference. In this book D. H. Mellor discusses the three basic kinds of probability – physical, epistemic, and subjective – and introduces and assesses the main theories and interpretations of them. The topics and concepts covered include: * chance * frequency * possibility * propensity * credence * confirmation * Bayesianism. _Probability: A Philosophical Introduction_ is essential reading for all philosophy students and others who encounter or need to apply ideas of probability. (shrink)

The contributions to this special collection concern issues and problems discussed in or related to the work of Wesley C. Salmon. Salmon has long been noted for his important work in the philosophy of science, which has included research on the interpretation of probability, the nature of explanation, the character of reasoning, the justification of induction, the structure of space/time and the paradoxes of Zeno, to mention only some of the most prominent. During a time of increasing preoccupation with historical (...) and sociological approaches to under standing science (which characterize scientific developments as though they could be adequately analysed from the perspective of political movements, even mistaking the phenomena of conversion for the rational appraisal of scientific theories), Salmon has remained stead fastly devoted to isolating and justifying those normative standards distinguishing science from non-science - especially through the vindi cation of general principles of scientific procedure and the validation of specific examples of scientific theories - without which science itself cannot be (even remotely) adequately understood. In this respect, Salmon exemplifies and strengthens a splendid tradi tion whose most remarkable representatives include Hans Reichenbach, Rudolf Carnap and Carl G. Hempel, all of whom exerted a profound influence upon his own development. (shrink)

This selection of D. H. Mellor's work demonstrates the wide ranging originality of his work. It gathers together sixteen major papers on related topics. Together they form a complete modern metaphysics. The first five papers are on aspects of the mind: on our 'selves', their supposed subjectivity and how we refer to them, on the nature of conscious belief and on computational and physicalist theories of the mind. The next five papers deal with dispositions, natural kinds, laws of nature and (...) how they involve natural necessity, universals and objective chances, and the relation between properties and predicates. Then follow three papers about the relations between time, change and causation, the nature of individual causes and effects and of the causal relation between them, and how causation depends on chance. The last three papers discuss the relation between chance and degrees of belief, give a solution to the problem of induction, and argue for an objective interpretation of decision theory. (shrink)

For a helpful presentation of the various views on probability and inductive logic as well as a thorough survey of the present literature on these topics, one could hardly do better than this work. Kyburg presents, in separate chapters, classical, frequency, logical, subjectivist and epistemological theories of probability, referring to major classical and contemporary works where each of these views is defended. He presents the common criticisms of each view as well as some criticisms of his own and brings (...) out what he takes to be of value in each view. These chapters are preceded by a brief but clear presentation of the probability calculus and a chapter on informal interpretations of probability in ordinary language. A descriptive bibliography follows each chapter in which Kyburg comments on the leading works in each area. The same format applies to his discussion of inductive logic in part II. Inductive inference is discussed in ordinary language and in formal contexts. Statistical inference, confirmation theories, acceptance theories, and demonstrative induction are discussed in separate chapters. There are also discussions of the role of simplicity in inductive inference and the problem of justifying induction. Exercises are added to each chapter and the work might serve well as a text in this field. A forty-eight page bibliography at the end of the book is another one of its assets.--R. H. K. (shrink)

A careful presentation of the foundations of probability theory, containing many valuable innovations. Two accounts of probability are adduced: probability as a measure on the subsets of a probability set, and as a measure on the sentences of a formal language. The book stresses connections between these two accounts; of particular interest is its thesis that statistical probabilities may be regarded as estimates of inductive probabilities.—R. H. T.

In this paper, we consider recent attempts to metaphysically explain agentive modality in terms of conditionals. We suggest that the best recent accounts face counterexamples, and more worryingly, they take some agentive modality for granted. In particular, the ability to perform basic actions features as a primitive in these theories. While it is perfectly acceptable for a semantics of agentive modal claims to take some modality for granted in getting the extension of action claims correct, a metaphysical explanation of agentive (...) modality cannot, at least not in the way that conditional approaches to agentive modality do. We argue that this problem was present even in the classical conditional analysis. By a pessimistic induction, we suggest that, probably, no conditional approach to agentive modality will succeed. (shrink)

The purpose of this paper is to provide a systematic appraisal of the covering law and statistical relevance theories of statistical explanation advanced by Carl G. Hempel and by Wesley C. Salmon, respectively. The analysis is intended to show that the difference between these accounts is inprinciple analogous to the distinction between truth and confirmation, where Hempel's analysis applies to what is taken to be the case and Salmon's analysis applies to what is the case. Specifically, it is argued (a) (...) that statistical explanations exhibit the nomic expectability of their explanandum events, which in some cases may be strong but in other cases will not be; (b) that the statistical relevance criterion is more fundamental than the requirement of maximal specificity and should therefore displace it; and, (c) that if statistical explanations are to be envisioned as inductive arguments at all, then only in a qualified sense since, in particular, the requirement of high inductive probability between explanans and explanandum must be abandoned. (shrink)

The contributions to this special collection concern issues and problems discussed in or related to the work of Wesley C. Salmon. Salmon has long been noted for his important work in the philosophy of science, which has included research on the interpretation of probability, the nature of explanation, the character of reasoning, the justification of induction, the structure of space/time and the paradoxes of Zeno, to mention only some of the most prominent. During a time of increasing preoccupation with historical (...) and sociological approaches to under standing science (which characterize scientific developments as though they could be adequately analysed from the perspective of political movements, even mistaking the phenomena of conversion for the rational appraisal of scientific theories), Salmon has remained stead fastly devoted to isolating and justifying those normative standards distinguishing science from non-science - especially through the vindi cation of general principles of scientific procedure and the validation of specific examples of scientific theories - without which science itself cannot be (even remotely) adequately understood. In this respect, Salmon exemplifies and strengthens a splendid tradi tion whose most remarkable representatives include Hans Reichenbach, Rudolf Carnap and Carl G. Hempel, all of whom exerted a profound influence upon his own development. (shrink)

This recent addition to the well-known "Studies in Logic" series is sure to be of first importance to serious students of inductive logic, confirmation theory, and related issues. The book is an anthology of fourteen papers, which are classified under five different headings: "Extensions of Inductive Logic," "Induction and Information," "Prospects of Confirmation Theory," "The Paradoxes of Confirmation," and "Probability and Foundational Problems." Needless to say, all of the papers are of uniformly high quality. Especially worthy (...) of mention are two papers by Hintikka and Hilpinen which deal with an interesting generalization of Carnap's continuum of inductive methods, and which lead to a somewhat more plausible treatment of non-logically-true closed sentences. Suppes contributes two papers dealing with the recently revived Bayesian methods and their significance for concept formation in psychology and confirmation theory in the philosophy of science. Also under the heading of confirmation theory, one might mention Max Black's paper, "Notes on the Paradoxes of Confirmation," a lucid and rather novel approach to this problem. There is also an important paper by Dana Scott and Peter Krauss entitled "Assigning Probabilities to Logical Formulas." This piece of work presents a set-theoretical method for bridging the gap between the standard treatment of probability by means of axioms defining a real measure over a Boolean algebra and the usual logical inquiries into "degree of confirmation" and the like. The reference value of the book is enhanced by a subject index of terms and concepts dealt with in the various papers.—H. P. K. (shrink)

According to the one-fallacy theory, the only real fallacy is equivocation. In particular, the fallacy of incomplete evidence draws a conclusion inductively from parts of our evidence while ignoring other parts of it which undermine the conclusion. T his is an equivocation on the relative term 'probable': the conclusion is probable relative to a part of our evidence but not relative to the whole of it. Unfortunately, this view is not entirely consistent with my meta-theory of fallacies which (...) allows t hat some failures of rationality are errors simply in inductive reasoning rather than being equivocations. (shrink)

Dans ses recherches empiriques, philosophiques et métaphysiques la conscience humaine ne sort pas de sa propre sphère. C'est toujours la conscience qui parle. Par sa connaissance l'homme ne peut dépasser la conscience directe. Par sa pensée il tend à dépasser médiatement la conscience. Cette constatation nous est dictée par le fait scientifiquement fondé que tant la conscience humaine que son contenu sont tirés, c.a.d. révélés, des profondeurs cachées où ils sont recélés. C'est ce qui rend évident que l'homme possède un (...) merveilleux "sens sondeur", lui permettant de reconnaître les hauteurs et les profondeurs de notre conscience et aspirant à la transcendance. Le domaine de l'expérience se borne nécessairement aux phénomènes, et tandis que celui de la philosophie s'étend au fondement de ces phénomènes et à leurs rapports réciproques, la métaphysique, la science des principes, se propose de pénétrer l'origine et le sens profond de toute chose, du néant à l'ultime perfection. Après Kant qui a voulu en finir avec la métaphysique dogmatique unilatéralement déductive, la méthode inductive a pris définitivement le dessus. Cette méthode ne s'arroge pas le droit de juger d'une façon apodictique en ce qui touche aux problèmes de l'existence, qui ont donné naissance aux dispositions de la conscience humaine. Elle s'efforce, au contraire, de faire en cette matière une large part à l'inconnu en démontrant que les résultats sont heuristiques, hypothétiques et problématiques. Ainsi la théorie de la connaissance, la philosophie et la théologie s'accordent à dire que les données microcosmiques dans la sphère de la conscience humaine peuvent être les représentants des entités macrocosmiques. Si la conscience humaine poursuit ses recherches philosophiques et métaphysiques, c'est qu'elle doit sa genèse à une relation universelle dont elle est la représentation. (shrink)

This second volume in the series designed to review the work done in various areas of philosophy during the period 1956-1966 is concerned with the philosophy of science. There are forty essays on a variety of topics in the philosophy of science describing the work done in that area in the past decade and a bibliography covering the same period. Most are in English, some in French or German. Some representative topics and their authors are: Laws, Models, Causality, Induction and (...) Probability, Scientific Methodology, Time, Space, Cosmology, Philosophy and Physics, Quantum Theory, Biology and Philosophy. In addition there are several general essays on the influence of various philosophers and scientists on current developments in the philosophy of science, on the ethical and philosophical implications of science, on Cybernetics, Information Theory, Game theory and a number of essays on the development of philosophy of science in different countries of Western and Eastern Europe and Japan. Like the first volume of this series, this book is an indispensable guide to anyone interested in the field, and a place should be made for it on every library shelf---where there is an interest in philosophy of science.--R. H. K. (shrink)

This volume claims to offer first a correct interpretation of Hume's theory of causation, and second, a philosophical defense of it against many recent criticisms. The first two chapters try to reconcile Hume's two definitions of "cause," and to prove that Hume was not a skeptic about induction. The authors contend that Hume's views on causation can be rationally reconstructed as a unified theory that is, they believe, faithful to his intentions, namely that causation involves regularities or constant (...) conjunctions, and some kind of necessity. (shrink)

Definitions of stronger and weaker versions of physical realism are offered, The first relating to the existence of physical objects and the second to the independence of their properties. It is argued that recent debates about the commensurability and convergence of scientific theories and the causal theory of reference are irrelevant to the truth of these theses, Although their proponents seem to think them linked. It is then argued that support for realist positions must be inductive. Such support (...) is provided for both the weaker and stronger theses. (shrink)

This chapter argues that epistemologists should replace a “standard alternatives” picture of knowledge, assumed by many fallibilist theories of knowledge, with a new “multipath” picture of knowledge. The chapter first identifies a problem for the standard picture: fallibilists working with this picture cannot maintain even the most uncontroversial epistemic closure principles without making extreme assumptions about the ability of humans to know empirical truths without empirical investigation. The chapter then shows how the multipath picture, motivated by independent arguments, saves fallibilism (...) from this problem. The multipath picture is based on taking seriously the idea that there can be multiple paths to knowing some propositions about the world. An overlooked consequence of fallibilism is that these multiple paths to knowledge may involve ruling out different sets of alternatives, which should be represented in a fallibilist picture of knowledge. The chapter concludes by considering inductive knowledge and strong epistemic closure from this multipath perspective. (shrink)

This work is divided into two parts. Part I contains sixteen critical es says by prominent philosophers and computer scientists. Their papers offer insightful, well-argued contemporary views of a broad range of topics that lie at the heart of philosophy in the second half of the twen tieth century: semantics and ontology, induction, the nature of prob ability, the foundations of science, scientific objectivity, the theory of naming, the logic of conditionals, simulation modeling, the relatiOn be tween minds and (...) machines, and the nature of rules that guide be havior. In this volume honoring Arthur W. Burks, the philosophical breadth of his work is thus manifested in the diverse aspects of that work chosen for discussion and development by the contributors to his Festschrift. Part II consists of a book-length essay by Burks in which he lays out his philosophy of logical mechanism while responding to the papers in Part I. In doing so, he provides a unified and coherent context for the range of problems raised in Part I, and he highlights interesting relationships among the topics that might otherwise have gone un noticed. Part II is followed by a bibliography of Burks's published works. (shrink)

This anthology collects readings from important nineteenth and early twentieth century figures who contributed to the philosophy of science before that discipline emerged in the last 40 years as an area of study in its own right. It begins with a seldom-read selection by Kant ) and ends with a selection from Bridgman's The Logic of Modern Physics. Each selection is preceded by a three-page biography of the author together with a bibliography of his major writings and some writings on (...) his work. Many familiar names appear, e.g., Mill, Mach, Pearson, Hertz, Poincare, Peirce, Duhem, Russell, Whitehead, and Campbell. But there are others represented whose actual writings are not so familiar to many students of the philosophy of science, e.g., J. F. W. Herschel, William Whewell, Hermann Von Helmholtz, J. B. Stallo, Emile Boutroux and William Ostwald. With the exception of Stallo, the writings of these figures have been long out of print. In one case, a selection from Ludwig Boltzmann on the nature of mechanics, the editor has translated the selected passage into English expressly for this volume. A wide range of topics are considered in the readings: physical laws, theories, induction, observation, space, time, and others; but, as the nature of the case requires, the focus of attention is on classical science. For this reason most existing courses in the philosophy of science could use this collection only as a supplementary text. But it would function well in such a role. Moreover, specialized courses in the history of philosophical thinking about science will find it very useful.--R. H. K. (shrink)

The essays collected in this volume to honor Ernest Nagel reflect his wide interest in all topics relating philosophy to the natural and social sciences. The essays, written by distinguished philosophers and scientists form a mixed bag, but most of them are very good. The first part, "Science and Inquiry" begins with notes taken by Patrick Suppes of Nagel's lectures on Dewey's logic delivered in 1947. It follows with essays on knowledge by Stuart Hampshire, on intensions and the law of (...) inverse variation by R. M. Martin, and four essays on problems of induction and confirmation which contribute markedly to this well-worn field. The eleven essays of the second part, "Structure of Science" range from discussions of physics and ontology, mechanism and evolution to essays on functionalism in anthropology and ethics and legal theory. In between there are very good essays by C. Hempel on reduction, S. Morgenbesser on the realist-instrumentalist controversy, essays on the identity thesis, extensive measurement, causation and action, philosophy of language, and the differences between the natural and social sciences. Part three contains six essays on the role of values in various settings, e.g., ethical theory, the social sciences, legal theory and existentialism. The fourth and final part contains a variety of historical studies: Clagett on the quadrature of lunes in medieval science, I. Bernard Cohen on Newton, A. Koslow on the law of inertia, Charles Parsons on Kant's philosophy of arithmetic, Philip Wiener on a Soviet view of Peirce's pragmatism and S. Diamond on John D. Rockefeller and the historians.--R. H. K. (shrink)

Originally published as a long essay in Mind and Cosmos, Volume II of the University of Pittsburgh series in the philosophy of science, this study admirably fills the need for an elementary survey of problems in the area of probability and induction. But it is more than an introduction. The author is working on the general thesis that Bayes' theorem of the probability calculus holds the key to the understanding of scientific inference. Guided by this idea he attempts to salvage (...) what he thinks is of value in various current theories of probability and scientific inference, particularly, the frequency theory of probability as defended by Reichenbach, Popper's views on the falsifiability of theories, and Hanson's work on the logic of discovery. These attempts to develop a theory in the latter part of the book follow discussions of Hume's critique of induction, the probability calculus and five past and present interpretations of the calculus. This is a well-written and challenging introduction to the field.—R. H. K. (shrink)

Torporley's ‘Congestor analyticus’, completed in 1627 in the library of the Earl of Northumberland at Petworth, was seen by Rigaud in the 1830s among the mathematical manuscript collection of the Earl of Macclesfield. Torporley's additional copy of the introductory part, preserved at Sion College, has been used for the present report. Torporley's prime objective was the presentation of some of Harriot's work. His first example concerns a classical problem in number theory. The complete solution, by an inductive process (...) based on tables of differences, is given in a few folios of the British Library collection of Harriot manuscripts. Torporley's transcription and commentary contrast forcibly today with the immediate illuminating impact of Harriot's original. (shrink)

This paper is a sequel to the joint publication of Scott and Krauss in which the first aspects of a mathematical theory are developed which might be called "First Order Probability Logic". No attempt will be made to present this additional material in a self-contained form. We will use the same notation and terminology as introduced and explained in Scott and Krauss, and we will frequently refer to the theorems stated and proved in the preceding paper. The main objective (...) of this study is to show that the probability of symmetric probability systems may be represented as a "weighted average" of what might be called "product probabilities". We then discuss some applications of our results to Carnap's "Principle of instantial relevance", which plays an important role in his system of inductive logic. (shrink)

This collection of papers in epistemic logic is oriented towards applications to game theory and individual decision theory. Most of these papers were presented at the inaugural conference of the LOFT (Logic for the Theory and Games and Decisions) conference series, which took place in 1994 in Marseille. Among the notions dealt with are those of common knowledge and common belief, infinite hierarchies of beliefs and belief spaces, logical omniscience, positive and negative introspection, backward induction and rationalizable (...) equilibria in game theory. (shrink)

The pessimistic induction and the problem of underdetermination in the philosophy of science have a rich history. In their recent incarnation as the problem of unconceived alternatives, most fully articulated by Kyle Stanford (2010) in Exceeding Our Grasp, the induction is more specific and underdetermination is construed more epistemically than is typical…The problem is not that there are empirically equivalent alternatives, that is, alternative between which no empirical evidence could ever distinguish. The problem is that multiple radically different alternative that (...) are empirically inequivalent might be equally well-confirmed by current evidence, and we might fail to even conceive one or more of those alternatives… In “Of German Tanks and Scientific Theories: Estimating the Number of Unconceived Alternatives,” Burkay Ozturk (2016) challenges Stanford on a distinct front. By applying a method of statistical estimation to scientific alternatives, Ozturk argues that the possibility space within which the alternatives are located allows for probable knowledge. The particular frequentist estimation method Ozturk employs requires that we assume the alternative pool is finite, which seems to be both false and wildly implausible. At first glance. I argue in this comment that Ozturk’s postulate of finitude is actually defensible in circumstances that might actually hold for ordinary scientific contexts. (shrink)

Systematics based solely on structuralist principles is non-science because it is derived from first principles that are inconsistent in dealing with both synchronic and diachronic aspects of evolution, and its evolutionary models involve hidden causes, and unnameable and unobservable entities. Structuralist phylogenetics emulates axiomatic mathematics through emphasis on deduction, and “hypotheses” and “mapped trait changes” that are actually lemmas and theorems. Sister-group-only evolutionary trees have no caulistic element of scientific realism. This results in a degenerate systematics based on patterns of (...) fact or evidence being treated as so fundamental that all other data may be mapped to the cladogram, resulting in an apparently well-supported classification that is devoid of evolutionary theory. Structuralism in systematics is based on a non-ultrametric analysis of sister-group informative data that cannot detect or model a named taxon giving rise to a named taxon, resulting in classifications that do not reflect macroevolutionary changes unless they are sister lineages. Conservation efforts are negatively affected through epistemological extinction of scientific names. Evolutionary systematics is a viable alternative, involving both deduction and induction, hypothesis and theory, developing trees with both synchronic and diachronic dimensions often inferring nameable ancestral taxa, and resulting in classifications that advance evolutionary theory and explanations for particular groups. (shrink)

Systematics based solely on structuralist principles is non-science because it is derived from first principles that are inconsistent in dealing with both synchronic and diachronic aspects of evolution, and its evolutionary models involve hidden causes, and unnameable and unobservable entities. Structuralist phylogenetics emulates axiomatic mathematics through emphasis on deduction, and “hypotheses” and “mapped trait changes” that are actually lemmas and theorems. Sister-group-only evolutionary trees have no caulistic element of scientific realism. This results in a degenerate systematics based on patterns of (...) fact or evidence being treated as so fundamental that all other data may be mapped to the cladogram, resulting in an apparently well-supported classification that is devoid of evolutionary theory. Structuralism in systematics is based on a non-ultrametric analysis of sister-group informative data that cannot detect or model a named taxon giving rise to a named taxon, resulting in classifications that do not reflect macroevolutionary changes unless they are sister lineages. Conservation efforts are negatively affected through epistemological extinction of scientific names. Evolutionary systematics is a viable alternative, involving both deduction and induction, hypothesis and theory, developing trees with both synchronic and diachronic dimensions often inferring nameable ancestral taxa, and resulting in classifications that advance evolutionary theory and explanations for particular groups. (shrink)

Dans ses recherches empiriques, philosophiques et métaphysiques la conscience humaine ne sort pas de sa propre sphère. C'est toujours la conscience qui parle. Par sa connaissance l'homme ne peut dépasser la conscience directe. Par sa pensée il tend à dépasser médiatement la conscience. Cette constatation nous est dictée par le fait scientifiquement fondé que tant la conscience humaine que son contenu sont tirés, c.a.d. révélés, des profondeurs cachées où ils sont recélés. C'est ce qui rend évident que l'homme possède un (...) merveilleux "sens sondeur", lui permettant de reconnaître les hauteurs et les profondeurs de notre conscience et aspirant à la transcendance. Le domaine de l'expérience se borne nécessairement aux phénomènes, et tandis que celui de la philosophie s'étend au fondement de ces phénomènes et à leurs rapports réciproques, la métaphysique, la science des principes, se propose de pénétrer l'origine et le sens profond de toute chose, du néant à l'ultime perfection. Après Kant qui a voulu en finir avec la métaphysique dogmatique unilatéralement déductive, la méthode inductive a pris définitivement le dessus. Cette méthode ne s'arroge pas le droit de juger d'une façon apodictique en ce qui touche aux problèmes de l'existence, qui ont donné naissance aux dispositions de la conscience humaine. Elle s'efforce, au contraire, de faire en cette matière une large part à l'inconnu en démontrant que les résultats sont heuristiques, hypothétiques et problématiques. Ainsi la théorie de la connaissance, la philosophie et la théologie s'accordent à dire que les données microcosmiques dans la sphère de la conscience humaine peuvent être les représentants des entités macrocosmiques. Si la conscience humaine poursuit ses recherches philosophiques et métaphysiques, c'est qu'elle doit sa genèse à une relation universelle dont elle est la représentation. (shrink)

In their logical analysis of theorems about disjoint rays in graphs, Barnes, Shore, and the author (hereafter BGS) introduced a weak choice scheme in second-order arithmetic, called the $\Sigma ^1_1$ axiom of finite choice (hereafter finite choice). This is a special case of the $\Sigma ^1_1$ axiom of choice ( $\Sigma ^1_1\text {-}\mathsf {AC}_0$ ) introduced by Kreisel. BGS showed that $\Sigma ^1_1\text {-}\mathsf {AC}_0$ suffices for proving many of the aforementioned theorems in graph theory. While it is not (...) known if these implications reverse, BGS also showed that those theorems imply finite choice (in some cases, with additional induction assumptions). This motivated us to study the proof-theoretic strength of finite choice. Using a variant of Steel forcing with tagged trees, we show that finite choice is not provable from the $\Delta ^1_1$ -comprehension scheme (even over $\omega $ -models). We also show that finite choice is a consequence of the arithmetic Bolzano–Weierstrass theorem (introduced by Friedman and studied by Conidis), assuming $\Sigma ^1_1$ -induction. Our results were used by BGS to show that several theorems in graph theory cannot be proved using $\Delta ^1_1$ -comprehension. Our results also strengthen results of Conidis. (shrink)

This book is a clear, concise, and conceptually unified treatment of various problems, both formal and philosophical, of inductive logic and probability. Ackermann's main concern throughout the book is the problem of adducing inductive support for various hypotheses, and of deciding between two competing hypotheses which is more reasonable given the available evidence. The author begins with a general consideration of the criteria to be met by satisfactory rules of inductive inference: accordance with intuitive notions of reasonableness (...) in simple cases, sensitivity to the given evidence, capacity for unambiguous intersubjective application. Ackermann quickly disposes of the argument that valid inductive rules must be made to rest upon a "postulate of the uniformity of nature": "If past projections of regularities suddenly begin to go wrong, nondeductive rules satisfying the criteria suggested above will begin to select regularities other than the ones which have failed." This clears the way for a consideration of the general problem of evidential support or confirmation, with its well-known paradoxes and difficulties. Ackermann, like Goodman, locates the source of these in problems bearing on the semantics of scientific language, and cautiously points to Goodman's theory of projection and entrenchment as the way out of most of the muddle. Succeeding chapters deal with the notion of probability of hypotheses, statistical inference, and the application of Bayesian techniques and decision theory to science. A well-chosen bibliography completes this modest but rewarding little book.—H. P. K. (shrink)

Among the dubious theses "proved" by the author of this classic example of pseudo-scientific literature are: relativistic physics is incorrect, the quantum theory is incorrect, "the success of quantum theory is purely mathematical," time, like space, has three dimensions, inductance and mass are equivalent, there is such a thing as absolute motion, and "All properties which are possessed by either space or time individually are.... properties of both space and time." What makes this book unusual is the fact (...) that the immense number of citations and footnotes refer to almost all of the important books and articles in the field of the philosophical foundations of physics. Larson therefore has accomplished one outstanding task: he has succeeded in immersing himself in some of the most philosophically and scientifically compelling literature of recent times and has emerged unscathed by a single intelligible idea.—H. P. K. (shrink)

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by C. (...) Neumann, Mach, Friedländer and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t2. In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation $\dot{\alpha}$ of the parameter α is the order of magnitude $\dot{\alpha}=-H_0 \alpha$ , where H0 is the instantaneous value of the Hubble constant: $H_0 =\left({\dot{R}/R} \right)_0 \approx \left( {0.5-1.0} \right) \times 10^{-10}a^{-1}$ . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed. (shrink)

ABSTRACTIn this polemical book, Francesco Boldizzoni argues that economic history is so moribund as to require resurrection. He maintains that economic history has been converted into a subfield of economics and has embraced the antihistorical and a priori intellectual style of mainstream economics departments: it has, in effect, ceased to be a form of history. Boldizzoni hopes to force a recognition of contemporary economic history's bankruptcy and to show the way toward a revitalization.He criticizes both economic history as retrospective econometrics, (...) as in the work of Robert Fogel, and economic history as a branch of the new institutional economics, as in the work of Douglas North. Boldizzoni suggests that economic history should return to the sort of research and models that prevailed earlier in its own history—models based on induction from observed economic life rather than on deduction from the theories of contemporary microeconomics. He particularly singles out the work of Witold Kula, Moses Finley, and the Annales historians for emulation, but also praises the perspectives of economic sociology and economic anthropology.Boldizzoni's call for a return to a more inductive form of economic history is welcome, and his discussions of his heroes should remind us that economic history was once a vibrant and creative part of the history profession. But the book's advice is more useful for historians working on premodern than on modern economic life. The claim that self‐governing markets and interest‐maximizing individual actors are pure figments of economists' imaginations seems far less certain for recent than for premodern times. And his insistence that each society has its own distinct form of economic life that must be discovered inductively leaves unconceptualized the world‐spanning forces of capitalist development that increasingly shape societies everywhere. Boldizzoni's critique and his positive suggestions are certainly valuable, but he by no means supplies a sufficient recipe for economic history's resurrection as a vibrant field. (shrink)

Nelson Goodman's new riddle of induction wears many faces. In one of its guises the new riddle of induction appears as the problem of providing a general account of the distinction between projectible and non-projectible predicates. This is the form of the riddle which is supposed to point up a lacuna in the foundations of confirmation theories such as Carnap's which, Goodman charges, work only to the extent that one builds into them just the right predicates. As a new riddle (...) of induction, the problem of distinguishing projectible from non-projectible predicates has the virtue that it is in fact new—a virtue not shared by some other forms of the riddle.Philosophers had recognized previously that some predicates are more projectible than others in the sense that, for instance, the prediction that a certain toss of a die will turn up an even face is safer and more likely to be true than the prediction that the same toss will turn up six. (shrink)

The social exchange theory of reasoning, which is championed by Leda Cosmides and John Tooby, falls under the general rubric “evolutionary psychology” and asserts that human reasoning is governed by content-dependent, domain-specific, evolutionarily-derived algorithms. According to Cosmides and Tooby, the presumptive existence of what they call “cheater-detection” algorithms disconfirms the claim that we reason via general-purpose mechanisms or via inductively acquired principles. We contend that the Cosmides/Tooby arguments in favor of domain-specific algorithms or evolutionarily-derived mechanisms fail and that the (...) notion of a social exchange rule, which is central to their theory, is not correctly characterized. As a consequence, whether or not their conclusion is true cannot be established on the basis of the arguments they have presented. (shrink)

Twenty-four scientists and philosophers contribute to this volume, which constitutes the proceedings of the 1959 meetings of the American Association for the Advancement of Science. Six symposia deal with theory construction; empirical and conventional elements in physical theory; induction, probability and simplicity; the logic of variables and constants; philosophical issues of quantum theory; and the methodology of psychology and the social sciences. Many of the contributions are excellent; most deal with controversial issues, and generate considerable life in (...) the discussions and commentaries.--B. J. H. (shrink)

Researchers are required to seek consent from Indigenous communities prior to conducting research but there is inadequate information about how Indigenous people understand and become fully engaged with this consent process. Few studies evaluate the preference or understanding of the consent process for research with Indigenous populations. Lack of informed consent can impact on research findings. The Picture Talk Project was initiated with senior Aboriginal leaders of the Fitzroy Valley community situated in the far north of Western Australia. Aboriginal people (...) were interviewed about their understanding and experiences of research and consent processes. Transcripts were analysed using NVivo10 software with an integrated method of inductive and deductive coding and based in grounded theory. Local Aboriginal interpreters validated coding. Major themes were defined and supporting quotes sourced. Interviews with Aboriginal leaders were facilitated by a local Aboriginal Community Navigator who could interpret if necessary and provide cultural guidance. Participants were from all four major local language groups of the Fitzroy Valley; aged 31 years and above; and half were male. Themes emerging from these discussions included Research—finding knowledge; Being respectful of Aboriginal people, Working on country, and Being flexible with time; Working together with good communication; Reciprocity—two-way learning; and Reaching consent. The project revealed how much more there is to be learned about how research with remote Aboriginal communities should be conducted such that it is both culturally respectful and, importantly, meaningful for participants. We identify important elements in community consultation about research and seeking consent. (shrink)

This second volume in the series designed to review the work done in various areas of philosophy during the period 1956-1966 is concerned with the philosophy of science. There are forty essays on a variety of topics in the philosophy of science describing the work done in that area in the past decade and a bibliography covering the same period. Most are in English, some in French or German. Some representative topics and their authors are: Laws, Models, Causality, Induction and (...) Probability, Scientific Methodology, Time, Space, Cosmology, Philosophy and Physics, Quantum Theory, Biology and Philosophy. In addition there are several general essays on the influence of various philosophers and scientists on current developments in the philosophy of science, on the ethical and philosophical implications of science, on Cybernetics, Information Theory, Game theory and a number of essays on the development of philosophy of science in different countries of Western and Eastern Europe and Japan. Like the first volume of this series, this book is an indispensable guide to anyone interested in the field, and a place should be made for it on every library shelf---where there is an interest in philosophy of science.--R. H. K. (shrink)

The question of how we apply knowledge from biomedical science to medical and public health practice has been the subject of heated debates about generalizability and related concepts, such as applicability and inductive inference. In this essay, I interpret the term from the perspective of two causal models: determinism and indeterminism. I suggest that theories of generalizability can be formulated on the basis of both models and take the form of testable but unverifiable hypotheses, an attribute that is common (...) to all scientific theories. Nonetheless, there is one noteworthy difference between the two models: determinism allows one to rationalize a decision to treat a certain kind of patient but only indirectly a decision to treat any particular patient, whereas indeterminism accommodates both types of decisions. (shrink)