Showing papers in "Synthese in 1985"

Could man be an irrational animal

Abstract: Aristotle thought man was a rational animal. From his time to ours, however, there has been a steady stream of writers who have dissented from this sanguine assessment. For Bacon, Hume, Freud, or D. H. Lawrence, rationality is at best a sometimes thing. On their view, episodes of rational inference and action are scattered beacons on the irrational coastline of human history. During the last decade or so, these impressionistic chroniclers of man's cognitive foibles have been joined by a growing group of experimental psychologists who are subjecting human reasoning to careful empirical scrutiny. Much of what they have found would appall Aristotle. Human subjects, it would appear, regularly and systematically invoke inferential and judgmental strate gies ranging from the merely invalid to the genuinely bizarre. Recently, however, there have been rumblings of a reaction brewing a resurgence of Aristotelian optimism. Those defending the sullied name of human reason have been philosophers, and their weapons have been conceptual analysis and epistemological argument. The central thrust of their defense is the claim that empirical evidence could not possibly support the conclusion that people are systematically irra tional. And thus the experiments which allegedly show that they are must be either flawed or misinterpreted. In this paper I propose to take a critical look at these philosophical defenses of rationality. My sympathies, I should note straightaway, are squarely with the psychologists. My central thesis is that the philoso phical arguments aimed at showing irrationality cannot be experiment ally demonstrated are mistaken. Before considering these arguments, however, we would do well to set out a few illustrations of the sort of empirical studies which allegedly show that people depart from nor mative standards of rationality in systematic ways. This is the chore that will occupy us in the following section.

How to give it up: A survey of some formal aspects of the logic of theory change

Abstract: The paper surveys some recent work on formal aspects of the logic of theory change. It begins with a general discussion of the intuitive processes of contraction and revision of a theory, and of differing strategies for their formal study. Specific work is then described, notably Gardenfors' postulates for contraction and revision, maxichoice contraction and revision functions and the condition of orderliness, partial meet contraction and revision functions and the condition of relationality, and finally the operations of safe contraction and revision. Verifications and proofs are omitted, with references given to the literature, but definitions and principal results are presented with rigour, along with discussion of their significance.

Wittgenstein and the Vienna Circle

Abstract: With the publication of the Tractatus Wittgenstein felt that he had made what contribution he could to philosophy. Perhaps it was for this reason, along with other, inner reasons connected with the defeat of Austria-Hungary in the War, that he retired into the Austrian countryside to teach at elementary schools. Frank Ramsey, the brilliant young logician at Cambridge, came to visit Wittgenstein and prevailed upon him to discuss philosophy. But a proper return to that vocation seemed out of the question: Wittgenstein wrote to Keynes: You ask in your letter whether you could do anything to make it possible for me to return to scientific work. The answer is, no: there is nothing to be done in that way, because I myself no longer have any strong inner drive towards that sort of activity. Everything that I really had to say I have said, and so the spring has run dry. That sounds queer, but it’s how things are.

Organism-environment mutuality epistemics, and the concept of an ecological niche

Abstract: The concept of an ecological niche (econiche) has been used in a variety of ways, some of which are incompatible with a relational or functional interpretation of the term. This essay seeks to standardize usage by limiting the concept to functional relations between organisms and their surroundings, and to revise the concept to include epistemic relations. For most organisms, epistemics are a vital aspect of their functional relationships to their surroundings and, hence, a major determinant of their econiche. Rejecting the traditional dualism of organism and environment, an econiche is defined as the reciprocal (dual) of a functionally specified class of organisms (FSTU). From this perspective, an econiche necessarily implies a certain type of organism, and a class of functionally similar organisms implies a special econiche. The econiche concept is also discussed in relation to other ecological terms that reflect the distributional patterns of organisms, such as “habitat’, and the concept of an “empty niche” is criticized.

Destroying the consensus

Abstract: Should the U.S. government proceed with the development of the MX missile? This is a complex question. Answering it involves considering many factors including assessments of alternative defense systems, national priorities and so on. One of the factors is whether or not the MX system will survive a Soviet first strike. There is a range of expert opinion on this question. There are also differences of opinion concerning who the experts are and the extent to which their opinions are to be relied on. Given this diversity of views what is a policy maker, in this case the president, to do? Is there some rational way to generate a consensus out of this wealter of opinions? In their book Rational Consensus in Science and Society 1 Keith Lehrer and Carl Wagner claim that under certain circumstances there does exist a uniquely rational way of combining the opinions of 'experts ' into a consensus. They argue that even though the experts disagree they may be rationally commit ted to a consensus. As they construe it, the consensus should embody all the information contained in the individual views. The experts, recognizing this are, under certain conditions, rationally commit ted to changing their views to the consensus. The president might be able to employ Lehrer and Wagner 's method to extract a consensus from his advisors which he could use in his own deliberations. Lehrer and Wagner develop their account of consensus within a Bayesian framework. They imagine a group of individuals each with a subjective probability distribution over some language. According to them consensus, if it exists, is also represented by a probability distribution. The consensus distribution is a weighted average of the individual distributions. The determination of the weights is crucial in their account and will be discussed later. The authors see their account of consensus as contributing to the solution of a number of related problems. (1) It is intended as an analysis of the concept of consensus as in, for example, \"The re is a consensus among geologists that the earth is at least 4 billion years old.\

Formal Systems of Dialogue Rules

Abstract: Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a ‘chain of arguments’. From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs. Section 3 contains a — relatively quick — proof of the equivalence of the four systems. It follows that each of them yields intuitionistic logic.

On the formal properties of weighted averaging as a method of aggregation

Abstract: I first encountered Keith Lehrer's work on consensus during the summer of 1977,l and was immediately intrigued by the possibility of developing a formal account of his model of rational group decision making. I adopted as a model for this enterprise the axiomatic method of social choice theory and was not surprised to discover that the question of how to aggregate probabilities was as complex and prob lematic as the question of how to aggregate preferences and utilities. The former issue has only recently received the kind of attention which has been directed at the latter for several decades, and is finally beginning to be as vigorously debated, as attested to by the essays in this volume. I am grateful to Barry Loe wer for organizing this forum on Rational Consensus in Science and Society. My replies to the preceding critical essays follow.

Probability kinematics, conditionals, and entropy principles

Abstract: treatment of marginalization requires axioms that govern the interaction between composition, pairing, and margining. The axioms are as follows: (i) T.o = (Tv).; ( i i ) (ST), = $~T; (iii) ( T; S), x ~ = T,; T~, where u x v is the usual Cartesian product of propositional (measurable) maps. At this point the framework of relative probabilities is rich enough to express a number of notions providing a foundation to statistical reasoning. One such notion is independence. Given a diagram P u ; v 1--~X-~ Y x Z , we say that the propositional (measurable) maps u and v are Pindependent iff P,,v = P,; P,. It is not hard to check that this definition coincides with the usual definition of statistical independence of two random variables. (Here the pairing u; v is defined by u; v(x)= (u(x), v(x))). Unquestionably, the most important concept by far in statistics and probability kinematics is conditionalization. In fact much of our groundworkup to this point was intended for the introduction of conditionals. K I N E M A T I C S , C O N D I T I O N A L S , E N T R O P Y P R I N C I P L E S 99 We know that every propositional map u:X--> Y induces a family of equational propositions [u = y] = {xl u(x) = y} which partitions the sample space X. These propositions in turn convert every probability P on X into a standard conditional Pt,=y] (including 0), defined by the usual operations of restriction and normalization Pt,=y](A) = P(A N [u = y]): P([u = y]). Note the important fact that the conditional is a function of the fixed map u and state y. It may be possible to glue these 'local' conditionals together so as to get one 'global' conditional, a relative probability P~: Y --~ X, defined by P\"(y, A) = P[,=y](A). The problem is that we would like this definition to work for all propositions and not just the equational ones. A leading idea is to define pu by the limit of standard Bayesian conditionals P~(y, A) = Lim [P(A n u-l( U)): P,( U)], U-->y where U is a proposition satisfying P~(U) ~ 0 in ~3y, and approaching the state y, relative to a suitable convergence structure. As U becomes: increasingly smaller, still close to y, in the limit the standard conditionals (P~)u merge into a 'point' conditional P~(y,-). Of course, the limit may not exist, and even if it does exist, it is not clear what the underlying convergence structure is. It turns out that a construction on filters does the job. To avoid additional technicalities, we wind up this brief discussion of generalized conditionals by pointing out that if Y has given a topology, then the set Azy of possible proposition-open set pairs (U, V), satisfying P . ( U ) ~ O, y~ V and U c V, forms a directed system of elements, ordered by ( U, V) <( U', V') iff V' c V. Now if the net of standard Bayesian conditionals {(Pu) u l( U, V) e JC'y} converges at all, its limit is unique and is equal to P\"(y, .). In standard texts of statistics the conditional P\" : Y ~ X is a relative probability, defined implicitly by the integral equation 100 Z O L T A N D O M O T O R P( A A u-~( B)) = JB P\"(Y' A) P,( dy). (10) Although this definition does provide a natural extension of Bayesian conditionals, in general, contrary to the actual practice of statistics, it • does not single out a unique relative probability P% No matter which definition is adapted, its axiomatization leads to the following: AXIOM 4. Generalized Bayesian Conditionalization of Belief States P u I ~ X , X ~ Y

Consensus as shared agreement and outcome of inquiry

Abstract: When two or more agents disagree concerning what is true, concerning how likely it is that a hypothesis is true or concerning how desirable it is that a hypothesis be true, they may, of course, be prepared to rest content with the disagreement and treat each other's views with contemptuous toleration. The mere fact that someone disagrees with one's judgments is insufficient grounds for opening up one's mind. Most epistemologists forget that it is just as urgent a question to determine when we are justified in opening up our minds as it is to determine when we are justified in closing them. Nonetheless, the context of disagreement sometimes offers good reasons for the participants initiating some sort of investigation to settle their dispute. When this is so, an early step in such a joint effort is to identify those shared agreements which might serve as the noncontroversial basis of subsequent inquiry. Once this is done, investigation may proceed relative to that background of shared agreements according to those methods acknowledged to be appropriate to the problem under consideration. On this view of disagreement and its resolution through inquiry, the notion of consensus may be used in two quite distinct ways: (a) One can speak of that consensus of the participants at the beginning of inquiry which constitutes the background of shared agreements on which the investigation is initially grounded, (b) Sometimes inquiry of this kind may terminate with a satisfactory conclusion. We may then say that a consensus has been reached as to the outcome of inquiry.

The Relation Between Epistemology and Psychology

Abstract: In the wake of Frege’s attack on psychologism and the subsequent influence of Logical Positivism, psychological considerations in philosophy came to be viewed with suspicion. Philosophical questions, especially epistemological ones, were viewed as ‘logical’ questions, and logic was sharply separated from psychology. Various efforts have been made of late to reconnect epistemology with psychology. But there is little agreement about how such connections should be made, and doubts about the place of psychology within epistemology are still much in evidence. It therefore remains to be clarified just how such links should be established, and what impact they would have on the direction of epistemology.

Circumstances and dominance in a causal decision theory

Abstract: Rational choices reflect beliefs and preferences in certain orderly ways. According to Bayesian decision theories, rational choices maximize expected utility. More precisely, according to a Bayesian decision theory, an option in an appropriate partition of options is rational if and only if its expected utility is at least as great as the expected utility of any option in that partition. The expected utility of an option is a weighted average of values for its possible total upshots, weights in this average being probabilities for these upshots given this option: if Ua is the set of a's possible total upshots,

Some random observations

Abstract: Of course, the rationale of PME is so different from what has been taught in “orthodox” statistics courses for fifty years, that it causes conceptual hangups for many with conventional training. But beginning students have no difficulty with it, for it is just a mathematical model of the natural, common sense way in which anybody does conduct his inferences in problems of everyday life. The difficulties that seem so prominent in the literature today are, therefore, only transient phenomena that will disappear automatically in time. Indeed, this revolution in our attitude toward inference is already an accomplished fact among those concerned with a few specialized applications; with a little familarity in its use its advantages are apparent and it no longer seems strange. It is the idea that inference was once thought to be tied to frequencies in random experiments, that will seem strange to future generations.

Some foundational problems in mathematics suggested by physics

Abstract: It is largely recognized that physics has represented an important source of suggestions in the historical development of mathematics and, in more recent times, even of logic. At the same time, if we look to the foundational investigations about both sciences in our century, one cannot help but notice that these researches have very rarely inter acted. Further, a number of discussions about the foundations of mathematics seem to go along with a somewhat naive and old fashioned image of physics, whereas foundational investigations about physics often propose an oversimplified image of the world of mathe matics (stressing for instance the characterization of mathematics as a merely analytical science). I would like to discuss in what sense contemporary physics might provide some interesting arguments and theoretical results, which could have a bearing on the foundational studies about mathematics. Let me start with a traditional philosophical question. It is well known that many discussions of the golden period of the foundational studies in mathematics in our century are essentially founded on a somewhat schematic contraposition between a platonistic view according to which, roughly, mathematical objects are described) and a concep tualista view (according to which mathematical objects are invented or constructed). Now, such a contraposition is clearly based on an extrapolation from the theoretical constructs of empirical sciences. Namely, the starting point of the traditional platonist in mathematics seems to be founded on a very uncritical concept of physical object, to which the platonist intends to assimilate even the concept of mathema tical object. In other words (according to the classical platonistic view), the concept of mathematical object should share the same logical and gnoseological characters as the concept of physical object. But what are the relevant properties of the concept of physical object? It is well known that contemporary physics has submitted to a strong criticism the traditional concept of object, developed by classical macrophysics [10]. I would like to recall only four main reasons, which in my opinion confirm the thesis according to which the concept of

Justification, reasons, and reliability

Abstract: Some time ago, F. P. Ramsey (1960) suggested that knowledge is true belief obtained by a reliable process. This suggestion has only recently begun to attract serious attention. In 'Discrimination and Perceptual Knowledge', Alvin Goldman (1976) argues that a person has knowledge only if that person's belief has been formed as a result of a reliable cognitive mechanism. In Belief, Truth, and Knowledge, David Armstrong (1973) argues that one has knowledge only if one's belief is a comPletely reliable sign of the truth of the proposition believed. On both of these theories, the reliability of one's belief is a necessary condition of that belief's being an instance of knowledge. These reliability theories have another interesting feature in common, namely, that neither of them explicitly requires or includes the traditional justification requirement for knowledge. Reliability has taken over the role of justification. This naturally leads to the question whether reliability and justification are related in some philosophically interesting fashion. In this paper I shall investigate this question. The result will be a positive proposal to the effect that justified belief is reliable belief. This result, in turn, explains why reliability can take over the role of justification in an account of knowledge. Moreover, the identification of justification with reliability constitutes a step toward the naturalization of normative epistemological concepts.

Mathematical logic: Tool and object lesson for science

Abstract: The object lesson concerns the passage from the foundational aims for which various branches of modern logic were originally developed to the discovery of areas and problems for which logical methods are effective tools. The main point stressed here is that this passage did not consist of successive refinements, a gradual evolution by adaptation as it were, but required radical changes of direction, to be compared to evolution by migration. These conflicts are illustrated by reference to set theory, model theory, recursion theory, and proof theory. At the end there is a brief autobiographical note, including the touchy point to what extent the original aims of logical foundations are adequate for the broad question of the heroic tradition in the philosophy of mathematics concerned with the ‘nature’ of the latter or, in modern jargon, with the architecture of mathematics and our intuitive resonances to it.

Genetic epistemology, history of science and genetic psychology

Abstract: Genetic epistemology analyzes the growth of knowledge both in the individual person (genetic psychology) and in the socio-historical realm (the history of science). But what the relationship is between the history of science and genetic psychology remains unclear. The biogenetic law that “ontogeny recapitulates phylogeny” is inadequate as a characterization of the relation. A critical examination of Piaget's Introduction a l'Epistemologie Genentique indicates these are several examples of what I call stage laws common to both areas. Furthermore, there is at least one example of a paradoxical inverse relation between the two — geometry. Both similarities and differences between the two domains require an explanation, a developmental explanation. Although such an explanation seems to be psychological in nature, it is not merely empirical but also normative (since psychology is both factual and normative according to Piaget). Hence genetic epistemology need not be reduced to psychology (narrowly conceived), but rather should be seen as being both empirical and normative and thus similar to certain types of contemporary philosophy of science.