Gilboa and Schmeidler provide a paradigm for modelling decision making under uncertainty. Unlike the classical theory of expected utility maximization, case-based decision theory does not assume that decision makers know the possible 'states of the world' or the outcomes, let alone the decision matrix attaching outcomes to act-state pairs. Case-based decision theory suggests that people make decisions by analogies to past cases: they tend to choose acts that performed well in the past in similar situations, and to avoid acts (...) that performed poorly. It is an alternative to expected utility theory when both states of the world and probabilities are neither given in the problem nor can be easily constructed. The authors describe the general theory and its relationship to planning, repeated choice problems, inductive inference, and learning; they highlight its mathematical and philosophical foundations and compare it with expected utility theory as well as with rule-based systems. (shrink)

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler. A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with (...) state-dependent utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable. (shrink)

Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a “Grand State Space”, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing (...) the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs. (shrink)

This note argues that, under some circumstances, it is more rational not to behave in accordance with a Bayesian prior than to do so. The starting point is that in the absence of information, choosing a prior is arbitrary. If the prior is to have meaningful implications, it is more rational to admit that one does not have sufficient information to generate a prior than to pretend that one does. This suggests a view of rationality that requires a compromise between (...) internal coherence and justification, similarly to compromises that appear in moral dilemmas. Finally, it is argued that Savage's axioms are more compelling when applied to a naturally given state space than to an analytically constructed one; in the latter case, it may be more rational to violate the axioms than to be Bayesian. (shrink)

Published as a tribute to the memory of Elisha Pazner, this book contains a collection of essays providing a comprehensive view of the design and evaluation of economic mechanisms, written and edited by the major contributors to the field. Amongst the topics included are bargaining theory and the economics of competitive bidding. The surveys are preceded by 'A Perspective', by Leo Hurwicz which contains a systematic account of the development of the literature on mechanism design, and this provides a context (...) for both the surveys and the six published papers authored or co-authored by Elisha Pazner that complete the book and demonstrate Pazner's interest in and contribution to the study of economic mechanisms. Leonid Hurwitcz is the Nobel Prize Winner 2007 for The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, along with colleagues Eric Maskin and Roger Myerson, for his work on the effectiveness of markets. (shrink)

A decision maker has to choose one of several random variables whose distributions are not known. As a Bayesian, she behaves as if she knew the distributions. In this paper we suggest an axiomatic derivation of these (subjective) distributions, which is more economical than the derivations by de Finetti or Savage. Whereas the latter derive the whole joint distribution of all the available random variables, our approach derives only the marginal distributions. Correspondingly, the preference questionnaire needed in our case is (...) less smaller. (shrink)

Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a “Grand State Space”, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing (...) the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs. (shrink)

We propose a model of an agent’s probability and utility that is a compromise between Savage (The foundations of statistics, Wiley, 1954) and Jeffrey (The Logic of Decision, McGraw Hill, 1965). In Savage’s model the probability–utility pair is associated with preferences over acts which are assignments of consequences to states. The probability is defined on the state space, and the utility function on consequences. Jeffrey’s model has no consequences, and both probability and utility are defined on the same set of (...) propositions. The probability–utility pair is associated with a desirability relation on propositions. Like Savage we assume a set of consequences and a state space. However, we assume that states are comprehensive, that is, each state describes a consequence, as in Aumann (Econometrica 55:1–18, 1987). Like Jeffrey, we assume that the agent has a preference relation, which we call desirability, over events, which by definition involves uncertainty about consequences. For a given probability and utility of consequences, the desirability relation is presented by conditional expected utility, given an event. We axiomatically characterize desirability relations that are represented by a probability–utility pair. We characterize the family of all the probability–utility pairs that represent a given desirability relation. (shrink)

We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

Do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how can they benefit from representation theorems, which are no more than equivalence results? We address these questions. We propose several ways in which representation results can be useful and discuss their implications for axiomatic decision theory.

The interpretation of economic theories varies along several dimensions. First, models can describe reality, illustrate a recommended state of affairs, or analyze the structure and implications of a theory. Second, theories can be used for prediction or for explanation. Third, theories can relate to reality in a rule-based or case-based manner. Fourth, theories can be statements about economic reality or about the act of economic reasoning itself. Fifth, theories can offer predictions or merely critique reasoning. We argue that theories are (...) often open to multiple interpretations which can shift depending on the context in which the theory is applied, the surrounding economic literature, and the argument made by the interpreter. (shrink)

Ellsberg's (1961) famous paradox shows that decision-makers give events with ‘known’ probabilities a higher weight in their outcome evaluation. In the same article, Ellsberg suggests a preference representation which has intuitive appeal but lacks an axiomatic foundation. Schmeidler (1989) and Gilboa (1987) provide an axiomatisation for expected utility with non-additive probabilities. This paper introduces E-capacities as a representation of beliefs which incorporates objective information about the probability of events. It can be shown that the Choquet integral of an E-capacity (...) is the Ellsberg representation. The paper further explores properties of this representation of beliefs and provides an axiomatisation for them. (shrink)

In this book, which thoroughly revises and greatly expands his classic work Sameness and Substance, David Wiggins retrieves and refurbishes in the light of twentieth-century logic and logical theory certain conceptions of identity, of substance and of persistence through change that philosophy inherits from its past. In this new version, he vindicates the absoluteness, necessity, determinateness and all or nothing character of identity against rival conceptions. He defends a form of essentialism that he calls individuative essentialism, and then a (...) form of realism that he calls conceptualist realism. In a final chapter he advocates a human being-based conception of the identity and individuation of persons, arguing that any satisfactory account of personal memory must make reference to the life of the rememberer himself. This important book will appeal to a wide range of readers in metaphysics, philosophical logic, and analytic philosophy. (shrink)

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative (...) principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration. (shrink)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised learning (...) methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

A collection of 14 essays honoring the life and work of Oxford philosopher Wiggins touching on topics from ancient philosophy to ethics, metaphysics and the theory of meaning. The contributing scholars debate many of the seminal issues of Wiggins' work, including the determinancy of distinctness, relative identity, naturalism in ethics, logic and truth in moral judgments, and the practical wisdom of Aristotle. The collection uniquely features replies by Wiggins to each of the papers. Annotation copyright by Book News, Inc., Portland, (...) OR. (shrink)

Drawing on work of the past decade, this volume brings together articles from the philosophy, history, and sociology of science, and many other branches of the biological sciences. The volume delves into the latest theoretical controversies as well as burning questions of contemporary social importance. The issues considered include the nature of evolutionary theory, biology and ethics, the challenge from religion, and the social implications of biology today (in particular the Human Genome Project).

According to dispositionalism about modality, a proposition <p> is possible just in case something has, or some things have, a power or disposition for its truth; and <p> is necessary just in case nothing has a power for its falsity. But are there enough powers to go around? In Yates (2015) I argued that in the case of mathematical truths such as <2+2=4>, nothing has the power to bring about their falsity or their truth, which means they come out both (...) necessary and not possible. Combining this with axiom (T), it is easy to derive a contradiction. I suggested that dispositionalists ought to retreat a little and say that <p> is possible just in case either p, or there is a power to bring it about that p, grounding the possibility of mathematical propositions in their truth rather than in powers. Vetter’s (2015) has the resources to provide a response to my argument, and in her (2018) she explicitly addresses it by arguing for a plenitude of powers, based on the idea that dispositions come in degrees, with necessary properties a limiting case of dispositionality. On this view there is a power for <2+2=4>, without there being a power to bring about its truth. In this paper I argue that Vetter’s case for plenitude does not work. However, I suggest, if we are prepared to accept metaphysical causation, a case can be made that there is indeed a power for <2+2=4>. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

The typical kind of color realism is reductive: the color properties are identified with properties specified in other terms (as ways of altering light, for instance). If no reductive analysis is available — if the colors are primitive sui generis properties — this is often taken to be a convincing argument for eliminativism. That is, realist primitivism is usually thought to be untenable. The realist preference for reductive theories of color over the last few decades is particularly striking in light (...) of the generally anti-reductionist mood of recent philosophy of mind. The parallels between the mind—body problem and the case of color are substantial enough that the difference in trajectory is surprising. While dualism and non-reductive physicalism are staples, realist primitivism is by and large a recent addition to the color literature. And it remains a minority position, although one that is perhaps gaining support. In this paper, we investigate whether it should be accepted, and conclude it should not be. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

This is an in-depth study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that (...) are grasped through geometrical or intelligible intuition. -/- Accordingly, this study classifies Fichte’s philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the Wissenschaftslehre itself may be read as an attempt at a new philosophical mathesis, or “mathesis of the mind.” -/- “This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched.” Professor Dr. Marco Ivaldo -/- “This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the Wissenschaftslehre and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious.” Professor Dr. Emmanuel Cattin. (shrink)

In 1962, the philosopher Richard Taylor used six commonly accepted presuppositions to imply that human beings have no control over the future. David Foster Wallace not only took issue with Taylor's method, which, according to him, scrambled the relations of logic, language, and the physical world, but also noted a semantic trick at the heart of Taylor's argument. _Fate, Time, and Language_ presents Wallace's brilliant critique of Taylor's work. Written long before the publication of his fiction and essays, Wallace's (...) thesis reveals his great skepticism of abstract thinking made to function as a negation of something more genuine and real. He was especially suspicious of certain paradigms of thought-the cerebral aestheticism of modernism, the clever gimmickry of postmodernism-that abandoned "the very old traditional human verities that have to do with spirituality and emotion and community." As Wallace rises to meet the challenge to free will presented by Taylor, we witness the developing perspective of this major novelist, along with his struggle to establish solid logical ground for his convictions. This volume, edited by Steven M. Cahn and Maureen Eckert, reproduces Taylor's original article and other works on fatalism cited by Wallace. James Ryerson's introduction connects Wallace's early philosophical work to the themes and explorations of his later fiction, and Jay Garfield supplies a critical biographical epilogue. (shrink)

I argue that virtual reality is a sort of genuine reality. In particular, I argue for virtual digitalism, on which virtual objects are real digital objects, and against virtual fictionalism, on which virtual objects are fictional objects. I also argue that perception in virtual reality need not be illusory, and that life in virtual worlds can have roughly the same sort of value as life in non-virtual worlds.

Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der fonnalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet fUr die Logik eine ahnliche Fonnel­ sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebrauchlich ist. In der Mathematik wurde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewohnlichen Sprache bedienen. Die groBen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum (...) wesentlichen Teil mit dadurch bedingt, daB es gelang, einen brauchbaren und leistungsfahigen Fonnalismus zu finden. - Was durch die Formel­ sprache in der Mathematik erreicht wird, das solI auch in der theoretischen Logik durch diese erzielt werden, namlich eine exakte, wissenschaftliche Behandlung ihres Gegenstandes. Die logischen Sachverhalte, die zwischen Urteilen, Begriffen usw. bestehen, finden ihre Darstellung durch Formeln, deren Interpretation frei ist von den Unklarheiten, die beim sprachlichen Ausdruck leicht auftreten konnen. Der Dbergang zu logischen Folgerungen, wie er durch das SchlieBen geschieht, wird in seine letzten Elemente zerlegt und erscheint als fonnale Umgestaltung der Ausgangsfonneln nach gewissen Regeln, die den Rechenregeln in der Algebra analog sind; das logische Denken findet sein Abbild in einem LogikkalkUl. Dieser Kalkiil macht die erfolgreiche Inangriffnahme von Problemen moglich, bei denen das rein inhaltliche Denken prinzipiell versagt. Zu diesen gehort z. B. (shrink)

Interpretation -- Introduction -- Interpreting Plato -- The political culture of Plato's early dialogues -- Dialogue -- Character and history -- The mouthpiece principle -- Forms of evidence -- Desire -- Socrates and eros -- The subjectivist conception of desire -- Instrumental and terminal desire -- Rational and irrational desires -- Desire in the critique of Akrasia -- Interpreting Lysis -- The deficiency conception of desire -- Inauthentic friendship -- Platonic desire -- Antiphilosophical desires -- Knowledge -- Excellence as wisdom (...) -- The epistemic unity of excellence -- Dunamis and technê -- Goodness and form -- The epistemological priority of definitional knowledge -- Ordinary ethical knowledge -- Method -- The Socratic fallacy -- Socrates' pursuit of definitions -- Hupothesis -- Two postulates -- The geometrical illustration -- Geometrical analysis -- The method of reasoning from a postulate -- Elenchus and hupothesis -- Knowledge and aitia -- F-conditions -- Cognitive security -- Aporia -- Forms of aporia -- Dramatic aporia -- The example of Charmides -- Charmides as autobiography -- The politics of Sôphrosunê -- Critias' Philotimia -- Self-knowledge and the knowledge of knowledge -- Knowledge of knowledge and knowledge of the good -- Philosophy and the polis. (shrink)

First published in 1995, The Visual Brain in Action remains a seminal publication in the cognitive sciences. For this new edition, a very substantial and illustrated epilogue has been added to the book in which Milner and Goodale review the key developments that support or challenge the views that were put forward in the first edition.

Japan and the Enemies of Open Political Science argues that Eurocentric blindness is a scientific failing, not a moral one. In a way true of no other political system, Japan's greatness has the potential to enliven and reform almost all the main branches of Western Political Science. David Williams criticizes Western social science, Anglo-American Philosophy and French Theory and explains why mainstream economists, historians of political thought and postculturalists have ignored Japan's modern achievements. Williams demonstrates why the renewal of (...) social science and the nurturing of a "a philosophy of the Pacific Century" requires a sustained act of intellectual demolition. (shrink)

There have been serious controversies in the latter part of the 20th century about the roles and functions of scientific and medical research. In whose interests are medical and biomedical experiments conducted and what are the ethical implications of experimentation on subjects unable to give competent consent? From the decades following the Second World War and calls for the global banning of medical research to the cautious return to the notion that in controlled circumstances, medical research on human subjects is (...) in the best interest of the given individual and the broader population, this book addresses the key implications of experimentation on humans. This volume covers major ethical themes within biomedical research providing historical, philosophical, legal and policy reflections on the literature and specific issues in the field of research on human subjects. Focusing on special populations (the elderly, children, prisoners and the cognitively impaired) it represents the most up-to-date review of the special ethical and legal conflicts that arise with relation to experimentation on subjects from these groups. In the light of current initiatives for law reform pertaining to research ethics the world over, this volume provides a timely, comprehensive and provocative exploration of the field. The volume has been carefully organized to present important philosophical perspectives on organizing principles that should underlie any practical application. A forward-looking historical review of the regulatory regimes of principal jurisdictions, including of the legal controls already in place, provides the backdrop for future policy initiatives. Additionally, in the light of global restructuring of health care systems, several chapters have been devoted to epidemiological research and related issues. (shrink)

While there are many legal textbooks on the laws of armed conflict and academic works on ethical issues in international relations, this is the first text on the relevance of legal and normative issues in military practice. It covers the entire spectrum of military operations and is written with military deicision-makers particularly in mind.

Extant theoretical work on the political resource curse implies that dependence on resource revenues should decrease autocracies’ likelihood of democratizing but not necessarily affect democracies’ chances of survival. Yet most previous empirical studies estimate models that are ill-suited to address this claim. We improve upon earlier studies, estimating a dynamic logit model that interacts a continuous measure of resource dependence with an indicator of regime type using data from 166 countries, covering the period from 1816-2006. We find that an increase (...) in resource dependence at time t - 1 increases the likelihood of autocratic persistence at t, but has no appreciable effect on democratic survival. We go beyond existing empirical studies to show that increases in resource dependence have persistent and substantial cumulative effects on autocracies' likelihood of becoming democratic over the long-term, showing that the total effect of resource dependence on regime type is much larger than the short-term (one period) effect indicates. (shrink)

Fichte-Studien, volume 49 (Leiden: Brill/Rodopi Publishers, 8 April 2021), edited by David W. Wood, 471pp. -/- Presenting new critical perspectives on J.G. Fichte’s Wissenschaftslehre, this volume of articles in English by an international group of scholars addresses the topic of first principles in Fichte’s writings. Especially discussed are the central text of his Jena period, the 1794/95 Grundlage der gesammten Wissenschaftslehre, as well as later versions like the Wissenschaftslehre nova methodo (1796-99) and the presentations of 1804 and 1805. Also (...) included are new studies on the first principles of the particular sub-disciplines of Fichte’s system, such as the doctrines of aesthetics, nature, right, ethics, and history. The volume also contains a number of miscellaneous essays on Fichte research, as well as several book reviews. (shrink)