Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide (...) variety of disciplines. The material in the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)

There is widespread agreement about a combination of attributes that someone needs to possess if they are to be counted as a conservative. They need to lack definite political ideals, goals or ends, to prefer the political status quo to its alternatives, and to be risk averse. Why should these three highly distinct attributes, which are widely believed to be characteristic of adherents to a significant political position, cluster together? Here I draw on prospect theory to develop an (...) explanation for the clustering of attributes that is characteristic of conservatives. I argue that a lack of political ideals is the underlying driver of conservatism. I will provide reason to believe that people who lack political ideals are disposed to prefer the political status quo to its alternatives; and reason to believe that people who prefer the political status quo to its alternatives are disposed to be risk averse, at least with respect to significantly many of the risks that arise in the social and political domain. I also consider and reject some other potential explanations for the clustering of attributes that is characteristic of conservatives and sketch some policy implications that follow from the explanation I develop. (shrink)

Prospect theory is increasingly used to explain deviations from the traditional paradigm of rational agents. Empirical support for prospect theory comes mainly from laboratory experiments using student samples. It is obviously important to know whether and to what extent this support generalizes to more naturally occurring circumstances. This article explores this question and measures prospect theory for a sample of private bankers and fund managers. We obtained clear support for prospect theory. Our (...) financial professionals behaved according to prospect theory and violated expected utility maximization. They were risk averse for gains and risk seeking for losses and their utility was concave for gains and convex for losses. They were also averse to losses, but less so than commonly observed in laboratory studies and assumed in behavioral finance. A substantial minority focused on gains and largely ignored losses, behavior reminiscent of what caused the current financial crisis. (shrink)

In the theoretical description of prospect theory, distinct sets of parameters can control the curvature of the value function and the shape of the probability weighting function. There is one for the gain domain and one for the loss domain. However, in most estimations, behaviour over losses is assumed to perfectly reflect behaviour over gains, through a unique set of parameters. We examine the consequences of relaxing this simplifying assumption in the context of Tanaka et al.’s (Am Econ (...) Rev 100(1):557–571, 2010) risk-elicitation procedure based on multiple price lists. We show that subjects’ behaviour for gains is mostly reflected for losses at the aggregate and individual levels, and is consistent with the distinctive prospect theory fourfold pattern. Reflection is only partial as the mean curvature of the value function is slightly less convex for losses than it is concave for gains. These results are robust to a high-stake context. However, we demonstrate that assuming reflection can have huge consequences on loss-aversion measures. Incidentally, we also highlight the existence of a strong, negative and persistent pure loss-frame effect on elicited loss aversion. We recommend that future practitioners and modellers are particularly cautious about the loss-aversion values they obtain or use because these are especially sensitive to parametric assumptions and framing. (shrink)

We give a probabilistic justification of the shape of one of the probability weighting functions used in Prospect Theory. To do so, we use an idea recently introduced by Herzog and Hertwig. Along the way we also suggest a new method for the aggregation of probabilities using statistical distances.

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of (...) 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)

The introduction of the euro gave a unique opportunity to empirically disentangle two components of utility: intrinsic value, a rational component central in economics, and the numerosity effect (going by numbers while ignoring units), a descriptive and irrational component central in prospect theory and underlying the money illusion. We measured relative risk aversion in Belgium before and after the introduction of the euro, and could consider changes in intrinsic value while keeping numbers constant, and changes in numbers while (...) keeping intrinsic value constant. Intrinsic value significantly affected risk aversion, and the numerosity effect did not. Our study is the first to confirm the classical hypothesis of increasing relative risk aversion while avoiding irrational distortions due to the numerosity effect. (shrink)

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of (...) 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)

Prospect Theory (PT) is widely regarded as the most promising descriptive model for decision making under uncertainty. Various tests have corroborated the validity of the characteristic fourfold pattern of risk attitudes implied by the combination of probability weighting and value transformation. But is it also safe to assume stable PT preferences at the individual level? This is not only an empirical but also a conceptual question. Measuring the stability of preferences in a multi-parameter decision model such as PT (...) is far more complex than evaluating single-parameter models such as Expected Utility Theory under the assumption of constant relative risk aversion. There exist considerable interdependencies among parameters such that allegedly diverging parameter combinations could in fact produce very similar preference structures. In this paper, we provide a theoretic framework for measuring the (temporal) stability of PT parameters. To illustrate our methodology, we further apply our approach to 86 subjects for whom we elicit PT parameters twice, with a time lag of 1 month. While documenting remarkable stability of parameter estimates at the aggregate level, we find that a third of the subjects show significant instability across sessions. (shrink)

We conduct a standardized survey on risk preferences in 53 countries worldwide and estimate cumulative prospect theory parameters from the data. The parameter estimates show that significant differences on the cross-country level are to some extent robust and related to economic and cultural differences. In particular, a closer look on probability weighting underlines gender differences, economic effects, and cultural impact on probability weighting. The data set is a useful starting point for future research that investigates the impact of (...) risk preferences on the market level. (shrink)

Prospect theory is an alternative theory of choice under conditions of risk, and deviates from expected utility theory by positing that people evaluate choices with respect to gains and losses from a reference point. They tend to overweight losses with respect to comparable gains and engage in risk-averse behavior with respect to gains and risk-acceptant behavior with respect to losses. They also respond to probabilities in a non-linear manner. I begin with an overview of prospect (...) theory and some of the evidence upon which it is based, and then consider some of the implications of the theory for American politics, international relations, and the law. I end with a brief discussion of some of the conceptual and methodological problems confronting the application of prospect theory to the study of politics. (shrink)

Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk and Uncertainty (...) 5:297–323, 1992). We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are (...) characterized by objective probabilities). Our new elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the paradox, (...) the slope at zero has to be finite. (2) to account for the fourfold pattern of risk attitudes, the probability weighting has to be strong enough. (shrink)

Much behavioral welfare economics assumes that expected utility theory does not accurately describe most human choice under risk. A substantial literature instead evaluates welfare consequences by taking cumulative prospect theory as the natural default alternative, at least where description is concerned. We present evidence, based on a review of previous literature and new experimental data, that the most empirically adequate hypothesis about human choice under risk is that it is heterogeneous, and that where EUT does not apply, (...) more choice is characterized by rank-dependent utility models than by CPT. Most of the apparently loss-averse choice behavior results from probability weighting rather than from direct disutility experienced when an outcome is framed as a loss against an idiosyncratic reference point. We then consider implications of this finding for methodological debates about how to model welfare effects of policies, and argue that abandonment of a dogmatic belief in CPT as the correct theory of risk human choice exposes a conceptual error that is widespread in behavioral welfare economics. We provide concluding reflections on second-order, philosophical issues around the grounding of normative commitments in policy-focused economics. (shrink)

We discuss the bearing of Daniel Kahneman and Amos Tversky's Prospect Theory on some central issues in ethics. It has been argued that the theory provides a better explanation of our intuitive responses to some important ethical decision cases—like some famous cases put by Philippa Foot and others—than traditional and widely acknowledged ethical principles do. In this way, Prospect Theory contributes to the new wave of skepticism, emanating from the social sciences, about the role of (...) intuitive judgments in ethical theory and philosophy more generally. We focus on Kahneman and Tversky's famous Asian Disease Problem. We show that the case fails to support Prospect Theory over traditional ethical theory as an explanation of the most common intuitive responses to the case, and, moreover, fails as an account of the most common intuitive responses to Foot's famous trolley case and related cases. We maintain that careful critical attention to all these cases shows that Prospect Theory has not made a successful incursion into ethics, whatever it may have established about non-ethical decision-making. (shrink)

Third generation prospect theory is a theory of choices and of judgments of highest buying and lowest selling prices of risky prospects, i.e., of willingness to pay and willingness to accept. The gap between WTP and WTA is sometimes called the “endowment effect” and was previously called the “point of view” effect. Third generation prospect theory combines cumulative prospect theory for risky prospects with the theory that judged values are based on the (...) integration of price paid or price received with the consequences of gambles. In TGPT, the discrepancy between WTP and WTA is due to loss aversion-losses have greater absolute utility than gains of the same value. TGPT was developed independently of similar developments by Birnbaum and Zimmermann :145–187, 1998) and Luce. This paper reviews theoretical and empirical findings, to show that TGPT fails as a descriptive model of both choices and judgments. Evidence refutes three implications of TGPT, but they are consistent with configural weight models in which loss aversion is not needed to describe the results. In the configural weight models, buyers place greater weight on lower consequences, attributes or estimates of value compared to sellers, who place greater configural weight on higher aspects of an object or prospect. (shrink)

Whereas original prospect theory was introduced over 40 years ago, its formula for multi-outcome prospects has never yet been published, resulting in many misunderstandings. This note provides that formula.

Original and cumulative prospect theory differ in the composition rule used to combine the probability weighting function and the value function. We test the predictive power of these composition rules by performing a novel out-of-sample prediction test. We apply estimates of prospect theory’s weighting and value function obtained from two-outcome cash equivalents, a domain where original and cumulative prospect theory coincide, to three-outcome cash equivalents, a domain where the composition rules of the two theories (...) differ. Although both forms of prospect theory predict three-outcome cash equivalents very well, at the aggregate level, we find small but systematic under-prediction of cash equivalents for cumulative prospect theory and small but systematic over-prediction of cash equivalents for original prospect theory. We also observe substantial heterogeneity across subjects and types of gambles, some of which is accounted for by differences in the curvature and elevation of the weighting function across individuals. We also find differences in prediction related to whether the worst outcome is zero or non-zero. (shrink)

In this paper, we analyse higher-order risky choices by the representative cumulative prospect theory (CPT) decision maker from three alternative reference points. These are the status quo, average payout and maxmin. The choice tasks we consider in our analysis include binary risks, and are the ones employed in the experimental literature on higher order risk preferences. We demonstrate that the choices made by the representative subject depend on the reference point. If the reference point is the status quo (...) and the lottery choices exhibit symmetric risk, we demonstrate that there is no third order reflection effect of lottery choices but there is a fourth order reflection effect. When the average payout is the reference point, we demonstrate that any third or fourth order lottery choice is possible dependent upon the lottery payoffs. However, under the assumption of maxmin reference point, the risky choices are prudent and temperate. In addition to these results, our analysis reveals that the representative CPT subject can choose combinations of second with third and fourth order risky options that differ from those in other major models of decision under risk. We contrast our theoretical predictions with the empirical results reported in the literature on higher order risk preferences and are able to reconcile some conflicting experimental evidence. (shrink)

We investigate whether the display of portfolio performance as coming from one large portfolio or two smaller subportfolios matters to individuals and whether prospect theory can explain this preference. To this end, we run a large survey experiment of 3267 individuals in 5 European countries presenting an identical overall return as coming from one portfolio or two smaller subportfolios to individuals. We also elicited the coefficients of the prospect theory value function through price list lotteries. In (...) losses, following prospect theory and mental accounting predictions, we observe emprically a preference for the display of returns as coming from 2 subportfolios, one displaying a small gain and the other a large loss, over a unique portfolio displaying the aggregated resulting loss. As expected, for an overall gain, individuals favor one portfolio over two subportfolios, one displaying a small loss and the other a larger gain. The shape of the value function does not explain individuals’ preferences. The reference point seems to be the main factor involved in explaining individuals’ choice of two subportfolio presentations of the outcome. (shrink)

Advocates of Expressivism about basically any kind of language are best-served by abandoning a traditional content-centric approach to semantic theorizing, in favor of an update-centric or dynamic approach (or so this paper argues). The type of dynamic approach developed here — in contrast to the content-centric approach — is argued to yield canonical, if not strictly classical, "explanations" of the core semantic properties of the connectives. (The cases on which I focus most here are negation and disjunction.) I end the (...) paper by describing a distinctive sense in which mental states might play a fundamental role in the practice of semantic theorizing (as I understand it), and I connect this to a distinctive account of the pragmatic function of, e.g., a normatively laden claim in discourse. (shrink)

We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us (...) to rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics. (shrink)

Theory appears to have played the ideological-institutional role of enfranchiser, even if the role was ulti-mately an epiphenomenal one. Furthermore, the expectation of gold in "them thar hills" also encouraged too many university presses to invest in film publications, especially when the arcane peregrinations of Theory facilitated their rationalization of their relaxation of their traditional role as academic gatekeepers. Hence film studies has been flooded with repetitive decoctions of the Theory in search of the same market in (...) much the same way that con-sumers are confronted with so many marginally differentiated shampoos. (shrink)

This essay discusses ways in which contemporary mathematical logic may be reconciled with John Dewey’s logical theory. Standard formal techniques drawn from dynamic modal logic, situation theory, generative grammar, generalized quantifier theory, category theory, lambda calculi, game theoretic semantics, network exchange theory, etc., are accommodated within a framework consistent with Dewey’s Logic: The Theory of Inquiry (1938). This essay outlines some basic features of Dewey’s logical theory, working in a top-down fashion through various (...) technical notions pertaining to existential and ideational aspects of inquiry, from contextual notions of situations and ideologies, to primitive operational and empirical notions of modes of action and particular qualities. The aim here is to display the scope of Dewey’s logical theory and thus establish a framework relative to which details may be explored without losing sight of their larger significance. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, (...) they are identical. In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing (...) principle, known as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

In this article, I argue that there are three widely accepted views within contemporary theorising about justice that present barriers to accepting that non-human animals possess direct entitlements of justice. These views are that the basis of entitlements of justice is either contribution to a cooperative scheme for mutual advantage or the capacity to so contribute; political liberalism, that is, the view that requirements for coercive state action can be justified only by appeal to the ideal of citizens as free (...) and equal and the principles of justice that are entailed by that ideal; and that the principles of justice apply directly to the institutions of what John Rawls calls the ‘basic structure of society’, and not to the conduct of individuals. I then consider several attempts to ground direct entitlements of justice for animals via modest revisions to one or more of these widely accepted views, and argue that they fail, and that, more generally, any such attempt must fail. I claim that any theory that can include direct entitlements for animals must reject and at least one of and, and that there are reasons to think that those who are inclined to endorse direct entitlements for animals are unlikely to be satisfied with any view that does not reject all three of the widely accepted views. I conclude by briefly noting some of the important implications of rejecting all of these views. (shrink)

Primitivists about truth maintain that truth cannot be analysed in more fundamental terms. Defences of primitivism date back to the early years of analytic philosophy, being offered by G.E. Moore, Bertrand Russell, and Gottlob Frege. In more recent years, a number of contemporary philosophers—including Donald Davidson, Ernest Sosa, Trenton Merricks, Douglas Patterson, and Jamin Asay—have followed suit, defending their own versions of primitivism. I'll begin by offering a brief history of primitivism, situating each of these views within the landscape of (...) primitivist truth theories and detailing some of their core motivations and apparent shortcomings. To close the discussion, I'll offer a diagnosis of the prospects of primitivism, focusing on the mystery challenge, which has loomed large throughout the history of primitivist truth theories, and the methodology that should be used in evaluating primitivist (and other) truth theories going forward. (shrink)

Michael Tye has recently argued that the phenomenal character of conscious experiences is "one and the same as" (1) Poised (2) Abstract (3) Non-conceptual (4) Intentional Content (PANIC). Tye argues extensively that PANIC Theory accounts for differences in phenomenal character in representational terms. But another task of a theory of phenomenal consciousness is to account for the difference between those mental states that have phenomenal character at all and those that do not. By going through each of the (...) four qualifiers of PANIC, we argue that PANIC Theory fails to account for this difference in genuinely representational terms. We suggest, furthermore, that the reasons it fails are likely to be endemic to all representational theories of phenomenal consciousness. (shrink)

A distinction can be made between those who think that self-deception is frequently intentional and those who don’t. I argue that the idea that self-deception has to be intentional can be partly traced to a particular invalid method for analyzing reflexive expressions of the form ‘Ving oneself’ (where V stands for a verb). However, I take the question of whether intentional self-deception is possible to be intrinsically interesting, and investigate the prospects for such an alleged possibility. Various potential strategies of (...) intentional self-deception are examined in relation to Alfred Mele’s suggestion that doing something intentionally implies doing it knowingly. It is suggested that the best prospects for an intentionalist theory of self-deception lie with a strategy involving the control of attention. (shrink)

Acknowledgements Andrea Scarantino, Nicholas Shea, Mark Sprevak, and three anonymous referees provided incisive and constructive comments, for which I am very grateful. In 2012, earlier versions of this paper were delivered in Edinburgh, at the Joint Session in Stirling, and at a workshop on natural information in Aberdeen. I thank participants for their feedback.

Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper—drawing on graph-theoretic and topological ideas—I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out (...) that there is no unique method of decycling. An important upshot is that the notion of asymmetric ground may be indeterminate. (shrink)

The big question at the end of Feferman is: Is it possible to find a foundation for unlimited category theory? I show that the answer is no by showing that unlimited category theory is inconsistent.

Libertarian punishment theory was initially articulated by Murray N. Rothbard and Walter E. Block. It was broken down into four separate stages. To a great degree, this theory was accepted by Eduardo Blasco and Davie Marcos. However, they maintain it is in need of some slight adjustments and improvements, mainly dealing with the interest rate. The present paper claims their suggestion while valid, is unnecessary, since this theory already incorporates that element, at least implicitly.

Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy provides a reasonably gentle introduction to this new logic, thoroughly motivated by intuitive explanations of the need for all of its component parts, and illustrated through innovative applications of the calculus.

I see model theory as becoming increasingly detached from set theory, and the Tarskian notion of set-theoretic model being no longer central to model theory. In much of modern mathematics, the set-theoretic component is of minor interest, and basic notions are geometric or category-theoretic. In algebraic geometry, schemes or algebraic spaces are the basic notions, with the older “sets of points in affine or projective space” no more than restrictive special cases. The basic notions may be given (...) sheaf-theoretically, or functorially. To understand in depth the historically important affine cases, one does best to work with more general schemes. The resulting relativization and “transfer of structure” is incomparably more flexible and powerful than anything yet known in “set-theoretic model theory”.It seems to me now uncontroversial to see the fine structure of definitions as becoming the central concern of model theory, to the extent that one can easily imagine the subject being called “Definability Theory” in the near future.Tarski's set-theoretic foundational formulations are still favoured by the majority of model-theorists, and evolution towards a more suggestive language has been perplexingly slow. None of the main texts uses in any nontrivial way the language of category theory, far less sheaf theory or topos theory. Given that the most notable interactions of model theory with geometry are in areas of geometry where the language of sheaves is almost indispensable, this is a curious situation, and I find it hard to imagine that it will not change soon, and rapidly. (shrink)

Whatever the difference in the authors' positions, this collection gains its unity through their common interest in the significance and value of Critical ...

Knowing is something that we do not have much of a theory about., p. 365.)Interest has recently been shown in causal theories of perception, memory, inference, reference, truth, justification and belief, as well as in a more general “causal theory of knowledge” which would embrace and connect all of these concepts within a broad epistemological framework. The burden of this paper is that prospects are poor for an interesting and general enough causal theory of knowledge. A threat (...) to generality arises from the causal theory's difficulties with knowledge of general truths. A threat to interest arises when attempts to accommodate general truths lead to a weakening of the notion of “causal connection” appealed to, making dubious the explanatory force of such an appeal. (shrink)

The structural approach to alternatives :669–690, 2007; Fox and Katzir in Nat Lang Semant 19:87–107, 2011; Katzir in Semantics, pragmatics and the case of scalar implicatures, Palgrave Macmillan, London, pp 40–71, 2014) is the most developed attempt in the literature at solving the symmetry problem of scalar implicatures. Problematic data with indirect and particularised scalar implicatures have however been raised :249–270, 2015). To address these problems, Trinh and Haida proposed to augment the theory with the Atomicity Constraint. Here we (...) show that this constraint falls short of explaining minimal variants of the original problems, and moreover that it runs into trouble with the inferences of sentences involving gradable adjectives like full and empty. We furthermore discuss how the structural approach suffers at times from the problem of ‘too many lexical alternatives’ pointed out by Swanson :31–36, 2010), and at other times from the opposite problem of ‘too few lexical alternatives’. These three problems epitomise the challenge of constructing just enough alternatives under the structural approach to solve the symmetry problem in full generality. Finally, we also sketch another recent attempt at solving the symmetry problem, Bergen et al., 2016), which is based on relative informativity and complexity. We argue that Bergen et al. do not provide a general solution to the symmetry problem either, by pointing to some of the open problematic cases that remain for this approach as well. We conclude that while important progress has been made in the theory of alternatives for scalar implicatures in the last few years, a full solution to the symmetry problem has not yet been attained. (shrink)