Our results concern the existence of a countable extension U of the countable atomless Boolean algebra B such that U is a "nonconstructive" extension of B. It is known that for any fixed admissible indexing φ of B there is a countable nonconstructive extension U of B (relative to φ). The main theorem here shows that there exists an extension U of B such that for any admissible indexing φ of B, U is nonconstructive (relative to φ). Thus, in this (...) sense U is a countable totally nonconstructive extension of B. (shrink)

Given an admissible indexing φ of the countable atomless Boolean algebra B, an automorphism F of B is said to be recursively presented (relative to φ) if there exists a recursive function $p \in \operatorname{Sym}(\omega)$ such that F ⚬ φ = φ ⚬ p. Our key result on recursiveness: Both the subset of $\operatorname{Aut}(\mathscr{B})$ consisting of all those automorphisms which are recursively presented relative to some indexing, and its complement, the set of all "totally nonrecursive" automorphisms, are uncountable. This arises (...) as a consequence of the following combinatorial investigations: (1) A comparison of the cycle structures of f and f̄, where f is a permutation of some free basis of B and f̄ is the automorphism of B induced by f. (2) An explicit description of the permutations of ω whose conjugacy classes in $\operatorname{Sym}(\omega)$ are (a) uncountable, (b) countably infinite, and (c) finite. (shrink)

The two main psychological theories of the ordinary conditional were designed to account for inferences made from assumptions, but few premises in everyday life can be simply assumed true. Useful premises usually have a probability that is less than certainty. But what is the probability of the ordinary conditional and how is it determined? We argue that people use a two stage Ramsey test that we specify to make probability judgements about indicative conditionals in natural language, and we describe experiments (...) that support this conclusion. Our account can explain why most people give the conditional probability as the probability of the conditional, but also why some give the conjunctive probability. We discuss how our psychological work is related to the analysis of ordinary indicative conditionals in philosophical logic. (shrink)

The COVID-19 outbreak has simultaneously increased the need for mental health services and decreased their availability. Brief online self-help interventions that can be completed in a single session could be especially helpful in improving access to care during the crisis. However, little is known about the uptake, acceptability, and perceived utility of these interventions outside of clinical trials in which participants are compensated. Here, we describe the development, deployment, acceptability ratings, and pre–post effects of a single-session intervention, the Common Elements (...) Toolbox, adapted for the COVID-19 crisis to support graduate and professional students. Participants, who were not compensated, were randomly assigned to two of three modules: behavioral activation, cognitive restructuring, and gratitude. Over 1 week, 263 individuals began and 189 individuals completed the intervention. Participants reported that the intervention modules were acceptable, helpful, engaging, applicable to their lives, and could help them manage COVID-related challenges. Participants reported pre- to post-program improvements in secondary control and in the perceived negative impact of the COVID-19 crisis on their quality of life. On average, differences in their perceived ability to handle lifestyle changes resulting from the pandemic were positive, but small and at the level of a non-significant trend. Our results highlight the acceptability and utility of an online intervention for supporting individuals through the COVID-19 crisis. (shrink)

Stanovich & West distinguish between evolutionary rationality and normative rationality, and System 1 and System 2 mental processes. They hold that the main function of System 2 has to do with normative and not evolutionary rationality. We ask how System 2 could then be an adaptation, especially given S&W's own work on individual differences.

This Element is on new developments in the psychology of reasoning that raise or address philosophical questions. In traditional studies in the psychology of reasoning, the focus was on inference from arbitrary assumptions and not at all from beliefs, and classical binary logic was presupposed as the only standard for human reasoning. But recently a new Bayesian paradigm has emerged in the discipline. This views ordinary human reasoning as mostly inferring probabilistic conclusions from degrees of beliefs, or from hypothetical premises (...) relevant to a purpose at hand, and as often about revising or updating degrees of belief. This Element also covers new formulations of dual-process theories of the mind, stating that there are two types of mental processing, one rapid and intuitive and shared with other animals, and the other slow and reflective and more characteristic of human beings. The final topic covered is the new developments and rationality. (shrink)

What is truly beautiful? For Søren Kierkegaard the beautiful is to be found in an integrated self, one that is freely chosen. This article explores Kierkegaard's "aesthetic" stage of existence through the character of Augusto Pérez, the protagonist of Miguel de Unamuno's novel, Niebla. After establishing a solid link between Unamuno and Kierkegaard, Kierkegaard's "ethical" stage is used to critique the "aesthetic" stage on aesthetic grounds, on the basis of the beauty found in life's work, a calling. The conclusion is (...) that the sphere of the "aesthetic" does not achieve Kierkegaard's "aesthetics" of an integrated, fully existing self. (shrink)

Collaboration requires agents to coordinate their behavior on the fly, sometimes cooperating to solve a single task together and other times dividing it up into sub‐tasks to work on in parallel. Underlying the human ability to collaborate is theory‐of‐mind (ToM), the ability to infer the hidden mental states that drive others to act. Here, we develop Bayesian Delegation, a decentralized multi‐agent learning mechanism with these abilities. Bayesian Delegation enables agents to rapidly infer the hidden intentions of others by inverse planning. (...) We test Bayesian Delegation in a suite of multi‐agent Markov decision processes inspired by cooking problems. On these tasks, agents with Bayesian Delegation coordinate both their high‐level plans (e.g., what sub‐task they should work on) and their low‐level actions (e.g., avoiding getting in each other's way). When matched with partners that act using the same algorithm, Bayesian Delegation outperforms alternatives. Bayesian Delegation is also a capable ad hoc collaborator and successfully coordinates with other agent types even in the absence of prior experience. Finally, in a behavioral experiment, we show that Bayesian Delegation makes inferences similar to human observers about the intent of others. Together, these results argue for the centrality of ToM for successful decentralized multi‐agent collaboration. (shrink)

Dual-process and dual-system theories in both cognitive and social psychology have been subjected to a number of recently published criticisms. However, they have been attacked as a category, incorrectly assuming there is a generic version that applies to all. We identify and respond to 5 main lines of argument made by such critics. We agree that some of these arguments have force against some of the theories in the literature but believe them to be overstated. We argue that the dual-processing (...) distinction is supported by much recent evidence in cognitive science. Our preferred theoretical approach is one in which rapid autonomous processes are assumed to yield default responses unless intervened on by distinctive higher order reasoning processes. What defines the difference is that Type 2 processing supports hypothetical thinking and load heavily on working memory. (shrink)

Dienes' & Perner's proposals are discussed in relation to the distinction between explicit and implicit systems of thinking. Evans and Over (1996) propose that explicit processing resources are required for hypothetical thinking, in which mental models of possible world states are constructed. Such thinking requires representations in which the individuals' propositional attitudes including relevant beliefs and goals are made fully explicit.

Our commentary challenges Boyer's model by arguing that the extended-self is a more likely basis for ownership psychology. We outline how self-based principles of investment and control might structure thinking about ownership and related rights. We end by expanding the extended-self account to include welfare, as a way of understanding the contexts under which ownership is upheld or violated.

ANTHROPOLOGY AND HISTORY In 1950 I delivered the Marett Lecture at Oxford1. In it I said that I regarded social anthropology as being closer to certain kinds of history than to the natural sciences. I will not say that there was a storm of  ...

Miguel de Unamuno was profoundly influenced by Søren Kierkegaard's pseudonymous works at a time when Kierkegaard was virtually unknown in Southern Europe. This book explores the scope and character of that influence, clarifies misconceptions in the relationship between the authors, and offers an original, Kierkegaardian reading of three of Unamuno's best known novels: Niebla, San Manuel Bueno, mártir, and Abel Sánchez.

M. Oaksford and N. Chater presented a Bayesian analysis of the Wason selection task in which they proposed that people choose cards in order to maximize expected information gain as measured by reduction in uncertainty in the Shannon-Weaver information theory sense. It is argued that the EIG measure is both psychologically implausible and normatively inadequate as a measure of epistemic utility. The article is also concerned with the descriptive account of findings in the selection task literature offered by Oaksford and (...) Chater. First, it is shown that their analysis data reported in the recent article of K. N. Kirby is unsound; second, an EIG analysis is presented of the experiments of P. Pollard and J. St. B. T. Evans that provides a strong empirical disconfirmation of the theory. (shrink)