'The Probabilistic Mind' is a follow-up to the influential and highly cited 'Rational Models of Cognition'. It brings together developments in understanding how, and how far, high-level cognitive processes can be understood in rational terms, and particularly using probabilistic Bayesian methods.

The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean (...) algebra. We prove without choice principles that any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras. (shrink)

This article provides an algebraic study of the propositional system $\mathtt {InqB}$ of inquisitive logic. We also investigate the wider class of $\mathtt {DNA}$ -logics, which are negative variants of intermediate logics, and the corresponding algebraic structures, $\mathtt {DNA}$ -varieties. We prove that the lattice of $\mathtt {DNA}$ -logics is dually isomorphic to the lattice of $\mathtt {DNA}$ -varieties. We characterise maximal and minimal intermediate logics with the same negative variant, and we prove a suitable version of Birkhoff’s classic variety (...) theorems. We also introduce locally finite $\mathtt {DNA}$ -varieties and show that these varieties are axiomatised by the analogues of Jankov formulas. Finally, we prove that the lattice of extensions of $\mathtt {InqB}$ is dually isomorphic to the ordinal $\omega +1$ and give an axiomatisation of these logics via Jankov $\mathtt {DNA}$ -formulas. This shows that these extensions coincide with the so-called inquisitive hierarchy of [9].1. (shrink)

The purpose of this investigation is to develop a ranking of academic business ethics journals. For this, a revealed preference approach, also known as a citation impact method, was employed. The citation data were generated by using Google Scholar; h-index, g-index and hc-index were utilised to obtain a ranking. It was observed that the scores of these three indices correlated almost perfectly. This study also demonstrates that business ethics is a well-established discipline that should have its own set of recognised (...) academic outlets. (shrink)

In The Metaphysics of Beauty, Zangwill argues that it is essential to beauty that it depends on the ordinary features of things.

Social interaction is both ubiquitous and central to understanding human behavior. Such interactions depend, we argue, on shared intentionality: the parties must form a common understanding of an ambiguous interaction (e.g., one person giving a present to another requires that both parties appreciate that a voluntary transfer of ownership is intended). Yet how can shared intentionality arise? Many well-known accounts of social cognition, including those involving “mind-reading,” typically fall into circularity and/or regress. For example, A’s beliefs and behavior may depend (...) on her prediction of B’s beliefs and behavior, but B’s beliefs and behavior depend in turn on her prediction of A’s beliefs and behavior. One possibility is to embrace circularity and take shared intentionality as imposing consistency conditions on beliefs and behavior, but typically there are many possible solutions and no clear criteria for choosing between them. We argue that addressing these challenges requires some form of we-reasoning, but that this raises the puzzle of how the collective agent (the “we”) arises from the individual agents. This puzzle can be solved by proposing that the will of the collective agent arises from a simulated process of bargaining: agents must infer what they would agree, were they able to communicate. This model explains how, and which, shared intentions are formed. We also propose that such “virtual bargaining” may be fundamental to understanding social interactions. (shrink)

An influential line of thinking in behavioral science, to which the two authors have long subscribed, is that many of society's most pressing problems can be addressed cheaply and effectively at the level of the individual, without modifying the system in which the individual operates. We now believe this was a mistake, along with, we suspect, many colleagues in both the academic and policy communities. Results from such interventions have been disappointingly modest. But more importantly, they have guided many (though (...) by no means all) behavioral scientists to frame policy problems in individual, not systemic, terms: To adopt what we call the “i-frame,” rather than the “s-frame.” The difference may be more consequential than i-frame advocates have realized, by deflecting attention and support away from s-frame policies. Indeed, highlighting the i-frame is a long-established objective of corporate opponents of concerted systemic action such as regulation and taxation. We illustrate our argument briefly for six policy problems, and in depth with the examples of climate change, obesity, retirement savings, and pollution from plastic waste. We argue that the most important way in which behavioral scientists can contribute to public policy is by employing their skills to develop and implement value-creating system-level change. (shrink)

In 1995 Visser, van Benthem, de Jongh, and Renardel de Lavalette introduced NNIL-formulas, showing that these are exactly the formulas preserved under taking submodels of Kripke models. In this article we show that NNIL-formulas are up to frame equivalence the formulas preserved under taking subframes of frames, that NNIL-formulas are subframe formulas, and that subframe logics can be axiomatized by NNIL-formulas. We also define a new syntactic class of ONNILLI-formulas. We show that these are the formulas preserved in monotonic images (...) of frames and that ONNILLI-formulas are stable formulas as introduced by Bezhanishvili and Bezhanishvili in 2013. Thus, ONNILLI is a syntactically defined set of formulas axiomatizing all stable logics. This resolves a problem left open in 2013. (shrink)

Social interaction is both ubiquitous and central to understanding human behavior. Such interactions depend, we argue, on shared intentionality: the parties must form a common understanding of an ambiguous interaction. Yet how can shared intentionality arise? Many well-known accounts of social cognition, including those involving “mind-reading,” typically fall into circularity and/or regress. For example, A’s beliefs and behavior may depend on her prediction of B’s beliefs and behavior, but B’s beliefs and behavior depend in turn on her prediction of A’s (...) beliefs and behavior. One possibility is to embrace circularity and take shared intentionality as imposing consistency conditions on beliefs and behavior, but typically there are many possible solutions and no clear criteria for choosing between them. We argue that addressing these challenges requires some form of we-reasoning, but that this raises the puzzle of how the collective agent arises from the individual agents. This puzzle can be solved by proposing that the will of the collective agent arises from a simulated process of bargaining: agents must infer what they would agree, were they able to communicate. This model explains how, and which, shared intentions are formed. We also propose that such “virtual bargaining” may be fundamental to understanding social interactions. (shrink)

ABSTRACTIn ‘The Principles of Art’, R. G. Collingwood argues that art is the imaginative expression of emotion. So much the worse, then, for Collingwood. The theory seems hopelessly inadequate to the task of capturing art’s extension: of encompassing all the works we generally suppose should be rounded up under the concept. A great number of artworks, and several art forms, have nothing to do with emotion. But it would be surprising were Collingwood philistine enough to think that art is only (...) ever concerned with communicating quotidian affective states, like anger, fear or love. Surely he has some more sophisticated notion of emotion in mind, and quite probably of expression too. And it turns out that those sophisticated notions can be pushed towards a version of the expression theory that meets the extensional challenge. If we interpret Collingwood as saying that expression is a particular application of imagination, and that imagination is the faculty that refines ideas of emotions, and that ‘emotions’... (shrink)

I describe and defend the view in a philosophy of mind that I call 'Normative Essentialism', according to which propositional attitudes have normative essences. Those normative essences are 'horizontal' rational requirements, by which I mean the requirement to have certain propositional attitudes given other propositional attitudes. Different propositional attitudes impose different horizontal rational requirements. I distinguish a stronger and a weaker version of this doctrine and argue for the weaker version. I explore the consequences for knowledge of mind, and I (...) then consider objections to the view from mental causation, from empirical psychology, and from animals and small children. (shrink)

A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its extensions are structurally complete. Citkin (1978) proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem is not widely accessible. In this paper we offer (...) a self-contained proof of Citkin’s theorem, based on Esakia duality and the method of subframe formulas. As a corollary, we obtain a short proof of Citkin’s 2019 characterization of hereditarily structurally complete positive logics. (shrink)

I give an informal presentation of the evolutionary game theoretic approach to the conventions that constitute linguistic meaning. The aim is to give a philosophical interpretation of the project, which accounts for the role of game theoretic mathematics in explaining linguistic phenomena. I articulate the main virtue of this sort of account, which is its psychological economy, and I point to the casual mechanisms that are the ground of the application of evolutionary game theory to linguistic phenomena. Lastly, I consider (...) the objection that the account cannot explain predication, logic, and compositionality. (shrink)

In this paper we define the notion of frame based formulas. We show that the well-known examples of formulas arising from a finite frame, such as the Jankov-de Jongh formulas, subframe formulas and cofinal subframe formulas, are all particular cases of the frame based formulas. We give a criterion for an intermediate logic to be axiomatizable by frame based formulas and use this criterion to obtain a simple proof that every locally tabular intermediate logic is axiomatizable by Jankov-de Jongh formulas. (...) We also show that not every intermediate logic is axiomatizable by frame based formulas. (shrink)

We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive algebras determine Medvedev’s logic (...) of finite problems. In addition to the algebraic characterization of H(B), we give a topological characterization of H(B) in terms of the recently introduced choice-free duality for Boolean algebras using so-called upper Vietoris spaces (UV-spaces). In particular, while a Boolean algebra B is realized as the Boolean algebra of compact regular open elements of a UV-space dual to B, we show that H(B) is realized as the algebra of compact open elements of this space. This connection yields a new topological semantics for inquisitive logic. (shrink)

I argue against motivational internalism. First I recharacterise the issue over moral motivation. Second I describe the indifference argument against motivation internalism. Third I consider appeals to irrationality that are often made in the face of this argument, and I show that they are ineffective. Lastly, I draw the motivational externalist conclusion and reflect on the nature of the issue.

Social interaction is both ubiquitous and central to understanding human behavior. Such interactions depend, we argue, on shared intentionality: the parties must form a common understanding of an ambiguous interaction (e.g., one person giving a present to another requires that both parties appreciate that a voluntary transfer of ownership is intended). Yet how can shared intentionality arise? Many well-known accounts of social cognition, including those involving “mind-reading,” typically fall into circularity and/or regress. For example, A’s beliefs and behavior may depend (...) on her prediction of B’s beliefs and behavior, but B’s beliefs and behavior depend in turn on her prediction of A’s beliefs and behavior. One possibility is to embrace circularity and take shared intentionality as imposing consistency conditions on beliefs and behavior, but typically there are many possible solutions and no clear criteria for choosing between them. We argue that addressing these challenges requires some form of we-reasoning, but that this raises the puzzle of how the collective agent (the “we”) arises from the individual agents. This puzzle can be solved by proposing that the will of the collective agent arises from a simulated process of bargaining: agents must infer what they would agree, were they able to communicate. This model explains how, and which, shared intentions are formed. We also propose that such “virtual bargaining” may be fundamental to understanding social interactions. (shrink)

Noise in behavior is often viewed as a nuisance: while the mind aims to take the best possible action, it is let down by unreliability in the sensory and response systems. How researchers study cognition reflects this viewpoint – averaging over trials and participants to discover the deterministic relationships between experimental manipulations and their behavioral consequences, with noise represented as additive, often Gaussian, and independent. Yet a careful look at behavioral noise reveals rich structure that defies easy explanation. First, both (...) perceptual and preferential judgments show that sensory and response noise may potentially only play minor roles, with most noise arising in the cognitive computations. Second, the functional form of the noise is both non-Gaussian and non-independent, with the distribution of noise being better characterized as heavy-tailed and as having substantial long-range autocorrelations. It is possible that this structure results from brains that are, for some reason, bedeviled by a fundamental design flaw, albeit one with intriguingly distinctive characteristics. Alternatively, noise might not be a bug but a feature: indeed, we suggest that noise is fundamental to how cognition works. Specifically, we propose that the brain approximates probabilistic inference with a local sampling algorithm, one that uses randomness to drive its exploration of alternative hypotheses. Reframing cognition in this way explains the rich structure of noise and leads to a surprising conclusion: that noise is not a symptom of cognitive malfunction but plays a central role in underpinning human intelligence. (shrink)

If Bayesian Fundamentalism existed, Jones & Love's (J&L's) arguments would provide a necessary corrective. But it does not. Bayesian cognitive science is deeply concerned with characterizing algorithms and representations, and, ultimately, implementations in neural circuits; it pays close attention to environmental structure and the constraints of behavioral data, when available; and it rigorously compares multiple models, both within and across papers. J&L's recommendation of Bayesian Enlightenment corresponds to past, present, and, we hope, future practice in Bayesian cognitive science.

This chapter explores insights concerning the relations among imagination, imagined selves, and knowledge of one’s own self that are to be found in Fernando Pessoa’s The Book of Disquiet. The insights are explored via close reading of the text and comparison with contemporaries of Pessoa. First, a tempting account of the importance of imagination in The Book of Disquiet is set out. On this reading, Pessoa is immersed in miasmatic boredom, but able to temporarily rise above it through the restorative (...) powers of escapist imagination. But, it is suggested, Pessoa neither enjoys his prolific imaginings, nor returns from them restored. It is argued that Pessoa’s disquiet owes to failures of imagination; the book presents a sharp contrast between Pessoa’s keen awareness of the importance of a successful, active imaginative life, and his failure to maintain such a thing. It is further argued that these failures point us towards a better account of imagination’s importance to Pessoa, an account that both prefigures and goes beyond Sartre’s ideas about the relations between nothingness, imagination, and self-consciousness. (shrink)

I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objectionthe Mushroom Omelette Objectionis that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those rules have logical contents, or (...) following those conventional rules is done for logical reasons. Lastly, I compare this argument with other arguments found in Quine’s early work, and consider two attempts to reply to Quine. (shrink)

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)

We show that every proper normal extension of the bi-modal system S5 2 has the poly-size model property. In fact, to every proper normal extension L of S5 2 corresponds a natural number b(L) - the bound of L. For every L, there exists a polynomial P(·) of degree b(L) + 1 such that every L-consistent formula is satisfiable on an L-frame whose universe is bounded by P(||), where || denotes the number of subformulas of . It is shown that (...) this bound is optimal. (shrink)

Electronic dance music has much about it to interest philosophers. In this article, I explore facets of dance music cultures, using the issue of authenticity as a framing question. The problem of sorting real or authentic dance music from mainstream or commercial clubbing can be treated as a matter of history and genre-definition; as a matter of defining scenes or subcultures; and as a matter of blackness. In each case, electronic dance music, and critical discourse surrounding it, offers fresh illumination (...) of aesthetic questions. I briefly characterise the main genres of dance music, match conversations about the hardcore continuum with philosophers’ accounts of genre, survey sociologists’ ways of thinking about cultures and their connections to taste and personal identity, and link criticisms that dance music now lacks blackness to conceptions of black aesthetics. This article is Part I of two; Part II focusses on dancers, DJs, and the aesthetics and ontology of dance music itself. Video abstract. (shrink)

I argue that Hanslick was right to think that music should not be understood in terms of emotion. In particular, it is not essential to music to possess emotions, arouse emotions, express emotions, or represent emotions. All such theories are misguided.

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.

Beauty is an important part of our lives. Ugliness too. It is no surprise then that philosophers since antiquity have been interested in our experiences of and judgments about beauty and ugliness. They have tried to understand the nature of these experiences and judgments, and they have also wanted to know whether these experiences and judgments were legitimate. Both these projects took a sharpened form in the twentieth century, when this part of our lives came under a sustained attack in (...) both European and American intellectual circles. Much of the discourse about beauty since the Eighteenth century had deployed a notion of the ‘aesthetic’, and so that notion in particular came in for criticism. This disdain for the aesthetic may have roots in a broader cultural Puritanism, which fears the connection between the aesthetic and pleasure. Even to suggest, in the recent climate, that an artwork might be good because it is pleasurable, as opposed to cognitively, morally or politically beneficial, is to court derision. The twentieth century has not been kind to the notions of beauty or the aesthetic. Nevertheless, some thinkers — philosophers, as well as others in the study of particular arts — have persisted in thinking about beauty and the aesthetic in a traditional way. In the first part of this essay, I look at the particular rich account of judgments of beauty given to us by Immanuel Kant. The notion of a ‘judgment of taste’ is central to Kant's account and also to virtually everyone working in traditional aesthetics; so I begin by examining Kant's characterisation of the judgment of taste. In the second part, I look at the issues that twentieth century thinkers have raised. I end by drawing on Kant's accout of the judgement of taste to consider whether the notion of the aesthetic is viable. (shrink)

How far does a researcher’s responsibility extend when an incidental finding is identified? Balancing pertinent ethical principles such as beneficence, respect for persons, and duty to rescue is not always straightforward, particularly in neuroimaging research where empirical data that might help guide decision making are lacking. We conducted a systematic survey of perceptions and preferences of 396 investigators, research participants, and Institutional Review Board members at our institution. Using the partial entrustment model as described by Richardson, we argue that our (...) data supports universal reading by a neuroradiologist of all research MRI scans for incidental findings and providing full disclosure to all participants. (shrink)

Films typically provide an experience that is very much like the experience of ordinary motion. It is for this reason that they are commonly known as moving pictures or, slightly more broadly, moving images. Our focus in this chapter is on making sense of that experience. We begin our chapter by exploring the centrality of the experience of movement to film. We turn then to various explanations of that experience. Perhaps film images are transparent and allow us to indirectly see (...) the movement of the objects they depict. Or perhaps certain theories of depiction can make sense of the experience of motion in cinema. In the final section, we address a range of ontological issues raised by the question of cinematic movement. Is the motion of images real movement or merely illusory? What is a cinematic image? (shrink)

We show that every proper normal extension of the bi-modal system S52 has the poly-size model property. In fact, to every proper normal extension L of S52 corresponds a natural number b(L) - the bound of L. For every L, there exists a polynomial P(·) of degree b(L) + 1 such that every L-consistent formula ϕ is satisfiable on an L-frame whose universe is bounded by P(|ϕ|), where |ϕ| denotes the number of subformulas of ϕ. It is shown that this (...) bound is optimal. (shrink)

We generalize the notion of a monadic algebra to that of a pseudomonadic algebra. In the same way as monadic algebras serve as algebraic models of epistemic modal system S5, pseudomonadic algebras serve as algebraic models of doxastic modal system KD45. The main results of the paper are: Characterization of subdirectly irreducible and simple pseudomonadic algebras, as well as Tokarz's proper filter algebras; Ordertopological representation of pseudomonadic algebras; Complete description of the lattice of subvarieties of the variety of pseudomonadic algebras.

We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n -universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.

We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n-universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.

Many recent aestheticians have criticized the notion of disinterest. The aestheticians in question take the notion to have a vaguely Kantian pedigree. And in attacking this notion, they think of themselves as attempting to remove a cornerstone of Kant’s aesthetics. This procedure is hardly likely to be effective if what they attack bears little resemblance to Kant’s original notion. In this brief note, I want to show how far these anti-Kantian aestheticians have missed their mark.

Recently, two apparently quite different duality-based approaches to automata minimisation have appeared. One is based on ideas that originated from the controllability-observability duality from systems theory, and the other is based on ideas derived from Stone-type dualities specifically linking coalgebras with algebraic structures derived from modal logics. In the present paper, we develop a more abstract view and unify the two approaches. We show that dualities, or more generally dual adjunctions, between categories can be lifted to dual adjunctions between categories (...) of coalgebras and algebras, and from there to automata with initial as well as final states. As in the Stone-duality approach, algebras are essentially logics for reasoning about the automata. By exploiting the ability to pass between these categories, we show that one can minimize the corresponding automata. We give an abstract minimisation algorithm that has several instances, including the celebrated Brzozowski minimisation algorithm. We further develop three examples that have been treated in previous works: deterministic Kripke frames based on a Stone-type duality, weighted automata based on the self-duality of semimodules, and topological automata based on Gelfand duality. As a new example, we develop alternating automata based on the discrete duality between sets and complete atomic Boolean algebras. (shrink)