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)

This article proposes that a general theory of assessment of historical testimony should do justice to the long tradition of adjudication in accordance with maxims of reliability and competence. I argue that an explanatory genealogical theory (along lines first adumbrated by Charles Seignobos) satisfies this condition, and that it has further notable virtues: respect for the strengths of rival theories, regard for the links between adjudication of testimony and other basic procedures of historical inquiry, and the promise of profitable lines (...) of investigation. (shrink)

According to one understanding of the problem of dirty hands, every case of dirty hands is an instance of moral conflict, but not every instance of moral conflict is a case of dirty hands. So, what sets the two apart? The dirty hands literature has offered widely different answers to this question but there has been relatively little discussion about their relative merits as well as challenges. In this paper I evaluate these different accounts by making clear which understanding of (...) concept distinctness underlies them and which of them is, ultimately, the most plausible one in the case of dirty hands and ordinary moral conflict. In order to do so, I will borrow from the terminology employed in recent debates in the philosophy of evil which have tackled a similar problem to the one at hand, i.e. defining what sets evil apart from ordinary wrongdoing. Here it has been argued that concepts could be distinct in three ways: they can have a quantitative difference, a strong qualitative or a moderate qualitative difference. I conclude that the most convincing definition of dirty hands draws a moderate qualitative distinction between ordinary moral conflict according to which dirty hands are those moral conflicts that involve a serious violation or betrayal of a core moral value. (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)

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)

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)

Recent research suggests that language evolution is a process of cultural change, in which linguistic structures are shaped through repeated cycles of learning and use by domain-general mechanisms. This paper draws out the implications of this viewpoint for understanding the problem of language acquisition, which is cast in a new, and much more tractable, form. In essence, the child faces a problem of induction, where the objective is to coordinate with others (C-induction), rather than to model the structure of the (...) natural world (N-induction). We argue that, of the two, C-induction is dramatically easier. More broadly, we argue that understanding the acquisition of any cultural form, whether linguistic or otherwise, during development, requires considering the corresponding question of how that cultural form arose through processes of cultural evolution. This perspective helps resolve the “logical” problem of language acquisition and has far-reaching implications for evolutionary psychology. (shrink)

Gerd Buchdahl’s international reputation rests on his masterly writings on Kant. In them he showed how Kant transformed the philosophical problems of his predecessors and he minutely investigated the ways in which Kant related his critical philosophy to the contents and methods of natural science. Less well known, if only because in large part unpublished, are the writings in which Buchdahl elaborated his own views on the methods and status of the sciences. In this paper I examine the roles of (...) hermeneutics in Buchdahl’s reconstruction of Kant’s philosophical system and in his own ‘transcendental methodological’ approach to the philosophy of science. The first section looks at Buchdahl’s views on the theory and practice of historical interpretation and at the Husserlian hermeneutic scheme of reduction and realisation that he used in his later accounts of the philosophies of science of Kant and himself. The second section concentrates on Buchdahl’s treatment of the grounds of science in Kant; and the third on the hermeneutic strategies Buchdahl employed in articulating and justifying his own views. The paper closes with reflections on the impact and importance of Buchdahl’s interpretation of Kant’s critical philosophy in relation to the sciences and of his own hermeneutically based philosophy of science.Author Keywords: Buchdahl; Kant; Hermeneutics; Methodology; Transcendental philosophy. (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)

People are unable to report how they decide whether to move backwards or forwards to catch a ball. When asked to imagine how their angle of elevation of gaze would change when they caught a ball, most people are unable to describe what happens although their interception strategy is based on controlling changes in this angle. Just after catching a ball, many people are unable to recognise a description of how their angle of gaze changed during the catch. Some people (...) confidently choose incorrect descriptions that would guarantee failure of interception demonstrating unconscious knowledge co-existing with systematically different conscious beliefs. Where simple solutions to important evolutionary problems exist, unconscious perception needs to be impervious to conscious beliefs. (shrink)

morality? I want to pursue these questions by examining an argument against moral realism that Simon Blackburn has developed.' In parts 1 and 2, I consider..

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)

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)

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)

The problem of dirty hands is, roughly speaking, concerned with situations in which an agent is faced with a choice between two evils so that, no matter what they do, they will have to violate something of important moral value. Theorists have been primarily concerned with dirty hands choices arising in politics because they are thought to be particularly frequent and pressing in this sphere. Much of the subsequent discussion in the literature has focused on the impact that such choices (...) have on a well-functioning democracy and how, if at all, we can ensure that a politician dirtying their hands does not undermine core democratic values and processes. A particular concern has been whether dirty-handed politicians ought to publicly reveal their actions after the fact and whether they should be held accountable through some form of punishment. The first aim of this paper is to point out that the focus on what is required in the wake of a dirty-handed decision, based on the need to protect the democratic system ought to be balanced with a genuine concern for reparative justice and what is owed to the victims of dirty hands. In the second part of this paper, I then examine the suitability of one common way in which perpetrators partly repair the damage they have done to victims, namely apologizing, in the dirty hands context. (shrink)

This paper argues that the dirty hands literature has overlooked a crucial distinction in neglecting to discuss explicitly the issue of, what I call, symmetry. This is the question of whether, once we are confronted with a dirty hands situation, we could emerge with our hands clean depending on the action we choose. A position that argues that we can keep our hands clean I call “asymmetrical” and one that says that we will get our hands dirty no matter what (...) we do I call “symmetrical”. Not acknowledging this distinction is a problem because, firstly, it adds to the existing confusions about how best to define what dirty hands are. Secondly, it prevents the concept of dirty hands from being applied properly to other contexts such as, for example, the responsibility and accountability of politicians. I argue that we have good reason to favour a symmetrical understanding because it gives a more convincing account of what makes an action dirty and because it more accurately captures our complex moral decision-making when faced with dirty hands situations. The paper concludes by outlining possible implications that the distinction between the symmetry view and the asymmetry view has on wider debates surrounding the problem of dirty hands. (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.

This paper considers three arguments by David Shugarman and Maureen Ramsay for why dirty hands cannot be democratic. The first argues that it is contradictory, in principle, to use undemocratic means to pursue democratic ends. There is a conceptual connection between means and ends such that getting one’s hands dirty is incompatible with acting in accordance with democratic ends. The second claims that using dirty-handed means, in practice, will undermine democracy more than it promotes it and therefore cannot be justified. (...) The final criticism states that politicians with dirty hands are a sign that politics is no longer meeting the criteria necessary to be called democratic. The paper shows that such rejections of democratic dirty hands are based on misunderstandings of the nature of dirty hands and democratic politics. (shrink)

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)

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.

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)

What are the groundrules in the philosophy of art? What criteria of adequacy should we use for assessing theories of art?

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.

I reply to some recent comments by Brian Weatherson on my 'simulation argument'. I clarify some interpretational matters, and address issues relating to epistemological externalism, the difference from traditional brain-in-a-vat arguments, and a challenge based on 'grue'-like predicates.

In Higher Superstition, published early in 1994, biologist Paul R. Gross and mathematician Norman Levitt denounced an `Academic Left' at once militant and ill-informed in its criticisms of science. Gross and Levitt showed sharp eyes for the pretentious and absurd in the works of American postmodernists, feminists, multiculturalists, radical environmentalists and, alas, exponents of science studies -- that is, historians, philosophers and sociologists of science. In the Autumn of 94, physicist Alan Sokal, inspired by Gross and Levitt's book, submitted a (...) spoof article portentously entitled `Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity' to Social Text, a leading journal in the expanding field of cultural studies. As he later told Janny Scott of the New York Times : I structured the article around the silliest quotations about mathematics and physics from the most prominent academics, and I invented an argument praising them and linking them together. All this was very easy to carry off, because my article wasn't obliged to respect any standards of evidence or logic. The editors of Social Text were hoodwinked. By an unhappy coincidence, shortly after receiving Sokal's article they decided to produce a special `Science Wars' collection, including the unrefereed article together with responses to Higher Superstition. `Transgressing the Boundaries' duly appeared in the Spring/Summer 96 double issue, accompanied by articles from a number of those denounced by Gross and Levitt and lampooned by Sokal -- the perfect setting! (shrink)