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)

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)

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)

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..

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)

“Motivational externalism” is the externalism until they see more of what view that moral judgements have no motisuch a theory would be like. The mere posvational efficacy in themselves, and that sibility of such a theory is not sufficiently when they motivate us, the source of motireassuring, even given strong arguments vation lies outside the moral judgement in against the opposite position. For there may a separate desire. Motivational externalism also be objections to externalism. contrasts with “motivational internalism,” Moral philosophers (...) have not spent much which is either the view that our moral effort spelling out the details of an exterjudgements are partly constituted by motinalist model of moral motivation. Those vation, or else that they would be if we who have endorsed externalism include were rational. The major problem for mo- Philippa Foot, Michael Stocker, David tivational internalism—in either guise—is Brink, Al Mele, Sigrún Svavarsdóttir, and that it flies in the face of common obsermyself (Foot 1972, Stocker 1979, Brink vation and first-personal experience of the 1989, 1997, Mele 1996, Svavarsdóttir fact that we can, without irrationality, be 1999, Zangwill 1999). But even these phiindifferent to morality. Philippa Foot piolosophers concentrated mostly on arguing neered this argument (Foot 1972). The pheagainst internalism or defending moral renomenon of indifference encourages alism rather than articulating the externalist motivational externalism. alternative. As a consequence, it is not clear This paper will not revisit this difficulty how the externalism that can be gleaned for internalism, but will travel in the opfrom these writings can be defended posite dialectical direction. The aim is to against various objections to externalism. expound and defend externalism, not to This paper is concerned to fashion an atargue against internalism. This paper will tractive version of externalism, and show address, and try to soothe away, the reluchow it evades objections. tance of many philosophers to embrace In section 1, a particular version of motimotivational externalism.. (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)

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)

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.

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)

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)

Can a certain sort of property supervene on another sort of property without reducing to it? Many philosophers find the superveniencel irreducibility combination attractive in the philosophy of mind and in moral philosophy. They think that mental properties supervene upon physical properties but do not reduce to them, or that moral properties supervene upon natural properties without reducing to them. Other philosophers have tried to show that the combination is ultimately untenable, however attractive it might initially appear. Thus Ted Honderich (...) and Jaegwon Kim argue that the combination cannot explain the causal efhcacy of the supervening properties. And Simon. (shrink)

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.

Despite his longstanding silence regarding Marx’s Capital, I wish here to argue that Badiou has in fact, in the three volumes of Being and Event, produced the materials for a contemporary logic of the capitalist social form. He has done so, however, in the form of an arsenal of abstract concepts that have yet to be precisely measured against Marx’s critical and formal reproduction of capitalism, the systematic exposition of which consumes the three volumes of Capital. I first argue that (...) Badiou’s general disinterest in the logic of capitalism and Marx’s Capital specifically takes on a strongly symptomatic, spectral presence in the 1994-1995 seminar Lacan: Anti-philosophy 3. Secondly, while it is true that Badiou’s Logics of Worlds never discusses the logic of appearance that governs all capitalist things, it is possible nonetheless to read Logics as an abstract translation and formalisation of Marx’s Capital. In this view, Capital should quite simply be read as a systematic demonstration of the logic of what Marx calls the capitalist social form, which is to say, in Badiou’s jargon, the logic or science of the appearance of things in the capitalist world. In a sense, then, this means nothing more, though nothing less, than subjecting the Logics of Worlds to a Marxian torsion: in order to demonstrate that which Badiou has neglected, Marx has in fact already accomplished, i.e. the systematic, synthetic demonstration of the necessary forms of the appearance of commodities in the capitalist social form. (shrink)

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)

Responding to serious environmental problems, requires urgent and fundamental shifts in our day-to-day lifestyles. This paper employs a qualitative, cross-cultural approach to explore people’s subjective self-reflections on their experiences of pro-environmental behavioral spillover in three countries; Brazil, China, and Denmark. Behavioral spillover is an appealing yet elusive phenomenon, but offers a potential way of encouraging wider, voluntary lifestyle shifts beyond the scope of single behavior change interventions. Behavioral spillover theory proposes that engaging in one pro-environmental action can catalyze the performance (...) of others. To date, evidence for the phenomenon has been mixed, and the causal processes governing relationships between behaviors appear complex, inconsistent and only partly understood. This paper addresses a gap in the literature by investigating accounts of behavioral spillover in three diverse cultural settings using qualitative semi-structured interviews. The analysis shows that while around half of participants overall who were questioned recalled spillover effects, the other half had not consciously experienced spillover. There were few significant differences across cultures, though some forms of spillover effects were reported more in some cultures than others. More environmentally-engaged participants across all three countries were significantly more likely to experience spillover than those who were less engaged. Accounts of within-domain spillovers were most commonly reported, mainly comprising waste, resource conservation and consumption-related actions. Accounts of between-domain spillover were very rare. Recollection of contextual and interpersonal spillover effects also emerged from the interviews. Our findings suggest that more conscious behavioral spillover pathways may be limited to those with pre-existing environmental values. Behavioral spillover may comprise multiple pathways incorporating conscious and unconscious processes. We conclude that targeting behavioral catalysts that generate more socially diffuse spillover effects could offer more potential than conventional spillover involving a single individual. (shrink)

an article written with Tom Imbo for the forthcoming Compendium of Quantum Mechanics.

The quantum gravity program seeks a theory that handles quantum matter fields and gravity consistently. But is such a theory really required and must it involve quantizing the gravitational field? We give reasons for a positive answer to the first question, but dispute a widespread contention that it is inconsistent for the gravitational field to be classical while matter is quantum. In particular, we show how a popular argument (Eppley and Hannah 1997) falls short of a no-go theorem, and discuss (...) possible counterexamples. Important issues in the foundations of physics are shown to bear crucially on all these considerations. (shrink)

Much of our private and public ethical discourse occurs in the giving, receiving, or demanding of an apology, yet we suffer deep confusion regarding what an apology actually is. Most of us have never made explicit precisely what we expect from a full apology and therefore apologizing has become a vague and clumsy ritual. Full apologies can be morally and emotionally powerful, but, as with most valuable things, frauds masquerade as the genuine article. These semblances of apologies often deceive and (...) manipulate, and such duplicity is common between lovers, families, litigants, and nations. In response to this, I propose nine elements that an apology must satisfy in order to be considered categorical. I believe we have such a categorical apology in mind when we seek a full apology. The standards for a categorical apology are rigorous and precise, and I hope to disentangle the distinct elements of apologies. A categorical apology is a rare and burdensome act, and under certain circumstances full apologies may not be possible regardless of how badly we may desire them. While the leading social science accounts by Aaron Lazare and Nicolas Tavuchis aptly demonstrate how apologies lubricate reciprocally egoist relationships, such theories ultimately prove unsatisfying because apologies achieve their highest meaning as morally rich acts. Both Tavuchis and Lazare offer merely descriptive accounts when a prescriptive argument seems necessary. No philosopher, however, has ever devoted a monograph to the topic and only a handful of papers on apologies have appeared in philosophy journals. (shrink)

In sum, the non-cognitivist account of motivation is far from unproblematic. The non-cognitivist has trouble telling us what moral attitudes are in a way that is consistent with the phenomenon of variable motivation. Given that the cognitivist has an easy explanation of variable motivation, it seems that cognitivism is preferable to non-cognitivism on the score of motivation, which is a reversal of the way the issue is usually perceived.

In a recent paper in this journal, Ken Olum attempts to refute the doomsday argument by appealing to the self–indication assumption (SIA) that your very existence gives you reason to think that there are many observers. Unlike earlier users of this strategy, Olum tries to counter objections that have been made against (SIA). We argue that his defence of (SIA) is unsuccessful. This does not, however, mean that one has to accept the doomsday argument (or the other counter–intuitive results that (...) flow from related thought–experiments). A developed theory of observation selection effects shows why the doomsday argument is inconclusive, and how one can consistently reject both it and (SIA). (shrink)

We prove that every normal extension of the bi-modal system S52 is finitely axiomatizable and that every proper normal extension has NP-complete satisfiability problem.

Ethical leadership in any organisation is expected to come from the top. With business leaders taking a real stand on ethics, it is imperative that business schools instil strong values into their students. Deans of business schools must exhibit these ethical values to provide an example for faculty, students and staff to emulate. This study is an investigation of the ethical values of deans and associate deans in ten business schools in Canada. The results portray the ethical inclination of business (...) school leaders even with substantial monetary gains to be made. The moral climate as a result is discussed to provide further insight into the implications of the ethical values of these deans. Results indicate that although deans in Canadian business schools generally frown upon unethical behaviour, there are some fuzzy instances that still lead to questionable decisions and inconsistencies across the group. (shrink)