In this article, we report on eight grand challenges for value sensitive design, which were developed at a one-week workshop, Value Sensitive Design: Charting the Next Decade, Lorentz Center, Leiden, The Netherlands, November 14–18, 2016. A grand challenge is a substantial problem, opportunity, or question that motives sustained research and design activity. The eight grand challenges are: Accounting for Power, Evaluating Value Sensitive Design, Framing and Prioritizing Values, Professional and Industry Appropriation, Tech policy, Values and Human Emotions, Value Sensitive Design (...) and Intelligent Algorithms, and Value Tensions. Each grand challenge consists of a discussion of its importance and a set of tractable key questions. (shrink)

In this article, we introduce the Special Issue, Value Sensitive Design: Charting the Next Decade, which arose from a week-long workshop hosted by Lorentz Center, Leiden, The Netherlands, November 14–18, 2016. Forty-one researchers and designers, ranging in seniority from doctoral students to full professors, from Australia, Europe, and North America, and representing a wide range of academic fields participated in the workshop. The first article in the special issue puts forward eight grand challenges for value sensitive design to help guide (...) and shape the field. It is followed by 16 articles consisting of value sensitive design nuggets—short pieces of writing on a new idea, method, challenge, application, or other concept that engages some aspect of value sensitive design. The nuggets are grouped into three clusters: theory, method, and applications. Taken together the grand challenges and nuggets point the way forward for value sensitive design into the next decade and beyond. (shrink)

Drucilla Cornell engaged in scholarship and activism in South Africa for over a decade, and indeed she moved home from New York to Cape Town to participate more fully in the life and politics of the newly democratic country. This was not only a prolific period of scholarship and activism in her life, but also an inflection point in the country’s nascent constitutional jurisprudence. In this article, we memorialize Drucilla’s extraordinary contributions to the development of South Africa’s constitutional order and (...) of its legal academy. We situate these contributions in the broader set of concerns—about dignity and freedom, socialism and democracy, non-Western ideals, feminism, modernity, and the constitution of community—with which she had been engaged since the earliest days of her career. We include relevant anecdotes from her life in South Africa; not only her life as a scholar but also as a teacher, mentor, friend, and above all, a revolutionary activist. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

This paper examines an ideology I call techno-colonialism. I argue that techno-colonialism represents an attempt to selectively reproduce settler colonial practices adjusted to twenty-first century realities. This argument has implications for contemporary settler colonialism, the radical right, and climate change politics. In what follows, I discuss the techno-colonial doctrines of Nick Land, Curtis Yarvin, Peter Thiel, and Patri Friedman. These figures articulate a political theory about exploiting new technologies to escape the state and found new societies. To explore (...) techno-colonial ideology, I focus on Seasteading—the practice of creating floating city-states to colonize the ocean––as an attempted realization of techno-colonial ideals. As I claim, techno-colonialism attempts to humanize the politics of settlement. But I argue that techno-colonialism's ambitions fail, and techno-colonialism fails to create a harmless politics of settlement. I conclude that we should be attentive to the relations of political and economic power in which such exit projects are embedded. Moreover, this paper also promotes our understanding of climate change and the radical right's politics. While scholars most naturally associate the radical right with climate change denialism, the techno-colonists illustrate another possibility. They welcome catastrophe, and see rising-sea levels as an opportunity to start society afresh. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities cannot be smaller than the derived and so cannot ‘compose’ them in (...) any ordinary sense, would a formal derivation actually show the physical reality of localized entities? We address these questions via a survey of a range of theories of quantum gravity, and generally sketch how they may be answered positively. (shrink)

This is an opinionated guide to the literature on epistemic dilemmas. It discusses seven kinds of situations where epistemic dilemmas appear to arise; dilemmic, dilemmish, and non-dilemmic takes on them; and objections to dilemmic views along with dilemmist’s replies to them.

Epistemologists often appeal to the idea that a normative theory must provide useful, usable, guidance to argue for one normative epistemology over another. I argue that this is a mistake. Guidance considerations have no role to play in theory choice in epistemology. I show how this has implications for debates about the possibility and scope of epistemic dilemmas, the legitimacy of idealisation in Bayesian epistemology, uniqueness versus permissivism, sharp versus mushy credences, and internalism versus externalism.

This paper examines the impact of neoreactionary thinking – that of Curtis Yarvin, Nick Land, Peter Thiel and Patri Friedman in particular – on contemporary political debates manifest in ‘architectures of exit’. We specifically focus on Urbit, as an NRx digital architecture that captures how post-neoliberal politics imagines notions of freedom and sovereignty through a micro-fracturing of nation-states into ‘gov-corps’. We trace the development of NRx philosophy – and situate this within contemporary political and technological change to theorize (...) the significance of exit manifest within the notion of ‘dynamic geographies’. While technological programmes such as Urbit may never ultimately succeed, we argue that these, and other speculative investments such as ‘seasteading’, reflect broader post-neoliberal NRx imaginaries that were, perhaps, prefigured a quarter of a century ago in The Sovereign Individual. (shrink)

This article compares the concept of habitus, as formulated in the work of Mauss and Bourdieu, with the concept of habit, as formulated in the work of Merleau-Ponty and Dewey. The rationale for this, on one level, is to seek to clarify these concepts and any distinction that there may be between them – though the article notes the wide variety of uses of both concepts and suggests that these negate the possibility of any definitive definitions or contrasts. More centrally, (...) however, the purpose of the comparison is to draw out a number of important issues and debates which, it is argued, further work must address if the concepts of habit and habitus are to continue to prove useful and illuminating in social science. (shrink)

Epistemologists spend a great deal of time thinking about how we should respond to our evidence. They spend far less time thinking about the ways that evidence can be acquired in the first place. This is an oversight. Some ways of acquiring evidence are better than others. Many normative epistemologies struggle to accommodate this fact. In this article I develop one that can and does. I identify a phenomenon – epistemic feedback loops – in which evidence acquisition has gone awry, (...) with the result that even beliefs based on the evidence are irrational. Examples include evidence acquired under the influence of confirmation bias and evidence acquired under the influence of cognitively penetrated experiences caused by implicit bias. I then develop a theoretical framework which enables us to understand why beliefs that are the outputs of epistemic feedback loops are irrational. Finally, I argue that many popular approaches to epistemic normativity may need to be abandoned on the grounds that they cannot comfortably explain feedback loops. The scope of this last claim is broad: it includes almost all contemporary theories of justified/rational belief and of the epistemology of cognitive penetration. (shrink)

This paper investigates the significance of T-duality in string theory: the indistinguisha- bility with respect to all observables, of models attributing radically different radii to space – larger than the observable universe, or far smaller than the Planck length, say. Two interpretational branch points are identified and discussed. First, whether duals are physically equivalent or not: by considering a duality of the familiar simple harmonic oscillator, I argue that they are. Unlike the oscillator, there are no measurements ‘outside’ string theory (...) that could distinguish the duals. Second, whether duals agree or disagree on the radius of ‘target space’, the space in which strings evolve according to string theory. I argue for the latter position, because the alternative leaves it unknown what the radius is. Since duals are physically equivalent yet disagree on the radius of target space, it follows that the radius is indeterminate between them. Using an analysis of Brandenberger and Vafa (1989), I explain why – even so – space is observed to have a determinate, large radius. The conclusion is that observed, ‘phenomenal’ space is not target space, since a space cannot have both a determinate and indeterminate radius: instead phenomenal space must be a higher-level phenomenon, not fundamental. (shrink)

Daniel Greco (forthcoming) argues that there cannot be epistemic dilemmas. I argue that he is wrong. I then look in detail at a would-be epistemic dilemma and argue that no non-dilemmic approach to it can be made to work. Along the way, there is discussion of octopuses, lobsters, and other ‘inscrutable cognizers’; the relationship between evaluative and prescriptive norms; a failed attempt to steal a Brueghel; epistemic and moral blame and residue; an unbearable guy who thinks he’s God’s gift to (...) women; excuses; stupid games involving hats; radical permissivism; how I’ll never be able to afford to buy a house in Hampstead; and many other exciting topics. (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)

I consider a number of reasons one might think we should only accept epistemic dilemmas in our normative epistemology as a last resort and argue that none of them is compelling.

Weyl symmetry of the classical bosonic string Lagrangian is broken by quantization, with profound consequences described here. Reimposing symmetry requires that the background space-time satisfy the equations of general relativity: general relativity, hence classical space-time as we know it, arises from string theory. We investigate the logical role of Weyl symmetry in this explanation of general relativity: it is not an independent physical postulate but required in quantum string theory, so from a certain point of view it plays only a (...) formal role in the explanation. (shrink)

The point of departure for this article is the observation that, despite his own personal involvement as an engaged intellectual, Pierre Bourdieu offers a very thin account of social movement activism, and one pre-empted by the rather limited concept of ‘crisis’. The aim of the article, however, is to argue that the central concepts of Bourdieu’s theory of practice can be used to provide an effective and interesting basis for the analysis of social movements, protest and contention. To this end (...) the article demonstrates how the concepts of habitus, capital and field, in particular, resonate with important findings from the social movement literature. The focus of the article is limited to an engagement with Bourdieu. It connects with other work by the author, however, in which he has argued that Bourdieu’s framework can be used to address very serious problems in social movement theory. (shrink)

I argue that evidentialism should be rejected because it cannot be reconciled with empirical work on bias in cognitive and social psychology.

I argue that it is epistemically permissible to believe that P when it is epistemically rational to believe that P. Unlike previous defenses of this claim, this argument is not vulnerable to the claim that permissibility is being confused with excusability.

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)

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)

Since antiquity, natural philosophers have struggled to comprehend the nature of three tightly interconnected concepts: space, time, and motion. A proper understanding of motion, in particular, has been seen to be crucial for deciding questions about the natures of space and time, and their interconnections. Since the time of Newton and Leibniz, philosophers’ struggles to comprehend these concepts have often appeared to take the form of a dispute between absolute conceptions of space, time and motion, and relational conceptions. This article (...) guides the reader through some of the history of these philosophical struggles. Rather than taking sides in the (alleged) ongoing debates, or reproducing the standard dialectic recounted in most introductory texts, we have chosen to scrutinize carefully the history of the thinking of the canonical participants in these debates — principally Descartes, Newton, Leibniz, Mach and Einstein. Readers interested in following up either the historical questions or current debates about the natures of space, time and motion will find ample links and references scattered through the discussion and in the Other Internet Resources section below. (shrink)

I want to review some ways in which Quantum Mechanics seems to affront our “common-sense” notions of identity. Let’s start with a list.

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)

This is a brief response to Loïc Wacquant’s article, ‘Homines in extremis’. The response makes four contributions. First, I consider some of the reasons for the confusion surrounding the habitus concept, arguing that this confusion may be lessened (without any obvious loss) if we revert to ‘habit’ or ‘disposition’. Second, I argue that, irrespective of these terminological quibbles, it is vital that we do not conflate ‘habitus’ and ‘embodied actor’ as some accounts do. There is more to the embodied actor (...) than her habits and she can only have habits because this is so. Third, I begin to explore the point of view offered by ‘carnal ethnography’ and call for further clarification of that point of view. Finally, I note that Wacquant’s ethnography has the effect of rendering certain of Bourdieu’s ideas in a more concrete manner and foregrounding sociability, which the latter is sometimes inclined to ignore. This, I suggest, is a positive development. (shrink)

Drawing upon ethnographic data, this article analyses 'vocabularies of motive' amongst individuals who work out at a private health club in the Greater Manchester area (UK). The article draws a distinction between motives for starting at a gym and motives for continuing, and analyses each separately. It also seeks to draw out, in the latter case, the many motives which conflict with a stereotypical view of 'working out' found in some academic accounts. Working out is not only an instrumental means (...) of cultivating valued bodily attributes, it is argued, nor are its attractions necessarily all 'bodily' (at least narrowly defined) in nature. (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)

The consensus recommendations by Salter and colleagues (2023) regarding pediatric decision-making intentionally omitted adolescents due to the additional complexity their evolving autonomy presented. Using two case studies, one focused on truth-telling and disclosure and one focused on treatment refusal, this article examines medical decision-making with and for adolescents in the context of the six consensus recommendations. It concludes that the consensus recommendations could reasonably apply to older children.

This article examines how parents should make health decisions for one child when they may have a negative impact on the health interests or other interests of their siblings. The authors discuss three health decisions made by the parents of Alex Jones, a child with developmental disabilities with two older neurotypical siblings over the course of eight years. First, Alex’s parents must decide whether to conduct sequencing on his siblings to help determine if there is a genetic cause for Alex’s (...) developmental disabilities. Second, Alex’s parents must decide whether to move to another town to maximize the therapy options for Alex. Third, Alex’s parents must decide whether to authorize the collection of stem cells from Alex for a bone marrow transplant for his sibling who developed leukemia. We examine whether the consensus recommendations by Salter and colleagues (2023) regarding pediatric decision-making apply in families with more than one child. (shrink)

It is common to allocate scarce health care resources by maximizing QALYs per dollar. This approach has been attacked by disability-rights advocates, policy-makers, and ethicists on the grounds that it unjustly discriminates against the disabled. The main complaint is that the QALY-maximizing approach implies a seemingly unsatisfactory conclusion: other things being equal, we should direct life-saving treatment to the healthy rather than the disabled. This argument pays insufficient attention to the downsides of the potential alternatives. We show that this sort (...) of discrimination is one of four unpalatable consequences that any approach to priority setting in health care must face. We argue that, given the alternatives, it is far from clear that we should revise the QALY-maximizing approach in response to this objection. (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.

We conduct a case study analysis of a proposal for the emergence of time based upon the approximate derivation of three grades of temporal structure within an explicit quantum cosmological model which obeys a Wheeler-DeWitt type equation without an extrinsic time parameter. Our main focus will be issues regarding the consistency of the approximations and derivations in question. Our conclusion is that the model provides a self-consistent account of the emergence of chronordinal, chronometric and chronodirected structure. Residual concerns relate to (...) explanatory rather than consistency considerations. (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.

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 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)

In this paper we critically review the various attempts that have been made to understand quantum field theory. We focus on Teller's (1990) harmonic oscillator interpretation, and Bohm et al.'s (1987) causal interpretation. The former unabashedly aims to be a purely heuristic account, but we show that it is only interestingly applicable to the free bosonic field. Along the way we suggest alternative models. Bohm's interpretation provides an ontology for the theory--a classical field, with a quantum equation of motion. This (...) too has problems; it is not Lorentz invariant. (shrink)

I criticize a certain view of the 'quanta' of quantum mechanics that sees them as fundamentally non-atomistic and fundamentally significant for our understanding of quantum fields. In particular, I have in mind work by Redhead and Teller (1991, 1992 and Teller 1990). I prove that classical particles do not have the rather strong flavour of identity often associated with them; permuting positions and momenta does not produce distinct states. I show that even the label free excitation formalism is compatible with (...) a mild form of atomism. Finally, I summarise some of the principle objections to an 'oscillator' interpretation of quantum fields. (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.

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)

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 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)

It is often argued that the requirement that moral obligations be ‘action guiding’ motivates the claim that one can be obligated to ϕ only if one can ϕ. I argue that even on its most plausible interpretation, this argument fails, since the reasoning behind it leads to the absurd conclusion that one is permitted to ϕ if one cannot ϕ.

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)

Williamson (2000) appeals to considerations about when it is natural to say that a hypothesis is consistent with one’s evidence in order to motivate the claim that all and only knowledge is evidence. It is argued here that the relevant considerations do not support this claim, and in fact conflict with it.

Icons of knowledge -- Two small embryos in spirits of wine -- Like flies on the Parlon ceiling -- Drawing and Darwinism -- Illustrating the magic word -- Professors and progress -- Visual strategies -- Schematics, forgery, and the so-called educated -- Imperial grids -- Setting standards -- Forbidden fruit -- Creative copying -- Trials and tributes -- Scandal for the people -- A hundred Haeckels -- The textbook illustration -- Iconoclasm -- The shock of the copy.