This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory (...) of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov’s revolutionary approach to constructive proof theory. The editors also include Yankov’s contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics. (shrink)

Positive logics are $\{ \wedge, \vee, \to \}$-fragments of intermediate logics. It is clear that the positive fragment of $Int$ is not structurally complete. We give a description of all hereditarily structurally complete positive logics, while the question whether there is a structurally complete positive logic which is not hereditarily structurally complete, remains open.

Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and obeying treated in the same way. The suggested approach is based on the ideas of Łukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. More precisely, a consequence relation is defined on a set of statements of forms “proposition _A_ is accepted” and “proposition _A_ is rejected”, where _A_ is (...) a proposition,—a unified consequence relation. Accordingly, the rules defining a unified consequence relation,—the unified rules, have statements as premises and as conclusions. A special attention is paid to the logics in which each proposition is either accepted or rejected. If we express this property via unified rules and add them to a unified deductive system, such a unified deductive system defines a reversible unified consequence: a statement “proposition _B_ is accepted” is derived from the statement “proposition _A_ is accepted” if and only if a statement “proposition _A_ is rejected” is derived from the statement “proposition _B_ is rejected”. (shrink)

Propositional logic is understood as a set of theorems defined by a deductive system: a set of axioms and a set of rules. Superintuitionistic logic is a logic extending intuitionistic propositional logic \. A rule is admissible for a logic if any substitution that makes each premise a theorem, makes the conclusion a theorem too. A deductive system \ is structurally complete if any rule admissible for the logic defined by \ is derivable in \. It is known that any (...) logic can be defined by a structurally complete deductive system—its structural completion. The main goal of the paper is to study the following problem: given a superintuitionistic logic L, is the structural completion of L hereditarily structurally complete? It is shown that, on the one hand, there is continuum many of such logics, including \, and many of its standard extensions. On the other hand, there is continuum many superintutitionistic logics structural completion of which is not hereditarily structurally complete. It is observed that the class of hereditarily structurally complete superintuitionistic consequence relations does not have the smallest element and it contains continuum many members lacking the finite model property. The following statement is instrumental in obtaining negative results: if a Lindenbaum algebra of formulas on one variable is finite and has more than 15 elements, then a structural completion of such a logic is not hereditarily structurally complete. (shrink)

The goal of this paper is to generalize a notion of quasi-characteristic inference rule in the following way: with every finite partial algebra we associate a rule, and study the properties of these rules. We prove that any equivalential logic can be axiomatized by such rules. We further discuss the correlations between characteristic rules of the finite partial algebras and canonical rules. Then, with every algebra we associate a set of characteristic rules that correspond to each finite partial subalgebra of (...) this algebra. Finally, we demonstrate that in many respects these sets enjoy the same properties as regular quasi-characteristic rules. (shrink)

We give an example of a variety of Heyting algebras and of a splitting algebra in this variety that is not finitely presentable. Moreover, we show that the corresponding splitting pair cannot be defined by any finitely presentable algebra. Also, using the Gödel-McKinsey-Tarski translation and the Blok-Esakia theorem, we construct a variety of Grzegorczyk algebras with similar properties.

The paper studies admissibility of multiple-conclusion rules in positive logics. Using modification of a method employed by M. Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility of multiple-conclusion rules in the positive logics is equivalent to the problem of admissibility in intermediate logics defined by positive additional axioms. Moreover, a multiple-conclusion rule \ follows from a set of multiple-conclusion rules \ over a positive logic \ if and only if \ follows from (...) \ over \. (shrink)

A term td is called a ternary deductive term for a variety of algebras V if the identity td≈r holds in V and ∈θ yields td≈td for any A∈V and any principal congruence θ on A. A connective f is called td-distributive if td)≈ f,…,td). If L is a propositional logic and V is a corresponding variety that has a TD term td, then any admissible in L rule, the premises of which contain only td-distributive operations, is derivable, and the (...) substitution r↦td is a projective L-unifier for any formula containing only td-distributive connectives. The above substitution is a generalization of the substitution introduced by T. Prucnal to prove structural completeness of the implication fragment of intuitionistic propositional logic. (shrink)

The goal of this paper is to generalize a notion of characteristic (or Jankov) formula by using finite partial Heyting algebras instead of the finite subdirectly irreducible algebras: with every finite partial Heyting algebra we associate a characteristic formula, and we study the properties of these formulas. We prove that any intermediate logic can be axiomatized by such formulas. We further discuss the correlations between characteristic formulas of finite partial algebras and canonical formulas. Then with every well-connected Heyting algebra we (...) associate a set of characteristic formulas that correspond to each finite relative subalgebra of this algebra. Finally, we demonstrate that in many respects these sets enjoy the same properties as regular characteristic formulas. In the last section we outline an approach how to generalize these obtained results to the broad classes of algebras. (shrink)

With each superintuitionistic propositional logic L with a disjunction property we associate a set of modal logics the assertoric fragment of which is L . Each formula of these modal logics is interdeducible with a formula representing a set of rules admissible in L . The smallest of these logics contains only formulas representing derivable in L rules while the greatest one contains formulas corresponding to all admissible in L rules. The algebraic semantic for these logics is described.

With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$, providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is admissible. We prove that (...) any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. (shrink)

Response-dependence theories have historically been very popular in aesthetics, and aesthetic response-dependence has motivated response-dependence in ethics. This chapter closely examines the prospects for such theories. It breaks this category down into dispositional and fittingness strands of response-dependence, corresponding to descriptive and normative ideal observer theories. It argues that the latter have advantages over the former but are not themselves without issue. Special attention is paid to the relationship between hedonism and response-dependence. The chapter also introduces two aesthetic properties that (...) lead to wrong kinds of reasons problems for aesthetic response-dependence: insightfulness and the capacity to change one’s perspective. These properties do not have obvious parallels in the ethical domain, and so present an obstacle for response-dependence even in aesthetics. The chapter ends by examining replies on behalf of the response-dependence theorist, ultimately suggesting that a restricted form of response-dependence is the most promising way forward for fans of such theories. (shrink)

This chapter is centered around an apparent tension that research on implicit bias raises between virtue and social knowledge. Research suggests that simply knowing what the prevalent stereotypes are leads individuals to act in prejudiced ways—biasing decisions about whom to trust and whom to ignore, whom to promote and whom to imprison—even if they reflectively reject those stereotypes. Because efforts to combat discrimination obviously depend on knowledge of stereotypes, a question arises about what to do next. This chapter argues that (...) the obstacle to virtue is not knowledge of stereotypes as such, but the “accessibility” of such knowledge to the agent who has it. “Accessibility” refers to how easily knowledge comes to mind. Social agents can acquire the requisite knowledge of stereotypes while resisting their pernicious influence, so long as that knowledge remains, in relevant contexts, relatively inaccessible. (shrink)

Perceptual experiences justify beliefs—that much seems obvious. As Brewer puts it, “sense experiential states provide reasons for empirical beliefs” (this volume, xx). In Mind and World McDowell argues that we can get from this apparent platitude to the controversial claim that perceptual experiences have conceptual content: [W]e can coherently credit experiences with rational relations to judgement and belief, but only if we take it that spontaneity is already implicated in receptivity; that is, only if we take it that experiences have (...) conceptual content. (1994, 162) Brewer agrees. Their view is sometimes called conceptualism; nonconceptualism is the rival position, that experiences have nonconceptual content. One initial obstacle is understanding what the issue is. What is conceptual content, and how is it different from nonconceptual content? Section 1 of this paper explains two versions of each of the rival positions: state (non)conceptualism and content (non)conceptualism; the latter pair is the locus of the relevant dispute. Two prominent arguments for content nonconceptualism—the richness argument and the continuity argument—both fail (section 2). McDowell’s and Brewer’s epistemological defenses of content conceptualism are also faulty (section 3). Section 4 gives a more simple-minded case for conceptualism; finally, some reasons are given for rejecting the claim—on one natural interpretation—that experiences justify beliefs. (shrink)

There are at least two different aspects of our rational evaluation of agents’ doxastic attitudes. First, we evaluate these attitudes according to whether they are supported by one’s evidence (substantive rationality). Second, we evaluate these attitudes according to how well they cohere with one another (structural rationality). In previous work, I’ve argued that substantive and structural rationality really are distinct, sui generis, kinds of rationality – call this view ‘dualism’, as opposed to ‘monism’, about rationality – by arguing that the (...) requirements of substantive and structural rationality can come into conflict. In this paper, I push the dialectic on this issue forward in two main ways. First, I argue that the most promising ways of resisting the diagnosis of my cases as conflicts still end up undermining monism in different ways. Second, supposing for the sake of argument that we should understand the cases as conflicts, I address the question of what we should do when such conflicts arise. I argue that, at least in a prominent kind of conflict case, the coherence requirements take precedence over the evidential requirements. (shrink)

Context-sensitive expressions appear ill suited to the purpose of sharing content across contexts. Yet we regularly use them to that end (in regulations, textbooks, memos, guidelines, laws, minutes, etc.). This paper describes the utility of the concept of a metacontext for understanding cross-contextual content-sharing with context-sensitive expressions. A metacontext is the context of a group of contexts: an infrastructure that can channel non-linguistic incentives on content ascription so as to homogenize the content ascribed to context-sensitive expressions in each context in (...) the group. Documents composed of context-sensitive expressions can share content across contexts when supported by an appropriate metacontext. The bible has its church, the textbook its education system, the form its bureaucracy, and the manifesto its social movement. Some metacontexts support cross-contextual content-sharing. Some don’t. A promising research programme (one with practical importance) would take metacontexts as its unit of analysis. (shrink)

Comment on Brogaard's Seeing and Saying (OUP 2018).

A survey of color science and color vision.

Money isn’t everything, so what is? Many government leaders, social policy theorists, and members of the general public have a ready answer: happiness. This paper examines an opposing view due to Robert Nozick, which centres on his experience-machine thought experiment. Despite the example's influence among philosophers, the argument behind it is riddled with difficulties. Dropping the example allows us to re-version Nozick's argument in a way that makes it far more forceful - and less dependent on people's often divergent intutions (...) about the experience machine. [DOWNLOAD AVAILABLE at oro.open.ac.uk repository, link below]. (shrink)

Within the history of African American struggle against racist oppression that often verges on dystopia, a hidden tradition has depicted a transfigured world. Daring to speculate on a future beyond white supremacy, black utopian artists and thinkers offer powerful visions of ways of being that are built on radical concepts of justice and freedom. They imagine a new black citizen who would inhabit a world that soars above all existing notions of the possible. In Black Utopia, Alex Zamalin offers (...) a groundbreaking examination of African American visions of social transformation and their counterutopian counterparts. Considering figures associated with racial separatism, postracialism, anticolonialism, Pan-Africanism, and Afrofuturism, he argues that the black utopian tradition continues to challenge American political thought and culture. Black Utopia spans black nationalist visions of an ideal Africa, the fiction of W. E. B. Du Bois, and Sun Ra’s cosmic mythology of alien abduction. Zamalin casts Samuel R. Delany and Octavia E. Butler as political theorists and reflects on the antiutopian challenges of George S. Schuyler and Richard Wright. Their thought proves that utopianism, rather than being politically immature or dangerous, can invigorate political imagination. Both an inspiring intellectual history and a critique of present power relations, this book suggests that, with democracy under siege across the globe, the black utopian tradition may be our best hope for combating injustice. (shrink)

Skepticism about the internal world is actually more troubling than skepticism about the external world.

There is a correlation between positions taken on some scientific questions and political leaning. One way to explain this correlation is the cultural cognition hypothesis (CCH): people's political leanings are causing them to process evidence to maintain fixed answers to the questions, rather than to seek the truth. Another way is the different background belief hypothesis (DBBH): people of different political leanings have different background beliefs which rationalize different positions on these scientific questions. In this article, I argue for two (...) things. I argue that two attempts by proponents of the CCH to discredit the DBBH fail. And I argue that this matters, because while the CCH makes epistemic paternalistic interventions seem called for (as some philosophers have argued compellingly), the DBBH does not. The DBBH makes it much easier to stay closer to an ideal of deliberative democracy. (shrink)

What can we do—and what should we do—to fight against bias? This final chapter introduces empirically-tested interventions for combating implicit (and explicit) bias and promoting a fairer world, from small daily-life debiasing tricks to larger structural interventions. Along the way, this chapter raises a range of moral, political, and strategic questions about these interventions. This chapter further stresses the importance of admitting that we don’t have all the answers. We should be humble about how much we still don’t know and (...) dedicate efforts to gathering as much knowledge as possible. Even so, we know enough now to start making a difference, and this chapter ultimately aims to chip away at the gap between our abstract commitments to treat people fairly and our lived habits and experiences, which continue to be shaped by implicit and explicit prejudices and stereotypes about race, gender, and other social categories. (shrink)

A 20th anniversary edition of the art classic that celebrates the intersection of creative expression and spirituality—from one of the greatest living artists of our time Twenty years after the original publication of The Mission of Art, Alex Grey’s inspirational message affirming art’s power for personal catharsis and spiritual awakening is stronger than ever. In this special anniversary edition, Grey—visionary painter, spiritual leader, and best-selling author—combines his extensive knowledge of art history with his own experiences in creating art at (...) the boundaries of consciousness. Grey examines the roles of conscience and intention in the creative process, including practical techniques and exercises useful in exploring the spiritual dimensions of art. Challenging and thought-provoking, The Mission of Art will be appreciated by everyone who has ever contemplated the deeper purpose of creative expression. (shrink)

A survey of arguments for and against the view that colors are physical properties.

This paper argues that climate injustice will be compounded in the future as a result of the deferred nature of many climate impacts. My claim is that the temporal disconnect between emissions and climate harm threatens future people’s ability to access what I call “resistance goods,” which rely on forms of address, often realised in oppositional political action. I identify three resistance goods—self-assertion, solidarity and testimony—and show that each is threatened by the temporality of climate change. A compound of climate (...) injustice is that it will be experienced as demeaning, isolating and silencing by many future people. (shrink)

Siegel and Byrne debate whether perceptual experiences present rich properties or exclusively thin properties.

Speciesism, broadly understood as the view that species membership is a morally relevant property, has been a central topic of debate within animal ethics for around 50 years. However, in all this time, animal ethicists have paid relatively scant attention to the nature of species membership itself. This seems potentially regrettable, since species membership's precise nature is presumably highly pertinent to the question of its exact moral relevance. Here, I advocate for a ‘species-focused’ approach to assessing speciesism, arguing that, in (...) debating the merits of speciesism, animal ethicists should (i) centre the nature of species membership, and (ii) consult philosophers of biology. Adherence to this second prescription appears necessary since a lot of what philosophers of biology believe regarding the nature of species membership appears contrary to what many animal ethicists have seemingly assumed. (shrink)

Originally published in 1961. The essays in this volume focus on the awareness of science and art, evolution and Freudian psychology. Besides the chapter on Darwin and Freud, the author discusses criticism, the fantasy element in drama and popular literature, the history of the novel, the motivation of science and the function of erotic art.

This paper identifies the major failings of mainstream economics and the rational choice theory it relies upon. These failures were identified by the four figures mentioned in the title: economics treats agents as rational fools; by the time the long … More ›.

Excerpt: 1. Introduction This chapter provides insight into the diverse ethical debates on genetics and epigenetics. Much controversy surrounds debates about intervening into the germline genome of human embryos, with catchwords such as genome editing, designer baby, and CRISPR/Cas. The idea that it is possible to design a child according to one’s personal preferences is, however, a quite distorted view of what is actually possible with new gene technologies and gene therapies. These are much more limited than the editing and (...) design metaphors suggest. Such metaphors are therefore highly problematic phrases in the context of new gene technologies, for two reasons. On one hand, to design a child of choice by modifying the genome would require modifying any gene of choice, which is more than can be done with current gene technologies, such as CRISPR/Cas. On the other hand, a modification of genes would need to be enough to create any characteristic of choice in the future child. The latter presupposes the assumption of genetic determinism. Moreover, the CRISPR/Cas technology can not only be used in a potentially therapeutic manner at the germline level. In addition, there is the (more likely) scenario of a future clinical therapeutic use of these new gene technologies for modifying the DNA sequence of other cells of the body (somatic genome editing). There is also the option of modifying the epigenome, that is, the spatial configuration of DNA (epigenome editing) (see table 1). Like genetics and genome editing, epigenetics has been at the center of recent popular scientific and ethical discourse as well as scientific debates. The concept of epigenetics has given rise to very different notions of inheritability and responsibility for health, which, however, are oftentimes based on scientifically controversial basic assumptions. That there continues to be covert genetic determinism in the form of epigenetic determinism (see table 2) in debates about epigenetics has been pointed out in ethical analyses of epigenetics. Neither genetic determinism nor epigenetic determinism has been confirmed scientifically. It is therefore important to recognize the concepts that are discussed (and sometimes harshly criticized) in debates about genome editing and epigenetics—for example, concepts about the causal role of DNA for our own life course. This importance is based on the fact that if we understand such controversial concepts, we will be able to remain critical when evaluating scientific knowledge and ethical arguments about genome editing and epigenetics. This chapter, therefore, explains some of these concepts. For an ethical analysis of epigenetics as well as of genome editing, it is necessary to understand and critically reflect upon the underlying concepts of genetic determinism and other, related -isms. The following section offers a detailed introduction to these -isms (section 2; see also table 2). Section 3 provides an ethical analysis of genome editing and epigenetics based on the explanations in section 2. Section 3 focuses on inheritability and responsibility, justice, safety, the problem of consent, and the effects of genome editing and epigenetics on embryos and future generations. This section does not discuss in detail further points that can be found in ethical debates about epigenetics as well as in ethical debates about genome editing. These points include (among others): • fear that the findings of epigenetics and that the methods of genome editing are misused—this also with respect to eugenics and enhancement; • naturalness—an issue we mention in passing a few times in the following analysis; • a possible connection between the genome/epigenome and the concept of human dignity, and the derived danger of instrumentalization and infringement of autonomy when intervening in the genome or epigenome. Since current discourse about ethical issues associated with genome editing focuses mainly on germline interventions, which are, for instance, interventions into a human embryo’s genome, we mainly focus on germline interventions when comparing the debates on genome editing and on epigenetics in section 3. (shrink)

'What would happen if everyone acted that way?' This question is often used in everyday moral assessments, but it has a paradoxical quality: it draws not only on Kantian ideas of a universal moral law but also on consequentialist claims that what is right depends on the outcome. In this book, Alex Tuckness examines how the question came to be seen as paradoxical, tracing its history from the theistic approaches of the seventeenth century to the secular accounts of the (...) present. Tuckness shows that the earlier interpretations were hybrid theories that included both consequentialist and non-consequentialist elements, and argues that contemporary uses of this approach will likewise need to combine consequentialist and non-consequentialist commitments. (shrink)

The Art Experience: An Introduction to Philosophy and the Arts takes readers on an engaging and accessible journey that explores a series of fundamental questions about the nature of art and aesthetic value. Three of these questions serve as the major sections for the book's 12 chapters: What makes something a work of art? How should we experience art in order to get the most out of it? And once we understand art, how should we evaluate whether it is good (...) or bad? Philosophical theory is illustrated with concrete examples: the paintings of Frida Kahlo, the music of Johann Sebastian Bach, the masks of the Nso people, and many others. Classic questions are balanced with cutting-edge challenges, such as Linda Nochlin's work on the exclusion of women from the artistic canon. The Art Experience presupposes no prior knowledge of philosophy or art, and it will be of interest to any reader seeking an accessible and engaging introduction to this field. Along the way, readers learn how philosophical theories can affect our real-world experiences with painting, music, theater, and many more art forms. Key Features Accessible for any college student and assumes no knowledge of philosophy, art theory, or any artistic medium Organizes topics conceptually, rather than historically, allowing students to more easily grasp the core issues themselves rather than tracing their historical evolution Offers readers a large number of contemporary examples and a consistent focus on the way theory can affect people's real-world experiences with art Explores questions about bias - for example, whether the artistic canon has excluded some groups unfairly and whether definitions of art are Western-biased. (shrink)

This chapter focuses on what’s novel in the perspective that the prediction error minimization (PEM) framework affords on the cognitive-scientific project of explaining intelligence by appeal to internal representations. It shows how truth-conditional and resemblance-based approaches to representation in generative models may be integrated. The PEM framework in cognitive science is an approach to cognition and perception centered on a simple idea: organisms represent the world by constantly predicting their own internal states. PEM theories often stress the hierarchical structure of (...) the generative models they posit. The novel explanatory power of the PEM account derives largely from the way in which pairs of generative and recognition models interact. “Predictive coding” refers to an encoding strategy in which predicted portions of an input signal are subtracted from the actual signal received, so that only the difference between the two is passed as output to the next stage of information processing. (shrink)

This is Political Philosophy is an accessible and well-balanced introduction to the main issues in political philosophy written by an author team from the fields of both philosophy and politics. This text connects issues at the core of political philosophy with current, live debates in policy, politics, and law and addresses different ideals of political organization, such as democracy, liberty, equality, justice, and happiness. Written with great clarity, This is Political Philosophy is accessible and engaging to those who have little (...) or no prior knowledge of political philosophy and is supported with supplemental pedagogical and instructor material on the This Is Philosophy series site. (shrink)

The Dangerous Book for Boys Abstract: Seventeenth and eighteenth century discussions of the senses are often thought to contain a profound truth: some perceptible properties are secondary qualities, dispositions to produce certain sorts of experiences in perceivers. In particular, colors are secondary qualities: for example, an object is green iff it is disposed to look green to standard perceivers in standard conditions. After rebutting Boghossian and Velleman’s argument that a certain kind of secondary quality theory is viciously circular, we discuss (...) three main lines of argument for the secondary quality theory. The first is inspired by an intuitively compelling picture of perception articulated by Reid; the second is that the secondary quality theory is a conceptual truth; the third line of argument is presented in Johnston’s influential paper ‘How to speak of the colors’. We conclude that all these arguments fail, and that the secondary quality theory is unmotivated. Keywords: color, secondary quality, disposition, vision, perception.. (shrink)