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.

Intentionalism about demonstratives is the view that the referent of a demonstrative is determined solely by the speaker's intentions. Intentionalists can disagree about the nature of these intentions, but are united in rejecting the relevance of other factors, such as the speaker's gestures, her gaze, and any facts about the addressee or the audience. In this paper, I formulate a particular version of this view, and I defend it against six objections, old and new.

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Common principles for resource allocation in health care can prioritize the alleviation of small health burdens over lifesaving treatment. I argue that there is some evidence that these principles are at odds with a sizable share of public opinion, which holds that saving a life should take priority over any number of cures for minor ailments. I propose two possible explanations for this opinion, one debunking and one vindicatory. I also outline how well-designed surveys and moral inquiry could help decide (...) between them. Finally, I consider how priority-setting principles could be adjusted if the view that saving a life always trumps alleviating small burdens were vindicated. (shrink)

This essay surveys the varieties of disjunctivism about perceptual experience. Disjunctivism comes in two main flavours, metaphysical and epistemological.

This paper introduces a symposium on Equality versus Priority. It explains how cases involving risk are key to distinguishing these views and discusses a 'social egalitarian' critique of both 'telic egalitarians' and 'telic prioritarians'.

One very popular framework in contemporary epistemology is Bayesian. The central epistemic state is subjective confidence, or credence. Traditional epistemic states like belief and knowledge tend to be sidelined, or even dispensed with entirely. Credences are often introduced as familiar mental states, merely in need of a special label for the purposes of epistemology. But whether they are implicitly recognized by the folk or posits of a sophisticated scientific psychology, they do not appear to fit well with perception, as is (...) often noted. -/- This paper investigates the tension between probabilistic cognition and non-probabilistic perception. The tension is real, and the solution—to adapt a phrase from Quine and Goodman—is to renounce credences altogether. (shrink)

When A utters a declarative sentence in a context to B, typically A can mean a proposition by the sentence, the sentence in context literally expresses a proposition, there are propositions A and B can agree the sentence literally expressed, and B can acquire knowledge from this testimonial exchange. In recent work on linguistic communication, each of these four platitudes has been challenged, and on the same basis: viz. on the ground that exactly which proposition the sentence expressed in context (...) is not discernible given the information provided by the context. I argue that, even if this is true, there will be propositional parts of the proposition expressed by the sentence in context which can be identified and that, consequently, the partial understanding afforded by the existence of such identifiable parts undermines the soundness of the arguments against the platitudes. (shrink)

It seems possible to see a star that no longer exists. Yet it also seems right to say that what no longer exists cannot be seen. We therefore face a puzzle, the traditional answer to which involves abandoning naïve realism in favour of a sense datum view. In this article, however, I offer a novel exploration of the puzzle within a naïve realist framework. As will emerge, the best option for naïve realists is to embrace an eternalist view of time, (...) and claim that in the relevant case, one sees a still existent star‐stage located somewhere in the distant past. (shrink)

Traditionally, perceptual experiences—for example, the experience of seeing a cat—were thought to have two quite distinct components. When one sees a cat, one’s experience is “about” the cat: this is the representational or intentional component of the experience. One’s experience also has phenomenal character: this is the sensational component of the experience. Although the intentional and sensational components at least typically go together, in principle they might come apart: the intentional component could be present without the sensational component or vice (...) versa. (shrink)

Darwin in Argentina -- Conflicting Systems -- Francisco Javier Muniz (1795-1871) -- Hermann Burmeister (1807-1891) -- Francisco P. Moreno (1852-1919) -- Domingo F. Sarmiento (1811-1888) -- Eduardo Holmberg (1852-1937) -- Florentino Ameghino (1854-1911) -- Jose Ingenieros (1877-1925) -- Carlos Octavio Bunge (1875-1918).

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)

Endre Begby’s Prejudice: A Study in Non-Ideal Epistemology engages a wide range of issues of enduring interest to epistemologists, applied ethicists, and anyone concerned with how knowledge and justice intersect. Topics include stereotypes and generics, evidence and epistemic justification, epistemic injustice, ethical-epistemic dilemmas, moral encroachment, and the relations between blame and accountability. Begby applies his views about these topics to an equally wide range of pressing social questions, such as conspiracy theories, misinformation, algorithmic bias, discrimination, and criminal justice. Through it (...) all, the book’s central thesis is that prejudices can be epistemically rational, a corrective against what Begby takes to be the received view that prejudices are always and everywhere bad. However, Begby’s arguments do not engage consistently with relevant empirical literatures, misrepresent the positions of his interlocutors, and rehearse ideas already well-established across a range of intellectual traditions. (shrink)

Although decision‐making algorithms are not new to medicine, the availability of vast stores of medical data, gains in computing power, and breakthroughs in machine learning are accelerating the pace of their development, expanding the range of questions they can address, and increasing their predictive power. In many cases, however, the most powerful machine learning techniques purchase diagnostic or predictive accuracy at the expense of our ability to access “the knowledge within the machine.” Without an explanation in terms of reasons or (...) a rationale for particular decisions in individual cases, some commentators regard ceding medical decision‐making to black box systems as contravening the profound moral responsibilities of clinicians. I argue, however, that opaque decisions are more common in medicine than critics realize. Moreover, as Aristotle noted over two millennia ago, when our knowledge of causal systems is incomplete and precarious—as it often is in medicine—the ability to explain how results are produced can be less important than the ability to produce such results and empirically verify their accuracy. (shrink)

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)

This fascinating and thought-provoking book provides much-needed philosophical background for counselors, therapists, and healthcare workers looking for broader, deeper foundations in the struggle to help and make sense of others. While examining the best among 20th century philosophy it shows the wealth of inspiration of earlier centuries, and demonstrates with remarkable clarity the way in which the ideas of, and the relations between, these philosophers can inspire, inform, and underpin much of counseling and psychotherapy.

I defend Fricker’s virtue-theoretic proposals for grappling with epistemic injustice, arguing that her account is both empirically oriented and plausible. I agree with Fricker that an integral component of what we ought to do in the face of pervasive epistemic injustice is working to cultivate epistemic habits that aim to consistently neutralize the effects of such prejudices on their credibility estimates. But Fricker does not claim that her specific proposals constitute the only means through which individuals and institutions should combat (...) epistemic injustice. I therefore build on Fricker’s account by beginning to sketch a fuller picture of the structure of cultivating epistemic virtue. Virtue cultivation must, I argue, occur on two broad but interrelated fronts: first, the direct retraining of more automatic and unreflective patterns of thinking, feeling, and reacting to epistemic social reality, and second, the cultivation of more reflective, metacognitive virtues, such as the ability to swiftly identify contexts in which our first-order epistemic intuitions are likely astray. Although I articulate a range of individual-level obligations, my account is not individualistic. With Fricker, I argue that individual self-transformation is a necessary but not sufficient component of the struggle for epistemic justice. Accordingly, I sketch several ways in which individual virtue cultivation must be a socially and institutionally embedded process. Moreover, I argue that this process is ongoing. While most individuals cannot actually achieve such moral-epistemic ideals, many can (and therefore should try to) get much closer than they already are. (shrink)

Epistemologists typically assume that the acquisition of knowledge from testimony is not threatened at the stage at which audiences interpret what proposition a speaker has asserted. Attention is instead typically paid to the epistemic status of a belief formed on the basis of testimony that it is assumed has the same content as the speaker’s assertion. Andrew Peet has pioneered an account of how linguistic context sensitivity can threaten the assumption. His account locates the threat in contexts in which an (...) audience’s evidence under-determines which proposition a speaker is asserting. I argue that Peet’s epistemic uncertainty account of the threat is mistaken and I propose an alternative. The alternative locates the threat in contexts that provide factors that give audiences a mistaken psychological certainty or confidence that a speaker has asserted a proposition she has not. (shrink)

Millar has written a valuable monograph on perceptual knowledge. Knowing By Perceiving is careful and detailed, at times laborious, delivering many insights. Oc.

The terminology surrounding the dispute between higher-order and first-order theories of consciousness is piled so high that it sometimes obscures the view. When the debris is cleared away, there is a real prospect.

Does immorality necessarily involve irrationality? The question is often taken to be among the deepest in moral philosophy. But apparently deep questions sometimes admit of deflationary answers. In this case we can make way for a deflationary answer by appealing to dualism about rationality, according to which there are two fundamentally distinct notions of rationality: structural rationality and substantive rationality. I have defended dualism elsewhere. Here, I’ll argue that it allows us to embrace a sensible – I will not say (...) boring – moderate view about the relationship between immorality and irrationality: roughly, that immorality involves substantive irrationality, but not structural irrationality. I defend this moderate view, and argue that many of the arguments for less moderate views turn either on missing the distinction between substantive and structural rationality, or on misconstruing it. (shrink)

Research suggests that interventions involving extensive training or counterconditioning can reduce implicit prejudice and stereotyping, and even susceptibility to stereotype threat. This research is widely cited as providing an “existence proof” that certain entrenched social attitudes are capable of change, but is summarily dismissed—by philosophers, psychologists, and activists alike—as lacking direct, practical import for the broader struggle against prejudice, discrimination, and inequality. Criticisms of these “debiasing” procedures fall into three categories: concerns about empirical efficacy, about practical feasibility, and about the (...) failure to appreciate the underlying structural-institutional nature of discrimination. I reply to these criticisms of debiasing, and argue that a comprehensive strategy for combating prejudice and discrimination should include a central role for training our biases away. (shrink)

You know what someone else is thinking and feeling by observing them. But how do you know what you are thinking and feeling? This is the problem of self-knowledge: Alex Byrne tries to solve it. The idea is that you know this not by taking a special kind of look at your own mind, but by an inference from a premise about your environment.

This comment mainly examines Yli-Vakkuri and Hawthorne’s preferred framework for examining whether narrow content is viable, arguing that their framework is not well-suited to the task; once a more traditional framework is adopted, Y&H’s case against internalism is strengthened.

Can we trust our intuitive judgments of right and wrong? Are moral judgements objective? What reason do we have to do what is right and avoid doing what is wrong? In Conversations on Ethics, Alex Voorhoeve elicits answers to these questions from eleven outstanding philosophers and social scientists: -/- Ken Binmore; Philippa Foot; Harry Frankfurt; Allan Gibbard; Daniel Kahneman; Frances Kamm; Alasdair MacIntyre; T. M. Scanlon; Peter Singer; David Velleman; Bernard Williams. -/- The exchanges are direct, open, and sharp, (...) and give a clear account of these thinkers' core ideas about ethics. They also provide unique insights into their intellectual development - how they became interested in ethics, and how they conceived the ideas for which they became famous. Conversations on Ethics will engage anyone interested in moral philosophy. (shrink)

This article presents a semantic analysis of indirect speech reports. The analysis aims to explain a combination of two phenomena. First, there are true utterances of sentences of the form α said that φ which are used to report an utterance u of a sentence wherein φ's content is not u's content. This implies that in uttering a single sentence, one can say several things. Second, when the complements of these reports (and indeed, these reports themselves) are placed in conjunctions, (...) the conjunctions are typically infelicitous. I argue that this combination of phenomena can be explained if speech reports report (perhaps contingent) parts of the contents of the sentences reported. (shrink)

In what circumstances is it legitimate to use force? How should force be used? These are two of the most crucial questions confronting world politics today. The Just War tradition provides a set of criteria which political leaders and soldiers use to defend and rationalize war. This book explores the evolution of thinking about just wars and examines its role in shaping contemporary judgements about the use of force, from grand strategic issues of whether states have a right to pre-emptive (...) self-defence, to the minutiae of targeting. Bellamy maps the evolution of the Just War tradition, demonstrating how it arose from a myriad of sub-traditions, including scholasticism, the holy war tradition, chivalry, natural law, positive law, Erasmus and Kant's reformism, and realism from Machiavelli to Morgenthau. He then applies this tradition to a range of contemporary normative dilemmas related to terrorism, pre-emption, aerial bombardment and humanitarian intervention. (shrink)

What must linguistic knowledge be like if it is to explain our capacity to use language? All linguists and philosophers of language presuppose some answer to this critical question, but all too often the presupposition is tacit. In this collection of sixteen previously unpublished essays, a distinguished international line-up of philosophers and linguists address a variety of interconnected themes concerning our knowledge of language.

Treatment of sexual minority youth presents psychologists with a number of challenging ethical considerations. The APA Ethics Code is a valuable resource for addressing these issues, but psychologists require additional guidance in order to provide ethical treatment. This article provides relevant background, an overview of the ethical considerations of treating sexual minority youth, and recommendations to improve upon the current state of awareness and available resources. Psychologists must continually strive to improve our understanding of ethical decisions around treatment, training, and (...) research that will serve to address this vulnerable population's unmet mental health needs. (shrink)

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)

Theories and Narratives will interest all readers for whom the role of history in the understanding of contemporary civilizations is an essential issue.

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be that Theon is (...) destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

Three arguments for the thesis that sex is socially constructed are examined and rejected. No such argument could succeed, because sex is not socially constructed.

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)