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.

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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)

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).

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.

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)

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)

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)

Are women (simply) adult human females? Dictionaries suggest that they are. However, philosophers who have explicitly considered the question invariably answer no. This paper argues that they are wrong. The orthodox view is that the category *woman* is a social category, like the categories *widow* and *police officer*, although exactly what this social category consists in is a matter of considerable disagreement. In any event, orthodoxy has it that *woman* is definitely not a biological category, like the categories *amphibian* or (...) *adult human female*. -/- In the first part, a number of arguments are given for the view that women are adult human females; the second part turns to rebutting the main objections. Finally, a couple of morals are briefly noted: one for activist sloganeering, and one for ameliorative projects that seek to change the meaning of ‘woman’. (shrink)

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)

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)

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)

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.

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.

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.

The evolution of the equation of mass conservation in fluid mechanics is studied. Following early hydraulic approximations, and progress by Daniel and Johann Bernoulli, its first expression as a partial differential equation was achieved by d’Alembert, and soon given definitive form by Euler. Later reworkings by Lagrange, Laplace, Poisson and others advanced the subject, but all based their derivations on the conserved mass of a moving fluid particle. Later, Duhamel and Thomson gave a simpler derivation, by considering mass flow into (...) and out of a fixed portion of space. The later propagation of these derivations in nineteenth-century British textbooks and treatises is also examined, including Maxwell’s on the kinetic theory of gases. (shrink)

Most contemporary philosophical discussions of intentionality start and end with a treatment of the propositional attitudes. In fact, many theorists hold that all attitudes are propositional attitudes. Our folk-psychological ascriptions suggest, however, that there are non-propositional attitudes: I like Sally, my brother fears snakes, everyone loves my grandmother, and Rush Limbaugh hates Obama. I argue that things are as they appear: there are non-propositional attitudes. More specifically, I argue that there are attitudes that relate individuals to non-propositional objects and do (...) so not in virtue of relating them to propositions. I reach this conclusion by not only showing that attempted analyses of apparently non-propositional attitudes in terms of the propositional fail, but that some non-propositional attitudes don’t even supervene on propositional attitudes. If this is correct, then the common discussions of intentionality that address only propositional attitudes are incomplete and those who hold that all intentional states are propositional are mistaken. (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)

The 'content view', in slogan form, is 'Perceptual experiences have representational content'. I explain why the content view should be reformulated to remove any reference to 'experiences'. I then argue, against Bill Brewer, Charles Travis and others, that the content view is true. One corollary of the discussion is that the content of perception is relatively thin (confined, in the visual case, to roughly the output of 'mid-level' vision). Finally, I argue (briefly) that the opponents of the content view are (...) partially vindicated, because perceptual error is due to false belief. (shrink)

Using a combination of semantic theory and findings from conversation analysis, this paper describes a way in which questions, which incorporate presuppositions that are false, when used in a courtroom cross-examination wherein there are certain turn-taking rules, rights and restrictions, stop a rape victim from expressing the content that she wants to express in that context. This kind of silencing contrasts with other kinds of silencing that consist in the disabling of a speech act's force, rather than precluding the expression (...) of certain contents. -/- Content Note: there are explicit descriptions of sexual violence in this paper. (shrink)

Should we understand implicit attitudes on the model of belief? I argue that implicit attitudes are (probably) members of a different psychological kind altogether, because they seem to be insensitive to the logical form of an agent’s thoughts and perceptions. A state is sensitive to logical form only if it is sensitive to the logical constituents of the content of other states (e.g., operators like negation and conditional). I explain sensitivity to logical form and argue that it is a necessary (...) condition for belief. I appeal to two areas of research that seem to show that implicit attitudes fail spectacularly to satisfy this condition—although persistent gaps in the empirical literature leave matters inconclusive. I sketch an alternative account, according to which implicit attitudes are sensitive merely to spatiotemporal relations in thought and perception, i.e., the spatial and temporal orders in which people think, see, or hear things. (shrink)

This book investigates context-sensitivity in natural language by examining the meaning and use of a target class of theoretically recalcitrant expressions. These expressions-including epistemic vocabulary, normative and evaluative vocabulary, and vague language -exhibit systematic differences from paradigm context-sensitive expressions in their discourse dynamics and embedding properties. Many researchers have responded by rethinking the nature of linguistic meaning and communication. Drawing on general insights about the role of context in interpretation and collaborative action, Silk develops an improved contextualist theory of CR-expressions (...) within the classical truth-conditional paradigm: Discourse Contextualism. The aim of Discourse Contextualism is to derive the distinctive linguistic behavior of a CR-expression from a particular contextualist interpretation of an independently motivated formal semantics, along with general principles of interpretation and conversation. It is shown how in using CR-expressions, speakers can exploit their mutual grammatical and world knowledge, and general pragmatic reasoning skills, to coordinate their attitudes and negotiate about how the context should evolve. The book focuses primarily on developing a Discourse Contextualist semantics and pragmatics for epistemic modals. The Discourse Contextualist framework is also applied to other categories of epistemic vocabulary, normative and evaluative vocabulary, and vague adjectives. The similarities/differences among these expressions, and among context-sensitive expressions more generally, have been underexplored. The development of Discourse Contextualism in this book sheds light on general features of meaning and communication, and the variety of ways in which context affects and is affected by uses of language. Discourse Contextualism provides a fruitful framework for theorizing about various broader issues in philosophy, linguistics, and cognitive science. (shrink)

Would suppressing deepfakes violate freedom of expression norms? The question is pressing because the deepfake phenomenon in its more poisonous manifestations appears to call for a response, and automated targeting of some kind looks to be the most practically viable. Two simple answers are rejected: that deepfakes do not deserve protection under freedom of expression legislation because they are fake by definition; and that deepfakes can be targeted if but only if they are misleadingly presented as authentic. To make progress, (...) following a discussion of why freedom of expression deserves protection in a democracy, the question is reframed. At issue is not whether the arrival of deepfakes brings new and potentially serious dangers (it does), nor whether these dangers call for measures that potentially limit freedom of expression (they do), but whether the need for such measures raises any new and unfamiliar freedom-of-expression challenges. The answer to that question, surprisingly, is no. The balancing act needed to cope with the arrival of deepfakes brings plenty of difficulties, certainly, but none of the measures likely to be effective in tackling deepfake harms raises freedom-of-expression concerns that aren’t familiar from consideration of non-deepfake harms. In that respect, at least, the arrival of deepfakes makes no difference. (shrink)

A linguistic theory is correct exactly to the extent that it is the explicit statement of a body of knowledge possessed by a designated language-user. This popular psychological conception of the goal of linguistic theorizing is commonly paired with a preference for idiolectal over social languages, where it seems to be in the nature of idiolects that the beliefs one holds about one’s own are ipso facto correct. Unfortunately, it is also plausible that the correctness of a genuine belief cannot (...) consist merely in that belief’s being held. This paper considers how best to eliminate this tension. (shrink)

How do cognition and affect interact to produce action? Research in intergroup psychology illuminates this question by investigating the relationship between stereotypes and prejudices about social groups. Yet it is now clear that many social attitudes are implicit. This raises the question: how does the distinction between cognition and affect apply to implicit mental states? An influential view—roughly analogous to a Humean theory of action—is that “implicit stereotypes” and “implicit prejudices” constitute two separate constructs, reflecting different mental processes and neural (...) systems. On this basis, some have also argued that interventions to reduce discrimination should combat implicit stereotypes and prejudices separately. We propose an alternative framework. We argue that all putative implicit stereotypes are affect-laden and all putative implicit prejudices are “semantic,” that is, they stand in co-activating associations with concepts and beliefs. Implicit biases, therefore, consist in “clusters” of semantic-affective associations, which differ in degree, rather than kind. This framework captures the psychological structure of implicit bias, promises to improve the power of indirect measures to predict behavior, and points toward the design of more effective interventions to combat discrimination. (shrink)

Infallibilism is commonly rejected because it is apparently subject to easy counter-examples. I describe a strategy that infallibilists can use to resist this objection. Because the sentences used in the counter-examples to express evidence and belief are context-sensitive, the infallibilist can insist that such counter-examples trade on a vacillation between different readings of these sentences. I describe what difficulties await those who try to produce counter-examples against which the proposed strategy is ineffective.

Much of our ordinary thought and talk about responsibility exhibits what I call the ‘pie fallacy’—the fallacy of thinking that there is a fixed amount of responsibility for every outcome, to be distributed among all those, if any, who are responsible for it. The pie fallacy is a fallacy, I argue, because how responsible an agent is for some outcome is fully grounded in facts about the agent, the outcome and the relationships between them; it does not depend, in particular, (...) on how responsible anyone else is for that same outcome. In this paper, I explore how the pie fallacy can arise by considering several different kinds of case in which two or more agents are responsible for the same outcome. I’ll end with some brief remarks on the potential consequences of my arguments for how to think about responsibility in war. (shrink)