What responsibilities do audiences have in engaging with artworks? Certain audience responses seem quite clear: for example, audiences should not vandalize or destroy artworks; they should not disrupt performances. This paper examines other kinds of resisting responses that audiences sometimes engage in, including petitioning the artist to change their works, altering copies of artworks, and creating new artworks in another artist’s fictional world. I argue for five claims: (1) while these actions can sometimes infringe on the rights of artists, the (...) rights of artists are not absolute; (2) the fact that such actions are based on mistaken interpretations of the artworks has no normative weight; (3) there can be reason to object to additions and alterations whose conception of the artwork is morally worse than the original (and so, there can be reason to support additions and alterations whose conception is morally better); (4) petitioning raises special moral problems; and, most important, (5) some of these actions are valuable because they involve creative and aesthetic activity. Those acts of audience resistance that are creative, morally improve on the original work, and that minimize the infringement of the artists’ rights are good, and should be encouraged. (shrink)

Aesthetic internalism claims a link between judgement and motivation: aesthetic judgements bring with them motivations to act in characteristic ways. Critics object that there is a difference between merely liking something and judging it to be aesthetically good, and that it is our likings, not our aesthetic judgements, that motivate us. This paper develops a version of aesthetic internalism that can respond to this criticism. Wholehearted aesthetic judgements are characterized by stability, attention, and motivation. Making such judgements is an important (...) part of a good life, and so at least some aesthetic judgements are motivating. So we have reason to think that this version of aesthetic internalism is true. This paper defends wholehearted aesthetic internalism against objections, and assesses an argument from aesthetic internalism to aesthetic non-cognitivism. While wholehearted aesthetic internalism can only offer qualified support to non-cognitivism, it nonetheless offers a number of fruitful avenues for further work. (shrink)

This paper has three aims: to define autonomism clearly and charitably, to offer a positive argument in its favour, and to defend a larger view about what is at stake in the debate between autonomism and its critics. Autonomism is here understood as the claim that a valuer does not make an error in failing to bring her moral and aesthetic judgements together, unless she herself values doing so. The paper goes on to argue that reason does not require the (...) valuer to make coherent her aesthetic and moral evaluations. Finally, the paper shows that the denial of autonomism has realist commitments that autonomism does not have, and concludes that issues of value realism and irrealism are relevant to the debates about autonomism in ways that have not hitherto been recognized. (shrink)

© British Society of Aesthetics 2018. Published by Oxford University Press on behalf of the British Society of Aesthetics. All rights reserved. For Permissions, please email: [email protected] adaptation of literary works into films has been almost completely neglected as a philosophical topic. I discuss two questions about this phenomenon:What do we mean when we say that a film is faithful to its source?Is being faithful to its source a merit in a film adaptation?In response to, I set out two distinct (...) senses of fidelity: story fidelity and thematic fidelity. I then argue, in response to, that thematic fidelity, but not story fidelity, is an aesthetic merit in a film adaptation. The key steps in this argument involve showing that merely preserving the story from one medium to another does not typically involve an aesthetically... (shrink)

Immoralists hold that in at least some cases, moral fl aws in artworks can increase their aesthetic value. They deny what I call the valence constraint: the view that any effect that an artwork’s moral value has on its aesthetic merit must have the same valence. The immoralist offers three arguments against the valence constraint. In this paper I argue that these arguments fail, and that this failure reveals something deep and interesting about the relationship between cognitive and moral value. (...) In the fi nal section I offer a positive argument for the valence constraint. (shrink)

One important but infrequently discussed difficulty with expressivism is the attitude type individuation problem.1 Expressivist theories purport to provide a unified account of normative states. Judgments of moral goodness, beauty, humor, prudence, and the like, are all explicated in the same way: as expressions of attitudes, what Allan Gibbard calls “states of norm-acceptance”. However, expressivism also needs to explain the difference between these different sorts of attitude. It is possible to judge that a thing is both aesthetically good and morally (...) bad. While the realist can explain the difference by suggesting that each judgment makes reference to a different property (or set of properties), the expressivist cannot. She must show that what is expressed by the speaker is different in each case. This has proven to be difficult to do. (shrink)

In recent years it has become more and more difficult to distinguish between metaethical cognitivism and non-cognitivism. For example, proponents of the minimalist theory of truth hold that moral claims need not express beliefs in order to be (minimally) truth-apt, and yet some of these proponents still reject the traditional cognitivist analysis of moral language and thought. Thus, the dispute in metaethics between cognitivists and non-cognitivists has come to be seen as a dispute over the correct way to characterize our (...) psychology: are moral judgments beliefs, or a kind of pro-attitude? In this paper, I argue that this distinction, too, is difficult to maintain in the light of a reasonable skepticism about folk psychology. I conclude by suggesting some new possibilities for the analysis of moral language that look beyond this distinction. I begin by briefly reviewing some contemporary positions in metaethics on cognitivism and non-cognitivism, that are intended to emphasize the supposed psychological differences between the two views. I show that the appearance of a clear difference between these views depends on one's having a very strong commitment to the context-independence and completeness of certain concepts of folk psychology. I then argue for a moderate skepticism about folk psychology. I conclude that folk concepts like ?belief? are not sufficiently well-defined to settle this metaethical dispute. (shrink)

Ancient Chinese and Greek thinkers alike were preoccupied with the moral value of music; they distinguished between good and bad music by looking at the music’s effect on moral character. The idea can be understood in terms of two closely related questions. Does music have the power to affect the ethical character of either listener or performer? If it does, is it better as music for doing so? I argue that an affirmative answers to both questions are more plausible than (...) it might seem at first. (shrink)

The topic of this essay is how non-realistic novels challenge our philosophical understanding of the moral significance of literature. I consider just one case: Joseph Heller’s Catch-22. I argue that standard philosophical views, based as they are on realistic models of literature, fail to capture the moral significance of this work. I show that Catch-22 succeeds morally because of the ways it resists using standard realistic techniques, and suggest that philosophical discussion of ethics and literature must be pluralistic if it (...) is to include all morally salient literature, and not just novels in the “Great Tradition” and their ilk. (shrink)

I explore the claim that “fictive imagining” – imagining what it is like to be a character – can be morally dangerous. In particular, I consider the controversy over William Styron’s imagining the revolutionary protagonist in his Confessions of Nat Turner. I employ Ted Cohen’s model of fictive imagining to argue, following a generally Kantian line of thought, that fictive imagining can be dangerous if one has the wrong motives. After considering several possible motives, I argue that only internally directed (...) motives can satisfy the moral concern. Finally, I suggest that when one has the right motives, fictive imagining is morally praiseworthy since it improves one’s ability to imagine the lives of others. (shrink)

In this essay I argue that if Kantian and consequentialist ethical theories are vulnerable to the so-called “problem of alienation,” a virtue ethics based on Xunzi’s ethical writings will also be vulnerable to this problem. I outline the problem of alienation, and then show that the role of ritual ( li ) in Xunzi’s theory renders his view susceptible to the problem as it has been traditionally understood. I consider some replies on Xunzi’s behalf, and also discuss whether the problem (...) affects other Confucian and eudaimonian approaches to virtue ethics. I close by considering some solutions to the problem and the affect that this result has on the argumentative dialectic between the three major ethical traditions. (shrink)

Some films scare us; some make us cry; some thrill us. Some of the most interesting films, however, leave us suspended between feelings – both joyous and sad, or angry and serene. This paper attempts to explain how this can happen and why it is important. I look closely at one film that creates and exploits these conflicted responses. I argue that cases of conflict in film illuminate a pair of vexing questions about emotion in film: (1) To what extent (...) are emotional responses rational, or in need of rationalization?; and (2) What relationship is there between emotional response and value (moral, filmic, or otherwise)? Conflict, I argue, can be revealing, and can help us better understand emotional responses to narrative film1 in general. The paper is divided into four sections. First, I sketch a theory of emotional engagement that makes sense of the notion of a “conflicted emotional response” to a film. Second, I turn to a particular case of a film that produces this sort of conflict, Fritz Lang’s M (1931), and show that the conflict engendered by that film is both more significant and less unusual than it may appear. In the final two sections, I argue that there is no need to rationalize or make consistent such mixed emotional responses, and that there is real moral, aesthetic, and cognitive value to be had from such conflict. (shrink)

Two recent novels, Ian McEwan’s Atonement and Margaret Atwood’s The Blind Assassin, are philosophically instructive. These books are interesting, I argue, because they reveal something about understanding and appreciating narrative. They show us that audience’s participation in narrative is much more subtle and complex than philosophers generally acknowledge. An analysis of these books reveals that narrative imagining is not static or unified, but dynamic and multipolar. I argue that once the complexity of narrative engagement is better understood, some prominent philosophical (...) problems and debates concerning narrative dissolve. (shrink)

Psychopaths are the bugbears of moral philosophy. They are often used as examples of perfectly rational people who are nonetheless willing to do great moral wrong without regret; hence the disorder has received the epithet “moral insanity” (Pritchard 1835). But whereas philosophers have had a great deal to say about psychopaths’ glaring and often horrifying lack of moral conscience, their aesthetic capacities have received hardly any attention, and are generally assumed to be intact or even enhanced. Popular culture often portrays (...) psychopaths in ways that suggest a great gap between their amorality and their aesthetic sensitivity. In The Silence of the Lambs (Jonathan Demme, 1991), Hannibal Lecter appreciates fine art, fashion, and wine, while he eats his way through his enemies. His real-life counterparts, however, do not demonstrate the same sensitivities. There is no evidence that psychopaths are capable of real aesthetic appreciation, and some evidence that they are not. In this paper, we set out the limited evidence for the psychopath’s deficient aesthetic sensitivity. The best explanations of what the psychopath lacks turn out to implicate abilities that are also thought to be central to moral thought and action: an impaired capacity for empathizing with others and deficient ability to take a disinterested attitude towards things (socalled distance). We endorse the latter explanation. Thinking about what underlies the psychopath’s deficient aesthetic understanding turns out to throw light on a difficult problem: the connection between ethics and aesthetics. (shrink)

The hermeneutic pragmatism explored in this article timely examines how “post-truth” claims over-estimate semantic freedoms while at the same time underestimating semantic and pre-semantic restraints. Such pragmatism also timely examines how formalists err by committing the reverse errors. Drawing on insights from James, Peirce, Putnam, Rorty, Gadamer, Derrida, and others, such hermeneutic pragmatism explores (1) the necessary role of both internal and objective experience in meaning, (2) the resulting instrumental nature of concepts required to deal with such experience, (3) (...) the related need for workability to apply to the “the collectivity of experience’s demands, nothing being omitted,” (4) the inherent role of morality and other norms in measuring such workability, (5) the semantic as well as experiential nature of our workable realities, (6) the semantic freedoms involved in constructing, framing, and retaining our workable realities and concepts, and (7) the semantic, pre-semantic, and other restraints on constructing, framing, and retaining our workable realities and concepts. -/- Such hermeneutic pragmatism also introduces Eunomia, a real-world alternative to Dworkin’s superhuman judge Hercules. Named after the Greek goddess of good order, the human Eunomia represents the reasonable judge excellently versed in (among other things) legal theory, legal practice, linguistics, and philosophy of language. Additionally, in its appendices, this article surveys the pragmatic restraints of “implementives” and provides a detailed overview of pragmatic “workability” restraints for both law and fact. -/- (By “sense” the title of this article means not only “meaning conveyed or intended” but also “capacity for effective application of the powers of the mind as a basis for action or response.” See Sense, MERRIAM-WEBSTER’S COLLEGIATE DICTIONARY (11th ed. 2014) “Workable” has the broad meaning discussed in Sections II, IV, and Appendix C of the Article, and "good" is further explored in the section on Eunomia, namesake of the Greek goddess of good order.) -/- Keywords: Pragmatism, Hermeneutic, Truth, Rule of Law, William James, C.S. Peirce, Hilary Putnam, Richard Rorty, Gadamer, Habermas, Derrida, Lon Fuller, H.L.A. Hart, Post-truth, Postmodernism, Trump, Rhetoric, Meaning, Interpretation, Metaphor, Category, Lifeworld, Formalism, Framing, Deconstruction. (shrink)

This chapter presents the formalist account of the moral status of an artwork as an aesthetically significant and autonomous form, with due emphasis on the Anglo-American art-for-art’s-sake aesthetic, as it developed between 1870 and 1960. The author shows that the formalist art-is-above-morals approach is a substantive moral stance in itself. Formalist aesthetics is usually presented in the literature as evincing a purist indifference to ethics, construing moral properties as external to art, in opposition to the internal pure properties of art’s (...) composition. The chapter demonstrates that this is a misrepresentation of the complex formalist prescriptive idea of the relations between art and ethics. Through its autonomy and imperviousness to external co-opting—which is accomplished by due focus on aesthetic form—art on the formalist account is held to be a paradigm of the liberalist principles of individual freedom and self-fulfillment, thus an inherent means to the good. (shrink)

This essay develops standards for grading religions including various forms of spiritualism. First, I examine the standards proposed by William James, John Hick, Paul Knitter, Dan Cohn-Sherbok, and Harold Netland. Most of them are useful in grading religions with or without conditions. However, those standards are not enough for refined and piercing evaluation. Thus, I introduce standards used in spiritualism. Although those standards are for grading spirits and their teachings, they are useful in refined and piercing evaluation of (...) religious phenomena. The spiritual standards complement James's, Hick's, Knitter's, and Netland's standards. Although most of the spiritual standards are rationally unjustifiable, they have practical value. (shrink)

Experiments are presented showing that visual search for Mueller-Lyer (ML) stimuli is based on complete configurations, rather than component segments. Segments easily detected in isolation were difficult to detect when embedded in a configuration, indicating preemption by low-level groups. This preemption—which caused stimulus components to become inaccessible to rapid search—was an all-or-nothing effect, and so could serve as a powerful test of grouping. It is shown that these effects are unlikely to be due to blurring by simple spatial filters at (...) early visual levels. It is proposed instead that they are due to more sophisticated processes that rapidly bind contour fragments into spatially-extended assemblies. These results support the view that rapid visual search cannot access the primitives formed at the earliest stages of visual processing; rather, it can access only higher-level, more ecologically-relevant structures. (shrink)

We offer philosophical motivations for a method we call Virtual World Cognitive Science (VW CogSci), in which researchers use virtual embodied agents that are embedded in virtual worlds to explore questions in the field of Cognitive Science. We focus on questions about mental and linguistic representation and the ways that such computational modeling can add rigor to philosophical thought experiments, as well as the terminology used in the scientific study of such representations. We find that this method forces researchers to (...) take a god’s-eye view when describing dynamical relationships between entities in minds and entities in an environment in a way that eliminates the need for problematic talk of belief and concept types, such as the belief that cats are silly, and the concept CAT, while preserving belief and concept tokens in individual cognizers’ minds. We conclude with some further key advantages of VW CogSci for the scientific study of mental and linguistic representation and for Cognitive Science more broadly. (shrink)

Within-category induction is the projection of a generic property from a class to a subtype of that class. The modifier effect refers to the discovery reported by Connolly et al., that the subtype statement tends to be judged less likely to be true than the original unmodified sentence. The effect was replicated and shown to be moderated by the typicality of the modifier. Likelihood judgements were also found to correlate between modified and unmodified versions of sentences. Experiment 2 elicited justifications, (...) which suggested three types of reason for the effect-pragmatics, knowledge-based reasoning, and uncertainty about attribute inheritance. It is argued that the results provide clear evidence for the default inheritance of prototypical attributes in modified concepts, although a full account of the effect remains to be given. (shrink)

In this thesis, I will defend a new kind of compatibilist account of free action, indirect conscious control compatibilism (or indirect compatibilism for short), and argue that some of our actions are free according to it. My argument has three components, and involves the development of a brand new tool for experimental philosophy, and the use of cognitive neuroscience. The first component of the argument shows that compatibilism (of some kind) is a conceptual truth. Contrary to the current orthodoxy in (...) the free will literature, which is that our concept of free will is an incompatibilist concept - a concept according to which we have free will only if determinism is false - I will show that our concept of free will is in fact a compatibilist concept - a concept according to which we can have free will even if determinism is true - and I do so using a new experimental philosophy methodology inspired by two-dimensional semantics. -/- Of course, even if our concept of free will is a compatibilist concept, this does not mean that there are any free actions in the world: the current empirical evidence from the brain sciences appears to show that there might be no, or very few, free actions in the world, even on many compatibilist understandings of what it would take for there to be free will. The second component of the argument addresses this concern by extending our understanding of compatibilism. Agents act freely either when their actions are caused by compatibilistically acceptable psychological processes, or are indirectly caused by those same processes. Hence the name of my account: indirect compatibilism. -/- The final component of the argument defends my new account against some interesting objections and provides evidence from cognitive neuroscience that some of our actions count as free by the lights of indirect compatibilism. (shrink)

The Protein Ontology (PRO) provides a formal, logically-based classification of specific protein classes including structured representations of protein isoforms, variants and modified forms. Initially focused on proteins found in human, mouse and Escherichia coli, PRO now includes representations of protein complexes. The PRO Consortium works in concert with the developers of other biomedical ontologies and protein knowledge bases to provide the ability to formally organize and integrate representations of precise protein forms so as to enhance accessibility to results of protein (...) research. PRO (http://pir.georgetown.edu/pro) is part of the Open Biomedical Ontologies (OBO) Foundry. (shrink)

Within contemporary philosophy of mind, it is taken for granted that externalist accounts of meaning and mental content are, in principle, orthogonal to the matter of whether cognition itself is bound within the biological brain or whether it can constitutively include parts of the world. Accordingly, Clark and Chalmers (1998) distinguish these varieties of externalism as ‘passive’ and ‘active’ respectively. The aim here is to suggest that we should resist the received way of thinking about these dividing lines. With reference (...) to Brandom’s (1994; 2000; 2008) broad semantic inferentialism, we show that a theory of meaning can be at the same time a variety of active externalism. While we grant that supporters of other varieties of content externalism (e.g., Putnam 1975 and Burge 1986) can deny active externalism, this is not an option for semantic inferentialists: On this latter view, the role of the environment (both in its social and natural form) is not ‘passive’ in the sense assumed by the alternative approaches to content externalism. (shrink)

Central to Sellars’ account of human cognition was a clear distinction, expressed in varying terminology in his different works, “between conceptual and nonconceptual representations.” Those who have come to be known as ‘left-wing Sellarsians’, such as Richard Rorty, Robert Brandom, and John McDowell, have tended to reject Sellars’ appeals to nonconceptual sensory representations. So-called ‘right-wing Sellarsians’ such as Ruth Millikan and Jay Rosenberg, on the other hand, have embraced and developed aspects of Sellars’ account, in particular the central underlying idea (...) that human perceptual cognition involves a certain naturalistic ‘mapping’ correspondence or structural ‘picturing’ isomorphism between internal mental representations and the layout and behavior of objects in the surrounding environment. Sellars, despite his defenses of nonconceptual representational content throughout his career, has with no small irony come to be cited as one of the “founding fathers of conceptualism.” While recognizing the strong conceptualist elements in Sellars’ Kantian account of perceptual cognition, I argue that a central core of Sellars’ account of nonconceptual sensory contents does not by itself fall afoul of the philosophical worries raised by the left-leaning Sellarsians, and that in fact it has significant merits in its own right. (shrink)

I argue that Zhuangist Daoism manifests what I label the spiritual aspiration to emulation, and then use this to challenge some of John Cottingham's attempts to confine authentic spiritual experience to theistic traditions.

This article tackles the sole surviving ancient commentary on what was perhaps the second most important Platonic work, with special interest for the manner in which the ancients tackled the setting of Plato's dialogues, Socratic ignorance, Socratic eros, the central myth-like Palinode, and the question of oral as against written teaching.

This essay is my review of Philip Booth’s ...and the Pursuit of Happiness: Wellbeing and the Role of Government. The book is an anthology of original articles by eminent researchers in modern happiness economics, such as: Booth himself; Paul Omerod; David Sacks, Betsey Stephenson, and Justin Wolfers; Christopher Snowden; J. R. Shackleton; Christian Bjornskov; Peter Boettke and Christopher Coyne; and Pedro Schwartz. I conclude by offering several criticisms of the work.

[A Polish translation of Steven James Bartlett, “Phenomenology of the Implicit,” Dialectica: Revue international de philosophie de la connaissance, Vol. 29, Nos. 2-3, 1975, pp. 173-188.] -/- This paper marks a juncture between the author’s studies in phenomenology and the transition he made to a study of what he has called a “metalogic of reference.” Published in 1974 in Polish translation, followed by its publication in English in 1975, “Phenomenology of the Implicit” describes the author’s “translation schema” that permits (...) certain of the central goals of Husserlian transcendental philosophy to be transposed to a framework that studies the preconditions of valid reference. The result of this translation was the development of the author’s “de-projective” approach to phenomenology, which he later dissociated from phenomenology in the form of a pure metalogic of reference. (shrink)

In this essay, I look at two films as possible exemplars of the Nietzschean view of egoism. Compulsion is based on the infamous 1924 Leopold and Loeb murder case. In the movie, two arrogant young men—one of whom admires Nietzsche and preaches the (apparently Nietzschean) view that the strong and superior don’t need to follow conventional morality—kill a boy to prove they can outsmart the unter-menschen police. For a different take on what Nietzsche may have had in mind as “the (...) Overman,” I also look at the film The Moon and Sixpence. Here the protagonist isn’t violent or aggressive, but a completely self-absorbed artist, who paints with genius but uses others without feeling any gratitude or friendship, let alone love. (shrink)

Respect for victims requires that we have social systems for punishing and condemning (reproving) serious crimes. But, the conditions of social marginalization and political subordination of the communities from which an overwhelming number of prisoners in the United States come place serious barriers in the face of effective reprobation. Mass incarceration makes this problem worse by disrupting and disrespecting entire communities. While humanities education in the prisons is far from a total solution, it is one way to make reprobation meaningful, (...) so long as the prison classroom is a place where the educators’ values are also put at risk. (shrink)

In this essay, I use four war movies to explore conflicts of loyalty and how they are resolved, all to illustrate W.D. Ross’ multiple rule deontologism. The films are all fine WWII movies: The Enemy Below; Decision Before Dawn; John Rabe; and The Bridge on the River Kwai. In my analysis of each, I show how the protagonists face conflicts of their loyalty to themselves, their countrymen, their friends, and humanity in general, and resolve them in the face of changing (...) factual backgrounds. (shrink)

In this essay, I take up the question of why so many of the movies made by Hollywood are endless sequels, “prequels,” and remakes of prior blockbuster hits and so many are based on comic books (X-men, Superman, Batman, and so on). I tie the explanation in part to the aforementioned 1950 Supreme Court ruling prohibiting production companies, and in part to broader cultural changes. In particular, I argue that precisely because film producers can no longer make money from the (...) concessions (i.e., the purchases within the theater), but only of the ticket sales, the producers keep producing remakes of known popular movies, rather than make deeply original movies. (shrink)

In this volume, leading philosophers of psychiatry examine psychiatric classification systems, including the Diagnostic and Statistical Manual of Mental Disorders, asking whether current systems are sufficient for effective diagnosis, treatment, and research. Doing so, they take up the question of whether mental disorders are natural kinds, grounded in something in the outside world. Psychiatric categories based on natural kinds should group phenomena in such a way that they are subject to the same type of causal explanations and respond similarly to (...) the same type of causal interventions. When these categories do not evince such groupings, there is reason to revise existing classifications. The contributors all question current psychiatric classifications systems and the assumptions on which they are based. They differ, however, as to why and to what extent the categories are inadequate and how to address the problem. Topics discussed include taxometric methods for identifying natural kinds, the error and bias inherent in DSM categories, and the complexities involved in classifying such specific mental disorders as "oppositional defiance disorder" and pathological gambling. -/- Contributors George Graham, Nick Haslam, Allan Horwitz, Harold Kincaid, Dominic Murphy, Jeffrey Poland, Nancy Nyquist Potter, Don Ross, Dan Stein, Jacqueline Sullivan, Serife Tekin, Peter Zachar. (shrink)

This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...) the model-theoretic concepts, based on those in [7], that guide the rest of this paper. Section 3 presents Natural Deduction systems IK and CK, formalizations of intuitionistic and classical one-step versions of K. In these systems, occurrences of step-markers allow deductions to display deductive structure that is covered over in familiar “no step” proof-theoretic systems for such logics. Box and Diamond are governed by Introduction and Elimination rules; the familiar K rule and Necessitation are derived (i.e. admissible) rules. CK will be the result of adding the 0-version of the Rule of Excluded Middle to the rules which generate IK. Note: IK is the result of merely dropping that rule from those generating CK, without addition of further rules or axioms (as was needed in [7]). These proof-theoretic systems yield intuitionistic and classical consequence relations by the obvious definition. Section 4 provides some examples of what can be deduced in IK. Section 5 defines some proof-theoretic concepts that are used in Section 6 to prove the soundness of the consequence relation for IK (relative to the class of models defined in Section 2.) Section 7 proves its completeness (relative to that class). Section 8 extends these results to the consequence relation for CK. (Looking ahead: Part 2 will investigate one-step proof-theoretic systems formalizing intuitionistic and classical one-step versions of some familiar logics stronger than K.). (shrink)

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between various (...) cut-conditions in the absence of finitariness or of monotonicity. (shrink)

Part 1 [Hodes, 2021] “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Part 1. For the systems associated with the intuitionistic counterparts (...) of D and T, these rules are “pure one-step”: their schematic formulations does not use □ or ♢. For the systems associated with the intuitionistic counterparts of K4, etc., these rules meet these conditions: neither □ nor ♢ is iterated; none use both □ and ♢. The join of the two systems associated with each of these familiar logics is the full one-step system for that intuitionistic logic. And further “blended” intuitionistic systems arise from joining these systems in various ways. Adding the 0-version of Excluded Middle to their intuitionistic counterparts yields the one-step systems corresponding to the familiar classical logics. Each proof-theoretic system defines a consequence relation in the obvious way. Section 10 examines inclusions between these consequence relations. Section 11 associates each of the above consequence relations with an appropriate class of models, and proves them sound with respect to their appropriate class. This allows proofs of some failures of inclusion between consequence relations. Section 12 proves that the each consequence relation is complete or weakly complete, that relative to its appropriate class of models. The Appendix presents three further results about some of the intuitionistic consequence relations discussed in the body of the paper. For Keywords, see Part 1. (shrink)