Irish literature after Yeats and Joyce, from the 1920s onwards, includes texts which have been the subject of much contention. For a start how should Irish literature be defined: as works which have been written in Irish or as works written in Englsih by the Irish? It is a period in whichideas of Ireland--of people, community, and nation--have been both created and reflected, and in which conceptions of a distinct Irish identity have been articulated, defended, and challenged; a period which (...) has its origins in a time of intense political turmoil. `after Yeats and Joyce' alsosuggests the immense influence of these two writers on the style, stances, and preoccupations of twentieth-century Irish literature. Neil Corcoran focuses his chapter on various themes such as `the Big House', the rural and provincial, with reference to authors from Kinsella and Beckett to WilliamTrevor, Seamus Heaney, and Mary Lavin, providing a lucid and far-reaching introduction to modern Irish writing. (shrink)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic (...) is a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

Essays devoted to the work of the late Neil Wilson, Canadian philosopher and contributor to the field of semantic analysis that emerged from the fusion of logic, pragmatism, and ontology. Many of the essays in this volume take their initial inspiration from Wilson's seminal work Substances Without Substrata.

Awarding rights to rivers, forests, and other environmental entities (EEs) is a new and increasingly popular approach to environmental protection. The distinctive feature of such rights of nature (RoN) legislation is that direct duties are owed to the EEs. This paper presents a novel rebuttal of the strongest argument against RoN: the no interest argument. The crux of this argument is that because EEs are not sentient, they cannot possess the kinds of interests necessary to ground direct duties. Therefore, they (...) cannot be legitimate rights-bearers. After considering and rejecting standard responses to this argument, the paper challenges its fundamental assumption: that rights-correlative duties must be grounded in the interests of the rights-bearer. The paper then presents the RoN critic with a dilemma. The critic must either accept that EEs are legitimate rights-bearers, or delegitimise many well-established rights-bearers along with EEs. Either way, the no interest argument loses its force. (shrink)

Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...) of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.Paul Rosenbloom 1950. (shrink)

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...) reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

One of the major contributions which Christopher Hookway has made to pragmatist epistemology is a critical exploration of the role that affective dispositions play in inquiry. According to Hookway, a well-functioning rational inquirer must rely upon a set of pre-reflective and affective dispositions which are not themselves fully available to rational evaluation. Despite their pre-reflective nature, on the pragmatist account these affective dispositions provide us with judgments and evaluations which are in many cases more reliable than those provided by explicit (...) rational reflection. -/- This chapter presents and defends Hookway’s account of the epistemic importance of our affective dispositions. The first section presents three roles which affective dispositions play within inquiry. The second section considers the concern that affective dispositions should be considered impositions upon our epistemic agency. In response, Hookway suggests that we must identify with our affective dispositions, and two interpretations of this claim are offered. The third section considers the possibility that the confidence we have in our affective dispositions might be appropriately shaken if we recognize that they are not shared by other inquirers. The chapter concludes by suggesting that Hookway’s position can overcome this worry by developing his notion of critical self-trust in three distinct ways. (shrink)

Develops a logical analysis of dialogue in which two or more parties attempt to advance their own interests. It includes a classification of the major types of dialogues and a discussion of several important informal fallacies.

Given the tremendous proliferation of student plagiarism involving the Internet, the purpose of this study is to determine which theory of ethical reasoning students invoke when defending their transgressions: deontology, utilitarianism, rational self-interest, Machiavellianism, cultural relativism, or situational ethics. Understanding which theory of ethical reasoning students employ is critical, as preemptive steps can be taken by faculty to counteract this reasoning and prevent plagiarism. Additionally, it has been demonstrated that unethical behavior in school can lead to unethical behavior in business; (...) therefore, correcting unethical behavior in school can have a positive impact on organizational ethics. To meet this objective, a content analysis was conducted on the written records of students formally charged with plagiarizing at a large West Coast university. Each case was classified according to the primary ethical reasoning that the student used to justify plagiarism. Results indicate that students predominately invoke deontology, situational ethics, and Machiavellianism. Based on these findings, specific recommendations are offered to curb plagiarism. (shrink)

Neil E. Williams develops a systematic metaphysics centred on the idea of powers, as a rival to neo-Humeanism, the dominant systematic metaphysics in philosophy today. Williams takes powers to be inherently causal properties and uses them as the foundation of his explanations of causation, persistence, laws, and modality.

This Element explores what it means for two theories in physics to be equivalent, and what lessons can be drawn about their structure as a result. It does so through a twofold approach. On the one hand, it provides a synoptic overview of the logical tools that have been employed in recent philosophy of physics to explore these topics: definition, translation, Ramsey sentences, and category theory. On the other, it provides a detailed case study of how these ideas may be (...) applied to understand the dynamical and spatiotemporal structure of Newtonian mechanics - in particular, in light of the symmetries of Newtonian theory. In so doing, it brings together a great deal of exciting recent work in the literature, and is sure to be a valuable companion for all those interested in these topics. (shrink)

This essay presents an ideal for modern Western romantic love.The basic ideas are the following: people want to form a distinctive sort of plural subject with another, what Nozick has called a "We", they want to be loved for properties of certain kinds, and they want this love to establish and sustain a special sort of commitment to them over time.

On his death in 2007, Richard Rorty was heralded by the New York Times as “one of the world’s most influential contemporary thinkers.” Controversial on the left and the right for his critiques of objectivity and political radicalism, Rorty experienced a renown denied to all but a handful of living philosophers. In this masterly biography, Neil Gross explores the path of Rorty’s thought over the decades in order to trace the intellectual and professional journey that led him to that (...) prominence. The child of a pair of leftist writers who worried that their precocious son “wasn’t rebellious enough,” Rorty enrolled at the University of Chicago at the age of fifteen. There he came under the tutelage of polymath Richard McKeon, whose catholic approach to philosophical systems would profoundly influence Rorty’s own thought. Doctoral work at Yale led to Rorty’s landing a job at Princeton, where his colleagues were primarily analytic philosophers. With a series of publications in the 1960s, Rorty quickly established himself as a strong thinker in that tradition—but by the late 1970s Rorty had eschewed the idea of objective truth altogether, urging philosophers to take a “relaxed attitude” toward the question of logical rigor. Drawing on the pragmatism of John Dewey, he argued that philosophers should instead open themselves up to multiple methods of thought and sources of knowledge—an approach that would culminate in the publication of Philosophy and the Mirror of Nature , one of the most seminal and controversial philosophical works of our time. In clear and compelling fashion, Gross sets that surprising shift in Rorty’s thought in the context of his life and social experiences, revealing the many disparate influences that contribute to the making of knowledge. As much a book about the growth of ideas as it is a biography of a philosopher, Richard Rorty will provide readers with a fresh understanding of both the man and the course of twentieth-century thought. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...) epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

This is a theoretical treatment of the term "Sha Zhu Pan" (杀猪盘) in Chinese, which translates to “Pig-Butchering” in English. The article critically examines the propagation and validation of "Pig Butchering," an animal metaphor, and its implications for the dehumanisation of victims of online fraud across various discourses. The study provides background information about this type of fraud before investigating its theoretical foundations and linking its emergence to the dehumanisation of fraud victims. The analysis highlights the disparity between academic literature, (...) subjected to rigorous peer-review processes, and sensationalised narratives prevalent in the media. While academic works subject "pig butchering" to critical scrutiny and refrain from endorsing derogatory terms to depict fraud victims, numerous media outlets employ this term uncritically, further worsening the predicament of these victims. "Pig butchering" is firmly rooted in the concept of dehumanisation, and this article underscores how language moulds perceptions of fraud and behaviour, extending to the development of preventive strategies. The role of law enforcement agencies in generating and disseminating materials is also a central theme, emphasising their responsibility as trusted sources of information. We suggest that these agencies should adopt non-victim shaming language to encourage victims to report crimes and alleviate the stigma attached to victimisation. Additionally, the article offers valuable cross-cultural insights by comparing metaphors from Chinese and Nigerian contexts. This comparative analysis enriches our comprehension of the global dimensions of online fraud and its cultural diversities, highlighting the substantial impact of language on perceptions and behaviours. We advocate for a departure from victim-blaming tendencies perpetuated by select media outlets, urging a more compassionate and accurate portrayal of those affected by online fraud. We, therefore, call for a more empathetic and accurate portrayal of individuals affected by online fraud, aligning with the broader objective of promoting understanding and support for these victims. (shrink)

Introduction HLA Hart: A biographical sketch Jurisprudence is the theoretical study of a practical subject. Its object is to achieve a systematic and ...

This paper develops a modal, Sentential logic having "not", "if...Then" and necessity as logical constants. The semantics (system of meanings) of the logic is the most obvious generalization of the usual truth-Functional semantics for sentential logic and its deductive system (system of demonstrations) is an obvious generalization of a suitable (jaskowski-Type) natural deductive system for sentential logic. Let a be a set of sentences and p a sentence. "p is a logical consequence of a" is defined relative to the semantics (...) and "p is demonstrable from a" is defined relative to the deductive system. Main meta-Theorem: p is demonstrable from a if and only if p is a logical consequence of a. Henkin-Type methods are used. The theorems of the logic are exactly those of s5. The deductive system is rigorously developed as a system of linear strings. (shrink)

This article draws attention to a pattern of development within science and other intellectual research communities that has received virtually no mention. We propose that subsequent dominance of a research community by a figure responsible for significant innovation often delays progress in the field. During the period in which the revolutionary continues to influence research in a community, far too frequently the effect is to freeze progress within the limited directions which the revolutionary sanctions.

Published with the aid of a grant from the National Endowment for the Humanities. Contains the only complete English-language text of The Concept of Truth in Formalized Languages. Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.

This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logical truth and logical (...) consequence. Adequacy criteria for systems of the first two types include: effectiveness, soundness, completeness, Post completeness, "strong soundness" and strong completeness. Consideration of a logical system as a theory of deduction leads us to attempt to formulate two adequacy criteria for systems of proofs. The first deals with the concept of rigor or "gaplessness" in proofs. The second is a completeness condition for a system of proofs. An historical note at the end of the paper suggests a remarkable parallel between the above hierarchy of systems and the actual historical development of this area of logic. (shrink)

In this paper, we make the case that a person who is considering or has already made a decision that appears seriously harmful to that person should in some cases be judged incapable of making that...

Philosophers from Hart to Lewis, Johnston and Bennett have expressed various degrees of reservation concerning the doctrine of double effect. A common concern is that, with regard to many activities that double effect is traditionally thought to prohibit, what might at first look to be a directly intended bad effect is really, on closer examination, a directly intended neutral effect that is closely connected to a foreseen bad effect. This essay examines the extent to which the commonsense concept of intention (...) supports a reasonably consistent and coherent application of double effect. Two important conclusions are these: (1) a number of traditionally proscribed activities involve a kind of “targeting” of innocents that can be taken to exhibit a direct intention to harm them; (2) a direct intention to harm need not involve a desire to harm in any ordinary sense of the latter expression. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and (...) his understanding of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

In Elements of Legislation, Neil Duxbury examines the history of English law through the lens of legal philosophy in an effort to draw out the differences between judge-made and enacted law and to explain what courts do with the laws that legislatures enact. He presents a series of rigorously researched and carefully rehearsed arguments concerning the law-making functions of legislatures and courts, the concepts of legislative supremacy and judicial review, the nature of legislative intent and the core principles of (...) statutory interpretation. (shrink)

In light of the growing need to pay attention to general public opinions and sentiments toward AI, this paper examines the levels of understandings amongst the Australian public toward the increased societal use of AI technologies. Drawing on a nationally representative survey of 2019 adults across Australia, the paper examines how aware people consider themselves to be of recent developments in AI; variations in popular conceptions of what AI is; and the extent to which levels of support for AI are (...) liable to alter with additional exposure to information about AI. While a majority of respondents consider themselves to have little knowledge and familiarity with the topic of AI, the survey nevertheless finds considerable range of relatively ‘plausible’ basic understandings of what AI is. Significantly, repeated questioning highlights a willingness among many people to reassess their opinions once having received further information about AI, and being asked to think through issues relating to AI and society. These patterns remain relatively consistent, regardless of respondents’ political orientation, income, social class and other demographic characteristics. As such, the paper concludes by considering how these findings provide support for the development of public education efforts to further enhance what might be termed ‘public understanding of AI’. (shrink)

Cognitive Science is a single-source undergraduate text that broadly surveys the theories and empirical results of cognitive science within a consistent computational perspective. In addition to covering the individual contributions of psychology, philosophy, linguistics, and artificial intelligence to cognitive science, the book has been revised to introduce the connectionist approach as well as the classical symbolic approach and adds a new chapter on cognitively related advances in neuroscience. Cognitive science is a rapidly evolving field that is characterized by considerable contention (...) among different views and approaches. Cognitive Science presents these in a relatively neutral manner. It covers many new orientations theories and findings, embedding them in an integrated computational perspective and establishing a sense of continuity and contrast with more traditional work in cognitive science. The text assumes no prerequisite knowledge, introducing all topics in a uniform, accessible style. Many topics, such as natural language processing and vision, however, are developed in considerable depth, which allows the book to be used with more advanced undergraduates or even in beginning graduate settings. A Bradford Book. (shrink)

A growth in consumer and media ethical consciousness has resulted in the need for organizations to ensure that members understand, share and project an approved and unified set of ethics. Thus understanding which variables are related to sharing and variation of ethical reasoning and moral intent, and the relative strength of these variables is critical. While past research has examined individual (attitudes, values, etc.), social (peers, significant others, etc.) and organizational (codes of conduct, senior management, etc.) variables, it has focused (...) on their influence on the individual – and not on their role in relation to patterns of group sharing and variation in an organization. Introduced as a new methodology to study ethics, microcultural analysis stipulates that to explain patterns of sharing and variation, one must understand how individual, social and organizational variables influence sharing and variation. Key hypotheses predict that managers who share in individual, social or organizational determinants will be more likely to share in ethical reasoning and moral intent. Qualitative and quantitative research supports the key hypotheses, finding social ties, personal moral intensity, Machiavellianism, locus of control and codes of ethics as significant determinants. Individuals who share in these determinants are more likely to share in ethical reasoning and moral intent. Additionally, regression analysis reveals social ties and personal moral intensity to be the strongest determinants. Based on these results, managerial recommendations focus on a holistic approach, manipulating these three determinants to cultivate a unified code of ethics within an organization. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis (...) of Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

The concept of recognition has been employed as a term of art in sovereign diplomacy, and in a philosophical tradition ranging from Plato to Hegel as an archetype of the emergence of political association leading to ethical civil relations. Recent liberal theorists have adapted the Hegelian 'struggle for recognition' to strengthen the argument for humane respect and human rights in the modern, multicultural state. This article emphasizes the cognitive processes and perceptual capacities of recognition. Drawing on Kant and Arendt, this (...) article argues for a broadly aesthetic view of politics as a basis for ethical and moral appraisal, and illustrates this approach with hypothetical and actual examples of politics and art. (shrink)