We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.

In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.

This paper explores proof-theoretic aspects of hybrid type-logical grammars, a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also present both a sequent and a proof net calculus for hybrid type-logical grammars. In addition to clarifying the logical foundations of hybrid type-logical grammars, the current study opens the way to variants and extensions of the original system, including but not limited to a non-associative version and (...) a multimodal version incorporating structural rules and unary modes. (shrink)

This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis, in the context for type-logical grammars, of the logical models and algorithms currently used in natural language semantics, defined as a function from a grammatical sentence to a set of logical formulas—because a statement can be ambiguous, it can correspond to multiple formulas, one for each (...) reading. We argue that as long as we do not explicitly compute the interpretation in terms of possible world models, one can compute the semantic representation of a given statement, including aspects of lexical meaning. This is a very generic process, so the results are, at least in principle, widely applicable. We also discuss the algorithmic complexity of this process. (shrink)

In this paper we present a logical system able to compute the semantics of both declarative and interrogative sentences. Our proposed analysis takes place at both the sentential and at the discourse level. We use syntactic inference on the sentential level for declarative sentences, while the discourse level comes into play for our treatment of questions. Our formalization uses a type logic sensitive to both the syntactic and semantic properties of natural language. We will show how an account of the (...) linguistic data follows naturally from the logical relations inherent in the type logic. (shrink)

Shareholders are sometimes considered to be, in moral terms, the owners of a company, they are after all the carriers of the residual liabilities and bear a higher proportion of the financial risk. However, in company law, the shareholders’ responsibility is limited, and in financial terms shareholders are only liable up to the fully paid value of the share certificate. Moreover, when the shares are sold, the responsibility and risk are transferred completely to the new bearer of the shares. Whether (...) this gap in moral and legal perceptions can be judged to be satisfactory in business ethics terms is a moot point and will be partly explored in this case study which seeks to analyse the shareholder’s responsibility towards a firm in which they own shares. The case study company chosen as a vehicle to explore these issues is that of Turner & Newall; a company that subjected its employees, communities and customers to a major health hazard – asbestosis. This paper will use the Turner & Newall archive materials to illustrate the moral hazards that can arise for shareholders. In particular it will examine the ethical responsibilities of shareholders towards those stakeholders who were exposed to the dangers of asbestos. This case is a significant test of the veracity of the legal system of company control, and exposes the ineffectiveness of that system in accountability terms. The case study also deals with specific issues that arose in the asbestos crisis, as well as with more general issues in our present system of corporate governance and shareholder responsibilities. (shrink)

Virtue Epistemology has come a long way since Ernest Sosa first mooted its possibility in ‘The Raft and the Pyramid’, a paper about the pitfalls of coherentism and foundationalism. What makes Virtue Epistemology distinctive, as opposed to other forms of reliabilist externalism, is that the epistemic agent becomes the locus for justification rather than the belief. In the midst of a small but growing literature in this focus on the agent, two clear trends are emerging that reflect a difference in (...) interest by the authors rather than any real underlying antagonism between camps. Where faculty reliabilists like Sosa and Greco are concerned about sceptical challenges, virtue responsibilists like Zazebski or Roberts and Wood prefer to write about intellectual flourishing. (shrink)

It is widely mooted that a plausible computational cognitive model should involve both symbolic and connectionist components. However, sound principles for combining these components within a hybrid system are currently lacking; the design of such systems is oftenad hoc. In an attempt to ameliorate this we provide a framework of types of hybrid systems and constraints therein, within which to explore the issues. In particular, we suggest the use of system independent constraints, whose source lies in general considerations about cognitive (...) systems, rather than in particular technological or task-based considerations. We illustrate this through a detailed examination of an interruptibility constraint: handling interruptions is a fundamental facet of cognition in a dynamic world. Aspects of interruptions are delineated, as are their precise expression in symbolic and connectionist systems. We illustrate the interaction of the various constraints from interruptibility in the different types of hybrid systems. The picture that emerges of the relationship between the connectionist and the symbolic within a hybrid system provides for sufficient flexibility and complexity to suggest interesting general implications for cognition, thus vindicating the utility of the framework. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Madness, Reason, and PrideRichard G.T. Gipps, PhD (bio)MadnessQuestions such as “what’s madness?” or “what’s reason?” carry no singular sense about with them wherever they go—which isn’t to say that, asked out of a particular interest in a particular context, they can’t be perfectly intelligible. Garson (2023) is wise to this when he follows “what is madness?” with “as opposed to what?”, even if this latter question itself hardly enjoys (...) a clear sense in the initial context of his asking. What counts as a satisfactory answer to “what’s x?” varies, so that sometimes we’ll be satisfied with a name, at other times by information about something’s genus, origin, function, or composition. Things get notoriously tricky when in the philosophical context the question is asked with a presumption of intelligibility despite ‘x’ being, say, an abstract noun formed from an adjective (‘consciousness’ out of ‘conscious’; ‘happiness’ out of ‘happy’; ‘madness’ out of ‘mad,’ etc.). For “what is?” questions are typically most perspicuously mooted when what’s being pursued are enquiries into (what we might call) the ‘essential nature’ of (what philosophers used to call) ‘substances’ or (of what are more ordinarily called) types of ‘thing’ or ‘entity.’ Invoke, by taking one’s lead from the fact that an ‘x’ is grammatically speaking a substantive, the specter of substance, and you can endlessly baffle yourself by now pondering the mysteries of the putative thing. (Vide discussions of “the nature of consciousness.”) Hence the boon of instead pursuing questions of an ‘opposed to what?’ sort; hence Wittgenstein considering using the Earl of Kent’s “I’ll teach you differences” (King Lear) as a motto for his Investigations. Rather more reflective wisdom regarding ‘x’ may thus be gained when we learn to contrast it with ‘y’ and ‘z’ than when peering into x’s non-existent constitution or groping for its never-instituted genus.Later, I make the case that Garson’s conception of reason itself might suffer from a form of substantialization and that, if I’m right in this, troubling implications follow for his approach to madness. But let’s begin by considering his enquiry into the relation of madness, idiocy and reason. So perhaps we’re reflecting on matters legal, and considering—since we’d hitherto been inclined to take ‘reason’ as univocal—what justifies our different treatments of the insane, the intellectually subnormal, and the normal. Or perhaps—proceeding from the same inclination—we’re puzzled by how someone may boast an exceptional IQ or demonstrate marvelous formal rationality (i.e., make deductions of a sort which would please the logician if no-one else) and yet still be quite mad. And then we realize that at which Garson’s Late Moderns seem to have been gesturing: The lack of reason qua intelligence in idiocy is a different [End Page 307] species from the lack of reason qua sanity in madness. An amethyst is lifeless in a different manner than an expired possum (it was never living, never moribund); the arational lack reason in a different sense than do the irrational (and a baobab cannot jump to conclusions.) There is, say his Late Modern theorists, something ‘perverse’ rather than simply deficient about the irrationality of madness.Now an important part of Garson’s thesis has it that “idiocy is a better candidate for the opposite of reason than madness.” One of the reasons for his making this claim is that he follows his Late Moderns in claiming that madness has reason somehow alive within it, albeit in an unconventional or surprising form. I return to his own explication of this below. Consider first, though, the different thought-referencing descriptions under which the speech acts of the thought-disordered, the speech-disordered, the delusional, and the learning disabled subject may be brought. The sufferer of speech disorder has difficulty with fluency or sound production, but once we get used to this we can find our way to the bona fide rational thought immanent within their discourse. The speech acts of the intellectually impaired subject aren’t chaotic, but instead want for invention and richness; they fail to express... (shrink)

This paper traces the history of artificial insemination by selected donors as a strategy for positive eugenic improvement. While medical artificial insemination has a longer history, its use as a eugenic strategy was first mooted in late nineteenth-century France. It was then developed as ‘scientific motherhood’ for war widows and those without partners by Marion Louisa Piddington in Australia following the Great War. By the 1930s AID was being more widely used clinically in Britain as a medical solution to male (...) infertility for married couples. In 1935 English postal clerk, Herbert Brewer, promoted AID as the socialization of the germ plasm in a eugenic scheme. The next year Hermann Muller, American Drosophila geneticist and eugenicist, presented his plan for human improvement by AID to Stalin. Some twenty years later, Muller, together with Robert Klark Graham, began planning a Foundation for Germinal Choice in California. This was finally opened in 1980 as the first practical experiment in eugenic AID, producing some 215 babies over the twenty years it functioned. While AID appeared to be a means of squaring a eugenic circle by separating paternity from love relationships, and so allowing eugenic improvement without inhibiting individual choice in marriage, it found very little favour with those who might use it, not least because of a couple’s desire to have their ‘own’ children has always seemed stronger than any eugenic aspirations. No state has ever contemplated using AID as a social policy. (shrink)

Focused sequent calculi are a refinement of sequent calculi, where additional side-conditions on the applicability of inference rules force the implementation of a proof search strategy. Focused cut-free proofs exhibit a special normal form that is used for defining identity of sequent calculi proofs. We introduce a novel focused display calculus fD.LG and a fully polarized algebraic semantics FP.LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FP.LG}$$\end{document} for Lambek–Grishin logic by generalizing the theory of multi-type calculi and their (...) algebraic semantics with heterogenous consequence relations. The calculus fD.LG has strong focalization and it is sound and complete w.r.t. FP.LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FP.LG}$$\end{document}. This completeness result is in a sense stronger than completeness with respect to standard polarized algebraic semantics, insofar as we do not need to quotient over proofs with consecutive applications of shifts over the same formula. We also show a number of additional results. fD.LG is sound and complete w.r.t. LG-algebras: this amounts to a semantic proof of the so-called completeness of focusing, given that the standard (display) sequent calculus for Lambek–Grishin logic is complete w.r.t. LG-algebras. fD.LG and the focused calculus fLG of Moortgat and Moot are equivalent with respect to proofs, indeed there is an effective translation from fLG-derivations to fD.LG-derivations and vice versa: this provides the link with operational semantics, given that every fLG-derivation is in a Curry–Howard correspondence with a directional λ¯μμ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{\lambda }\mu \widetilde{\mu }$$\end{document}-term. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

This study reconstructs the relationship between philosophy and politics in the way in which Heidegger's failure as a politician influenced the redevelopment of philosophy in the 1930s. The author also explains how Heidegger's failure influenced the content and direction of his later work.

Studies the politics of Heidegger in terms of "thrownness" or "existential contingency". Attempts to think through Heidegger's philosophy in a manner that parallels his own dialogue with other key western thinkers.

Despite their differences in origin, the three influential schools of twentieth-century continental cultural criticism--the Frankfurt School, existentialism, and poststructuralism--have long been treated as an ensemble and with critical hesitancy. Examining these schools as responses to the apparent collapse of Western civilization in the twentieth-century and as formidable intellectual challenges to the cultural legacies of the Enlightenment, this book provides a productive base for criticism and broadens our understanding of their histories and reception.

Having visited Ireland regularly during the 1930s, Ludwig Wittgenstein resigned his Cambridge philosophy professorship in 1947 and moved there, living in a fishing village on the Atlantic coast and hotels in Dublin and the Wicklow Mountains. Although Wittgenstein spent some time out of the country, Ireland was effectively his base for three very productive years during which he worked on what would become one of his key books, the posthumously published Philosophical Investigations. Wittgenstein in Ireland represents the first sustained account (...) of Wittgenstein's time in Ireland, placing it in its historical context. Wall pays a good deal of attention to the representation of the Irish landscape in which the Austrian philosopher found himself able to work; a large part of his writings were produced in the bleak landscapes of Ireland and Norway. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

This classic, provocative introduction to classical metaphysical questions focuses on appreciating the problems, rather than attempting to proffer answers.

Drawing on case studies from around the world - including Iran, Guatemala, USA and Mexico - this collection documents how transnational human rights discourses and legal institutions are materialised, imposed, resisted and transformed in a variety of contexts.

Written by a former student of Heidegger, this book examines the relationship between the philosophy and the politics of a celebrated teacher and the allure that Nazism held out for scholars committed to revolutionary nihilism.

In this study, Worsley argues that it is rational to believe in a loving God in the face of evil. Beginning with a critique of Alvin Plantinga, he shows that human freedom is highly complex, and so depends upon complex structures in nature. These are both necessary for freedom but also sufficient for natural evil. He offers close analysis of the evolution of the human brain. The book develops a parallel argument that human evil stems from the evolution of personality.

. History of the concept of economic efficiency . INTRODUCTION James Buchanan won the Nobel Prize by proving that the process by which elected officials ...

This book is the complete story of the creation of the universe, as it was understood by the ancient Egyptians. It is a collection of harmonic and radical 'Black Thoughts' and the pursuit of equality for all of this planet's inhabitants"--P. vii.

This book gives a descriptive analysis of specific Madhyamika texts. It compares the ideology of Kumarajiva (a translator of the four Madhyamika treatises 400 A.D.) with the ideologies of the three Chinese contemporaries - HuiYuan, Seng-Jui and Seng-Chao. It envisages an intercultural transmission of religious and philosophical ideas from India to China.

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...) or sidesteps problems that have been raised for previous work in this area. (shrink)

2010 Reprint of 1905 edition.This work is the magnum opus of Bucke's career, a project that he researched and wrote over many years. In it, Bucke described his own experience, that of contemporaries, and the experiences and outlook of historical figures including Buddha, Jesus, Paul, Plotinus, Muhammad, Dante, Francis Bacon, and William Blake. Bucke developed a theory involving three stages in the development of consciousness: the simple consciousness of animals; the self-consciousness of the mass of humanity ; and cosmic consciousness (...) - an emerging faculty and the next stage of human development. Among the effects of this progression, he believed he detected a lengthy historical trend in which religious conceptions and theologies had become less and less fearful. A classic work. (shrink)