Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...) explanation of the rules. (shrink)

That every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can (...) be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms. (shrink)

By considering the new notion of theinversesof syllogisms such asBarbaraandCelarent, we show how the rule ofIndirect Proof, in the form (no multiple or vacuous discharges) used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.

In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...) a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules. (shrink)

The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...) of derivations are collections of derivations in the associated “dedicated” natural-deduction proof-system, and functions therein (with no appeal to models, truth-values and elements of a domain). The compositionality of the semantics is analyzed. (shrink)

The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument does not (...) obtain, and assertions are always warranted, having grounds of assertion. The proof system is shown to satisfy Dummett’s harmony property, justifying the ND rules as meaning conferring. The semantics is suitable for incorporation into computational linguistics grammars, formulated in type-logical grammar. (shrink)

We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that a (...) particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoic axioms, the T1 rule and the instances of Cut with just two antecedent formulae in the first premiss. OPEN ACCESS. (shrink)

The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic.

"The papers in this volume are extended versions of presentations at the fourth International Workshop on Extensions of Logic Programming, held at the University of St Andrews, March/April 1993. Among the topics covered in the volume are: defintional reflection and completion, modules in lambda-Prolog, representation of logics as partial inductive definitions, non-procedural logic programming, knowledge representation, contradiction avoidance, disjunctive databases, strong negation, linear logic programming, proof theory and regular search spaces, finite sets and constraint logic programming, search-space pruning and universal (...) algebra, and implementation on transputer networks."--PUBLISHER'S WEBSITE. (shrink)

A major strategy to reduce transport congestion and other social costs of transport is to ensure that travellers make the best decisions, based on real time information. A wide range of technological systems have been developed to provide this information, but little is known about how travellers actually respond to it. This book offers an overview of various transport telematics options and provides an appropriate methodological framework, followed by a presentation of results from actual applications of these telematics systems from (...) a range of European countries in various transport sectors. The empirical results are supplemented by analytical models and geographic information systems representations with a view on generalizing these findings and identifying the key parameters which determine user response. (shrink)

The paper argues against Peacocke's moderate rationalism in modality. In the first part, I show, by identifying an argumentative gap in its epistemology, that Peacocke's account has not met the Integration Challenge. I then argue that we should modify the account's metaphysics of modal concepts in order to avoid implausible consequences with regards to their possession conditions. This modification generates no extra explanatory gap. Yet, once the minimal modification that avoids those implausible consequences is made, the resulting account cannot support (...) Peacocke's moderate rationalism. (shrink)

Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before (...) He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor. (shrink)

Suave, mari magno turbantibus aequora ventise terra magnum alterius spectare laborem;non quia vexari quemquamst iucunda voluptas,sed quibus ipse malis careas quia cernere suave est.suave etiam belli certamina magna tueri 5per campos instructa tua sine parte pericli.sed nil dulcius est, bene quam munita tenereedita doctrina sapientum templa serena,despicere unde queas alios passimque videreerrare atque viam palantis quaerere vitae, 10certare ingenio, contendere nobilitate,noctes atque dies niti praestante laboread summas emergere opes rerumque potiri.o miseras hominum mentes, o pectora caeca!qualibus in tenebris vitae quantisque (...) periclis 15degitur hoc aevi quodcumquest! nonne viderenil aliud sibi naturam latrare, nisi utquicorpore seiunctus dolor absit, mensque fruaturiucundo sensu cura semota metuque?(Lucr. 2.1–19)It is pleasant, when the winds stir up the waters on the great sea,to watch the great struggle of another from land;not because it is a great pleasure that anyone be troubled,but because it is pleasant to observe the troubles you yourself lack.It is also pleasant to watch the great contests of war 5spread out over the plains without taking any part in the danger.But nothing is more pleasing than to hold lofty yet calm templesthat are well defended by the teachings of wise men,from which you can look down and see others everywherego astray and wander while seeking the path of their life, 10competing in wits and contending over their nobility;throughout nights and days they strive with outstanding labourto come out at the peak of riches and have power over everything.O wretched minds of men, O blind hearts!In what shadows of life and in how many dangers 15is this bit of life, whatever it may be, being spent by you! Do you not seethat nature barks for nothing other than this – thatgrief be separated from the body and far away, and that the mind enjoypleasant feelings cut off from anxiety and fear?Epicurus' advice to his young friend Pythocles to ‘flee all education, raising up the top sail’ (παιδείαν δὲ πᾶσαν, μακάριε, ϕεῦγε τἀκάτιον ἀράμενος, Diog.Laert. 10.6 = Epicurus fr. 163 Us.) contains an allusion to Circe's advice to Odysseus inOdyssey12.37–58. For much of the Greek (and Roman) world, education was based on the Homeric epics, and thus Epicurus' statement represents a complicated position towards Homer in particular and poetry in general. Epicurean philosophy rejects poetry because it is misleading about the gods and the nature of the soul, but Epicurus and his followers, most notably Philodemus and Lucretius, engage in poetic allusion and even the composition of poetry. Much work has been done on allusions to poetry in all three writers, but I hope here to bring out a heretofore unnoticed poetic allusion at the start ofDe rerum naturaBook 2, in which Lucretius makes a programmatic statement about not only his philosophy, but also his poetry and its place in the poetic tradition. (shrink)

'As an introduction to early modern thinking and the impact of past ideas on present lives, this book can find few equals and no superiors. Porter is a witty, humane writer with an extraordinary vocabulary and a sparkling sense of fun. Whether he is quoting from obscure medical texts or analysing scabrous diaries, dishing the dirt on long-dead bigwigs or evoking sympathy for human suffering, his grasp is masterly and his erudition appealing. I wish I could read it again for (...) the first time: you can.' Times Educational Supplement, Book of the Week In this startlingly brilliant sequel to the prize-winning ENLIGHTENMENT Roy Porter completes his lifetime's work, offering a magical, enthusiastic and charming account of the writings of some of the most attractive figures ever to write English. (shrink)

The Indian film’s depiction of rape and sexual violence specifically on women, can provide a glimpse into the wider Indian cultural mores seeping into the thoughts and processes that are in play du...

The paper compares the suitability of two different epistemologies of counterfactuals—(EC) and (W)—to elucidate modal knowledge. I argue that, while both of them explain the data on our knowledge of counterfactuals, only (W)—Williamson’s epistemology—is compatible with all counterpossibles being true. This is something on which Williamson’s counterfactual-based account of modal knowledge relies. A first problem is, therefore, that, in the absence of further, disambiguating data, Williamson’s choice of (W) is objectionably biased. A second, deeper problem is that (W) cannot satisfactorily (...) elucidate modal knowledge. Third, from a naturalistic perspective, the nature of this second problem favours (EC) against (W). (shrink)

The paper presents a dilemma for both epistemic and non-epistemic versions of conceivability-based accounts of modal knowledge. On the one horn, non-epistemic accounts do not elucidate the essentialist knowledge they would be committed to. On the other, epistemic accounts do not elucidate everyday life de re modal knowledge. In neither case, therefore, do conceivability accounts elucidate de re modal knowledge.

Ockham's razor is popularly phrased as a prohibition against multiplying entities beyond necessity. This prohibition should extend to the receptacle for these entities. To state my thesis more positively and precisely, both qualitative and quantitative parsimony apply to space, time, and possibility. All other things equal, we ought to prefer a hypothesis that postulates less space. Smaller is better. Admittedly, scientists are ambivalent about economizing on the void. They praise simplicity. Yet astronomers have a history of helping themselves to as (...) much empty space as they wish—staggering common sense with the vastness of the universe. This largesse is abetted by an aesthetic bias for sublime hypotheses. Whereas abductions based on beauty converge with parsimony, abductions based on the sublime diverge from parsimony. Awe stifles our inner accountant. Both types of abduction are popular. Both are dubious because we lack independent assurance that the universe is beautiful or sublime. The analogy between space and time supports an extension of parsimony to time. Uniformitarian geologists regarded time as a free resource. However, geologists and cosmologists must justify their postulation of an immense past. Possibility follows suit. Contrary to David Lewis, possible worlds should be minimized. Parsimony about possibilities provides a rationale for parsimony about absences. Absences are possibilities that are not actual. So proliferation of absences entails proliferation of possibilities. We should admit only those absences which do explanatory work. (shrink)

Bumped from a flight? Relax with this defense of the big business practice of deliberately promising more services than one will provide. On a small scale, over‐promising yields a toxic moral dilemma and a lie. At a large scale, the dilemma becomes dilute, and the lie completely disappears. Overbooking is honest because there is a sufficiently high probability of fulfilling each promise. Overbooking is socially beneficial because the promised resources are used more efficiently. There are fewer wasted seats on jumbo (...) jets and hence cheaper tickets with less pollution. Widespread disapproval of overbooking is a fallacious scaling error. Instead of there being too much overbooking, there is too little. (shrink)

This book traces the evolution of Hindu theories of warfare in India from the dawn of civilization.

L’objectif de cet article est de laisser entrevoir pourquoi et comment il est possible de faire pivoter une approche esthétique fondée sur des idées vers une autre fondée sur des gestes. Mon point de pivotement sera ce que Kant affirme et présuppose de l’idée esthétique et du geste (dont il ne parle que brièvement et latéralement). Il ne s’agira donc pas d’exposer l’esthétique kantienne mais plutôt faire ressortir pourquoi cette dernière ne peut donner une pleine existence au geste et ce (...) qu’o... (shrink)

How did first millennia Indian Buddhists understand the emotions? What are the theoretical resources, methodologies and vocabularies they used to account for emotive phenomena, and how do these relate, if at all, to contemporary philosophy of the emotions? This essay focuses, as a case study, on the notion of ascetic solitude (viveka) presented by the Buddhist thinker and poet Aśvaghoṣa’s (second century CE) in his poetical work the Saundarananda. Approaching Aśvaghoṣa’s work as a lens through which to examine the broader (...) Buddhist philosophical conception of the emotions, it is demonstrated that solitude, far from being conceived as a physical withdrawal from the world (into an interior subjective space), is seen as a mode of engagement with the world, a dynamic and transformative experiential process. This understanding, it is argued, is set within a broader Buddhist philosophical conception of emotions primarily in terms of a shifting evaluative perceptual content. Within the Saundarananda, emotions are akin to “ways of seeing”—a matter of perceptual modes and patterns of salience and what they experientially pick and leave out. Outlining some of the features of this theory that are distinctively Buddhist, this essay join the scholarly critique of the practice of applying readymade contemporary emotive categories to the study of Indian Buddhist texts, and advocate the need to account for these texts as much as possible in their own terms. (shrink)

S(zp,zp) performs an innovative analysis of one of modern logic's most celebrated cornerstones: the proof of Gödel's first incompleteness theorem. The book applies the semiotic theories of French post- structuralists such as Julia Kristeva, Jacques Derrida and Gilles Deleuze to shed new light on a fundamental question: how do mathematical signs produce meaning and make sense? S(zp,zp) analyses the text of the proof of Gödel's result, and shows that mathematical language, like other forms of language, enjoys the full complexity of (...) language as a process, with its embodied genesis, constitutive paradoxical forces and unbounded shifts of meaning. These effects do not infringe on the logico-mathematical validity of Gödel's proof. Rather, they belong to a mathematical unconscious that enables the successful function of mathematical texts for a variety of different readers. S(zp,zp) breaks new ground by synthesising mathematical logic and post-structural semiotics into a new form of philosophical fabric, and offers an original way of bridging the gap between the "two cultures". (shrink)

We study shared intentions in what we call “loose groups”. These are groups that lack a codified organizational structure, and where the communication channels between group members are either unreliable or not completely open. We start by formulating two desiderata for shared intentions in such groups. We then argue that no existing account meets these two desiderata, because they assume either too strong or too weak an epistemic condition, that is, a condition on what the group members know and believe (...) about what the others intend, know, and believe. We propose an alternative, pooled knowledge, and argue that it allows formulating conditions on shared intentions that meet the two desiderata. (shrink)

An instructive comparison can be drawn between Jacques Ellul’s 1936 Esprit article portraying “Fascism as Liberalism’s Child” and Georges Bataille’s 1938 lecture on “The Sacred Sociology of Today’s World”. Both rely on Durkheim’s sociology in assuming modernity’s amorphousness, leaving passive masses of atomized individuals susceptible to mobilization into totalized entities by charismatic leadership. Bataille welcomes the postwar intensification of social aggregates but criticizes their militant, militaristic regimentation as not violent and sacred enough, whereas for Ellul, the resurgent social sacred (whether (...) orgiastic or dictatorial), as the active mass, is the enemy of the free person as the sole meaningful whole. (shrink)

Volume 39, Issue 2, April-June 2024, Page 140-142.

Volume 39, Issue 2, April-June 2024, Page 140-142.

This book examines the intricate dynamics of when individuals adhere to laws, taking into account the context in which laws attempt to shape human behavior. While existing literature touches upon various reasons why people comply with laws, the book focuses on a critical question which has been missing from the discussion: when do people obey laws? By treating law as a form of social communication, it develops an integrated framework to answer this question. It explores how social, psychological, and institutional (...) conditions shape compliance decisions of individuals. What does a law signify? When does the compulsion to obey arise? When do individuals comply out of a fear for legal sanctions or social repercussions? Why do some laws have high symbolic values and others fail despite harsh punishments? The book unveils the contextual intricacies that underlie obedience to law. It challenges conventional wisdom and offers a fresh perspective on the power and limitations of law in shaping human behavior. For scholars and academics seeking a deeper understanding of legal compliance and role of law in shaping behaviors, this book will be an indispensable resource. (shrink)

Originally published in 1989, Reclaiming Reality still provides the most accessible introduction to the increasingly influential multi-disciplinary and international body of thought, known as critical realism. It is designed to "underlabour" both for the sciences, especially the human sciences, and for the projects of human emancipation which such sciences may come to inform; and provides an enlightening intervention in current debates about realism and relativism, positivism and poststucturalism, modernism and postmodernism, etc. Elaborating his critical realist perspective on society, nature, science (...) and philosophy itself, Roy Bhaskar shows how this perspective can be used to undermine currently fashionable ideologies of the Right, and at the same time, to clear the ground for a reinvigorated Left. Reclaiming Reality contains powerful critiques of some of the most important schools of thought and thinkers of recent years—from Bachelard and Feyerabend to Rorty and Habermas; and it advances novel and convincing resolutions of many traditional philosophical problems. Now with a new introduction from Mervyn Hartwig, this book continues to provide a straightforward and stimulating introduction to current debates in philosophy and social theory for the interested lay reader and student alike. Reclaiming Reality will be of particular value not only for critical realists but for all those concerned with the revitalization of the socialist emancipatory project and the renaissance of the Marxist theoretical tradition. Roy Bhaskar is the originator of the philosophy of critical realism, and the author of many acclaimed and influential works including A Realist Theory of Science, The Possibility of Naturalism, Scientific Realism and Human Emancipation and Dialectic: The Pulse of Freedom. He is an editor of the recently published Critical Realism: Essential Readings and is currently chair of the Centre for Critical Realism. (shrink)

In this book, Roy Bhaskar sets out to revindicate ontology, critiquing the reduction of being in favor of knowledge, which he calls the "epistemic fallacy".

In today’s competitive economy, the war for talent has intensified. Organizations are increasingly investing in student engagement initiatives to build a robust talent pipeline. Among these initiatives, the offering of internship placements is a popular choice as it not only helps identify suitable talent, students can also benefit with valuable opportunities to develop work-related skills and gain experience. However, ensuring mutually beneficial outcomes for all stakeholders involved remains a challenge due to diverging expectations among stakeholder groups. This study aims to (...) enhance our understanding of high-quality internship design by applying stakeholder theory (ST) and the expectancy theory of motivation (ET) as theoretical frameworks. Qualitative research methods were employed, including semi-structured interviews with key stakeholders from higher education institutions, human resources managers, and front-line supervisors as well as a focus group with graduating business students. Thematic analysis of the data revealed several key themes related to stakeholder priorities and interests. The findings of this paper contribute to the fields of ST and ET by addressing an under-researched area: the motivations of supervisors as crucial stakeholders in delivering the internship experience. Scholars and practitioners have largely overlooked this aspect. From a managerial perspective, the findings highlight opportunities for fostering more synergistic partnerships between stakeholders, not only at the institutional level but also among internal stakeholder groups, including top management, human resources functions, and front-line supervisors. (shrink)