We introduce proof nets and sequent calculus for the multiplicative fragment of non-commutative logic, which is an extension of both linear logic and cyclic linear logic. The two main technical novelties are a third switching position for the non-commutative disjunction, and the structure of order variety.

This work is devoted to the relations between Lambek’s Syntactic Calculus and noncommutative variants of Girard’s Linear Logic; in particular the paper will consider: the geometrical representation of the laws of LC by means of proof-nets; the discovery - due to such a geometrical representation - of some laws of LC not yet considered; the discussion of possible linguistic uses of these new laws.

We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs. Our characterization is purely graph theoretical and works without further complication for proof nets with cuts, which are usually harder to handle in the non-commutative case. This also provides a new characterization of the proof nets for the Lambek calculus (with the empty sequence) which simply are a restriction on the formulas to be considered (which are asked to be intuitionistic).

Hilbert's conference lectures during the year 1922, Neuebegründung der Mathematik. Erste Mitteilung and Die logischen Grundlagen der Mathematik (both are published in (Hilbert [1935] 1965) pp. 157-195), contain his first public presentation of an axiom system for propositional logic, or at least for a fragment of propositional logic, which is largely influenced by the study on logical woks of Frege and Russell during the previous years.The year 1922 is at the beginning of Hilbert's foundational program in its definitive form. The (...) final public presentation by Hilbert of an axiom system for propositional logic is contained in the 1934 book Grundlagen der Mathematik, I (Hilbert and Bernays [1934] 1968). Sequent .. (shrink)

We study increasing F-sequences, where F is a dilator: an increasing F-sequence is a sequence (indexed by ordinal numbers) of ordinal numbers, starting with 0 and terminating at the first step x where F(x) is reached (at every step x + 1 we use the same process as in decreasing F-sequences, cf. [2], but with "+ 1" instead of "- 1"). By induction on dilators, we shall prove that every increasing F-sequence terminates and moreover we can determine for every dilator (...) F the point where the increasing F-sequence terminates. We apply these results to inverse Goodstein sequences, i.e. increasing (1 + Id) (ω) -sequences. We show that the theorem every inverse Goodstein sequence terminates (a combinatorial theorem about ordinal numbers) is not provable in ID 1 . For a general presentation of the results stated in this paper, see [1]. We use notions and results concerning the category ON (ordinal numbers), dilators and bilators, summarized in [2, pp. 25-31]. (shrink)

We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursuing this line of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, Type-raising, Composition, Geach (...) laws and Switching laws. (shrink)

We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursuing this line of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, Type-raising, Composition, Geach (...) laws and Switching laws. (shrink)

There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long (...) been known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. We show how the G-grammar can be oriented for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) to the free group over V, deep affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established can be considerable. (shrink)

Business ethics is a topic receiving much attention in the literature. However, the term 'business ethics' is not adequately defined. Typical definitions refer to the rightness or wrongness of behavior, but not everyone agrees on what is morally right or wrong, good or bad, ethical or unethical. To complicate the problem, nearly all available definitions exist at highly abstract levels. This article focuses on contemporary definitions of business ethics by business writers and professionals and on possible areas of agreement among (...) the available definitions. Then a definition is synthesized that is broad enough to cover the field of management in a sense as full as most managers might conceive of it. (shrink)

Purpose. The article is aimed to substantiate the view on the phenomenon of laughter as a subject of semiotic analysis, which leads to the following tasks: to reveal the possibilities of semiotics application in the study of laughter nature; to analyze the phenomenon of laughter as a cultural and natural phenomenon, as a sign and as an attribute; to consider the place of laughter in culture, which is understood as a sign system. Theoretical basis. The semiotic approach proceeds from the (...) fact that human lives in the world of signs, all the surrounding reality can be interpreted as a sign system. The basic concept of semiotics is the concept of a sign. The theoretical basis of the article is understanding the culture as a sign-symbolic system. Laughter is considered as a phenomenon ontologically rooted in human culture. At the same time, laughter is on the edge of culture. The research is based on the work of semiotic authors, cultural researchers, and the researchers of laughter. Originality. The originality lies in the application of the semiotic method to the research of laughter phenomenon, consideration of the dialectics of natural and cultural, signedness and non-signedness, manifested in the phenomenon of laughter. Conclusions. Laughter is considered as a psychophysiological phenomenon and as a cultural phenomenon. Laughter acts as an emotional manifestation, a physiological reaction, but socially and culturally mediated. In any case, laughter indicates an emotional or cognitive state of a human. Laughter acts as a process and result of the interpretation of a sign, a reaction to a sign. Laughter is a form and a means of communication. Being a natural phenomenon, in the process of social evolution, laughter acquires signedness, is integrated by culture as a sign system, and, at the same time, maintains a connection with nature. Thus, laughter occupies an ambivalent position between nature and culture. In the phenomenon of laughter, the dual state of human is revealed. In laughter, boundaries are blurred, the unity and opposition of natural and cultural, biological and social, soul and body, thought and feeling, sign and attribute are manifested. (shrink)

In the latest reform of the National Health Service great emphasis has been placed on the achievement and maintenance of quality. Mechanisms for ensuring this are being set up under the general title of “clinical governance”. What is the meaning of this term? The metaphor behind the phrase is of navigation through stormy seas, but who guides the helmsman? Clinical ethics committees could have a part to play in these changes, provided their role is properly understood. Clinical governance is concerned (...) with management according to an agreed set of aims. The task of ethics committees is Socratic rather than managerial. They should ask fundamental questions about the ethical norms of the services provided and give critical appraisal of the moral character of institutional policies. If these tasks are carried out then governance may become a watchword rather than just another buzzword. (shrink)

Zusammenfassung Der Beitrag widmet sich der Entstehung des Faches Religionsgeschichte in Frankreich. Die Vorgeschichte zu diesem Prozess beginnt mit Benjamin Constants Religionsphilosophie der 1810–1820er Jahre, in der die lokalen und diachronen Veränderungen des allgemein menschlichen religiösen Gefühls als ein Schlüssel zur Religionsgeschichte verstanden wurden. Nach einer langen Pause wird das Thema des religiösen Gefühls in Albert Révilles liberaltheologischem Projekt wieder aktuell. Ausgehend von Schleiermachers Voraussetzungen hoffte Réville dadurch die Apologetik zu modernisieren wie auch den Weg zum theologischen Inklusivismus zu bahnen. (...) Sein Sohn Jean, ebenfalls Theologe, neutestamentlicher Forscher und Sentimentalist, arbeitete mit dem Vater zusammen an der Institutionalisierung des Faches Religionsgeschichte in Frankreich. Albert Réville leitete von 1886 bis zu seinem Tod 1906 die fünfte (religionswissenschaftliche) Sektion der École Pratique des Hautes Études, gleichzeitig war Jean Réville seit 1884 Herausgeber der Fachzeitschrift Revue de l’histoire des religions. Révilles theoretischer Standpunkt wurde von É. Durkheim und seinen Gleichgesinnten H. Hubert und M. Mauss, die die weitere weltanschauliche Säkularisierung förderten, nach 1898 stark kritisiert. Diese Serie von Erwiderungen zeigt die Kluft zwischen der Methodologie der (dem Ursprung nach) evangelischen Religionsgeschichte und der durkheimischen Religionssoziologie. (shrink)

The primary aim of this study is to dissolve the mind-body problem. It shows how the ‘problem’ separates into two distinct sets of issues, concerning ontology on the one hand, and explanation on the other, and argues that explanation – whether or not human behaviour can be explained in physical terms – is the more crucial. The author contends that a functionalist methodology in psychology and neurophysiology will prove adequate to explain human behaviour. Defence of this thesis requires: an examination (...) of the mental/physical dichotomy, and its rejection in favour of a distinction between psychological and physical terms; a description and discussion of functionalism in psychology and neurophysiology, showing how the notorious problem of the necessary intensionality of psychological terms may be circumvented; an examination of the role of computer simulation in psycho-physical research; and an explanation of how the phenomena of sentience fit the functional framework. The book concludes that the thesis presented is in all essentials that of Aristotle; Aristotle had no ‘mind-body problem’, and were it not for a subsequent over-obsession with Cartesian scepticism, we need not have had one either. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Matter and Mathematics: An Essentialist Account of the Laws of Nature by Andrew YOUNANDominic V. CassellaYOUNAN, Andrew. Matter and Mathematics: An Essentialist Account of the Laws of Nature. Washington, D.C.: The Catholic University of America Press, 2023. xii + 228 pp. Cloth, $75.00Andrew Younan’s work situates itself between two opposing philosophical accounts of the laws of nature. In one corner, there are the Humeans (or Nominalists); in the (...) other, the Anti-Humeans (or Platonists). The goal of the book is to find an explanation for the orderliness of the natural world that avoids falling into the difficulties of the two opposing philosophies. For example, the Humeans treat “events” as fundamental, and the laws of nature follow from these “events.” For the Humeans, reality is essentially random, with any order being something of our own contrivance. Whereas for the Anti-Humeans, the laws of nature are fundamental and are treated as causing events, turning the effect of necessity into the cause of material [End Page 166] characteristics. Looking to Aristotle and Thomas Aquinas, Younan proposes the recovery of a third option, the Essentialist position. This Essentialist position understands substances, that is, individual beings, as fundamental and all else (for example, events and laws of nature) follow from these individual beings. The thesis of the book, generally understood, is that Essentialism evades the critiques that the Humeans and Anti-Humeans put against one another while retaining what is right in each approach.The book is divided into two parts. The book’s first part deals with general objections and replies and is divided into three chapters. Chapters 1 and 2 address the two opposing accounts of nature mentioned, while chapter 3 argues for the benefits of recovering an Essentialist position. Chapter 1 examines the objection that Aristotelian natural philosophy is incompatible with modern science, an objection raised by Descartes. Chapter 2 addresses the objections of the Humeans, namely, that natural philosophy and, with it, causality and induction have been debunked. Chapter 3 looks at the fathers of quantum theory, specifically Heisenberg, and argues that a return to Aristotle’s understanding of nature would benefit the modern scientific project. The book’s second part is an argument for the Essentialist position and is divided into three chapters. Chapters 4 and 5 are the foundation for chapter 6. Chapter 4 is an abstractive account of mathematics, differing from Descartes and his conceptions, which draws on the texts of Aristotle and Aquinas’s Division and Methods. Chapter 5 situates necessity and its role in Aristotelian natural philosophy. Chapter 6 is the author’s attempt at defining what it is to be a law of nature.Younan argues that adopting an essentialist understanding of nature in a system where all knowledge begins in the senses has three significant “payoffs.” The first is that it avoids governance language, that is, it avoids making laws themselves causes of necessity; the second is that it avoids the assertion of a priori knowledge; the third is that it understands individual things as the fundamental primitives in nature, restoring the substance to its proper place as the thing that “stands under” accidental being.The book is concluded with an appendix that explores and rearticulates Thomas Aquinas’s fifth way under the consideration of everything the author had argued for in the book’s main text. Taking as established by the rest of the book that necessity and teleology go hand in hand, Younan argues for a creator God who establishes a universe freely but within certain parameters that follow upon being itself. Younan concludes, with Thomas Aquinas, that laws of nature are “ordinances of reason” that must come from a rational mind. To be as consistent as they are, the laws of nature must be promulgated by God, and they are discoverable within the nature of matter itself.Younan’s book often engages its interlocutors on the big-picture scale, frequently giving generalizations and not going into details to avoid getting bogged down in the weeds. The author is very aware of what he is doing. [End Page 167] It is appropriate since engaging the multiheaded hydra of the schools of thought that Younan... (shrink)

"This book is an augmented and updated translation by the author of Theorie des Subjekts: Subjectiviteat und Identiteat zwischen Moderne und Postmoderne, Teubingen, Francke-UTB, 2010 (3rd ed.)"--Title page verso.

The ethics of citation has attracted increased attention in recent discussions of research and publication ethics, fraud and plagiarism. Little attempt has been made, however, to situate specific citation misbehaviors in terms of broader ethical practices and principles. To investigate researchers’ perceptions of citation norms, we surveyed active US researchers receiving federal funding from the National Institutes of Health (NIH), the National Science Foundation (NSF), and the National Endowment for the Humanities (NEH). Participants (_n_ = 257) were asked about citation (...) norms they endorse (norm reports), the behaviors they perceive others to engage in (peer reports), and their own citation behaviors (self-reports). Our analyses showed that while considerable discrepancies exist between norm reports, peer reports and self-reports, respondents’ discipline has no significant effect on these. Participants indicated that their own practices and that of their peers falls short of the norms they endorse, but that their own behavior is much less ethically deficient than that of their peers. An exploratory factor analysis revealed that ethically questionable citation behaviors could be grouped usefully into three categories: strategic citations, neglectful citations, and blind citations. Contrary to our hypothesis, the survey showed that greater experience does not always result in better citation practices. A particularly divisive issue pertained to intentionally citing authors from underrepresented demographic groups for reasons of social justice, but broad support for this practice is lacking, although arts and humanities scholars are slightly more supportive. Most researchers view questionable citation practices as negatively affecting their disciplines. Our findings suggest the need for clearer articulations of the citation norms and improved guidance and training about citations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Opining the articuli fidei:Thomas Aquinas on the Heretic’s Assent to the Articles of FaithM. V. DoughertyTHOMAS AQUINAS’S ACCOUNT of the infused virtue (habitus) of faith presupposes that some intrinsically intelligible truths are beyond the range of the natural cognitive abilities of human beings. The possession of the virtue of faith allows the believer to transcend certain natural epistemic limitations so that he can assent to truths that are necessary (...) for salvation. Consonant with the Catholic theological tradition, Aquinas refers to such truths as the articles of faith (articuli fidei), and stock examples include propositions concerning the Trinity and the Incarnation.1In light of the many and well-known texts from the Corpus Thomisticum that highlight the disproportion or incommensurability between the articles of faith and the natural cognitive abilities of human beings, it would not be unreasonable for one to assume that faith is required to assent to such articles of faith [End Page 1] in this life. Such an interpretive assumption could be expressed as:A1: A human being can assent to the articles of faith in this life if and only if the human being is fortified with the infused virtue of faith.One might be led to ascribe A1 to Aquinas when one considers that he criticizes the Pelagians precisely for maintaining that the assent to matters of faith is caused by nothing other than free will.2 Still further, one might think that strong evidence for A1 is Aquinas’s claim that “free will does not suffice for believing, since those things that are of faith are above reason.”3I argue, however, that A1’s identification of the virtue of faith as a necessary condition for the assent to the articles of faith does not adequately reflect Aquinas’s position, despite the many texts that may suggest such a view.4 That Aquinas does not endorse A1 can be made evident by examining his largely overlooked account of the epistemic state of the heretic (haereticus). To be sure, most commentators who explore the Thomistic treatment of heresy focus on the psychology of error underlying the heretic’s denial of one or more of the articles of faith.5 In the present paper I take an alternate path, however, focusing on those epistemic acts whereby the heretic gets its [End Page 2] right, so to speak, by correctly assenting to some of the articles of faith. Aquinas maintains that the heretic does not possess the infused virtue of faith yet still assents to all the articles of faith except for the one or more articles that he denies. Bereft of faith, the heretic “holds those things that are of faith by another mode than through faith.”6 This seemingly anomalous epistemic condition deserves consideration.7I. Intellects without FaithThe heretic appears to be cognitively privileged, since without faith he assents to the things that are of faith, seemingly overcoming without divine assistance the aforementioned disproportion between the limited range of reason and the articles of faith. Aquinas is aware of the apparent difficulty; in the Summa theologiae he defuses the rather unusual objection that heretics appear to have greater cognitive capacities than the faithful, since heretics routinely and unassistedly assent to those higher truths without possessing the virtue of faith.8 Aquinas concludes that the heretic holds the articles of faith by opinion (opinio), not faith.What makes one a heretic? Frequently Aquinas identifies obstinacy (pertinacia, instantia) as a necessary condition for heresy.9 The cause of heresy is at times identified with pride [End Page 3] (superbia).10 On Aquinas’s account, heresy is a species of unbelief (infidelitas) and every heretic is a schismatic.11 But the heretic does get many things right. If one were to deny all of the articles of faith, one would not qualify as a heretic, but would simply be a nonbeliever or an apostate. So, apart from the denial of an article (or a few articles) that specifies heretics as the distinct kind of heretic they happen to be, heretics for the most part succeed in assenting to most—but not all—of the articles of faith.Although the... (shrink)

The paper aims to analyze three discussions pertaining to the artificial intelligence project that took place on both sides of the “Iron Curtain” since the 1960s: 1) E.V. Ilyenkov – D.I. Dubrovsky (USSR), 2) H. Dreyfus – computer scientists (USA), 3) H. Dreyfus – H. Collins (USA – UK). The authors observe the originality of the arguments of Soviet philosophers in comparison with the discussions in the US and UK. The basis for a comparative analysis of these discussions is the (...) typology of social intercourse paradigms, which assumes the existence of three fundamentally different views of humans as social beings: the information-instrumental, the existential-phenomenological, and the social-institutional paradigms. These views correlate with the ideas about humans within different theoretical structures examining artificial intelligence. The information-instrumental paradigm poses the problem of social intercourse regarding communication, material, and informational exchange (D.I. Dubrovsky, computer scientists). The social-institutional paradigm considers social intercourse as personification, actualization, and implementation of the structural characteristics of social relations (E.V. Ilyenkov). The existential-phenomenological paradigm characterizes social intercourse as the realization of the internal potency of a self-conscious individual (H. Dreyfus). The paper exposes that the theoretical and methodological foundations of the discussions under consideration are similar to the paradigmatic foundations of the analysis of social intercourse in social philosophy and social sciences. There are “two and a half floors” in the research of problems associated with the entry of artificial intelligence technologies into the everyday life of society: 1) philosophy, computer and cognitive sciences; 2) social sciences; 3) interdisciplinary research. A particular paradigmatic structure and a unique research problem characterize each of them. In conclusion, “new old questions” are highlighted that structure the field of contemporary social analytics for studying artificial intelligence and artificial sociality. (shrink)