Phenomenology is the general study of the structure of experience, from thought and perception, to self-consciousness, bodily-awareness, and emotion. It is both a fundamental area of philosophy and a major methodological approach within the human sciences. Experiencing Phenomenology is an outstanding introduction to phenomenology. Approaching fundamental phenomenological questions from a critical, systematic perspective whilst paying careful attention to classic phenomenological texts, the book possesses a clarity and breadth that will be welcomed by students coming to the subject for (...) the first time. Accessibly written, each chapter relates classic phenomenological discussions to contemporary issues and debates in philosophy. The following key topics are introduced and explained: the methodological foundations of phenomenology intentionality as the ‘mark of the mental’ and the problem of non-existent objects perceptual experience, including our awareness of things, properties, and events the experience of body, self, and others imaginative and emotional experience detailed discussions of classical phenomenological texts, including: Brentano's _Psychology from an Empirical Standpoint _ Husserl's _Logical Investigations_, _Cartesian Meditations, _and On_ the Phenomenology of the Consciousness of Internal Time _ Heidegger’s _History of The Concept of Time,_ and _Being and Time _ Stein's _On the Problem of Empathy _ Sartre's _Transcendence of the Ego_, _Sketch for a Theory of the Emotions,_ and _The Imaginary _ Merleau-Ponty's Phenomenology of Perception. Also included is a glossary of key terms and suggestions for further reading, making this book an ideal starting point for anyone new to the study of phenomenology, not only in Philosophy but related disciplines such as Psychology and Sociology. (shrink)

The operators of first-order logic, including negation, operate on whole formulae. This makes it unsuitable as a tool for the formal analysis of reasoning with non-sentential forms of negation such as predicate term negation. We extend its language with negation operators whose scope is more narrow than an atomic formula. Exploiting the usefulness of subatomic proof-theoretic considerations for the study of subatomic inferential structure, we define intuitionistic subatomic natural deduction systems which have several subatomic (...) operators and an additional operator for formula negation at their disposal. We establish normalization and subexpression property results for the systems. The normalization results allow us to formulate a proof-theoretic semantics for formulae composed of the subatomic operators. We illustrate the systems with applications to reasoning with combinations of sentential negation, predicate term negation, subject term negation, and antonymy. (shrink)

It is well-known that intuitionistic logics can be formalized by means of Heyting algebras, i.e. relatively pseudocomplemented semilattices. Within such algebras the logical connectives implication and conjunction are formalized as the relative pseudocomplement and the semilattice operation meet, respectively. If the Heyting algebra has a bottom element |$0$|⁠, then the relative pseudocomplement with respect to |$0$| is called the pseudocomplement and it is considered as the connective negation in this logic. Our idea is to consider an arbitrary meet-semilattice (...) with |$0$| satisfying only the Ascending Chain Condition (these assumptions are trivially satisfied in finite meet-semilattices) and introduce the operators formalizing the connectives negation |$x^{0}$| and implication |$x\rightarrow y$| as the set of all maximal elements |$z$| satisfying |$x\wedge z=0$| and as the set of all maximal elements |$z$| satisfying |$x\wedge z\leq y$|⁠, respectively. Such a negation and implication is ‘unsharp’ since it assigns to one entry |$x$| or to two entries |$x$| and |$y$| belonging to the semilattice, respectively, a subset instead of an element of the semilattice. Surprisingly, this kind of negation and implication still shares a number of properties of these connectives in intuitionistic logic, in particular the derivation rule Modus Ponens. Moreover, unsharp negation and unsharp implication can be characterized by means of five, respectively seven simple axioms. We present several examples. The concepts of a deductive system and of a filter are introduced as well as the congruence determined by such a filter. We finally describe certain relationships between these concepts. (shrink)

This is the definitive companion to the study of metaphysics. It provides students with an accessible, comprehensive and philosophically rigorous introduction to all the key concepts, issues and debates. Ideal for use on undergraduate courses, the structure and content of this textbook closely reflect the way metaphysics is studied. Thematically structured, the text introduces all the various philosophical problems addressed by metaphysics through the idea of truth-making, a useful lens through which the topic is clearly and concisely explicated. (...) With a particular focus on method in contemporary metaphysics, the book examines a variety of metaphysical topics, including the nature of properties, time, causation and objects. The book offers lucid and incisive coverage of the field of metaphysics, its key concepts and current debates. Jonathan Tallant's cogent and thorough analysis is supplemented by student-friendly features, including chapter summaries, study questions and a comprehensive guide to further reading. Each chapter includes a series of specially designed mind-maps to help students visualise the logical space being explored and how the arguments push in different directions. (shrink)

Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, (...) still holds for the Boolean extended logic. (shrink)

According to Frege a proposition—or, in his terms, a thought—is an abstract structured entity constituted by senses which satisfies, at least, the three following properties: it can be semantically assessed as true or as false, it is the object of so called propositional attitudes and it can be grasped. What Frege meant by 'grasping' is the peculiar way in which we can have epistemic access to propositions. The possibility for propositions to be grasped is put by Frege as a (...) warrant for their existence: to challenge their graspability would amount to jeopardise their ontological reality. But is it true, as Frege uncritically maintained, that the "graspability requirement" is satisfied as far as propositions are concerned? This is the topic of the present work. A negative answer to the above mentioned question has been given in recent time by the representatives of what has come to be labelled the "cognitive turn" in analytical philosophy. People such as Fodor and Johnson-Laird patently denied the possibility for propositions, conceived Frege, to be accessed by the grasping relation. What grounds their position is, to put it roughly, the following train of thought: in order for something to be the target of the grasping relation it must enter the mind. Nothing which is different from a mental entity can enter the mind. Therefore, what can be grasped must be mental. The upshot of this move implies, among other things, the rejection of that radical anti-psychologism which was characteristic of the forefathers of the analytical tradition. In our work we shall try to resist their conclusion by showing that it is not necessary to zero the distinction between propositions and mental entities in order to provide an adequate account of the grasping relation. What one has to give up, instead, is only Frege's late Platonism of the "third realm" which, in our view, is a wholly unnecessary and dispensable accretion of his picture. For, as we shall show, if Platonism is in place it is difficult to provide an account of the grasping relation which makes no use of the "representationalist hypothesis" — i.e. of the hypothesis that mediate our access to whatever can be given to us. But representationalism, once in place, makes the theoretical role of the notion of sense dispensable or purely additional. (shrink)

In this article, I discuss Alain Badiou’s 2008 address titled “The Three Negations.” Though the text was originally presented in a symposium concerning the relationship of law to Badiou’s theory of the event, I discuss the way this brief address offers an introduction to the broad sweep of Badiou’s metaphysics, outlining his accounts of being, appearing, and transformation. To do so, Badiou calls on the resources of three paradigms of negation: from classical Aristotelian logic, from Brouwer’s intuitionist (...) logic, and in paraconsistent logics developed by DaCosta. I explain Badiou’s use of negation in the three primary areas of his metaphysics, as well as to diagnose the degrees of transformation that may have occurred in a situation. My analysis of Badiou’s use of negation in this text is aided by examples from his broader ontological oeuvre. I also explain the underlying requirement in Badiou’s work that formal considerations - mathematical or logical - get their sense by being tethered to readily-identifiable political, aesthetic, scientific, or interpersonal concerns. I conclude by addressing the foundation Badiou’s work establishes for pursuing a new metaphysics, and by discussing certain of the liabilities that remain in the wake of his account. (shrink)

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major (...) logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. (shrink)

The Logic & Structure project is about the language of mathematical logic and how it can be of use in the visual arts. It involves a conversation between a mathematical logician and a group of artists. The project is ongoing, and this is a report on its first two phases. This text has two parts. The first, “Logic”, is a short introduction to certain aspects of logic, as it was presented to the participants. The (...) second part, “Structures”, describes some of the outcomes.The inspiration for the project comes from modern model theory whose advances revealed the extent to which formal methods may be helpful in describing and analysing mathematical structures. While the structures that are studied are often immensely complex, the formal language in which their properties can be expressed is simple. Its syntax is precisely defined and well understood, and this understanding often successfully guides us in our explorations of the rich world of mathematical objects. Our goal is to see the extent to which a similar approach could be of value when talking about works of art as structures. To this end, one could try to describe existing art objects in terms of suitably chosen formal languages, but we follow a reverse route. The language is described first, and the participating artists are asked to come up with artwork in which formal elements and their relations are chosen in advance, making it easier to identify those features of the created pieces that can be formally expressed. In other words, we are not thinking of applying formal methods to create art; rather we want to begin with samples that can serve as material for discussion. (shrink)

In a 2010 paper Daley argues, contra Fodor, that several syntactically simple predicates express structured concepts. Daley develops his theory of structured concepts within Tichý’s Transparent Intensional Logic . I rectify various misconceptions of Daley’s concerning TIL. I then develop within TIL an improved theory of how structured concepts are structured and how syntactically simple predicates are related to structured concepts.

A theory of substructural negations as impossibility and as unnecessity based on bi-intuitionistic logic, also known as Heyting-Brouwer logic, has been developed by Takuro Onishi. He notes two problems for that theory and offers the identification of the two negations as a solution to both problems. The first problem is the lack of a structural rule corresponding with double negation elimination for negation as impossibility, DNE, and the second problem is a lack of correspondence between certain (...) sequents and a characterizing frame property. While the identification of negation as impossibility and negation as unnecessity does solve Onishi’s problems, in general it nevertheless seems desirable to keep the two notions separate. The present paper addresses the first problem by introducing a reformulation of Onishi’s display sequent calculus in a language of sequents that incorporates Boolean negation. Instead of identifying negation as impossibility and negation as unnecessity, a notion of weak frame correspondence is defined. It is observed that DNE weakly corresponds with a certain frame property, and two structural sequent rules are presented that together also weakly correspond with that frame property and allow one to derive DNE. Moreover, the reformulated display calculus has an independent motivation by considerations on proof-theoretic semantics. (shrink)

A celebrated result by Davis, Putnam, Robinson, and Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic. We investigate analogues of this result over structures endowed with a listable presentation. When such an analogue holds, the structure is said to have the DPRM property. We prove several results addressing foundational aspects around this problem, such as uniqueness of the listable presentation, transference of the DPRM (...) property under interpretation, and its relation with positive existential bi-interpretability. A first application of our results is the rigorous proof of (strong versions of) several folklore facts regarding transference of the DPRM property. Another application of the theory we develop is that it will allow us to link various Diophantine conjectures to the question of whether the DPRM property holds for global fields. This last topic includes a study of the number of existential quantifiers needed to define a Diophantine set. (shrink)

Broad in scope, this introduction to environmental ethics considers both contemporary issues and the extent of humanity’s responsibility for distant future life. John Nolt, a logician and environmental ethicist, interweaves contemporary science, logical analysis, and ethical theory into the story of the expansion of ethics beyond the human species and into the far future. Informed by contemporary environmental science, the book deduces concrete policy recommendations from carefully justified ethical principles and ends with speculations concerning the deepest problems of environmental (...) ethics. Pedagogical features include chapter outlines, annotated suggestions for further readings, the explanations of key terms when first mentioned, and an extensive glossary. (shrink)

Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi (...) is proved, and used to conclude that the considered logical systems are PSPACE-complete. (shrink)

One of Da Costa’s motives when he constructed the paraconsistent logic C! was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to C!. Tableau and natural deduction systems for the logic are (...) produced, as are appropriate algebraic structures. The paper then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature ‘Brouwerian logic’ or ‘closed-set logic’. (shrink)

Hoping to overcome the deficiencies of Bailey and Dewitt, and taking into account the insights of Diano, Kleve, and Merlan, Rist presents this book as an accurate and complete doxology of Epicurus’ philosophy. The book is written in a condensed style where doctrines treated early in the book are not fully explained until the completion of later parts. In trying to pin down Epicurus, distinct from the Epicureans, he depends heavily upon Lucretius and the few extant writings of Epicurus himself, (...) but he does range over the works of all the later students and commentators. Even so, much is left either vaguely outlined or problematic, and what is accepted from the more distant or biased sources is judiciously measured against the more accepted teachings. There are seven major chapters dealing with the canonic, physics, man and the cosmos, soul and mind and body, pleasure, friendship, and gods and religion. Certain of the teachings presented have a bearing, one upon the other, throughout the book and do much toward showing some consistency and richness to Epicurus’ philosophy: In the canonic, three types of criteria for judging as to the existence of a thing or the truth of a proposition are explained, viz., sensation, general concepts, and feeling. In the physics, a crucial topic is the role of the swerve with its logical priority. In the cosmos, there is the developmental, evolutionary character of the universe. In the soul and body of man, the animus/anima distinction is worked out. The interrelation of all these is brought to bear on the central theme of pleasure and the gods. Pleasure, as the stable condition of the flesh and confident expectation of the future on this score, with complete absence of pain and anxiety, involves the physics, friendship, the soul of man, and the canonic. Also important to his teaching on pleasure is the interplay of those pleasures based upon want and that pleasure which is a state of untroubledness. Rist makes good use of the teachings of the canonic to establish the existence of the gods. In describing their structure, he shows how the gods, as detached exemplars, fit in with the physics and canonic, and with the teaching on pleasure and friendship. He assiduously refrains from interpreting the role of the gods in Epicurus’ philosophy, but with their existence so presented future interpretations should be much enriched. This book is a superb piece of scholarship and an invaluable aid to the study of Greek philosophy.—W. A. F. (shrink)

In Ontology, quality determines beings. The quality-quantity bipolarity reveals that a conceptual logical comprehension that can include negation must be a dialectical logic. Quality is a precise characteristic of something capable of augmentation or diminution while remaining identical through differences or quantitative changes. Thus, quality and in opposition quantity are inextricably linked, giving definition to each other, so constituting a logical bipolarity. The theory is that a magnitude G is never separated from secondary qualities α and β, and (...) therefore, a measure depends on a concrete quality Gα or Gβ, that is to say on one pole of a logical bi-pole. However, the particular number, the unit, that expresses the result of a measure is the quality G alone. Examples drawn from physical and chemical experiments illustrate these ideas and elaborate the structure of the concept of opposition between the secondary qualities α and β of a magnitude G. (shrink)

There are properties of finite structures that are expressible with the use of Hilbert's ε-operator in a manner that does not depend on the actual interpretation for ε-terms, but not expressible in plain first-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in first-order logic over finite structures. The present result also implies that certain non-deterministic choice constructs, which have been considered in database theory, properly enhance the expressive power of (...) first-order logic even as far as deterministic queries are concerned, thereby answering a question raised by Abiteboul and Vianu. (shrink)

This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or (...) some other wave energy is directed at the material in question, "imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry. (shrink)

The concept of _substructural logic_ was originally introduced in relation to limitations of Gentzen’s structural rules of Contraction, Weakening and Exchange. Recent years have witnessed the development of substructural logics also challenging the Tarskian properties of Reflexivity and Transitivity of logical consequence. In this introduction we explain this recent development and two aspects in which it leads to a reassessment of the bounds of classical logic. On the one hand, standard ways of defining the notion of logical consequence (...) in classical logic naturally induce substructural logics when admitting more than two truth values; on the other hand, these substructural logics give rise to hierarchies of _metainferences_ that can be used to approximate classical logic at different levels. (shrink)

The work is concerned with the so called display property of display logic. The motivation behind it is discussed and challenged. It is shown using one display calculus for intuitionistic logic as an example that the display property can be abandoned without losing subformula, cut elimination and completeness properties in such a way that results in additional expressive power of the system. This is done by disentangling structural connectives so that they are no longer context-sensitive. A (...) recipe for characterizing structural extensions of display calculi is provided. (shrink)

This well-written book introduces the reader step by step and in a pedagogical way to an aspect of Lacan's thought: the claim that the unconscious is structured like a language. A number of commentators have already introduced two crucial concepts of Lacan into the American intellectual community: the imaginary and the symbolic. Thus the now standard introduction and companion volume to Lacan's Ecrits: Lacan and Language, by John P. Muller and William J. Richardson, gives in the introduction a (...) good presentation of these two concepts. A brief look at the table of contents of the book by Dor allows us to see that Dor takes a further step in the presentation of Lacan's ideas. The first part, "Linguistics and the formation of the unconscious", is only an expansion of the introduction of the Muller-Richardson book, while the second part, "The paternal metaphor as structuring pivot for subjectivity", goes beyond it. The ideas developed in the second part can be usefully complemented by the chapter on the paternal metaphor in the book by De Waelhens Schizophrenia and by my essay on the paternal metaphor or the one on "Fatherhood and Subjectivity". In these other pieces we do not find a clarification of a Lacanian distinction between the subject of the enunciation and the subject of the enunciated. We also do not find in these other pieces a clarification of Lacan's famous schema L. Dor clarifies both admirably in this part of the book. (shrink)

This book provides an introduction to the study of words, their main properties and how we use them to create meaning. It offers a detailed description of the organizational principles of the lexicon, and of the categories used to classify various lexical phenomena, including polysemy, meaning variation, behaviour in composition, and the interface with pragmatics. Elisabetta Ježek uses empirical data from digitalized corpora and speakers' judgements, combined with the formalisms developed in the field of general and theoretical linguistics, to (...) propose representations for each of these phenomena. The book's clear structure and accessible approach make it an ideal textbook for all students of linguistics and a valuable resource for scholars and students of language in the fields of cognitive science and philosophy. (shrink)

Philosophy for Linguists provides students with a clear, concise introduction to the main topics in the philosophy of language. Focusing on what linguists need to know and how philosophy relates to modern linguistics, the book is structured around key branches of linguistics: semantics, pragmatics, and language acquisition. Assuming no prior knowledge of philosophy, Siobhan Chapman traces the history and development of ideas in the philosophy of language and outlines the contributions of specific philosophers. The book is highly accessible and (...) includes: a general introduction and introductions to each chapter; numerous examples and quotations; comprehensive suggestions for further reading and an extensive glossary of linguistic terms. (shrink)

We consider a family of differential algebras of real functions on real euclidean spaces, stable under right composition by affine maps. We prove that under a weak finiteness property, there is an o-minimal expansion of the ordered field of real numbers in which all these functions are definable.

The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC.

Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| (...) for c|$\vee $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

We show that modal logics characterized by a class of frames satisfying the insertion property are suitable for Reiter's default logic. We refine the canonical fix point construction defined by Marek, Schwarz and Truszczyński for Reiter's default logic and thus we addrress a new paradigm for nonmonotonic logic. In fact, differently from the construction defined by these authors. we show that suitable modal logics for such a construction must indeed contain K D4. When reflexivity is added (...) to the modal logic used for the fix point construction then we come to the Marek Schwarz and Truszczyński framework for Reiter's default logic. Our framework, in fact, is appropriate also to the family of modal logics in between S4 and S4f. If, instead, reflexivity is dropped, then we show that a new family of modal logics is gained, namely the modal logics in between KD4 and KD4Z. The upper bound can be extended to the modal logic KD4LZ whenever the propositional language taken into account is finite. (shrink)

RésuméDans l'article qui précède, l'auteur s'efforce, à l'intention surtout de ceux qui enseignent les Eléments, de mettre en lumière la signification et l'importance de deux ouvrages concernant la géométrie. Le court écrit de M. G. Bouligand fait apparaǐtre la structure algébrique et logique de cette science et présente une ȧxiomatique introduisant les notions d'ensemble et de groupe de transformation. Ainsi s'élabore une classification progressive des problèmes selon le genre des solutions qui leur conviennent. Le livre beaucoup plus étendu de (...) M. F. Gonseth analyse les aspects intuitif, expérimental et théorique de ce qui constituait l'élémentaire dans les traités classiques, puis expose les recherches suscitées par le postulat d'Euclide qui ont amené au développement de la méthode axiomatique. Le triomphe de l'atomisme, découvrant un monde où les notions élémentaires de la géométrie ne s'applíquent plus intégralement, vient rendre plus aigu encore le problème du fondement de la vérité géométrique et celui de la nature de l'espace. Grǎce à l'introduction de notions telles que celle de correspondance schématique et celle de modèle, la géométrie apparaǐt comme une science rationnelle en évolution et à laquelle l'axiomatique sert de critère. Mais bien loin de présenter les caractères d'une pure rationalité, cette axiomatique retient certaines données intuitives, měme dans son application aux géométries non euclidiennes; elle organise un contrǒle de nos intuitions les plus élémentaires les unes par les autres, et assure par leur intermédiaire la portée expérimentale et la cohérence de la géométrie. On assiste ainsi à une véritable mutation de l'élémentaire; mais celle‐ci n'est pas due au hasard. La méthode qui a présidé à cette transformation, dont les étapes historiques sont décrites, est clairement dégagée et il est visible qu'elle régit également les formes nouvelles de la physique dont la constitution théorique ne diffère pas essentiellement de la géométrie considérée comme la science rationnelle de l'espace. Cette méthode est le statut d'une science ouverte. Ainsi se trouve pleinement légitimé un exposé comme celui de M. Bouligand. En s'illustrant l'un l'autre, les deux ouvrages offrent des horizons nouveaux à l'enseignement, měme élémentaire, de la géométrie. La portée philosophique de ces ouvrages n'est pas moindre que leur portée pédagogique.ZusammenfassungIn der voranstehenden Besprechung möchte der Rezensent insbesondere diejenigen unter den Lesern, die die Elemente unterrichten, auf zwei bedeutende Geometriewerke hinweisen. G. Bouligands knapp gehaltene Schrift stellt den algebraisch‐logischen Aufbau dieser Wissenschaft ins Licht und bietet eine Axiomatik, die die Begriffe der Menge und der Transformations‐gruppe einführt. Ausgehend von der passenden Lösungsart gelangt der Verfasser zu einer fortschreitenden Klassifizierung der Aufgaben. In seinem viel breiter angelegten Werk untersucht F. Gonseth das in den klassischen Lehrbüchern als das Elementare angesehene vom intuitiven, experimentellen und theoretischen Gesichtspunkte aus und macht daran anschliessend mit den von Euklids Postulat ausgehenden Nachforschungen, die zur Entwicklung der axiomatischen Methode geführt haben, bekannt. Der eigentliche Siegeszug des Atomismus und die mit dieser Wissenschaft verbundene Entdeckung einer Welt, in der die grundsätzlichen Begriffe der Geometrie ihre volle Bestätigung nicht mehr erfahren, macht die Frage nach den Grundlagen der Geometrie und die nach dem Wesen des Raums besonders brennend. Die Einführung von Begriffen wie Schema und Modell lässt die Geometrie als eine in Entwicklung begriffene Rationalwissenschaft erscheinen, welcher die Axiomatik als Prüfstein dient. Letztere trägt aber durchaus nicht die Züge reiner Vernunftmässigkeit, sie hält vielmehr, selbst in ihrer Anwendung auf die nichteuklidischen Geometrien, an gewissen intuitiven Voraussetzungen fest; sie ermöglicht eine wechselseitige Kritik unserer elementarsten intuitiven Erkenntnisse unter sich und gewährleistet so die experimentelle Tragweite und die Kohärenz der Geometrie. Es findet also eine eigentliche Mutation des Elementaren statt, doch bleibt dieser Wandel nicht dem Zufall überlassen. Die Planmässigkeit, mit der er sich vollzog, wird unter Beschreibung der geschichtlichen Entwicklungsstufen klar dargelegt, womit erkennbar wird, dass er auch die neueren Formen der Physik bestimmt, die sich ja nach ihrem theoretischen Grundgesetz von der Geometrie als der rationalen Wissenschaft vom Raume nicht wesentlich unterscheidet. Eine solche Methode erfüllt das Lebensgesetz einer offenen Wissenschaft. Durch sie finden Ausführungen wie die Bouligands ihre volle Rechtfertigung. Sich gegenseitig ergänzend und erläuternd eröffnen beide Werke selbst dem Elementarunterricht in der Geometrie neue Möglichkeiten. Der pädagogischen kommt ihre philosophische Bedeutung gleich.In the foregoing article the author endeavours—especially for all who are teaching the Elements—to set forth the significance and importance of two books about geometry. Mr. G. Bouligand's short writing brings out the algebraic and logical structure of that science and presents an »axiomatic« introducing both the notions of »whole« and »group of transformation«. A progressive classification of problems is thus elaborated according to the kinds of solutions that suit them. Mr. F. Gonseth, in his far more comprehensive work, analyses the intuitive, experimental and theoretical aspects of what used to constitute the elementary in classical treatises, then states the researches raised up by Euclid's postulate and leading to the development of the axiomatic method. The triumph of atomism, discovering a world to which the elementary notions of geometry do no longer apply fully, makes it still more difficult to solve the problems of the basing of both geometrical truth and the nature of space. Thanks to his introducing such ideas as »schematic correspondence« and »model«, geometry appears as a rational science in progress using the »axiomatic« as its criterion. But far from offering the characteristics of pure rationality, such an »axiomatic« retains some intuitive bases, even when applied to non‐Euclidian geometries; it organizes a control of our most elementary intuitions by setting them against one another, and secures through their medium the experimental significance and coherence of geometry. Thus a real mutation of the elementary takes place; but it is not owing to mere chance. The method which has presided over that transformation, the historical changes and stages of which are described, is clearly shown, and it is made evident that it also determines the new forms of physics, the theoretical constitution of which does not differ essentially from geometry considered as the rational science of space. That method is the statute of an open science. So Mr. Bouligand's account is fully justified. By elucidating each other, both books open new horizons to the teaching—even elementary—of geometry. The philosophical significance of those books is of no less importance than the pedagogical one. (shrink)

The Industrial Revolution caused an expansion of our ideas of property to include other forms of wealth, such as innovations and productive techniques. And the modern age has caused a further expansion of our ideas of property to include inchoate items, particularly information. The Framers of the U.S. Constitution presumed that government not only took an expansive view of the nature of property rights, they also believed that such rights should be protected. To James Madison and the (...) other Framers, property was a “broad and majestic term” that “embraces everything which may have a value to which man may attach a right.”. (shrink)

We prove that each Σ 0 2 set which is hypersimple relative to $\emptyset$ ' is noncuppable in the structure of the Σ 0 2 enumeration degrees. This gives a connection between properties of Σ 0 2 sets under inclusion and and the Σ 0 2 enumeration degrees. We also prove that some low non-computably enumerable enumeration degree contains no set which is simple relative to $\emptyset$ '.

"Annamarie Jagose knows that queer theory did not spring full-blown from the head of any contemporary theorist. It is the outcome of many different influences and sources, including the homophile movement, gay liberation, and lesbian feminism. In pointing to the history of queer theory-a history that all too often is ignored or elided-Jagose performs a valuable service." -Henry Abelove, co-editor of The Lesbian and Gay Studies Reader The political and academic appropriation of the term queer over the last several years (...) has marked a shift in the study of sexuality from a focus on supposedly essential categories as gay and lesbian to more fluid or queer notions of sexual identity. Yet queer is a category still in the process of formation. In Queer Theory , Annamarie Jagose provides a clear and concise explanation of queer theory, tracing it as part of an intriguing history of same-sex love over the last century. Blending insights from prominent theorists such as Judith Butler and David Halperin, Jagose argues that queer theory's challenge is to create new ways of thinking, not only about fixed sexual identities such as heterosexual and homosexual, but also about other supposedly essential notions such as sexuality and gender and even man and woman. (shrink)

A hundred years ago, Ramsey (1927) devised a new system of notation to more perspicuously represent the idea that ‘p’ and ‘¬¬p’ express the same fact. Recently, Monroy Pérez (2023) has argued that we can apply Ramsey’s insight to solve a recalcitrant problem for logical elitism — the thesis, most famously defended by Sider (2011), that the world’s fundamental metaphysical structure includes logical structure. Here, I discuss the general role of language in the framing of logical elitism and (...) present four arguments that show that the Ramseyan strategy for defending logical elitism fails. First, it does not eliminate all arbitrariness even for zeroth-order classical logic (§3). Second, it is a case of a more general strategy that exploits the fact that classical negation is an involution; then, choosing the Ramseyan proposal among the other cases is arbitrary (§4). Third, there are proposals to solve the riddle that are simpler than every case of the involutory strategy (§5). The discussion has consequences for logical elitism at large: in my fourth argument I contend, contrary to a fairly favoured opinion, that logical elitism should not be thought of as a thesis about languages, but as a thesis about joints in metaphysical tructure (§6). (shrink)

This book is a concise, readable introduction to the Greek author Thucydides, who is widely regarded as one of the foremost historians of all time.Why does Thucydides continue to matter today? Perez Zagorin answers this question by examining Thucydides' landmark History of the Peloponnesian War, one of the great classics of Western civilization. This history, Zagorin explains, is far more than a mere chronicle of the conflict between Athens and Sparta, the two superpowers of Greece in the fifth century (...) BCE. It is also a remarkable story of politics, decision-making, the uses of power, and the human and communal experience of war. Zagorin maintains that the work remains of permanent interest because of the exceptional intellect that Thucydides brought to the writing of history, and to the originality, penetration, and the breadth and intensity of vision that inform his narrative. The first half of Zagorin's book discusses the intellectual and historical background to Thucydides' work and its method, structure, and view of the causes of the war. The following chapters deal with Thucydides' portrayal of the Athenian leader Pericles and his account of some of the main episodes of the war, such as the revolution in Corcyra and the Athenian invasion of Sicily. The book concludes with an insightful discussion of Thucydides as a thinker and philosophic historian.Designed to introduce both students and general readers to a work that is an essential part of a liberal education, this book seeks to encourage readers to explore Thucydides--one of the world's greatest historians--for themselves. (shrink)

Linguistic Semantics: An Introduction is the successor to Sir John Lyons's important textbook Language, Meaning and Context (1981).While preserving the general structure of the earlier book, the author has substantially expanded its scope to introduce several topics that were not previously discussed, and to take account of new developments in linguistic semantics over the past decade. The resulting work is an invaluable guide to the subject, offering clarifications of its specialised terms and explaining its relationship to formal (...) and philosophical semantics and to contemporary pragmatics. With its clear and accessible style it will appeal to a wide student readership. Sir John Lyons is one of the most important and internationally renowned contributors to the study of linguistics. His many publications include Introduction to Theoretical Linguistics (1968) and Semantics (1977). (shrink)

Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation ( ${\neg}$ ) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns (...) out to be a formula-dependent notion and the second one is that the characterization (i.e. equivalence) appears to be pertinent to a class of paraconsistent logics which have double negation property. (shrink)

We don’t always know why we do the things we do. Some of the greatest stories in the history of mankind are built on that tragic fact of human life . A first important theoretical account of this fact was given by ‘les maîtres du soupçon’ at the end of the 19th century . They argued that unconscious motives, social structures and cultural particularities guide our actions beyond our knowledge, a fortiori beyond our control. The last three decades have witnessed (...) the rise of a new generation of masters of suspicion, this time with a background in experimental psychology. Many of these suspicion-inducing experiments will be discussed throughout the special issue. Let us just mention one paradigmatic study by the psychologists Nisbett and Wilson from 1977. One study will suffice to open up the full range of philosophical questions addressed in the contributions to follow.In the Nisbett and Wilson study people are invited .. (shrink)

We introduce an extended intuitionistic linear logic with strong negation and modality. The logic presented is a modal extension of Wansing's extended linear logic with strong negation. First, we propose three types of cut-free sequent calculi for this new logic. The first one is named a subformula calculus, which yields the subformula property. The second one is termed a dual calculus, which has positive and negative sequents. The third one is called a triple-context (...) calculus, which is regarded as a natural extension or generalization of Hodas and Miller's dual-context calculus appearing in a linear logic programming language. Second, we present a concurrent process calculus based on the logic. This calculus is an extension of Okada's process calculus. Third, we introduce a Kripke type semantics for a fragment of the logic, and show the completeness theorems with respect to the semantics. Finally, we mention a logic programming language based on the triple-context calculus. (shrink)

In this book review, I assess the merits of John Nolt's Environmental Ethics for the Long Term: An Introduction. Although the book is written as a primary text for an environmental ethics course, some of its later chapters are clearly written more for academic philosophers than undergraduate students. As a textbook, Nolt's book is excellent and an ideal choice for those who want to emphasize the long-term impacts of various environmental problems (e.g., climate change, biodiversity loss) in their courses. (...) Regarding the more rigorous arguments in the book's latter chapters, although they are novel and provocative, I raise two worries about them that pose challenges for the views that Nolt tries to defend. (shrink)

The structuralist program has developed a useful metascientific resource: ontological reductive links (ORLs) between the constituents of the potential models of reduced and reducing theories. This resource was developed initially to overcome an objection to structuralist ``global'' accounts of the intertheoretic reduction relation. But it also illuminates the way that concepts at a higher level of scientific investigation (e.g., cognitive psychology) become ``structured through reduction'' to lower-level investigations (e.g., cellular/molecular neuroscience). After (briefly) explaining this structuralist background, I demonstrate how this (...) resource illuminates an actual, emerging scientific example: the link between the psychological concept of a ``consolidation switch'' from short-term to long-term memory and the cellular/molecular mechanisms of the transition from early- to late-phases of long-term potentiation (LTP) (an important type of synaptic plasticity in mammalian hippocampus and cortex). (shrink)

Among several recent short introductions to the thought and work of Martin Heidegger, this is perhaps the best, especially for beginning students, since for the most part it faithfully represents Heidegger’s thought while remaining free of excessive German terminology. The author stays close to the standard translations of Heidegger’s basic words, but also sometimes offers fresh versions of key terms that shed light on Heidegger’s thought in ways that will stimulate specialists; for example, “minding” for Sorge and “facing up (...) [to]” for Vorlaufen. Polt’s introduction to Heidegger contains important discussions of the relevance of Heidegger’s thought to logic, language, and art, as well as to his political stance during the period of dominance of National Socialism in Germany. (shrink)

_Engaging Bioethics: An Introduction with Case Studies_ draws students into this rapidly changing field, helping them to actively untangle the many issues at the intersection of medicine and moral concern. Presuming readers start with no background in philosophy, it offers balanced, philosophically based, and rigorous inquiry for undergraduates throughout the humanities and social sciences as well as for health care professionals-in-training, including students in medical school, pre-medicine, nursing, public health, and those studying to assist physicians in various capacities. Written (...) by an author team with more than three decades of combined experience teaching bioethics, this book offers Flexibility to the instructor, with chapters that can be read independently and in an order that fits the course structure Up-to-date coverage of current controversies on topics such as vaccination, access to health care, new reproductive technologies, genetics, biomedical research on human and animal subjects, medically assisted death, abortion, medical confidentiality, and disclosure Attention to issues of gender, race, cultural diversity, and justice in health care Integration with case studies and primary sources Pedagogical features to help instructors and students, including Chapter learning objectives Text boxes and figures to explain important terms, concepts, and cases End-of-chapter summaries, key words, and annotated further readings Discussion cases and questions Appendices on moral reasoning and the history of ethical issues at the end and beginning of life An index of cases discussed in the book and extensive glossary/index A companion website with a virtual anthology linking to key primary sources, a test bank, topics for papers, and PowerPoints for lectures and class discussion. (shrink)

This accessible introduction to formal, and especially Montague, semantics within a linguistic framework, presupposes no previous background in logic, but takes students step-by-step from simple predicate/argument structures and their interpretation to Montague's intentional logic.

The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a (...) constraint model, which includes relevant theories. These three modelings have been seriously confused in the modern literature: untangling them helps motivate the main themes advanced concerning traditional negation and natural negation. Firstly, the dominant traditional view, except around scholastic times when the explosion view was in ascendency, has been the cancellation view, so that the mainstream negation of much of traditional logic is distinctively nonclassical. Secondly, the primary negation determinable of natural negation is ·relevant negation. In order to picture relevant negation the traditional idea of negation as otherthanness is progressive) refined, to nonexclusive restricted otherthanness. Several pictures result, a reversal picture, a debate model, a record cabinet (or files of the universe) model which help explain relevant negation. Two appendices are attached, one on negation in Hegel and the Marxist tradition, the other on Wittgenstein's treatment of negation and contradiction. (shrink)

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities (...) between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (shrink)

This paper is a reaction to the following remark by grzegorczyk: "the compound sentences are not a product of experiment. they arise from reasoning. this concerns also negations; we see that the lemon is yellow, we do not see that it is not blue." generally, in science the truth is ascertained as indirectly as falsehood. an example: a litmus-paper is used to verify the sentence "the solution is acid." this approach gives rise to a (very intuitionistic indeed) conservative extension of (...) the heyting logic satisfying natural duality laws. (shrink)

The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relevant logics; a defense of dialetheic (...) theory of negation; stable negation in logic programming; antirealism and falsity; and negation, denial, and language change in philosophical logic. Suited to scholars and graduate students in the fields of philosophy, logic mathematics, computer science, and linguistics. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

The ways in which space-time points and elementary particles are modeled share a curious feature: neither seems to specify which basic object has which properties. This chapter sketches the motivation for this claim and searches for an explanation for it. After reviewing several proposals, it argues for a view according to which objects occupy their place in a given relational structure essentially. This view, which is termed minimal structural essentialism, provides a metaphysical grounding for the physical equivalence of models (...) related by permutation. An interesting consequence of this position is that space-time points and elemental particles turn out to be individuals, albeit of a rather different sort than has traditionally been considered. (shrink)