In this paper are studied the properties of the proofs in PRA of provability logic sentences, i.e. of formulas which are Boolean combinations of formulas of the form PIPRA, where h is the Gödel-number of a sentence in PRA. The main result is a Normal Form Theorem on the proof-trees of provability logic sequents, which states that it is possible to split the proof into an arithmetical part, which contains only atomic formulas and has an essentially intuitionistic character, and into (...) a logical part, which is merely instrumental. Moreover, the induction rules which occur in the arithmetical part are implicit. Some applications of the Normal Form Theorem are shown in order to obtain some syntactical results on the PRA-completeness of modal logic. In particular a completeness theorem for Boolean combinations of modalities is given. (shrink)

In this paper the PA-completeness of modal logic is studied by syntactical and constructive methods. The main results are theorems on the structure of the PA-proofs of suitable arithmetical interpretationsS of a modal sequentS, which allow the transformation of PA-proofs ofS into proof-trees similar to modal proof-trees. As an application of such theorems, a proof of Solovay's theorem on arithmetical completeness of the modal system G is presented for the class of modal sequents of Boolean combinations of formulas of the (...) form p i,m i=0, 1, 2, ... The paper is the preliminary step for a forthcoming global syntactical resolution of the PA-completeness problem for modal logic. (shrink)

This paper is the second part of the syntactic demonstration of the Arithmetical Completeness of the modal system G, the first part of which is presented in [9]. Given a sequent S so that ⊢GL-LIN S, ⊬G S, and given its characteristic formula H = char(S), which expresses the non G-provability of S, we construct a canonical proof-tree T of ~ H in GL-LIN, the height of which is the distance d(S, G) of S from G. T is the syntactic (...) countermodel of S with respect to Gand is a tool of general interest in Provability Logic, that allows some classification in the set of the arithmetical interpretations. (shrink)

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G). (shrink)

This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, (...) so that ⊢GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢PA Sξ and d(S, G) > 0 imply the inconsistency of PA. (shrink)

A conjectural inference is proposed, aimed at producing conjectural theorems from formal conjectures assumed as axioms, as well as admitting contradictory statements as conjectural theorems. To this end, we employ Paraconsistent Informational Logic, which provides a formal setting where the notion of conjecture formulated by an epistemic agent can be defined. The paraconsistent systems on which conjectural deduction is based are sequent formulations of the C-systems presented in Carnielli-Marcos [CAR 02b]. Thus, conjectural deduction may also be considered to be a (...) tool for investigating the properties of paraconsistency in general. (shrink)

Italian political thinker Paolo Virno argues that the category of "multitude" is a far better tool to analyze contemporary issues than the Hobbesian concept of "people." Globalization is forcing us to rethink some of the categories—such as "the people"—that traditionally have been associated with the now eroding state. Italian political thinker Paolo Virno argues that the category of "multitude," elaborated by Spinoza and for the most part left fallow since the seventeenth century, is a far better tool to (...) analyze contemporary issues than the Hobbesian concept of "people," favored by classical political philosophy. Hobbes, who detested the notion of multitude, defined it as shunning political unity, resisting authority, and never entering into lasting agreements. "When they rebel against the state," Hobbes wrote, "the citizens are the multitude against the people." But the multitude isn't just a negative notion, it is a rich concept that allows us to examine anew plural experiences and forms of nonrepresentative democracy. Drawing from philosophy of language, political economics, and ethics, Virno shows that being foreign, "not-feeling-at-home-anywhere," is a condition that forces the multitude to place its trust in the intellect. In conclusion, Virno suggests that the metamorphosis of the social systems in the West during the last twenty years is leading to a paradoxical "Communism of the Capital.". (shrink)

The philosophical analysis of mathematical explanations concerns itself with two different, although connected, areas of investigation. The first area addresses the problem of whether mathematics can play an explanatory role in the natural and social sciences. The second deals with the problem of whether mathematical explanations occur within mathematics itself. Accordingly, this entry surveys the contributions to both areas, it shows their relevance to the history of philosophy and science, it articulates their connection, and points to the philosophical pay-offs to (...) be expected by deepening our understanding of the topic. (shrink)

At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of .

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

The temporality of intentions and actions in situations of social interaction can sometimes be paradoxical. I argue that in these situations it may sometimes be possible to conceive of individual acts that can, in a strong sense, be intended retroactively. This could happen when the relational patterns in social interaction literally alter the virtual structure of a participant's past corporeal intentions resulting in an odd experience of having intended something all along without knowing it. I propose that this possibility should (...) be interpreted as more than just a narrowly epistemic phenomenon. Examining this claim involves clarifying the enactive perspective on intentionality, which I do here. The enactive approach rejects the model of a causal relation between intention and action for one of an intrinsic qualitative relation between the two as facets of sense-making. I develop this idea and compare it with Merleau-Ponty's Fundierung model of the mutual relation between corporeal and reflexive intentionality to show that co-regulated moves/affections during social interaction may modulate both arcs of this relation, creating the possibility of a re-signification that alters not the actuality but the virtual tendencies that preceded the social act. (shrink)

This paper explores the epistemology of extrapolation from model organisms to humans in molecular medicine. We take into account two common views on the issue, the homology view and the disanalogy view. In response to both interpretations, we argue that the foundational basis of extrapolations cannot simply be provided by homology and that relevant disanalogies can, thanks to the techniques of molecular biology, be experimentally controlled and exploited to allow useful and reliable extrapolations. The case of "humanised mice" in the (...) context of cancer stem cell research provides evidence of how animal models can be construed to approximate bona fide causal analogue models of human diseases. To supplement this view we show how the epistemology of model organisms needs to take into account the engineering side of molecular medicine. Model organisms are often manipulated to create analogies or remove disanalogies with the target system. We maintain that highlighting this feature is fundamental to explain what warrants extrapolation in the search for the molecular causes of disease. (shrink)

Bringing together contributors from philosophy, international relations, security studies, and strategic studies, New Wars and New Soldiers offers a truly interdisciplinary analysis reflective of the nature of modern warfare. This comprehensive approach allows the reader to see the broad scope of modern military ethics, and to understand the numerous questions about modern conflict that require critical scrutiny. Aimed at both military and academic audiences, this paperback will be of significant interest to researchers and students in philosophy, sociology, military and strategic (...) studies, international relations, politics, and security studies, acting as an ideal course text or as supplementary reading. (shrink)

A novel theoretical framework for an embodied, non-representational approach to language that extends and deepens enactive theory, bridging the gap between sensorimotor skills and language. -/- Linguistic Bodies offers a fully embodied and fully social treatment of human language without positing mental representations. The authors present the first coherent, overarching theory that connects dynamical explanations of action and perception with language. Arguing from the assumption of a deep continuity between life and mind, they show that this continuity extends to language. (...) Expanding and deepening enactive theory, they offer a constitutive account of language and the co-emergent phenomena of personhood, reflexivity, social normativity, and ideality. Language, they argue, is not something we add to a range of existing cognitive capacities but a new way of being embodied. Each of us is a linguistic body in a community of other linguistic bodies. The book describes three distinct yet entangled kinds of human embodiment, organic, sensorimotor, and intersubjective; it traces the emergence of linguistic sensitivities and introduces the novel concept of linguistic bodies; and it explores the implications of living as linguistic bodies in perpetual becoming, applying the concept of linguistic bodies to questions of language acquisition, parenting, autism, grammar, symbol, narrative, and gesture, and to such ethical concerns as microaggression, institutional speech, and pedagogy. (shrink)

Christ as symbol in Kant¿s religion -- Hegel's conception of God -- The reality of religion in Hegel's idealist metaphysics -- Hegel's version of the ontological argument for the existence of God -- The trinity and the I -- The death of God and recognition of the self -- Beyond subjectivism -- The relevance of Hegel's philosophy of religion today.

Summary This article presents three hitherto unpublished letters by Frank Plumpton Ramsey on the foundations of mathematics with commentary. One of the letters was sent to Abraham Fraenkel and the other two letters to Heinrich Behmann. The transcription of the letters is preceded by an account that details the extent of Ramsey's known contacts with mathematical logicians on the Continent.

The Relationship of Philosophy to Religion Today is a collection of texts authored by philosophers with an interest in contemporary philosophy of religion, its merits and its limitations. The collection has been stimulated by such questions as: "What ought philosophy of religion be?" and "How ought philosophy relate to religion today?" In pursuing such questions, the editors have asked the contributors to offer their insights and reflections on issues that they see as important to contemporary philosophy of religion, with the (...) goal of producing a collection of texts offering the reader a variety of perspectives without privileging any particular philosophical, religious or irreligious orientation. The book covers such themes as the relationship between religion and modernity, faith in keeping with reason, contemplation, the merits and limitations of the atheism, and the relationship between philosophy, religion and politics. (shrink)

In Cabo Delgado, Mozambique, the year of 2020 marked a dramatic escalation of military activities of the Islamist insurgent group locally known as Al-Shabab or mashababe. This intensification was accompanied by a more immaterial phenomenon: the rise in prominence of social media, both as battleground and as public forum. While the insurgents sacked and occupied major towns and district headquarters, the Web 2.0 networks - Facebook and WhatsApp especially - became the central arena in which the war was apprehended and (...) discussed. This essay is an exploration of the entwining of social media with the 'new war' in Cabo Delgado, focussing on the events that surround the conquest of the Makonde plateau, mythical cradle of the Mozambican liberation struggle. Building on a budding literature on digital militarism, the essay dwells especially on orality and the use of the voice note as a medium to convey information deemed to be more trustworthy and stable than images. Tracking these media and their interrelations, the essay establishes a narrative, however fragmentary, of the downfall of the Makonde plateau; highlights recurring features of violence in the Cabo Delgado conflict; and provides fresh insight into the formation of the Local Force (Força Local), a State-sponsored militia largely constituted by war veterans. (shrink)

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on (...) the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

Le but de cet ouvrage est de montrer la teneur philosophique unitaire de la pensée critique de Diderot par delà le caractère éclaté et dispersé de son œuvre. Diderot philosophe est présenté comme un penseur critique et systématique, c'est-à-dire un philosophe dont la réflexion, d'une part, s'inscrit dans le cadre du courant de pensée moderne qui vise à dépasser les perspectives du « premier regard géomètre de la raison », celui de Descartes, de Malebranche et des post-cartésiens. D'autre part, elle (...) atteint un « second regard critique », plus profond, jeté sur le monde de la nature et surtout, sur lui-même (une philosophie de l'aperception : Spinoza, Wolff, les Moralistes anglais et Kant), qui se rattache intimement à un matérialisme biologique tout à fait original, issu de la confrontation de Diderot avec les naturalistes et les médecins de son temps. C'est ce matérialisme élaboré dans l'usine encyclopédique qui met en cause la notion clé d'« individualité naturelle » (jouée en couplet avec une « communauté du désir ») - néologisme dont Le Neveu de Rameau et Le Rêve de D'Alembert développeront les tenants et les aboutissants philosophiques -, et qui témoigne de la nouveauté d'approche propre à cette philosophie, à l'intérieur de la pensée des Lumières européennes. Avec Diderot, c'est une nouvelle figure historique de la philosophie elle-même - celle de la subjectivité individuelle complexe, uni-totalité de penser-sentir-agir - qui monte sur la scène de la modernité, comme étant la substance première, incontournable et insaisissable, de la pensée critique de nos jours. (shrink)