Categorical proof theory is an approach to understanding the structure of proofs. We illustrate the idea first by analyzing G0̈del's Dialectica interpretation and the Diller-Nahm variant in categorical terms. Then we consider the problematic question of the structure of classical proofs. We show how double negation translations apply in the case of the Dialectica interpretations. Finally we formulate a proposal as to how to give a more faithful analysis of proofs in the sequent calculus.

Cramer et al. contrast two possible explanations for psychological symptoms: latent variables (i.e., specific cause) versus a network of causality between symptoms. There is a third explanation: The reason for comorbidity and the reported network structure of psychological symptoms is that the underlying biological cause is a psychoneuroimmunoendocrine information network which, when dysregulated, leads to several maladaptive psychological and somatic symptoms.

Subjects and Simulations presents essays focused on suffering and sublimity, representation and subjectivity, and the relation of truth and appearance through engagement with the legacies of Jean Baudrillard and Philippe Lacoue-Labarthe.

We examined the hypothesis that a tendency to experience the world in terms of a sense of ‘special’ connection is responsible for the self-transcendent value dimension identified by multi-dimensional scaling and constitutes a common factor for different religious and non-religious interpretations of spirituality. Eight different groups were studied including: six different types of faith leaders in India and the UK, people who self-rated as spiritual but not religious, and those self-rating as neither spiritual nor religious. They completed a questionnaire that (...) assessed the strength of their spirituality irrespective of type and the experience of special connection to the following categories: people, nature, places and the universe, with and without using the term spiritual. For all eight samples the different types of connection were highly inter-correlated, and self-perceived spirituality correlated with the sum of connection items irrespective of whether items included the term spiritual or not. Variation between groups in the size of the latter correlation was consistent with different interpretations of spirituality in those groups. Although the meaning of spirituality is socially constructed, variability within faith leader groups suggests that its interpretation is also affected by personality. (shrink)

When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove consistency of first order arithmetic by reducing it to a quantifier-free theory with finite types. Like other functional interpretations Gödel’s Dialectica interpretation gives rise to category theoretic constructions that serve both as new models for logic and semantics and as tools for analysing and understanding various aspects of the Dialectica interpretation itself. Gödel’s Dialectica interpretation gives rise to the Dialectica categories , in: Contemp. (...) Math., vol. 92, Amer. Math. Soc., Providence, RI, 1989, pp. 47–62] and J.M.E. Hyland in [J.M.E. Hyland, Proof theory in the abstract, Ann. Pure Appl. Logic 114 43–78, Commemorative Symposium Dedicated to Anne S. Troelstra ]). These categories are symmetric monoidal closed and have finite products and weak coproducts, but they are not Cartesian closed in general. We give an analysis of how to obtain weakly Cartesian closed and Cartesian closed Dialectica categories, and we also reflect on what the analysis might tell us about the Dialectica interpretation. (shrink)

Peter Eli Gordon - Heidegger and the Greeks: Interpretive Essays - Journal of the History of Philosophy 46:1 Journal of the History of Philosophy 46.1 178-179 Muse Search Journals This Journal Contents Reviewed by Peter E. Gordon Harvard University Drew A. Hyland and John Panteleimon Manoussakis, editors. Heidegger and the Greeks: Interpretive Essays. Bloomington-Indianapolis: University of Indiana Press, 2006. Pp. xiii + 194. Paper, $24.95. Heidegger's troubled and over-determined interest in Greek philosophy is well known. In the 1933 rectoral (...) address, he declared that genuine science would become possible only "if we again place ourselves under the power of the beginning of our spiritual-historical existence. This beginning is the departure, the setting out, of Greek philosophy." All of Western science, Heidegger concluded, "remains bound to that beginning of philosophy. From it science draws the strength of its essence, assuming that it still remains at all equal to this beginning." Such claims bear witness to his life-long interpretive confrontation with the dawning figures of Western philosophy: Aristotle, Plato, and the pre-Socratics. Heidegger's.. (shrink)

Kleene's realizability interpretation for first-order arithmetic was shown by Hyland to fit into the internal logic of an elementary topos, the “Effective topos” . In this paper it is shown, that there is an internal realizability definition in , i.e. a syntactical translation of the internal language of into itself of form “n realizes ” , which extends Kleene's definition, and such that for sentences , the equivalence [harr]n is true in . The internal realizability definition depends on finding (...) separated covers for non-separated objects of . However, for the objects arising in higher-order arithmetic, canonical covers are available, which are definable in higher-order arithmetic. These canonical covers yield “covering axioms”. It is shown that these covering axioms, together with uniformity principles and Extended Church's Thesis, axiomatize a formalized extension of Kleene realizability to a constructive system of higher-order arithmetic. The details are worked out for second and third-order arithmetic, but the method can be extended to any order. As an application, it is shown in the final section that a certain completeness property of the category of “modest sets” can be derived in third-order arithmetic from the realizability axioms. (shrink)

A highly contentious issue in recent philosophy of logic has been the question of whether there can be contingently true identity statements. In this paper I want to investigate a possible loop-hole in the standard argument of the necessitarians (i.e., those who maintain that any true identity statement is necessarily true).

Tutte le dottrine tradizionali, da quelle più arcaiche e "primitive" a quelle più evolute e articolate, hanno sempre affermato che l'uomo non è un essere solamente corporeo, sia pur dotato di ingegno e di intelligenza, ma è un essere dalla natura composita, formato da una parte materiale e da una o più componenti invisibili e "sottili" e che in lui risiede un principio immortale di origine divina o comunque soprannaturale. Secondo il modo di vedere tradizionale, l'uomo, per conoscere e realizzare (...) se stesso, deve pertanto prendere coscienza, in primo luogo ed essenzialmente, di questa sua natura di essere composito e immortale, e questa è una di quelle idee universali (per noi forse la più importante) che troviamo diffuse presso tutte le popolazioni del pianeta, anche se con sfumature diverse nelle varie tradizioni..."--Cover flap. (shrink)

This book looks at facets in the history of capitalism from the Enlightenment period, through the emergence of the American Empire in the Pacific, and to the contemporary era of neoliberal globalization. This re-telling of history is done by drawing from the works of E. San Juan, Jr., considered arguably one of the great contemporary cultural and literary critics of our time. In this author's view, San Juan's lifetime of works offer a living documentation of, among others, the history and (...) thought of the modern world highlighted by the rise of capitalism through the contemporary era of neoliberal globalization, and shepherded to its hegemonic status by what stands today as the preeminent empire of the United States. The book underscores the symbiosis between contemporary capitalism as an economic system based on accumulation on the one hand, and the American imperial state on the other, just as it revisits the colonial project that was carried out in capitalism's wake, the violence and subjugation inflicted on its victims, and how this colonial project has morphed into a new form of colonialism maintained and enforced through the rules and institutional mechanisms of what is popularly known as neoliberal globalization that also provides the ideological and legal rationale for the commodification and the ultimate grab of the global commons reminiscent of the classical, albeit cruder, form of colonialism. (shrink)

Throughout the long history of Classic Maya hieroglyphs, a logosyllabic writing system used from the late first millennium BCE through the mid-second millennium CE in southern Mesoamerica, the most commonly recorded phonetic value was the syllable u (/ʔu/). With over a dozen different u hieroglyphs, Classic Maya scribes had more options for recording /ʔu/ than any other syllable or logograph. Cognitive approaches to writing systems typically attribute graphemic variation (i.e., alternation between signs with equivalent linguistic value) to semantic differences like (...) animacy or to non-linguistic factors like identity. Distribution of Classic Maya u hieroglyphs, however, suggests that morphosyntactic context influenced which grapheme scribes wrote and when. This case suggests that scribal knowledge of Classic Maya hieroglyphs included ideas about writing's relationship to language. It also highlights the cognitive relevance of morphosyntax for a writing system's users as they differentiate among graphic signs with identical linguistic denotation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.3 (2001) 505-522 [Access article in PDF] Mary Astell's Ironic Assault on John Locke's Theory of Thinking Matter E. Derek Taylor Mary Astell (1666-1731), most famous today for her call for the establishment of Protestant nunneries in Serious Proposal to the Ladies, Part I (1694) and for her acute Reflections Upon Marriage (1700), has lurked for years at the edges of that infinitely (...) contentious category "feminism," but she is only now beginning to receive her rightful inheritance as a theological and philosophical thinker, probably the title she would most have preferred. 1 This is not to say that Astell's Christian-Platonism has been ignored. In her 1986 biography Ruth Perry gave cogent expression to the centrality of Astell's idealist Christianity to all aspects of her thought 2 and in the same year, Bridget Hill thoughtfully warned her readers against attempting to force Astell, a religious conservative, "into some preconceived idea of what late seventeenth and early eighteenth century feminism ought to have been." 3 More recently, Patricia Springborg has written two significant essays that rely in part on Astell's more neglected theological-philosophical works, Letters concerning the Love of God (1695), a collection of Astell's correspondence with John Norris of Bemerton (1657-1711), and The Christian Religion, As Professed by a Daughter of the Church of England (1705; 3d edition 1730), far and away her most developed theological-philosophical [End Page 505] statement. 4 Despite these important forays, however, both Letters and Christian Religion continue to be largely ignored, as is suggested by the relative dearth of scholarly work on either text and the short shrift each receives in anthologies of Astell's works. 5 Despite the great popularity of Letters throughout the eighteenth century and despite the fact that, as Springborg points out, Astell considered Christian Religion "her magnum opus," neither text has found new life in a modern edition. 6This omission creates a rather vexing problem for would-be scholars of Astell's philosophical and theological ideas. The major primary texts themselves not being available, we have little choice but to rely on the limited accounts of other scholars for our information. Over a decade ago, for instance, The Journal of the History of Philosophy published a long note by Kathleen M. Squadrito on "Mary Astell's Critique of John Locke's View of Thinking Matter," and hers has since been the standard (if not quite only) account of this historically fascinating and important philosophical comment in Christian Religion.7 Squadrito wants, she writes, to "present a short account of [Astell's] work and her criticism of Locke's view of thinking matter." 8 Unfortunately, Squadrito's account of Astell's "work" is significantly flawed, which leads her to serious mischaracterizations of Astell's "criticism" of Locke's hypothesis. Briefly put, Astell's "own philosophy" in Christian Religion does not, as Squadrito claims, emerge "as an attempted reconciliation of the views of Norris and Locke" 9 ; because she supposes it does, however, Squadrito is able to present Astell's critique of Locke's theory [End Page 506] of thinking matter as a respectful, even-handed philosophical analysis, a theoretical bridge, as it were, between the Platonism of Norris and the Empiricism of Locke. As we shall see, Astell's critique of Locke's hypothesis actually amounts to a bitterly ironic assault, wherein Astell does not so much build bridges as burn them. Just why Astell in Christian Religion decided not to strike a middling position between Locke and Norris, and how this decision invigorated her attack on Locke's materialist hypothesis, are the primary questions this essay seeks to answer. In order to arrive at such answers, however, it is necessary first to examine the text in which Astell does attempt to carve out a position between Locke and Norris, namely Astell and Norris's Letters.The basic history of Letters is well enough understood. Mary Astell, a well-read young woman of significant perspicacity, first wrote in... (shrink)

Decisions related to animal welfare standards depend on farmer’s multiple goals and values and are constrained by a wide range of external and internal forces. The aim of this paper is twofold, i.e., to develop a theoretical framework for farmers’ AW decisions that incorporates farmers’ goals, use and non-use values and to present an approach to empirically implement the theoretical framework. The farmer as a head of the farm household makes choices regarding production to maximize the utility of the household. (...) The overall utility of the farmer is determined by his multiple objectives. For the analysis of multi-objective problems, the multiple criteria decision - making paradigm provides an appropriate theoretical framework. However, theories from the field of social-psychology are needed to facilitate the identification of all relevant aspects in the decision making. The practical use of the conceptual framework is demonstrated using a simple numerical application of a multi-objective programming model. Two workshops were devoted to examining the scientific consistency and the practical usefulness of the approach. Implementing this approach will increase knowledge of the main factors and barriers that determine farmers’ decisions with regard to AW standards. This knowledge is relevant during the development of new AW concepts that aims to supply products that comply with above-legal AW standards for middle-market segments. (shrink)

Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form S=∫ L 1 Φ d 4 x+∫ L 2 $\sqrt{-g}$ d 4 x where the volume element Φ d 4 x is independent of the metric. For global scale invariance, a “dilaton” φ has to be introduced, with non-trivial potentials V(φ)=f 1 eαφ in L 1 and U(φ)=f 2 e 2αφ in L 2 . This leads to non-trivial (...) mass generation and a potential for φ which is interesting for inflation. Interpolating models for natural transition from inflation to a slowly accelerated universe at late times appear naturally. This is also achieved for “Quintessential models,” which are scale invariant but formulated with the use of volume element Φ d 4 x alone. For closed strings and branes (including the supersymmetric cases), the modified measure formulation is possible and does not require the introduction of a particular scale (the string or brane tension) from the begining but rather these appear as integration constants. (shrink)

E. Jayne Whitea, Catherine Matsuob and Fiona WestbrookcaUniversity of Canterbury; bFukuoka University; cAuckland University of Technology (AUT)This collective writing piece takes its points of depa...

In the fourth section of Goethe’s Zahme Xenien we find the quatrain from which I have taken the theme of such an old and new controversy, which, as I hope, concerns both Germanic studies and the other humanities: “What was it that kept you from us so apart?” I always read Plutarch again and again. “And what was the lesson he did impart?” “They were all human beings—so much is plain.”1 In the very years when Goethe wrote these lines, that (...) is in the 1820s, Hegel repeatedly gave his lectures on the philosophy of history. Right at the beginning he formulated the opposite view which I should like briefly to characterize as “cultural relativism.”Every age has such peculiar circumstances, such individual conditions that it must be interpreted, and can only be interpreted, by reference to itself…. Nothing is shallower in this respect than the frequent appeal to Greek and Roman example which so often occurred among the French at the time of their Revolution. Nothing could be more different than the nature of these peoples and the nature of our own times.2 What is at issue here is not, of course, Hegel’s assertion that ages and peoples differ from each other. We all know that, and Goethe, the attentive reader and traveler, also knew, for instance, that the Roman carnival differed in its character from the celebrations of the Feast of Saint Rochus at Bingen, both of which he had described so lovingly. What makes the cultural historian into a cultural relativist is only the conclusion which we saw Hegel draw, that cultures and styles of life are not only different but wholly incommensurable, in other words that it is absurd to compare the peoples of a region or an age with human beings of other zones because there is no common denominator that would justify us in doing so. 1. ‘Was hat dich nun von uns entfernt?’ Hab immer den Plutarch gelesen. ‘Was has du den dabei gelernt?’ Sind eben alles Menschen gewesen.’ Johann Wolfgang von Goethe, Sämtlich Werke. Jubiläums-ausgabe in 40 Bänden 4:73; with commentary.2. See Georg Wilhelm Friedrich Hegel, Vorselungen über die Philosophie der Geschichte, Werke, 20 vols. , 12:17. E. H. Gombrich was director of the Warburg Institute and Professor of the History of the Classical Tradition at the University of London from 1959 to 1976. His many influential works include The Story of Art, Art and Illusion, Meditations on a Hobby Horse, The Sense of Order, Ideals and Idols, The Image and the Eye, Tributes, Aby Warburg, and New Light on Old Masters. His previous contributions to Critical Inquiry include “The Museum: Past, Present and Future” , “Standards of Truth: The Arrested Image and the Moving Eye” , and “Representation and Misrepresentation”. (shrink)