We show that arbitrary tautologies of Johansson’s minimal propositional logic are provable by “small” polynomial-size dag-like natural deductions in Prawitz’s system for minimal propositional logic. These “small” deductions arise from standard “large” tree-like inputs by horizontal dag-like compression that is obtained by merging distinct nodes labeled with identical formulas occurring in horizontal sections of deductions involved. The underlying geometric idea: if the height, h(∂), and the total number of distinct formulas, ϕ(∂), of a given tree-like deduction ∂ of a minimal (...) tautology ρ are both polynomial in the length of ρ, |ρ|, then the size of the horizontal dag-like compression ∂ᶜ is at most h(∂)×ϕ(∂), and hence polynomial in |ρ|. That minimal tautologies ρ are provable by tree-like natural deductions ∂ with |ρ|-polynomial h(∂) and ϕ(∂) follows via embedding from Hudelmaier’s result that there are analogous sequent calculus deductions of sequent ⇒ρ. The notion of dag-like provability involved is more sophisticated than Prawitz’s tree-like one and its complexity is not clear yet. Our approach nevertheless provides a convergent sequence of NP lower approximations of PSPACE-complete validity of minimal logic. (shrink)

This paper is a continuation of dag-like proof compression research initiated in [9]. We investigate proof compression phenomenon in a particular, most transparent case of propositional DNF Logic. We define and analyze a very efficient semi-analytic sequent calculus SEQ*0 for propositional DNF. The efficiency is achieved by adding two special rules CQ and CS; the latter rule is a variant of the weakened substitution rule WS from [9], while the former one being specially designed for DNF sequents. We show that (...) dag-like SEQ*0 has good deterministic proof search strategy. Furthermore, we expose six examples showing that dag-like deducibility in SEQ*0 admits exponential-size proof compression, as compared to familiar proof systems like cutfree sequent calculi, resolution and cutting plane proof systems. (shrink)

It is part of an old folklore that logic should not have existential theo- rems or existential validities. One should not prove in pure logic the existence of anything whatsoever; nothing could be proved by means of logic alone to necessarily exist. Whatever exists might not exist. This standpoint has been expressed by several philosophers from different traditions, such as Hume, Kant, Orenstein and Quine. We now set the stage by examining some issues. Our main question is: “Do we actually (...) have existential theorems in logic?” Two possible attitudes towards this question are as follows. A desideratum: logic should not have any existential theorems. A fact: logic does not have any existential theorems. (shrink)

The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to extend (...) Seldin's normalization strategy to Peirce's rule by showing that every derivation Π in the implicational fragment can be transformed into a derivation Π' such that no application of Peirce's rule in Π' occurs above applications of →-introduction and →-elimination. As a corollary of Seldin's normalization strategy we obtain a form of Glivenko's theorem for the classical {→}-fragment. (shrink)

A lógica não contém teoremas puramente existenciais: as únicas sentenças existenciaisválidas são aquelas com análogas universais válidas. Aqui, mostramos que istorealmente é assim quando corretamente interpretado: toda validade ex- istencial possuiuma análoga universal simples, que também é válida. Também caracterizamos validadesuniversais e existenciais em termos de tautologias.

This is the report on the XVI BRAZILIAN LOGIC CONFERENCE (EBL 2011) held in Petrópolis, Rio de Janeiro, Brazil between May 9–13, 2011 published in The Bulletin of Symbolic Logic Volume 18, Number 1, March 2012. -/- The 16th Brazilian Logic Conference (EBL 2011) was held in Petro ́polis, from May 9th to 13th, 2011, at the Laboratório Nacional de Computação o Científica (LNCC). It was the sixteenth in a series of conferences that started in 1977 with the aim of (...) congregating logicians from Brazil and abroad, furthering interest in logic and its applications, stimulating cooperation, and contributing to the development of this branch of science. EBL 2011 included more than one-hundred and fifty participants, all of them belonging to prominent research institutes from Brazil and abroad, especially Latin America. The conference was sponsored by the Academia Brasileira de Ciências (ABC), the As- sociation for Symbolic Logic (ASL), Universidade Estadual de Campinas (UNICAMP), Centre for Logic, Epistemology and the History of Sciences (CLE), Laboratório Nacional de Computação o Científica (LNCC), Pontif ́ıcia Universidade Cato ́lica do Rio de Janeiro (PUC- Rio), Sociedade Brasileira de Lógica (SBL), and Universidade Federal Fluminense (UFF). Funding was provided by Conselho Nacional de Desenvolvimento Cient ́ıfico e Tecnolo ́ gico (CNPq), Fundac ̧a ̃o de Amparo `a Pesquisa do Estado de São Paulo (FAPESP), Fundação Euclides da Cunha (FEC), and Universidade Federal Fluminense (UFF). The members of the Scientific Committee were: Mário Folhadela Benevides (COPPE- UFRJ), Fa ́bio Bertato (CLE-IFCH-UNICAMP), Jean-Yves Béziau (UFRJ), Ricardo Bianconi (USP), Juliana Bueno-Soler (UFABC), Xavier Caicedo (Universidad de Los An- des), Walter Carnielli (CLE-IFCH-UNICAMP), Oswaldo Chateaubriand Filho (PUC-Rio), Marcelo Esteban Coniglio (CLE-IFCH-UNICAMP), Newton da Costa (UFSC, President), Antonio Carlos da Rocha Costa (UFRG), Alexandre Costa-Leite (UnB), I ́tala M. Loffredo D’Ottaviano (CLE-IFCH-UNICAMP), Marcelo Finger (USP), Edward Hermann Haeusler (PUC-Rio), Décio Krause (UFSC), João Marcos (UFRN), Ana Teresa de Castro Martins (UFC), Maria da Paz Nunes de Medeiros (UFRN), Francisco Miraglia (USP), Luiz Car- los Pereira (PUC-Rio and UFRJ), Elaine Pimentel (UFMG), and Samuel Gomes da Silva (UFBA). The members of the Organizing Committee were: Anderson de Araujo (UNICAMP), Walter Carnielli (CLE-IFCH-UNICAMP), Oswaldo Chateaubriand Filho (PUC-Rio, Co- chair), Marcelo Correa (UFF), Renata de Freitas (UFF), Edward Hermann Haeusler (PUC- RJ), Hugo Nobrega (COPPE-UFRJ), Luiz Carlos Pereira (PUC-Rio e IFCS/UFRJ), Leandro Suguitani (UNICAMP), Rafael Testa (UNICAMP), Leonardo Bruno Vana (UFF), and Petrucio Viana (UFF, Co-chair). (shrink)

Upshot: In view of Kenny’s clinical insights, Hug’s notes on the intricacies of rational vs. a-rational “knowing” in the design sciences, and Chronaki & Kynigos’s notice of mathematics teachers’ meta-communication on experiences of change, this response reframes the heuristic power of bisociation and suspension of disbelief in the light of Kelly’s notion of “as-if-ism” (constructive alternativism. Doing as-if and playing what-if, I reiterate, are critical to mitigating intra-and inter-personal relations, or meta-communicating. Their epistemic status within the radical constructivist framework is (...) cast in the context of mutually enriching conversational techniques, or language-games, inspired by Maturana’s concepts of “objectivity in parenthesis” and the multiverse. (shrink)

The papers in Richard Vallée's Words and Contents span twenty-one years. The author navigates the discovery and exploration of different expressions and perspectives on language in this volume. Beginning with referring expressions and later addressing context sensitivity, the book examines how specific words contribute to the contents of utterances and the philosophical issues that surround them.

William Abraham studied Philosophy at the University of Ghana, and even more Philosophy at Oxford University. Thereafter, he gained permission to take part in the competitive examination and interview for a fellowship at All Souls' College. The examination was once described, with some exaggeration, as 'the hardest exam in the world!' It included a three-hour essay. Following his success in becoming the first African fellow of All Souls, his interest in African politics quickly developed into a Pan-African perspective. The Mind (...) of Africa, written while he was still at All Souls, was a fruit of that enlarged perspective. After several years as a Fellow, he had occasion to visit Ghana in 1962. There Kwame Nkrumah, then President of Ghana, successfully persuaded him to return to Ghana to teach at the University of Ghana, Legon and he subsequently resigned from All Souls. In 1968, he went to the United States as a visiting professor. This was followed by invitations to teach at various academic institutions there, including Berkeley and Stanford. He subsequently settled in California, where he continued to teach and research philosophy in the University of California at Santa Cruz until his retirement. The Mind of Africa appeared at a time when a number of African countries were obtaining, or fighting for, their political freedom from their colonial rulers and becoming independent nations and expecting to build new societies in accordance with their own visions and conceptions, though not necessarily jettisoning all the features of their colonial heritage. Building new societies requires appropriate ideologies and philosophies fashioned within the crucible of their cultural and historical experiences. Thus, the relation between ideology and society is taken up at the very outset of the book... The Mind of Africa is important for Africa's future and identity. (shrink)

À l'école d'Édith Stein -- À la recherche du geste intérieur -- Révéler la presence -- Anthropologie phénoménologique et théorie de l'éducation dans l'oeuvre d'Édith Stein (Résumé).

The Kyoto Protocol on global warming has provoked great controversy in part because it calls for heavier burdens on wealthy countries than on developing countries in the effort to control climate change. The U.S. Senate voted unanimously to oppose any agreement that does not require emissions reductions in low-income countries. The ethics of this position are examined in this paper which shows that there are good moral reasons for supporting the provisions of the Kyoto Protocol. Such a conclusion follows easily (...) from considerations of distributive justice but can also be supported by more narrowly self-interested arguments. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Augustine's Intellectual Conversion: The Journey from Platonism to ChristianityTravis E. AblesBrian Dobell. Augustine's Intellectual Conversion: The Journey from Platonism to Christianity. Cambridge-New York: Cambridge University Press, 2010. Pp. xvii + 250. Cloth, $82.00.The question of Augustine's Platonism is famously vexed. Since Peter Brown, the standard reading holds that Augustine did not move beyond the Neoplatonism of his early dialogues until he studied the writings of the apostle Paul (...) in the mid-390s CE, after which his distinctive theology begins to emerge. In this book, Brian Dobell's basic claim is that, whatever the validity of the "volitional conversion" of book 8, Augustine is not truly converted to orthodox Christianity until he discards the Photinian (adoptionist) Christology he admits to in Confessions [hereafter conf.] 7.19.25, and discards the Platonic ascent as a means to contemplative union with God, both of which take place with the reading of Paul. But the book is equally motivated by a concern to defend the historicity of conf.; Dobell claims it is perfectly reliable, once we understand the latter half of book 7 not as a few months in 386, but as a compressed narrative spanning Augustine's entire development until his true conversion to Christianity around 395. [End Page 137]Dobell develops this argument by isolating Augustine's twofold way of salvation in the writings of the late 380s. First is the "way of authority," in which Augustine's putative Photinian Christology portrays Christ as a kind of "poor man's Plato, sent to provide a path to salvation for the uneducated masses" (96). The human Jesus is "assumed" by God and is as "a man of outstanding wisdom" (73) but is not the incarnate Son. Dobell analyzes the homo assumptus/susceptus language of the early writings, arguing that Augustine does not truly hold an orthodox Christology until 396, concordant with the development of his theology of operative grace. The second, much longer section of the book concerns the "way of reason," the intellectualist path of salvation expressed in Augustine's early obsession with the liberal disciplines. Dobell dissects the Platonic ascents of conf. 7, adducing verbal and conceptual parallels from texts ca. 387–390 (De immortalitate animae, De ordine, De libero arbitrio, De vera religione) showing how Augustine's métaphysique des degrés d'être, a concept Dobell borrows from Olivier Du Roy, provides both a means of articulating these ascents and an answer to the problem of evil. But by De doctrina christiana, Augustine has decisively rejected the Platonic ascent and the liberal disciplines, and it simply remains for his Christology to come in line for the "intellectual conversion" to be complete.Dobell's book is a significant addition to the current debate. His knowledge of the first decade or so of Augustine's literary output is impressive, and his familiarity with the secondary literature is considerable, though not encyclopedic—he misses the work of J. Patout Burns, which complicates the Pauline thesis through consideration of the anti-Donatist literature. Dobell offers magisterial and invaluable discussions of famously fraught topics such as Augustine's indecisiveness about the preexistence of the soul, or the volitional solution to the problem of evil. There are some problems with Dobell's argument, though. While his main thesis that conf. 7.9.13ff. is a kind of précis of almost a decade of intellectual development deserves serious consideration, and is an elegant solution to debates about the historicity of Augustine's narrative in conf., the supporting arguments Dobell employs are less persuasive. A major portion of his book revolves around the contention that Augustine's early, heretical Photinian Christology extends much longer than modern scholarship has realized, that Augustine rectifies this Christology in conjunction with a Pauline soteriology of grace, and that all of this has to happen before Augustine's conversion is complete. If we suspend the question of normativity inherent in deciding Augustine's "orthodoxy" (particularly prior to Chalcedon), Dobell still does not succeed in showing that the early "pedagogical" homo assumptus Christology is, in fact, adoptionist; indeed, his evidence is often rather weak (for a tacit admission, see 73). On the flip... (shrink)

'Jousse - il a trouvé un filon, comme on dit', confie Bergson dans un entretien avec Lydie Adolphe. La relation que Marcel Jousse, chercheur, professeur, homme d'Église, entretient tout au long de ses quelque quarante ans d'enseignement avec le philosophe Henri Bergson est pour le moins paradoxale. Entre admiration et rejet, Jousse revendique 'sa' lecture de Bergson. Libre et inspirante, souvent critique, voire frôlant la caricature, cette lecture tonique agit en retour sur le lecteur, qu'il soit connaisseur de l'œuvre de (...) Bergson ou pas. Selon Jousse, le geste corporel-manuel, le geste global, est au cœur de la pensée du philosophe. Bergson joue sa pensée avec ses mains, avec tout son corps avant de la jeter dans ses livres. La connaissance des lois anthropologiques du Style oral formulées par Jousse permet de mieux saisir la particularité du style de Bergson, proche de celui de Péguy, et qui s'apparente au style oral des rythmo-mimeurs. Jousse, Bergson : deux noms qui ont marqué leur époque. Le lien fort qui unit les deux penseurs est au cœur de cette enquête - que l'on pourrait aussi écrire 'en quête' - à la fois philosophique et historique. Ce livre s'inscrit dans la longue liste des 'lecteurs de Bergson' qu'ils soient ou non bergsoniens."--Page 4 of cover. (shrink)

Linguistic study of Mongolian traditional classical translation.

The article examines Husserl's work On the Phenomenology of the Consciousness of Internal Time. Firstly, it seeks to show the surplus of cosmic time with regard to the temporality of consciousness. Secondly, an attempt is made to establish whether the Husserlian description of the form of the flow of consciousness is circular, i.e., whether it does not presupposes the objective time that it purports to constitute. Thirdly, a critical analysis of the self-manifestation of the absolute flow of consciousness is advanced. (...) Finally, a reference is made to the aporetics that befalls any investigation that tries to reduce one form of time to the other or to apprehend them independently. (shrink)

This book intends to introduce readers to the work of Charles E. Butterworth, and thereby to introduce students to Medieval islamic political philosophy, of which Butterworth is one of the world's most prominent scholars. In a wider sense, the Festschrift introduces its readers to the current debates on Medieval islamic political philosophy, related as they are to the questions of the relationship between islam and Christianity, the Medieval to the Modern world, and reason and revelation. Butterworth's scholarship spans six decades, (...) primarily translating, editing, and interpreting the works of the Muslim political philosopher Alfarabi (d. 950) and Averroes (Ibn Rushd, d. 1198). He began his studies of Muslim political philosophy at a time when the Middle East and islam did not have the political salience they have acquired in more recent years. instead, Butterworth's reason for engaging with islam was rooted in the question of the relationship between reason and revelation. While one possible answer was pursued in the Christian, latin West, the islamic borderlands of Greek, Roman, and Muslim civilization offered another. By exploring Averroes, who provides the possibility of an Aristotelian-Islamic political philosophy, and Alfarabi, who pursues a Platonic-islamic political philosophy, Butterworth showed how islamic civilization provided a viable alternative to the theologico-political question reason v revelation, as well as serving as an inspiration to the latin West. (shrink)

Existe-t-il une chose de tel qu'une conception herméneutique du langage? C'est à cette question que cet ouvrage se propose de répondre, de façon positive, en opérant une mise en dialogue des herméneutiques de Hans-Georg Gadamer et Paul Ricoeur. Malgré les différences indéniables entre les oeuvres de ces deux philosophes, l'auteur montre qu'elles ont en commun de penser le langage comme étant un principe fondamental de notre expérience du monde et de tout événement de compréhension. Une articulation entre les deux oeuvres, (...) qui mise sur une dialectique entre les notions d'appartenance et de distanciation, est possible à partir de cet accord de fond sur notre appartenance essentielle au langage. De ce point de vue, tout effort pour mettre à distance le langage afin d'en faire un objet d'étude doit tenir compte du caractère premier et irréductible de cette appartenance, s'il veut éviter de n'offrir qu'une vision réductrice du langage. Comme le révèlent les analyses de ce livre, les recherches de Gadamer et Ricoeur se caractérisent par la prise en compte de ce fait dans leurs réflexions sur le dialogue, le texte et la traduction, ainsi que dans leurs travaux sur la puissance créatrice du langage qui se manifeste dans la métaphore, le dire poétique et le récit. Cependant, le plus important pour l'herméneutique est que cette appartenance fondamentale ne soit pas synonyme d'un enfermement dans le langage, mais que le langage offre au contraire une ouverture sur l'être et permette à ce qui est de se dire et de se penser. (shrink)

The author of this study has a single-minded goal--the construction of a social ethic for the Hispanic Pentecostal Church in America that both coheres with the ...

The author offers an outline of the contemporary pragmatist scene in American philosophy. He shows the continuity and common features of classic and recent pragmatisms of which the most crucial are antifoundationalism and antirepresentationalism. In his analysis he distinguishes two main currents of neopragmatist philosophy: 1. post-analytic , and 2. neo-classic lines. Finally he focuses on some characteristics of the Rortyan post-analytic neopragmatism as expressed in his last book Philosophy and Social Hope.

1. El acto humano, deber y derecho -- 2. Derechos individuales, familia y sociedad.