In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- and (...) η-conversions) that the authors have investigated in recent work. (shrink)

The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical system of the Grundgesetze and (...) the one given by Martin-Löf for the intuitionistic type theory with a type of all types.The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast domain for foundational research. (shrink)

Developing a suggestion by Russell, Prawitz showed how the usual natural deduction inference rules for disjunction, conjunction and absurdity can be derived using those for implication and the second order quantifier in propositional intuitionistic second order logic NI\. It is however well known that the translation does not preserve the relations of identity among derivations induced by the permutative conversions and immediate expansions for the definable connectives, at least when the equational theory of NI\ is assumed to consist only of (...) \- and \-equations. On the basis of the categorial interpretation of NI\, we introduce a new class of equations expressing what in categorial terms is a naturality condition satisfied by the transformations interpreting NI\-derivations. We show that the Russell–Prawitz translation does preserve identity of proof with respect to the enriched system by highlighting the fact that naturality corresponds to a generalized permutation principle. Finally we sketch how these results could be used to investigate the properties of connectives definable in the framework of higher-level rules. (shrink)

In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...) predicative fragment of System F, called atomic System F. In this paper we show that this approach finds a general explanation within our equational study of second-order natural deduction, and a clear semantic justification in terms of parametricity. (shrink)

A proof-theoretic test for paradoxicality was famously proposed by Tennant: a paradox must yield a closed derivation of absurdity with no normal form. Drawing on the remark that all derivations of a given proposition can be transformed into derivations in normal form of a logically equivalent proposition, we investigate the possibility of paradoxes in normal form. We compare paradoxes à la Tennant and paradoxes in normal form from the viewpoint of the computational interpretation of proofs and from the viewpoint of (...) proof-theoretic semantics. (shrink)

A comparison between the standard adiabatic piston dynamics and that of a perfectly conducting (diathermal) piston helps to clarify their different behaviors and, in particular, the anomalously large random displacement of the adiabatic piston as compared to the diathermal one. It is shown to be associated with a situation where the presence of a single massive “particle” (the piston), acting as an internal constraint in a many-particle system, plays a somewhat unexpected relevant role. A significant physical insight accounting for the (...) above difference is gained by means of a simple analysis of the phase space available to our system. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (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 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 mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, Logic and the Art of Memory Italian philosopher and historian Paolo Rossi argues that this view is belied by an (...) examination of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book (originally titled Clavis Universalis ) remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, Logic and the Art of Memory documents an essential chapter in the development of human reason. (shrink)

The influential Italian thinker offers three essays in the political philosophy of language. Multitude between Innovation and Negation by Paolo Virno translated by James Cascaito. The publication of Paolo Virno's first book in English, Grammar of the Multitude, by Semiotext in 2004 was an event within the field of radical political thought and introduced post-'68 currents in Italy to American readers. Multitude between Innovation and Negation, written several years later, offers three essays that take the reader on a (...) journey through the political philosophy of language. “Wit and Innovative Action” explores the ambivalence inevitably arising when the semiotic and the semantic, grammar and experience, rule and regularity, and right and fact intersect. Virno unravels the infinite potential and wonders of everyday linguistic praxis and ambiguity. Wit, he argues, is a public performance, and its modus operandi characterizes human action in a state of emergency; it is a reaction, an articulate response, and a possible solution to a state of crisis. “Mirror Neurons, Linguistic Negation, and Mutual Recognition” examines the relationship of language and intersubjective empathy: without language, would human beings be able to recognize other members of their species? And finally, in “Multitude and Evil,” Virno challenges the distinction between the state of nature and civil society and argues for a political institution that resembles language in its ability to be at once nature and history. Few thinkers take the risks required by innovation. Like a philosophical entrepreneur, Virno is engaged in no less than rewriting the dictionary of political theory, an urgent and ambitious project when language, caught in a permanent state of emergency impossible to sustain, desperately needs to articulate and enact new practices of freedom for the multitude. Paolo Virno is the author of several books, including A Grammar of the Multitude, 2004). (shrink)

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.

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 aim of the paper is to discuss the influence exercised by Russell's thought inGöttingen in the period leading to the formulation of Hilbert's program in theearly twenties. I show that after a period of intense foundational work, culminatingwith the departure from Göttingen of Zermelo and Grelling in 1910 we witnessa reemergence of interest in foundations of mathematics towards the end of 1914. Itis this second period of foundational work that is my specific interest. Through theuse of unpublished archival sources (...) I will describe how Hilbert, Behmann, and Bernays,among others, were influenced by and reacted to the technical and philosophical thesespresented in Principia Mathematica. I also argue that there are some elements of continuity between Russell's approach and Hilbert's program as it was presented inthe early twenties. (shrink)

In Sophistical Refutations 8 Aristotle claims that every sophistical refutation depends on a false belief which is implicitly held by the victim of the fallacy and can normally be elicited from him as an explicit additional premiss. In this case the fallacious argument will be turned into a valid one, albeit with a false premiss. The paper discusses the nature of the FVP and tries to discover how it works when it tacitly causes the false appearance of a fallacious argument.

The paper examines Posterior Analytics II 11, 94a20-36 and makes three points. (1) The confusing formula ‘given what things, is it necessary for this to be’ [τίνων ὄντων ἀνάγκη τοῦτ᾿ εἶναι] at a21-22 introduces material cause, not syllogistic necessity. (2) When biological material necessitation is the only causal factor, Aristotle is reluctant to formalize it in syllogistic terms, and this helps to explain why, in II 11, he turns to geometry in order to illustrate a kind of material cause that (...) can be expressed as the middle term of an explanatory syllogism. (3) If geometrical proof is viewed as a complex construction built on simpler constructions, it can in effect be described as a case of purely material constitution. (shrink)

Art, Beauty and Imitation in Plato's Philosophy -- Art and Imitation in Aristotle -- Horace, Pseudo-Longinus and the Aesthetics of Literature in Hellenism -- Plotinus, Neo-Platonic and Christian Conception of Beauty -- The Middle Ages and Dante Alighieri -- The Heritage of Kantian Philosophy in Romanticism -- Moritz: Beyond the Concept of Imitation -- Theory of Poetry of Early German Romanticism -- Hegel: Art as a Form of the Absolute Spirit -- Schopenhauer: Art as Disinterestedness and Knowledge of Reality -- (...) Nietzsche: Knowledge and Art -- Symbolism and Aestheticism -- Benedetto Croce: Art and intuition -- Linguistics and Criticism -- Antonio Gramsci: The Role of Intellectuals in Culture -- Structuralism -- Martin Heidegger: The Work of Art and Truth -- Hans-Georg Gadamer: Poetry and Interpretation -- Critical Theory: A New Attitude towards Art and Society -- Perspectives of Post-Structuralism -- The Practice of Deconstruction -- Contemporary Schools and Traditions in Literary and Critical Theory -- Postmodern and the New Character of the Literary Work. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Beginning in the 20s of the last century, historical research into Eiximenis's life and writings has thrown into relief his contribution to the language and political ideas of the kingdoms and towns of the Catalan-Aragonese Crown. Of fundamental importance has been the work of medievalists from North America, and in particular that of Canadian scholars during the last decades of the twentieth century.More recently, a number of studies have (...) underlined the decisive contribution of Eiximenis – a representative of a European textual tradition among friars of the Minor Observance that extended from Oxford to Florence – to the establishment of a system of ethical values for the economic sphere and for trading practices that continued to be developed by members of the Franciscan Order throughout the high middle ages and early modern period.As a follow-up to these studies, I believe that a program of textual analysis and systematic investigation of Eximenis's work could provide further information about the range and significance of his political thinking, based as it was on applying, in typically Franciscan fashion, experimental observation to gain an understanding of the nature both of the societas and of the market, the latter being thought of as a defining expression of civic institutions in Western Europe. This same experimental approach can be found in Franciscan thinking from the catalan-aragonese realm not only in the work of Arnau de Vilanova and Ramon Llull, but also in that of Pere Tomas and Anselm Turmeda, two figures fundamental to the preparation and political engagement of the Friar of Girona.1. The concept of contractIn Eiximenian texts, the communitarian dimension is defined as one that is of necessity based on contract. It is expounded in the long opening section of the Dotzè del Crestià, where Eiximenis outlines the political value of the civitas, as well as setting out the elements that constitute civic life.Borrowing from Aristotle's discussion in the First Book of the Politics , the Franciscan friar strongly affirms that one of the principal reasons behind the civitas is the "necessitat de contractes," the need for contracts. Going far beyond the highly qualified analysis of money and coinage set out by the Greek philosopher, Eiximenis here maintains that the aims of the community is the profit that the citizenry realises by means of different forms of exchange, through buying and selling, through contracts, and through trading. Moreover, that the binding nature of trading-contracts is a matter of concern not of the city in the narrow sense, but of each and every kind of human social organization.Even before contract-law, or, better said, conventional or foral procedure, Eiximenis views the idea of the contract as an essential part of the ethical and organizational principles of living as a community, the essence of the civitas. And it is of great significance that when he is discussing the value and function of money, Eiximenis chooses to call the sorts of exchange that to-day we term economic or financial les civils conmutacions, or exchanges between citizens.These lexical hints allow us to capture the strength of meaning and value, the ethical perspective by which the Gerundense defines the inextricable union of the market and civic society. But it is not only an analytical perspective, significant as that is, that unites market and civic ethics; we are presented with a value judgment of contract and economic exchange as elements that determine the very idea of civilitas.The "bona civilitas," an expression that can be roughly translated as "good civic culture," is in fact founded on a concept of economic ethics that has as its distinguishing feature the logic of profitable exchange, of the distribution of that profit, of contractualization, and of the circulation of goods and money. It is characterised by redefining the anti-value of avaritia as a real.. (shrink)

Il volume, frutto della rielaborazione della tesi di dottorato, costituisce una retrospettiva sull'antropologia filosofica moderna attraverso due dei suoi massimi esponenti. Più specificamente mostra come la mitologia, la filosofia della storia e del linguaggio, la concezione vichiana dell'uomo abbiano avuto come costante punto di riferimento la psicologia d'impostazione cartesiana di Malebranche.

Reconociendo la insoslayable ambigüedad que afecta a la relación entre retórica y filosofía en la obra viquiana, este trabajo se preocupa por resaltar la continuidad entre el Vico retórico y el Vico filósofo, antes que por indagar las diferencias entre ambos. Semejante continuidad se percibe en la imaginación y en la persuasión. Ambos tópicos son tratados en profundidad en la Scienza Nuova, pero ponen de manifiesto consideraciones teóricas sobre la retórica que arrancan especialmente de las Institutiones Oratoriae.

Normal 0 0 1 91 520 .. 4 1 638 11.1280 0 14 0 0 Moving among historical material and contemporary debates on xenophobia and war, this paper is an exploration of the self-representation “ Italiani Brava Gente ”, an image claiming the intrinsic goodness of the Italian people. Originated during the first Italian colonial enterprises, it has been used also for overcoming the horrors of Fascism and is evoked in contemporary Italy too for justifying traumatic and violent events. Functioning (...) as an ideological laundry for reformulating and then setting aside disquieting moments of national shame, “ Italiani Brava Gente ” is central to the construction of a modern Italian identity. (shrink)

Una puesta a punto erudita y crítica acerca del género biográfico en Roma, de Cornelio Nepote al Tácito biógrafo, de Suetonio a los escritores de la Historia Augusta1. A learned and critical update about biographical genre in Rome, from Cornelius Nepos to Tacitus the biographer, from Suetonius to the authors of the Historia Augusta.

L’opera raccoglie nove lezioni introduttive alla gnoseologia: esse scaturiscono da un’esperienza d’insegnamento concreta e si configurano come un approccio teoretico all’universo composito della filosofia della conoscenza, rappresentando un supporto didattico in grado di accompagnare pedetentim – tanto gli studenti quanto i cultori della materia – alla scoperta di una disciplina di fondamentale importanza per le sue attinenze con la metafisica e l’etica.