Il libro di C., che costituisce il quinto volume della nuova promettente collana diretta da E.V. Maltese, nella quale sono già apparsi importanti contributi ed altri sono annunciati, comprende l'edizione critica e il commento di una parte delle poesie anacreontiche giunte sino a noi nella ben nota raccolta tramandata, mutila, come dimostra l'indice antico dei ff. 1-7, dal codice Barb. gr. 310, e più precisamente i componimenti classicheggianti sopravvissuti nella prima parte del manoscritto, con l'esclusione delle anacreontiche di Sofronio di (...) Gerusalemme, tutte già ripubblicate in edizione critica nel 1957, e dell'anacreontica di Michele Sincello, riedita in anni recenti. Anche i poemetti dei cinque autori scelti da C. — Elia Sincello, Ignazio Diacono, Leone Magistro, Giovanni di Gaza e Giorgio Grammatico — sono stati, per la verità, già pubblicati (e taluni tradotti in italiano) una o più volte, e forse, almeno da un punto di vista utilitaristico, sarebbe valsa la pena di ripubblicare tutta la sezione di anacreontiche classicheggianti della Silloge. Tanto più che questa nuova edizione ha soprattutto il merito di consentire al lettore italiano, anche non bizantinista, una uniforme consultazione di testi complessi ed eterogenei, degli apparati, della traduzione a fronte, accompagnata da note di commento; sebbene l'indice generale del volume, poco dettagliato, e non preceduto da un indice dei nomi, non aiuti il lettore nell'individuazione immediata dei testi e degli argomenti. (shrink)

The proofs of universally quantified statements, in mathematics, are given as “schemata” or as “prototypes” which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, including Herbrand. In this constructive approach where propositions are types, proofs are viewed as terms of λ-calculus and act as “proof-schemata”, as for universally quantified types. We examine here the critical case of Impredicative Type Theory, i. e. Girard's (...) system F, where type-quantification ranges over all types. Coherence and decidability properties are proved for prototype proofs in this impredicative context. (shrink)

Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed (...) the revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.”. (shrink)

Os sistemas de cômputo do tempo na Índia são extremamente complexos, devido a dois factores: em primeiro lugar a coexistência não só de diversas teorias e tabelas astronómicas mas também de diferentes calendários, que em parte resulta de a Índia raramente ao longo da sua história ter constituído uma unidade política; em segundo lugar uma grande preocupação, quiçá de origem mágica, com a objectividade astronómica dos dados utilizados no cômputo do tempo. Do primeiro factor indicado resultam, por exemplo, a (...) coexistência de calendários solares, predominantes em certas regiões, com calendários luni-solares nas restantes, a contagem dos meses a partir da lua-nova ou da lua-cheia, consoante as zonas, etc. Do segundo resultam por exemplo: a adopção de estranhas unidades de tempo, como o tithi (que se pode definir como a trigésima parte de uma lunação, ou, em outros termos, o tempo que, após uma conjunção com o Sol ou seja uma lua-nova, a Lua demora a afastar-se deste 12° sobre o zodíaco); a entrada em conta da precessão dos equinócios para efeitos de determinação do início dos signos do zodíaco; etc. O presente artigo procura resumir e explicar essa diversidade de uma perspectiva histórica, pondo-a em relação com a evolução da astronomia indiana. (shrink)

Esta coletânea é um tributo a Peter Frederick Strawson pelo centenário de seu nascimento (1919-2019). Diferentemente de outras coletâneas, esta propõe colocar em relevo a interlocução de Strawson com a tradição filosófica. Em outras palavras, por um lado, queremos evidenciar as discussões que Strawson travou com os seus contemporâneos (Austin, Quine, Russell e Wittgenstein), e, por outro, a influência que recebeu e as críticas que dirigiu àqueles que o precederam na história da filosofia (Aristóteles, Descartes, Hume, Kant). Poderíamos ter enriquecido (...) a lista acima com o nome de muitos outros filósofos com os quais Strawson teve contato, mas julgamos que o trabalho ficaria bastante extenso. Por esse motivo, optamos por aqueles nomes mais significativos que figuram na construção da história intelectual de Strawson. O presente volume reúne nove capítulos que levam como título o nome de Strawson e do filósofo com o qual ele dialogou ao longo de suas obras. Essa opção na nomeação dos capítulos por si só já permite colocar em evidência os principais filósofos pelos quais Strawson se interessou e com os quais se confrontou ao longo de seu trabalho filosófico. Com exceção do capítulo sobre Wittgenstein, que é uma versão revisada de um texto publicado anteriormente, todos os outros capítulos são inéditos e foram escritos especialmente para esta coletânea. O volume inclui na abertura a tradução de “Um fragmento de autobiografia intelectual”, de P. F. Strawson. Quando elegemos como título desta obra, Strawson e a tradição filosófica, não estamos insinuando que Strawson é um historiador da filosofia e muito menos que se interesse por historiografia. O título desta obra apenas quer indicar que Strawson, por um lado, transita na história da filosofia com alguma facilidade, além de nutrir um grande apreço por ela e, por outro, que ele discute com os principais nomes da história da filosofia no que concerne aos temas de seu interesse. A sua proposta filosófica é alimentada e irrigada por esse conhecimento, o que lhe dá a possibilidade de assumir na maioria das vezes posições ponderadas e equilibradas acerca de temas complexos por ele tratados. ​ ISBN: 978-85-5696-689-6. Nº de pág.: 244. (shrink)

Considerando retrospectivamente os desdobramentos da filosofia, é possível observar que, antes de reconhecer e reafirmar as singularidades de seu exercício, o discurso filosófico tem sua origem intimamente associada à poesia. Evidenciando alguns momentos de cisão e outros momentos de contato entre o discurso poético e o discurso filosófico, o presente ensaio visa abordar e refletir sobre o diálogo entre esses dois discursos ao longo do tempo. Nesse horizonte, consideraremos estrategicamente os trabalhos de autores como Homero, Platão, Goethe, F. Schlegel (...) e Schelling, a fim de evidenciar as oscilações e salientar alguns movimentos específicos dentro desse longo diálogo. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) (151 E-152C); as opposed to what he may have taught secretly to his pupils (152C-160D). Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) ; as opposed to what he may have taught secretly to his pupils. Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken.In that part of the dialogue where the question is under examination whether or not knowledge and perception are the same, Socrates uses an idealized concept of knowledge. That is, he restricts the use of the word by setting down what he will consider to be the essential characteristics of knowledge, the sufficient and necessary conditions of its being instantiated. An excellent piece of philosophical procedure. (shrink)

We experience our own body through both touch and vision. We further see that others’ bodies are similar to our own body, but we have no direct experience of touch on others’ bodies. Therefore, relations between vision and touch are important for the sense of self and for mental representation of one’s own body. For example, seeing the hand improves tactile acuity on the hand, compared to seeing a non-hand object. While several studies have demonstrated this visual enhancement of touch (...) effect, its relation to the ‘bodily self’, or mental representation of one’s own body remains unclear. We examined whether VET is an effect of seeing a hand, or of seeing my hand, using the rubber hand illusion. In this illusion, a prosthetic hand which is brushed synchronously—but not asynchronously—with one’s own hand is felt to actually be one’s hand. Thus, we manipulated whether or not participants felt like they were looking directly at their hand, while holding the actual stimulus they viewed constant. Tactile acuity was measured by having participants judge the orientation of square-wave gratings. Two characteristic effects of VET were observed: cross-modal enhancement from seeing the hand was inversely related to overall tactile acuity, and participants near sensory threshold showed significant improvement following synchronous stroking, compared to asynchronous stroking or no stroking at all. These results demonstrate a clear functional relation between the bodily self and basic tactile perception. (shrink)

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical (...) practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences. (shrink)

De l'antiquité à la Renaissance, la notion de certitude est au coeur de la structuration de la pensée. Cet ouvrage réunit les contributions de spécialistes, qui explorent tous la littérature latine en mettant cette notion à l'épreuve de différentes disciplines et époques.

La traduction latine des Dialoghi della historia du philosophe néo-platonicien Francesco Patrizi da Cherso est publiée à Bâle en 1570. L’étude de la circulation de ce texte et des choix de traduction permet de mieux comprendre la réception des artes historicae italiennes dans le Nord de l’Europe et les fluctuations ou limites du latin face à la montée en puissance de l’italien vernaculaire comme langue philosophique.

La traduction latine des Dialoghi della historia du philosophe néo-platonicien Francesco Patrizi da Cherso est publiée à Bâle en 1570. L’étude de la circulation de ce texte et des choix de traduction permet de mieux comprendre la réception des artes historicae italiennes dans le Nord de l’Europe et les fluctuations ou limites du latin face à la montée en puissance de l’italien vernaculaire comme langue philosophique.

Because anticipated and retrospective regret play important roles in practical deliberation and motivation, better understanding them can illuminate the contours of human agency. However, the possibility of self-ignorance and the fact that we change over time can make regret—especially anticipatory regret—not only a poor predictor of where the agent will be in the future but also an unreliable indicator of where the agent stands. Granting these, this paper examines the way in which prospective and, particularly, retrospective regret can nevertheless yield (...) important insight into the sorts of creatures we are, both generally and individually. The experience of retrospective regret can show a person she values something in a way she did not know or that she is (or was) a different person than she had thought, insights which can factor into forward-looking, or prospective, deliberation. Such instances of revelatory regret reveal something to the agent about herself as agent. I examine two cases of agential self-ignorance. In the first, the experience of regret reveals what the agent values, not only to others but even to the agent himself. In the second, the agent anticipates experiencing regret for an action but does not experience the regret, suggesting that the agent did not value the rejected alternative in the way she thought. Anticipatory regret is forward-looking and can play an important role in practical deliberation. But insofar as anticipatory regret flows from one’s imperfect judgment and prospection about oneself, retrospective regret can be an important corrective in helping the agent understand her own standpoint. (shrink)

In his newly updated version of The Anatomy of a Constitutional Law Case, Alan F. Westin provides a documentary portrait of historically important constitutional law case, 'Youngstown Sheet & Tube Co. v. Sawyer, ' from its rise in a bargaining dispute in the steel industry during 1952 to the aftermath of its decision by the United States Supreme Court. Westin has added to his classic book additional materials and personal commentaries collected since the work was first published. The new information (...) covers what went on within the Truman administration, what went on within the Supreme Court when analyzing and resolving issues that come before it. Westin includes selections from transcripts, briefs and other official proceedings, adds notes describing each phase of the constitutional process, and a section of commentary and questions relating this case to others. (shrink)

The “DNA is a program” metaphor is still widely used in Molecular Biology and its popularization. There are good historical reasons for the use of such a metaphor or theoretical model. Yet we argue that both the metaphor and the model are essentially inadequate also from the point of view of Physics and Computer Science. Relevant work has already been done, in Biology, criticizing the programming paradigm. We will refer to empirical evidence and theoretical writings in Biology, although our arguments (...) will be mostly based on a comparison with the use of differential methods (in Molecular Biology: a mutation or alike is observed or induced and its phenotypic consequences are observed) as applied in Computer Science and in Physics, where this fundamental tool for empirical investigation originated and acquired a well-justified status. In particular, as we will argue, the programming paradigm is not theoretically sound as a causal(as in Physics) or deductive(as in Programming) framework for relating the genome to the phenotype, in contrast to the physicalist and computational grounds that this paradigm claims to propose. (shrink)

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which all reality can (...) emerge in its material and sensible singularity, making possible all generalization and formal abstraction. (shrink)

In order to think of philosophy after automation, we have to ask if there is more in philosophy than the process of learning what philosophy is by inducing, from actual inferential practices, the future possible moves that are believed to produce philosophical truths. In the same way as the production of scientific hypothesis has been automated like a self-updating process which entails schemas of decisions and actions, philosophy itself, once conceived as a game where the truth of the statements is (...) measured with respect to the social reproduction of inferential moves, could be automated as well. (shrink)

This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, (...) in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field. (shrink)

Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relations, since regularities in very large databases are enough: “with (...) enough data, the numbers speak for themselves”. The “end of science” is proclaimed. Using classical results from ergodic theory, Ramsey theory and algorithmic information theory, we show that this “philosophy” is wrong. For example, we prove that very large databases have to contain arbitrary correlations. These correlations appear only due to the size, not the nature, of data. They can be found in “randomly” generated, large enough databases, which—as we will prove—implies that most correlations are spurious. Too much information tends to behave like very little information. The scientific method can be enriched by computer mining in immense databases, but not replaced by it. (shrink)

It is not quite as easy to see that there is in fact no formula of this modal language having the same truth conditions (in terms of S5 Kripke semantics) as (1). This was rst conjectured by Allen Hazen2 and later proved by Harold Hodes3. We present a simple direct proof of this result and discuss some consequences for the logical analysis of ordinary modal discourse.

How do we prove true but unprovable propositions? Gödel produced a statement whose undecidability derives from its ad hoc construction. Concrete or mathematical incompleteness results are interesting unprovable statements of formal arithmetic. We point out where exactly the unprovability lies in the ordinary ‘mathematical’ proofs of two interesting formally unprovable propositions, the Kruskal-Friedman theorem on trees and Girard's normalization theorem in type theory. Their validity is based on robust cognitive performances, which ground mathematics in our relation to space and time, (...) such as symmetries and order, or on the generality of Herbrand's notion of ‘prototype proof’. (shrink)

This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. It summarizes some basic ideas in information theory and very informally hints at their mathematical properties. In order to introduce Turing’s two main theoretical contributions, in Theory of Computation and in Morphogenesis, the fundamental divide between discrete vs. continuous structures in mathematics is presented, as it is also a divide in his scientific life. The reader who is familiar with these notions, and (...) is convinced that they are relevant in the mathematical understanding of phenomena, may skip this introduction and go directly to the Letter. (shrink)

Manufacturing and industry practices are undergoing an unprecedented revolution as a consequence of the convergence of emerging technologies such as artificial intelligence, robotics, cloud computing, virtual and augmented reality, among others. This fourth industrial revolution is similarly changing the practices and capabilities of operators in their industrial environments. This paper introduces and explores the notion of the Operator 4.0 as well as how this novel way of conceptualizing the human operator necessarily implicates human values in the technologies that constitute it. (...) The design approach known as value sensitive design (VSD) is used to explore how these Operator 4.0 technologies can be designed for human values. Expert elicitation surveys were used to determine the values of industry stakeholders and examples of how the VSD methodology can be adopted by engineers in order to design for these values is illustrated. The results provide preliminary adoption strategies that industrial teams can take to Operator 4.0 technology for human values. (shrink)