Conceptualism is the thesis that, for any perceptual experience E, (i) E has a Fregean proposition as its content and (ii) a subject of E must possess a concept for each item represented by E. We advance a framework within which conceptualism may be defended against its most serious objections (e.g., Richard Heck's argument from nonveridical experience). The framework is of independent interest for the philosophy of mind and epistemology given its implications for debates regarding transparency, relationalism and representationalism, demonstrative (...) thought, phenomenal character, and the speckled hen objection to modest foundationalism. (shrink)
I. In analytic philosophy, so-called 'univocalism' is the prevailing interpretation of the meaning of terms such as 'being' or 'existence', i.e. the thesis that these terms have only one meaning (see Russell, White, Quine, van Inwagen). But some analytical philosophers, inspired by Aristotle, maintain that 'being' has many senses (Austin, Ryle). II. Aristotle develops an argument in favour of this last thesis, observing that 'being' and 'one' cannot be a single genus, because they are predicated of their differences (Metaph. B (...) 3). III. But 'being' for Aristotle has also a unity, i.e. 'focal meaning', which coincides with substance (Metaph. Γ 2), and substance has not only an ontological priority, but also a logical priority, in respect to the other beings, as was shown by G. E. L. Owen. IV. This 'focal meaning' cannot be identified with primary substance, i.e. with the unmovable mover, as some interpreters pretend, because this latter has only an ontological, not a logical, priority in respect to the world. V. The impossibility of this interpretation results from Aristotle's rejection of an essence and a substance of being (Metaph. B 4), i.e. the rejection of what the Christian philosophers called esse ipsum subsistens. (shrink)
Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction between determinism and nondeterminism (...) W. Hugh Woodin; 6. Concept calculus: much better than Harvey M. Friedman; Part IV. Perspectives on Infinity from Physics and Cosmology: 7. Some considerations on infinity in physics Carlo Rovelli; 8. Cosmological intimations of infinity Anthony Aguirre; 9. Infinity and the nostalgia of the stars Marco Bersanelli; 10. Infinities in cosmology Michael Heller; Part V. Perspectives on Infinity from Philosophy and Theology: 11. God and infinity: directions for future research Graham Oppy; 12. Notes on the concept of the infinite in the history of Western metaphysics David Bentley Hart; 13. God and infinity: theological insights from Cantor's mathematics Robert J. Russell; 14. A partially skeptical response to Hart and Russell Denys A. Turner. (shrink)
The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still working (...) in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide. (shrink)
In “Mathematics is megethology,” Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology (...) and plural quantification are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, if—as Lewis maintains—MPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)
Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification (, ) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite (...) à la Dedekind, as the unique non-logical axiom. We will also sketch a virtual interpretation of the classical continuum involving no other infinite than a countable plurality of individuals. (shrink)
Social constructionists believe that experimental evidence plays a minimal role in the production of scientific knowledge, while rationalists such as myself believe that experimental evidence is crucial in it. As one historical example in support of the rationalist position, I trace in some detail the theoretical and experimental research that led to our understanding of beta decay, from Enrico Fermi’s pioneering theory of 1934 to George Sudarshan and Robert Marshak’s and Richard Feynman and Murray Gell-Mann’s suggestion in 1957 and (...) 1958, respectively, of the V–A theory of weak interactions. This is not a history of an unbroken string of successes, but one that includes incorrect experimental results, incorrect experiment-theory comparisons, and faulty theoretical analyses. Nevertheless, we shall see that the constraints that Nature imposed made the V–A theory an almost inevitable outcome of this theoretical and experimental research. (shrink)
The theory that ``consistency implies existence'' was put forward by Hilbert on various occasions around the start of the last century, and it was strongly and explicitly emphasized in his correspondence with Frege. Since (Gödel's) completeness theorem, abstractly speaking, forms the basis of this theory, it has become common practice to assume that Hilbert took for granted the semantic completeness of second order logic. In this paper I maintain that this widely held view is untrue to the facts, and that (...) the clue to explain what Hilbert meant by linking together consistency and existence is to be found in the role played by the completeness axiom within both geometrical and arithmetical axiom systems. (shrink)
In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal provability (...) and, on the other, by means of the operator K of epistemic logic. Intuitionistic logic, as reconstructed within this perspective, turns out to be a part of epistemic logic, so that it loses its traditional foundational role, antithetic to that of classical logic. In section 3 we uphold the view that certain consequences of the adoption of atemporal notion of truth, despite their apparent oddity, are quite acceptable from an antirealist point of view. (shrink)
This article explores Futurist technophilia and some more or less latent technophobia, in the period after 1918. Fuelled by the economic and industrial advancements of the so-called “Giolittian age,” as well as an extensive employment of war technology in the First World War, the Futurist technological imagination remains both robust and wide-ranging in the postwar period. Resonant of nineteenth-century French and Italian literary traditions, Filippo Tommaso Marinetti's official position clusters round the powerful, if hackneyed, images of the steam train and (...) the motorcar. A number of fellow Futurists, however, explore technology in more original and, in some cases, more persuasive fashions. From the technology of flying employed first-hand by Fedele Azari to Enrico Prampolini's mechanical applications on the European stage, from Anton Giulio Bragaglia's experimental cinema to Ivo Pannaggi's and Vinicio Paladini's technological rebirth in marxian key, the Futurists' approach to technology is characterised throughout by a problematic counterpoint of modernity and tradition. If the Futurist officialdom ultimately relies on the latter, numerous alternative experiences testify to their vibrant strife towards the former. (shrink)
In his recent edition, with translation and commentary, of Aristotle, Eth. Nic. VI, Hans-GeorgGadamer reproposes his interpretation of Aristotle's practical philosophy as a model for his own hermeneutics, confirming in this way his tendency to identify practical philosophy with the intellectual virtue of phronesis. Furthermore, although he recognizes the primacy attributed by Aristotle to the theoretical life, Gadamer tends to undervalue it and to consider phronesis and sophia at the same level. In particular he believes that (...) the theoretical life was for Aristotle an ideal accessible only to the gods. Unlike Heidegger, who refuses Aristotle's position because of the primacy of theoretical life, but appropriates his practical philosophy, Gadamer thinks that today is still possible to follow Aristotle, but only if we reduce that primacy. The article shows how, according to Gadamer, what Aristotle says about theoretical life, if rightly understood, can still be accepted. /// Na sua edição recente, com tradução e comentário ao Livro VI da Ética a Nicómaco de Aristóteles, Hans-GeorgGadamer reaflrma a sua interpretação dafllosofia prática de Aristóteles como modelo para a sua hermenêutica, confirmando deste modo a sua tendência a identificar a filosofia pratica de Aristóteles com a virtude dianoética da phronesis. Além disso, e apesar de reconhecer o primado atribuido por Aristóteles à vida teorética, Gadamer tende a desvalorizá-lo e a considerar a phronesis e a sophia como estando no mesmo piano. Gadamer parece especialmente convencido de que a vida teoretica para Aristóteles constitui um ideal apenas acessivel aos deuses. Ao contrário de Heidegger, que refuta a posição de Aristóteles por causa do primado atribuido à vida teorética, mas se apropria da sua filosqfia prática, Gadamer pensa ser ainda possivel seguir Aristóteles, para o efeito apenas se exigindo uma redimensionação desse primado. Enfim, o artigo demonstra como, segundo Gadamer, aquilo que Aristoteles diz acerca da vida teorética pode, se correctamente entendido, ser aceite ainda hoje. (shrink)
The present paper deals with natural intuitionistic semantics for intuitionistic logic within an intuitionistic metamathematics. We show how strong completeness of full first order logic fails. We then consider a negationless semantics à la Henkin for second order intuitionistic logic. By using the theory of lawless sequences we prove that, for such semantics, strong completeness is restorable. We argue that lawless negationless semantics is a suitable framework for a constructive structuralist interpretation of any second order formalizable theory (classical or intuitionistic, (...) contradictory or not). (shrink)
In this paper I set out to read Hägerström through his own eyes, adhering to the terminology he uses in his own original work and attempting to make sense of the variance and uniformity alike that one finds in his linguistic usage. The translations we have of Hägerström's works are quite liberal, using the same word in English where the original uses different ones, and, vice versa, using different words in English where the original uses a single one in different (...) contexts. These misleading translations of Hägerström have contributed in some measure to Hägerström's reputation for obscurity. Further, and most importantly, I will take seriously what Hägerström says about his own thought, namely, that it is dependent on that of Kant and independent of the currents of thought contemporary with Hägerström. In Section 1 , I will briefly take up the problem of consciousness that Hägerström proceeds from, and will recall something that Bertrand Russell once said, in 1928, in regard to the revolt staged in the early 20th century in Europe against German idealism. In Sections 2 and 4.1 , I will instead take up Kant for the purpose of clarifying Hägerström's theory of judgment as treated in Section 3 . In Section 4.2 , I will illustrate the difference between the notions of nothing, R-reality, and W-reality in Hägerström. In Sections 5 and 6 , I will examine the analysis that Hägerström offers of the principle of contradiction, and will summarize the three types of judgment he singled out, including the type he called impossible judgment (or, in my own words, pseudojudgment). In Section 7 , I will consider Hägerström views as grounding, in a transcendental way, the presupposition of the primacy of the external spatio-temporal world, a world independent of our representations: I will consider in particular the W-real complexes that are merely represented, as well as the spatio-temporal world as the only W-real complex that is not merely represented. Finally, in Section 8 , I will briefly consider some of those who have commented and translated Hägerström, this to conclude that R-reality and W-reality are coextensive but not synonymous. (shrink)
Comparaison entre la philosophie pratique aristotélisante d'aujourd'hui, représentée en Allemagne surtout par H.G. Gadamer, J. Ritter et leurs élèves, et les théories d'Aristote sur la phronesis et l'ethos, visant à montrer que ces dernières, dans la pensée du Stagirite, ne remplissent pas, contrairement à ce que croient ces interprètes, le rôle de la philosophie pratique toute entière. Contrast between the aristotelizing practical philosophy of today, represented in Germany especially by H.G. Gadamer, J. Ritter and their followers, and Aristotle's theories on (...) phronesis and ethos, in order to show that these theories, in the Stagirite's thought, don't play, against the opinion of those interpreters, the rôle of the whole practical philosophy. (shrink)
In this article, we describe an ontology aimed at the representation of the relevant entities and relations in the philosophical world. We will guide the reader through our modeling choices, so to highlight the ontology’s practical purpose: to enable an annotation of philosophical resources which is capable of supporting pedagogical navigation mechanisms. The ontology covers all the aspects of philosophy, thus including characterizations of entities such as people, events, documents, and ideas. In particular, here we will present a detailed exposition (...) of the entities belonging to the idea branch of the ontology, for they have a crucial role in the world of philosophy. Moreover, as an example of the type of applications made possible by the ontology we will introduce PhiloSurfical, a prototype tool we created to navigate contextually a classic work in twentieth century philosophy, Wittgenstein’s Tractatus Logico-Philosophicus. We discuss the potential usage of such navigation mechanisms in educational and scholarly contexts, which aim to enhance the learning process through the serendipitous discovery of relevant resources. (shrink)
Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like The Beatles sing Yesterday, a knowledge representation language should be able to express and reason about plural entities — like the Beatles — and their relationships — like sing — with any possible reading (cumulative, distributive or collective).In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the (...) semantics of sentences, is presented. A twofold extension of theA–C concept language is investigated: (1) special relations introduce collective entities either out of their components or out of other collective entities, (2) plural quantifiers on collective relations specify their possible reading. The formal syntax and semantics of the concept language is given, together with a sound and complete algorithm to compute satisfiability and subsumption of concepts, and to compute recognition of individuals. (shrink)
The aim of this paper is to reconsider several proposals that have been put forward in order to develop a Proof-Theoretical Semantics, from the by now classical neo-verificationist approach provided by D. Prawitz and M. Dummett in the Seventies, to an alternative, more recent approach mainly due to the work of P. Schroeder-Heister and L. Hallnäs, based on clausal definitions. Some other intermediate proposals are very briefly sketched. Particular attention will be given to the role played by the so-called Fundamental (...) Assumption. We claim that whereas, in the neo-verificationist proposal, the condition expressed by that Assumption is necessary to ensure the completeness of the justification procedure ( from the outside , so to speak), within the definitional framework it is a built-in feature of the proposal. The latter approach, therefore, appears as an alternative solution to the problem which prompted the neo-verificationists to introduce the Fundamental Assumption. (shrink)
Enrico Berti and others hold that Aquinas’s notion of God as ipsum esse subsistens conflicts with Aristotle’s view that positing an Idea of being treats being as a genus and nullifies all differences. The paper first shows how one of Aquinas’s ways of distinguishing esse from essence supposes an intimate tie between a thing’s esse and its differentia. Then it argues that for Aquinas the (one) divine essence differs from the (manifold) “essence of esse.” God is his very esse. (...) This somehow “contains” all esse, but it also transcends it, because although simple, it also “contains” all forms and differentiae. (shrink)
La discussion sur l'authenticité du deuxième livre de la Métaphysique d'Aristote (Petit Alpha), qui dure depuis un millénaire, a pour origine une scholie qui se trouve dans le Parisinus gr. 1853 (Xe siècle) à la jonction du premier et du deuxième livre. Or, cette scholie a été copiée par la même main que celle qui a ajouté une scholie d'un contenu comparable à la fin de la Métaphysique de Théophraste. Ce fait était passé inaperçu, parce que ce scribe a utilisé (...) différentes écritures: droite ou penchée, calligraphique ou cursive. L'ensemble des témoignages et indices déjà examinés par Gudrun Vuillemin-Diem, d'une part, et par Enrico Berti, d'autre part, est analysé et réinterprété à la lumière de cette nouvelle information, qui permet d'établir que c'est le premier livre de la Métaphysique, et non le deuxième, qui était attribué par certains à Pasiclès de Rhodes, comme en témoignait déjà Asclépios. Le contenu et la formulation très proches des deux scholies permettent de penser qu'elles viennent d'un même érudit: à l'aide, notamment, des commentaires d'Alexandre et d'Asclépios à la Métaphysique d'Aristote, de l'étude de Nicolas de Damas ou des catalogues d'Hermippe et d'Andronicos, il a préparé une 'édition' d'Aristote destinée à devenir un modèle de référence. Dans la tradition latine, Grand Alpha a été accidentellement attribué à Théophraste à cause de la seconde scholie. Mais la discussion dont témoigne la première scholie a pu également être provoquée dès l'origine par celle que rapporte la seconde scholie: la Métaphysique de Théophraste avait probablement été transmise comme un traité aristotélicien, jusqu'à ce que Nicolas de Damas en restitue la paternité à Théophraste; par suite, l'authenticité d'autres livres du corpus aristotélicien a pu également être mise en doute, mais parce qu'ils posaient des problèmes d'ordre éditorial, il y a deux millénaires déjà. (shrink)
Abstract. This paper discusses Kelsen's attempt at reducing the concept of subjektives Recht (what is subjectively right) to that of objektives Recht (what is objectively right). This attempt fails, it is argued, because in Kelsen's theory the concept of subjektives Recht survives concealed within the concept of individual norm (individuelle Norm), a norm that, pace Kelsen, is not a case of what is objectively right (objektives Recht) but is precisely what is subjectively right (subjektives Recht): We could call it "what (...) is individually right.". (shrink)
This essay suggests an interpretation of F. T. Marinetti and Fill a's La cucina futurista (The Futurist Cookbook) as a fundamentally utopian text that re-proposes and carries into the twentieth century some aspects of the nineteenth-century utopian tradition. In particular, it intends to further investigate the possibility that the alimentary discourse in La cucina shares some similarities with, and was influenced by the “gastrosophic” theory on the social role of meals and gastronomy, originally conceived by Charles Fourier (1772-1837), one of (...) the founding figures of the French utopian tradition. While strengthening the connection between futurism and French utopian thought and reasserting the centrality of food aesthetics in the avant-garde, this analysis provides another perspective on futurism's contradictory relation to tradition, exemplified in this additional re-appropriation and, to quote Cinzia Sartini Blum, “recycling of the past.”. (shrink)
Is a policy-friendly philosophy of science possible? In order to respond this question, I consider a particular instance of contemporary philosophy of science, the semantic view of scientific theories, by placing it in the broader methodological landscape of the integration of philosophy of science into STS (Science and Technology Studies) as a component of the overall contribution of the latter to science policy. In that context, I defend a multi-disciplinary methodological integration of the special discipline composing STS against a reductionist (...) interdisciplinary unification, arguing that if STS wants to contribute to policy advising by constructing narratives of science practice feasible for science policy both in terms of descriptive completeness and intelligibility, then it must avoid the explanatory reductionism tendencies of special disciplines in interdisciplinary contexts. This would favour, at the same time, a relaxation of esoteric language. On this basis, it seems that the semantic view is one right candidate among other approaches in the philosophy of science for facilitating the integration of the methodologically different contributions to STS toward policy objectives. In fact, besides offering a more realistic and descriptively complete picture of science practice with respect to its predecessor in the philosophy of science, namely the syntactic view, the semantic view is also able to capture some aspects of science practice that elude even sociological approaches to STS, thus inviting different perspective on the same subject matter. (shrink)
This essay discusses the problem of the two cultures. According to the author the problem arises because science is the source of a new way of conceiving reality and man, different from the mental conception entertained by nonscientific persons. The article suggests methodological guidelines for the philosopher interested in understanding the humanistic mentality of the scientists. The approach proposed is inductive-genetic. The aim is to help the philosopher explore science in its developmental becoming so that he may become aware of (...) the reasons for the characteristic mentality of scientists as regards humanistic issues. The essay concludes with a discussion of the new perspectives disclosed to scientific-humanistic dialogue. (shrink)
We introduce an epistemic version of validity and completeness of first order logic, based on the notions of ideal agent and fictional model. We then show how the perspective here considered may help to solve an epistemic puzzle arising from Gödel's second incompleteness theorem.
The present commentary addresses the Quartz & Sejnowski (Q&S) target article from the point of view of the dynamical learning algorithm for neural networks. These techniques implicitly adopt Q&S's neural constructivist paradigm. Their approach hence receives support from the biological and psychological evidence. Limitations of constructive learning for neural networks are discussed with an emphasis on grammar learning.
Brouwer's theorem of 1927 on the equivalence between virtual and inextensible order is discussed. Several commentators considered the theorem at issue as problematic in various ways. Brouwer himself, at a certain time, believed to have found a very simple counter-example to his theorem. In some later publications, however, he stated the theorem in the original form again. It is argued that the source of all criticisms is Brouwer's overly elliptical formulation of the definition of inextensible order, as well as a (...) certain ambiguity in his terminology. Once these drawbacks are removed, his proof goes through. (shrink)
This work presents a model-theoretic approach to the study of first-order theories of classes of BL-chains. Among other facts, we present several classes of BL-algebras, generating the whole variety of BL-algebras, whose first-order theory has quantifier elimination. Model-completeness and decision problems are also investigated. Then we investigate classes of BL-algebras having (or not having) the amalgamation property or the joint embedding property and we relate the above properties to the existence of ultrahomogeneous models.
What concept of Judaism is present in Schönberg’s philosophy of music? It is impossible to separate the musical texture from his experience of reconciliation with Judaism, and his new idea of musical drama is a confirmation that the dodecaphonic structure of musical thinking connects with Schönberg’s idea of the Jewish ethical and religious point of view. A comparative analysis of some essays with some operas shows the internal tie between music and Judaism in dodecaphony.
Previous research on the interpersonal effects of emotions in negotiation suggested that bargainers obtain higher outcomes expressing anger, when it is not directed against the counterpart as a person and it is perceived as appropriate. Instead, other studies indicated that successful negotiators express positive emotions. To reconcile this inconsistency, we propose that the direction of the effects of emotions depends on their perceived target, that is, whether the negotiatorsâ emotions are directed toward their opponentâs proposals or toward their own âexit (...) optionâ. An ultimatum game scenario experiment showed that negotiators who express positive emotion rather than negative, in addition to benefits in terms of relationship fortification, received better offers when participants perceived the negotiatorsâ emotions directed toward their own âexit optionâ. These findings indicate that positive emotions may signal the availability of better âexit optionâ, suggesting that happiness expressions can be strategically used to maximize both material and relational outcomes. (shrink)
I rely on Frascolla's interpretation of the Tractatus ontology to develop an account of depiction in which a picture is conceived of as a visual structure constituted by pixels that are conceived of, in their turn, as elementary propositions. Then I argue that such an account is complementary to the considerations about «noticing aspects» in the Philosophical Investigations, to the extent that the visual structure constituted by pixels provides a design allowing the picture’s viewer to notice aspects. Finally I argue (...) that a joint reading of the considerations about pictures in the Tractatus and in the Philosophical Investigations allows us to address some important issues in the contemporary philosophical debate about depiction. (shrink)
PG (Plural Grundgesetze) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. George Boolos’ plural semantics is replaced with Enrico Martino’s Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. Also, substitutional quantification is exploited to interpret quantification into predicate position. ACS provides a form of logicism which is (...) radically alternative to Frege’s and which is grounded on the existence of individuals rather than on the existence of concepts. (shrink)