In Part III of his Remarks on the Foundations of Mathematics Wittgenstein deals with what he calls the surveyability of proofs. By this he means that mathematical proofs can be reproduced with certainty and in the manner in which we reproduce pictures. There are remarkable similarities between Wittgenstein's view of proofs and Hilbert's, but Wittgenstein, unlike Hilbert, uses his view mainly in critical intent. He tries to undermine foundational systems in mathematics, like logicist or set theoretic ones, by stressing the (...) unsurveyability of the proof-patterns occurring in them. Wittgenstein presents two main arguments against foundational endeavours of this sort. First, he shows that there are problems with the criteria of identity for the unsurveyable proof-patterns, and second, he points out that by making these patterns surveyable, we rely on concepts and procedures which go beyond the foundational frameworks. When we take these concepts and procedures seriously, mathematics does not appear as a uniform system, but as a mixture of different techniques. (shrink)

Contre la metaphysique: questions de methode / par Felix Le Dantec,...Date de l'edition originale: 1912Collection: Bibliotheque de philosophie contemporaineCe livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF.Les oeuvres faisant partie de cette collection ont ete (...) numerisees par la BnF et sont presentes sur Gallica, sa bibliotheque numerique.En entreprenant de redonner vie a ces ouvrages au travers d'une collection de livres reimprimes a la demande, nous leur donnons la possibilite de rencontrer un public elargi et participons a la transmission de connaissances et de savoirs parfois difficilement accessibles.Nous avons cherche a concilier la reproduction fidele d'un livre ancien a partir de sa version numerisee avec le souci d'un confort de lecture optimal. Nous esperons que les ouvrages de cette nouvelle collection vous apporteront entiere satisfaction.Pour plus d'informations, rendez-vous sur www.hachettebnf.frhttp: //gallica.bnf.fr/ark: /12148/bpt6k5477903d. (shrink)

A travers la lecture du Visible et de l ‘Invisible, Guy-Félix Duportail se propose de montrer que la notion de chair connaît une structure topologique que l’on peut expliciter sous la forme de trois principes élémentaires : indivision, division, et réversibilité. Ceux-ci constituent l’infrastructure oubliée de la conscience et forment un inconscient phénoménologique (l’invisible- du visible). De plus, ces trois principes de la chair possèdent une signification· ontologique_ Dire que ľêtre est charnel, c’est ipso facto reconnaître la médiation nécessaire d’ (...) un troisième terme qui modifie le lien entre l’Être et le Néant. Ce troisième terme est ľ ouverture qui apparaît dans les phénomènes comme béance et qui s’apparente à l’objet du désir. L’ontologie de Merleau- Ponty dépasse ainsi la philosophie de la conscience de Husserl et de Sartre, de même que l’ontologie désincarnée de Heidegger. (shrink)

How does one arrive at a life in politics and policy? What happens to one's ideals when confronted with the reality that the only way to get things done in Washington is compromise? Who are the men and women who help shape our national agenda, and what drives their work? Dispatches From the Eastern Front provides fascinating, intensely personal, yet universal answers to these central questions. Recounting four decades inside Washington politics, Gerald Felix Warburg brings remarkable candor to a (...) most unusual memoir. An idealistic California baby boomer transported to the intimidating world of Capitol Hill policymaking at a young age, Warburg finds himself working to reform nuclear energy, strategic arms control, and foreign policy. As his access and power grow, greater challenges loom: how to maintain principles while cutting deals, and how to balance public purpose with private interests. An eclectic career reveals the slow and often painful development of emotional intelligence for work at the highest reaches of the public arena. (shrink)

The following definition of objective is proposed: A statement S is objective if and only if in S all parameters that are relevant to its truth value are made explicit. The objectivity of predicates and relations can be defined in a similar manner. This simple conception of objectivity-which could be called explicitness conception of objectivity-can be found in Hermann Weyl and plays a central part in the natural sciences. There are grades of objectivity depending on the quality and the number (...) of parameters our predicates are relativized to A relativistic Ockham principle has to be recognized: Relativization parameters are not to be multiplied beyond necessity. The explicitness conception of objectivity is accessible to mathematical specifications, is the core of the idea of invariance, has a lot of philosophical applications and leads to precise notions of subjectivity and a precise formulation of the problem of the limits of objectivity. (shrink)

The later Wittgenstein holds that the sole function of mathematical propositions is to determine the concepts they invoke. In the paper this view is discussed by means of a single example: Wittgenstein's investigation of the concept of a regular heptagon as used in Euclidean geometry (i.e., the Euclidean constructiongame with rulerand compass) andinCartesian analytic geometry. Going on from some well-known passages in Wittgenstein's Lectures on the Foundations of Mathematics, and completing these passages, it is shown that Wittgenstein'sview makes perfectly good (...) sense and can be very well defended. (shrink)

Peter Janichs konstruktiver Aufbau einer Chronometrie, wie er in der neuen Auflage seines Buches "Die Protophysik der Zeit" beschrieben ist, wird einer detaillierten Kritik unterzogen. Dabei kristallisieren sich drei ernste Probleme heraus: Das Problem der Eindeutigkeit der Leitlinie, das Problem der Transitivität der Begleitstellungen, und das Problem der eindeutigen Bestimmtheit der Uhren. Alle drei Probleme bleiben bei Janich unbewältigt, woraus folgt, daß seine Chronometrie in der vorliegenden Form zumindest unvollständig ist.

The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this (...) notion of fragment is axiomatized by the rules of the sequent calculus for the connectives involved. We also prove that these deductive systems are non-protoalgebraic, while the Gentzen systems are algebraizable with equivalent algebraic semantics the varieties of pseudocomplemented (commutative integral bounded) semilatticed and latticed monoids, respectively. All the logical systems considered are decidable. (shrink)

This paper studies, with techniques ofAlgebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sentential logics have been isolated. These logics are weaker than the positive implicative logic. We have determined their algebraic models (...) and the relationships between them, and have classified them according to several standard criteria of Abstract Algebraic Logic. One of the logics is protoalgebraic but neither equivalential nor weakly algebraizable, a rare situation where very few natural examples were hitherto known. In passing we have found new, alternative presentations of positive implicative logic, both in Hilbert style and in Gentzen style, and have characterized it in terms of the restricted Deduction Theorem: it is the weakest logic satisfying Modus Ponens and the Deduction Theorem restricted to at most 2 side formulas. The algebraic part of the work has lead to the class of quasi-Hilbert algebras, a quasi-variety of implicative algebras introduced by Pla and Verdú in 1980, which is larger than the variety of Hilbert algebras. Its algebraic properties reflect those of the corresponding logics and Gentzen systems. (shrink)

Wittgenstein was hostile towards set theory; see his remark in §22 of RFM II: ‘I believe and hope that a future generation will laugh at this hocus pocus’. At the same time, he says that what philosophy owes set theory is ‘tremendous’ and that this is something ‘deep’. I want to clarify these two statements and to reconcile them. The hocus‐pocus remark is mainly directed at the temptation to talk about an own world of sets, focussing on extensions and thereby (...) forgetting the actual mathematical manoeuvres leading to them. Wittgenstein does not shy away from using set‐theoretical symbols and expressions, but he regularly deprives them of their genuine set‐theoretical character. When speaking of the ‘depth’ we encounter with regard to set theory, what he means is the depth explained in PI §111: It arises ‘through a misinterpretation of our forms of language’, and this is particularly so in set theory. (shrink)

The sense of kairos is of time as having an event-like character. Fundamental here is a split between quantitative time and a qualitatively distinct moment. The decisive moment connects the kairological to crisis. By exploring the accounts of kairos in three contemporaries responding to the sense of crisis in 1920s Germany—Benjamin, Heidegger, and Tillich—this article shows the manner in action in the kairos can be understood as both responsive and non-opportunist. Themes such as the “tiger leap” (Benjamin), the “moment of (...) vision” (Heidegger), and the “shuddering” of time (Tillich) are analyzed to demonstrate how these accounts taken in dialogue with one another give an understanding of kairos, as a displacement and disruption of time as chronos and not simply as an interruption in chronological time. Such a disruption of chronological time is a necessary condition for responsible action, giving a measure also for the present. (shrink)

The threat of terrorism once again raises some of the classic questions about constitutionalism: is it possible for constitutions to do what they aim to do—channel and control political power in such a way as to make it safe and beneficent for those under its rule but also competent to govern? Does not terrorism reraise the Schmittian problem of “the exception”, i.e., the situation of emergency that necessarily escapes all constitutional limitations? Although they did not face the problem of terrorism (...) as we know it, the American founders developed three different models of constitutionalism, embodying three different ways of responding to emergent circumstances and yet remaining bound to the constitutionalist aspiration. We develop the main outlines of the three models both conceptually and historically and show how they continue to be relevant to current discussions of constitutionalism in the age of terror. Finally, we make a tentative effort to judge which of the three models is most able to do what constitutions should do in difficult times. (shrink)

Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 (Cambridge University Press, New York) is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic (“intuition” in the specific sense of Kant and Hilbert). Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic structure is the (...) so-called ‘intuitive model’ of arithmetic realized by Hilbert’s strings of strokes. This paper argues that Hilbert’s strings, considered as given in intuition, cannot play the role Parsons assigns to them: the criteria of identity of these strings do not have the sharpness that Parsons wants to see in them, and Parsons inadvertently projects abstract structures into his ‘intuitive model’. This diagnosis is exemplified with respect to (a) Parsons’ distinction between addition and multiplication on the one hand and exponentiation on the other and (b) his analysis of arithmetical knowledge in simple cases like “7 + 5 = 12”. All in all, it is claimed that Parsons book contains many important insights with respect to, for example, different versions structuralism, the notion of “natural number” and its uniqueness, induction, predicativity and other things, for which he is rightly famous, but that his way of drawing on the notion of intuition leaves too many questions unanswered. (shrink)

Name der Zeitschrift: Wittgenstein-Studien Jahrgang: 5 Heft: 1 Seiten: 145-162.

En las condiciones actuales, la exclusión por el color y el origen no pertenece al pasado. El pensamiento advertido y crítico mantiene su mirada sobre el tema de las razas, con perspectivas y enfoques nuevos. Sin embargo, en el pensamiento caribeño hay una curada historia de argumentos que ha dejado sin alas a valores de antaño, establecidos por la dominación colonial, para deshacer sus trampas y romper los universales de la �cultura universal�. El presente texto pretende hacer un recorrido por (...) la obra principal de los pensadores del área que han cuestionado el tema racial, uno de los más importantes de toda reflexión insular, sin apegos a tradiciones académicas disciplinares estrechas. (shrink)

This short document, appearing for the first time in English translation, concerns the prospects of a made-for-television cultural mini-series inspired by select episodes in Kafka's works. A window is opened onto Guattari's curatorial ambitions, cinematic projects, and theory of minor cinema, bringing into focus how he translated theoretical preoccupations into the cultural sector with reference to diverse semiotic media.

This book applies Augustine's thought to current questions of teaching and learning. The essays are written in an accessible style and is not intended just for experts on Augustine or church history.

The encyclical proclaims the centrality of human development, which includes acting with gratuitousness and solidarity in pursuing the common good. This paper considers first whether such relationships of gratuitousness and solidarity can be analysed through the prism of traditional theories of social psychology, which are highly influential in current management research, and concludes that certain aspects of those theories may offer useful tools for analysis at the practical level. This is contrasted with the analysis of such relationships through Aristotelian virtue (...) ethics (in particular as interpreted by MacIntyre 1985 , 1998 , 1999 ), which is emerging as a strong force in the field of business ethics, and which has strong conceptual similarities with the ideas put forward by Benedict XVI. Aristotelian virtue ethics offers a better fit with the aims of the encyclical at the theoretical level but it presents a number of challenges at the practical level, which the paper suggests may be addressed through the integration in its analysis of human action of models derived from social psychology. (shrink)