1,500 research outputs found

    Periods in the Use of Euler-type Diagrams

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    Logicians commonly speak in a relatively undifferentiated way about pre-euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of euler-type diagrams occurred within an expansive period, after a subsequent phase of regression the entire knowledge about the systematic application and the history of euler-type diagrams was lost. I will argue that the first expansive period lasted from Vives (1531) to Alsted (1614). The second period began around 1660 with Weigel and ended in 1712 with lange. The third period of expansion started around 1760 with the works of Ploucquet, euler and lambert. Finally, it is shown that euler-type diagrams became popular in the debate about intuition which took place in the 1790s between leibnizians and Kantians. The article is thus limited to the historical periodization between 1530 and 1800

    The Basic Laws of Cardinal Number

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    An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze

    Pure Nash Equilibria: Hard and Easy Games

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    We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is SigmaP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each players payoff depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players. The dependency structure of a game G can be expressed by a graph DG(G) or by a hypergraph H(G). By relating Nash equilibrium problems to constraint satisfaction problems (CSPs), we show that if G has small neighborhood and if H(G) has bounded hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems

    Frege – The Unintentional Linguist. On Frege’s Views of Language in the Context of 19th Century German Linguistics

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    Sein ganzes berufliches Leben hindurch betrachtete Frege die Sprache als eine gefĂ€hrliche Bedrohung des wissenschaftlichen Erkennens, der mit allen Mitteln der Logik zu begegnen war. Im ersten Teil des Aufsatzes wird aufgezeigt, wie Frege diese Auffassung in oft unbewusster und ungewollter Übereinstimmung mit gleichzeitigen Tendenzen sowohl in der deutschen Linguistik (Becker, Steinthal, Paul, Wundt) als auch in der deutschen Sprachkritik (Gruppe, Nietzsche, Mauthner) entwickelte und wie sein epistemologischer ‚Kampf gegen die Sprache’ mit einer bitteren persönlichen und professionellen Niederlage endete. Der zweite Teil des Aufsatzes enthĂ€lt eine Rekonstruktion von Freges logischer Grammatik sowie eine Darstellung des linguistischen Argumentes, das fĂŒr Freges endgĂŒltiges (und tragisches) Akzept vom Sprachskeptizismus entscheidend wurde (das sogenannte Fregesche Paradox). Der Aufsatz schließt mit einer Evaluierung der Relevanz des Fregeschen Paradoxes fĂŒr die heutige Linguistik

    Kant’s Deductions of Morality and Freedom

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    It is commonly held that Kant ventured to derive morality from freedom in Groundwork III. It is also believed that he reversed this strategy in the second Critique, attempting to derive freedom from morality instead. In this paper, I set out to challenge these familiar assumptions: Kant’s argument in Groundwork III rests on a moral conception of the intelligible world, one that plays a similar role as the ‘fact of reason’ in the second Critique. Accordingly, I argue, there is no reversal in the proof-structure of Kant’s two works

    Deep roots: A conceptual history of 'sustainable development' (Nachhaltigkeit)

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    In the last two decades, the concept of ‘Sustainable Development’ has made a steep career as a political and ethical guideline for dealing with the planet’s ecological and social crisis. The concept, globally inaugurated in 1987 by the World Commission on Environment and Development (socalled Brundtland Commission) is, however, not a brain-child of the modern environmental movement. Its blueprint can be found in the professional terminology of forestry. ‘Sustained yield’ had been the major doctrine of international forestry for almost two centuries. This formula is a translation of the German term ‘nachhaltiger Ertrag’. The roots of this concept can be traced back to the era of early ‘European Enlightenment’, when German Kameralists, inspired by the English author John Evelyn and the French statesman Jean Baptist Colbert, began to plan their dynasties’ woodlands ‘nachhaltig’ – in order to hand them along undiminished to future generations. The word itself was then coined in 1713 by Hanns Carl von Carlowitz, head of the Royal Mining Office in the Kingdom of Saxony, in order to meet the challenge of a predicted shortage of timber, the key resource of the time. This paper on the historical evolution of the concept of sustainability is thought to be a contribution to the 20th anniversary of the report of the Brundtland Commision. --

    Inferentialism and the reception of testimony

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    Ricoeur’s Transcendental Concern: A Hermeneutics of Discourse

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    This paper argues that Paul Ricoeur’s hermeneutical philosophy attempts to reopen the question of human transcendence in contemporary terms. While his conception of language as self-transcending is deeply Husserlian, Ricoeur also responds to the analytical challenge when he deploys a basic distinction in Fregean logic in order to clarify Heidegger’s phenomenology of world. Ricoeur’s commitment to a transcendental view is evident in his conception of narrative, which enables him to emphasize the role of the performative in literary reading. The meaning of the self in time provides Ricoeur with a discursive basis for distinguishing his own position from that of Kant and other philosophers in the transcendental tradition

    Frege, Carnap, and the Limits of Asserting

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    This paper applies the contemporary idea of the constitutive features of assertions to the texts of Gottlob Frege, Rudolf Carnap, and Ludwig Wittgenstein. The focus is in Frege and Carnap, but a connection to Wittgenstein’s remarks on philosophy is indicated at the end of the paper. I intend to study and compare the three philosophers’ views on philosophical asserting and philosophical assertions. The question about the limits of language is thus posed in pragmatic terms, because it is formulated as a question about the limits set to linguistic acts labelled as assertings. I focus on Frege’s Begriffschrift (1879) and his Grundlagen der Arithmetik (1884), and on Carnap’s article titled “Empiricism, Semantics, and Ontology” (1950/1956); I then make a few remarks on Wittgenstein’s Philosophical Investigations and On Certainty. I argue that there are important connections between Frege’s and Carnap’s views on the limits of asserting. Their otherwise diverging positions are connected in that, as they show, it is not easy for philosophers themselves to comply with the norms they give for judging and asserting. I argue that while Frege does not make his attitude towards philosophical assertions explicit, the common core in Carnap’s and Wittgenstein’s texts is that the epistemic norms they give to assertions lead both to deny the possibility of philosophical assertions.Peer reviewe

    Shrewdness, coup d'Ɠil, and genius: the cognitive attributes of the consummate general (Greek antiquity, Byzantine era, modern times)

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    Everett Wheeler's hypothesis that the Greek concept of ankhínoia finds its equivalent in eighteenth-century military writers' notion of the coup d'oeil is tested by comparing treatises on the art of war written in the two periods. After highlighting the different meanings of the coup d’oeil in 18th century military terminology, Clausewitz's approach is examined in the light of his concept of the genius for war
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