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Mathematics --- Number concept --- Algebra --- Logic, Symbolic and mathematical --- Mathématiques --- Concept de nombre --- Algèbre --- Logique symbolique et mathématique --- Philosophy --- Foundations --- Philosophie --- Fondations (Construction)

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Quels sont les problèmes philosophiques soulevés par les ordinateurs et par l'informatique ? Les réponses les plus fréquentes invoquent l'intelligence artificielle, la pensée des machines ou les théories computationnelles de l'esprit. Mais ces réponses occultent la possibilité d'une autre ouverture philosophique sur l'informatique, conçue à partir d'une réflexion sur la machine en logique. Comment comprendre que la logique, qui est à la fois une discipline de la pensée et un instrument d'analyse du langage, puisse devenir aussi bien une science des machines informatiques ? Pierre Wagner montre pourquoi la machine s'est progressivement imposée, depuis les années trente, comme l'un des objets majeurs de l'analyse logique ; et à partir de cette réflexion d'ordre historique, il trace les linéaments d'une philosophie des machines informatiques qui ne se réduit pas aux questions d'intelligence artificielle ou de théorie de l'esprit. L'ouvrage se présente également comme une introduction à certaines notions logiques fondamentales (les machines de Turing, le lambda-calcul, la correspondance de Curry-Howard...) dont l'auteur met en évidence la portée philosophique.

Computer science --- Logic, Symbolic and mathematical. --- Artificial intelligence. --- Informatique --- Logique symbolique et mathématique --- Intelligence artificielle --- Philosophy --- Philosophie --- Logic machines --- Logique mathématique --- Machines logiques --- Logique --- Histoire --- Intelligent machines --- Machines, Logic --- Logic --- Logic, Symbolic and mathematical --- Logique symbolique et mathématique --- Automation --- Logique mathématique. --- Philosophie. --- Histoire.

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One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.

Mathematical logic --- Mathematics --- Logic, Symbolic and mathematical. --- Mathématiques --- Logique symbolique et mathématique --- Philosophy. --- Philosophie --- Logic, Symbolic and mathematical --- -Math --- Science --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Philosophy --- -Philosophy --- Mathématiques --- Logique symbolique et mathématique --- Logic of mathematics --- Mathematics, Logic of --- Mathematical logic. --- Logic. --- Mathematics. --- History. --- Mathematical Logic and Foundations. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Reasoning --- Thought and thinking --- Methodology

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Das Buch beabsichtigt, mit den Mitteln einer phänomenologischen Semantik, einen Beitrag zum Verständnis der Modallogik und ihrer philosophischen Implikationen zu liefern. Es richtet sich in erster Linie an Phänomenologen, aber auch an analytische Philosophen und an philosophisch interessierte Logiker.Bereits im vorigen Jahrhundert begannen Mathematik und Logik, sich zu abstrakten Wissenschaften zu entwickeln. Husserl nannte die schließlich resultierende Einheit beider `Mathesis Universalis'. Diese bildet nicht nur den Boden aus dem Husserls philosophische Arbeit erwuchs, sondern auch den Rahmen, in den die moderne Modallogik zu stellen ist. Als abstrakte Disziplin der Mathesis Universalis erfordert ihre phänomenologische Aufklärung detaillierte Analysen der Genese von Modalisierung, die weit in die kognitiven Strukturen von (vorsprachlicher) Wahrnehmung hineinreichen. Das so gewonnene Verständnis von Modalisierung erbringt ein zweifaches Resultat: Zum einen kann die insbesondere im Rahmen der analytischen Philosophie geführte Diskussion der erkenntnistheoretischen und ontologischen Schwierigkeiten der Modallogik eine phänomenologische Aufklärung erfahren. Zum anderen erlaubt die Tatsache, daß der Beweisbegriff als mathematische Modalität zu verstehen ist, eine präzise phänomenologische Bestimmung des Verhältnisses von formaler Logik und Mathematik.

Fenomenologie --- Logic [Symbolic and mathematical ] --- Logica [Symbolische en wiskundige ] --- Logique symbolique et mathémathique --- Modaliteit (Logica) --- Modality (Logic) --- Modalité (Logique) --- Phenomenology --- Phénoménologie --- Logique symbolique et mathématique --- Logic, symbolic and mathematical --- Modal logic --- Nonclassical mathematical logic --- Bisimulation --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Phenomenology. --- Modality (Logic). --- Modalité (Logique) --- Logique symbolique et mathématique --- Phénoménologie --- Logic, Symbolic and mathematical --- Science --- Philosophy, Modern --- Logic --- Mathematical logic --- Mathematics --- Set theory --- Normal science --- Philosophy of science --- Philosophy --- Theory of knowledge --- Logic, Symbolic and mathematical. --- Philosophy. --- Sciences --- Philosophie --- Science - Philosophy --- Logique modale