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Beschreibung
These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic.
The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer… is a sort of equality where one side is “more equal than the other”: one thus discovers essentialist blind spots.
Starting with Gödel’s paradox (1931) – so to speak, the incompleteness of answers with respect to questions – the book proceeds with paradigms inherited from Gentzen’s cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra.
Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity.
This highly original course on logic by one of the world’s leading proof theorists challenges mathematicians, computer scientists, physicists and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way. Dieses Produkt haben wir gerade leider nicht auf Lager.
Handgeprüfte Gebrauchtware
Bis zu 50 % günstiger als neu
21 Tage Widerrufsrecht
Technische Daten
Erscheinungsdatum
24.09.2011
Sprache
Englisch
EAN
9783037190883
Herausgeber
EMS Press
Sonderedition
Nein
Autor
Jean-Yves Girard
Seitenanzahl
537
Auflage
1
Einbandart
Gebundene Ausgabe
Buch Untertitel
Lectures on Logic
Schlagwörter
proof-theory, sequent calculus, lambda-calculus, Logic, Curry–Howard isomorphism, incompleteness, natural deduction
Thema-Inhalt
PBCD - Mathematik: Logik
Höhe
240 mm
Breite
17 cm
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