The Blind Spot ; Lectures on Logic.

Format:

Book

Author/Creator:

Girard, Author.

Language:

English

Physical Description:

1 online resource (550 pages)

Other Title:

Blind Spot

Place of Publication:

EMS Press 2011

System Details:

text file PDF

Summary:

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 Gödels paradox (1931) - so to speak, the incompleteness of answers with respect to questions - the book proceeds with paradigms inherited from Gentzens 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 worlds 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.

ISBN:

3-03719-588-6