LEADER 03273nam 22004335a 450 001 9910151928603321 005 20110924234522.0 010 $a3-03719-588-6 024 70$a10.4171/088 035 $a(CKB)3710000000953872 035 $a(CH-001817-3)136-110924 035 $a(PPN)178155985 035 $a(EXLCZ)993710000000953872 100 $a20110924j20110925 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aThe Blind Spot$b[electronic resource] $eLectures on Logic /$fJean-Yves Girard 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (550 pages) 330 $aThese 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 Go?del'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. 517 $aBlind Spot 606 $aMathematical logic$2bicssc 606 $aMathematical logic and foundations$2msc 606 $aCategory theory; homological algebra$2msc 606 $aComputer science$2msc 615 07$aMathematical logic 615 07$aMathematical logic and foundations 615 07$aCategory theory; homological algebra 615 07$aComputer science 686 $a03-xx$a18-xx$a68-xx$2msc 700 $aGirard$b Jean-Yves$059717 801 0$bch0018173 906 $aBOOK 912 $a9910151928603321 996 $aThe Blind Spot$92565744 997 $aUNINA LEADER 01414nam2 22003133i 450 001 RAV0067917 005 20231121125628.0 020 $aIT$b641193 100 $a20140820d1965 ||||0itac50 ba 101 | $aita 102 $ait 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $a˜1: I œGermani; migrazioni e regni nell'Occidente già romano; i Franchi$f di O. Bertolini, C. Violante 210 $aMilano$cVallardi$d[1965! 215 $aXXVII, 651 p., [28! c. di tav.$cill.$d30 cm. 462 1$1001RAV0067915$12001 $a˜3: œNuove formazioni politiche nel mondo mediterraneo medioevale.$v1 700 1$aBertolini$b, Ottorino$3RAVV032259$4070$0210991 701 1$aViolante$b, Cinzio$3CFIV014616$4070$036487 801 3$aIT$bIT-01$c20140820 850 $aIT-RM028 $aIT-FR0084 $aIT-FR0017 899 $aBiblioteca Universitaria Alessandrina$bRM028 899 $aBiblioteca Del Monumento Nazionale Di Montecassino$bFR0084 899 $aBiblioteca umanistica Giorgio Aprea$bFR0017 $eN 912 $aRAV0067917 950 2$aBiblioteca umanistica Giorgio Aprea$cI/VIII$d 52UFF.PREST.NUOVE FORMAZIONI POLITIC$e 52MAG0000052655 VMN RS 3.1$fA $h20151204$i20151204 977 $a 01$a 25$a 52 996 $aGermani; migrazioni e regni nell'Occidente già romano; i Franchi$91043850 997 $aUNICAS