Some New Books on Logic

J. Lambek
1969 Canadian mathematical bulletin  
A well-known Hungarian mathematician has conjectured that, as soon as man discovers a proof that 1=0, the world will vanish. For fear of paradox intuitionists have been doing mathematics with one hand tied behind their back. Formalists still insist that metamathematics be done in this manner. Having been brought up on the books by Quine, Rosenbloom, and Kleene, one is left with the impression that logic is there to talk about mathematics, and that it may only utilize the most rudimentary of
more » ... rudimentary of constructive mathematics itself. Hence the emphasis on syntax, the science which deals with strings of symbols. Looking at the new books, one realizes that there has been a swing away from syntax to semantics, the science of meaning, and that the most powerful mathematical tools are now being used in logical investigations. To quote Fraissé: "One may say that semantics is to syntax as the theory of fields is to the methods for solving algebraic equations." Cours de logique mathématique, tome 1 ; relation, formule logique, compacité, complétude (Collection de logique mathématique, série A. No. 23) by R. Fraissé. Gauthier-Villars, Paris, 1967. xii+186.
doi:10.1017/s0008439500030654 fatcat:qha5k4j7h5gw5fc4nw5tgnn4xy