J.M.E. Hyland est professeur de logique mathématique au King’s College à Cambridge.
Logic, abstract mathematics and the science of information: an
unappreciated aspect of the heritage of Turing.
The science of information was born in the 1930s in the midst of the great discoveries of modern logic. In his famous 1937 paper Turing gave a definitive analysis of the notion of computability. The fact that this intuitive notion has a precise counterpart still seems remarkable today. Turing’s analysis has had an evident impact on practical computing. Computers are the most visible aspect of information science and even today we think of them as Turing machines. As a result perhaps the dominant idea of our time is that information science is information technology, that is to say that it is only concerned with practical questions.
However there is another aspect to computability. One should not forget that the notion first appeared within logic. Many links between logic, abstract mathematics and programming have since emerged and these form an important component of information science. Moreover information science itself has been a source of new mathematical structures. One example is given by the interplay between the Theory of Types from logic and Category Theory. I shall say something about this area and about Turing’s largely forgotten interest in related questions.