Published online by Cambridge University Press: 22 September 2009
The purpose of this chapter is to summarise some of the developments, associated with the formal sciences, that grew out of the foundations debates of the early decades of the twentieth century, and to examine the way in which they exerted an influence upon the formulation of linguistic theory. The basic strategy is to focus upon particular techniques or theories that were ultimately to be involved in the creation of TGG. Consequently, it should be remembered throughout that this chapter is necessarily selective, and that it does not attempt to provide an exhaustive coverage of all the associations between mathematics and linguistics that were mooted during the first half of the twentieth century. The first subject, discussed in section 3.2, is the use of the axiomatic-deductive method, and detailed attention is given to the work of Bloomfield, Bloch, and Harwood. Recursive function theory is considered next, in section 3.3, with specific reference to the work of Gödel, Kleene, Post, and Bar-Hillel. In section 3.4 the work of the Lvov-Warsaw school of logicians is assessed, and particular emphasis is placed upon the way in which some of Ajdukiewicz's research into logical systems was revived by Bar-Hillel in the early 1950s. The evolution of constructional system theory is considered in section 3.5, and the associations between Carnap and Goodman are explored, while, in section 3.6, the extreme philosophical stance that came to be known as constructive nominalism is presented.