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The purpose of this chapter is to summarise some of the movements within the formal sciences that occurred during the nineteenth and twentieth centuries, and which were ultimately to exert a profound ifluence over the development of TGG. Since the origins of TGG are the main focus of the following chapters, and since any search for origins necessarily entails an infinite regress if taken to an extreme, an arbitrary beginning is required, and the starting point chosen for this discussion is the emergence of the calculus as an identifiable set of algorithmic procedures in the late seventeenth century. Accordingly, the advent of the calculus is discussed in section 2.2 and some of the disputes associated with its appearance are reviewed, along with the main subsequent advances that led to the creation of the branch of mathematics known as ‘analysis’. In section 2.3 various attempts to provide a more secure foundation for analysis are briefly assessed, with particular attention being given to the endeavour to derive the calculus from the rudiments of number theory. The development of set theory, which grew out of the need to secure the basis of arithmetic, is summarised in section 2.4, and some of the resultant paradoxes are explored. The remaining sections of the chapter discuss the three main theories that emerged at the end of the nineteenth century and the beginning of the twentieth century in direct response to the foundations crisis prompted by set theory.
The main purpose of this chapter is to continue to reassess the development of TGG in the light of advances in the formal sciences. Consequently, Chomsky's writings from the years 1955–1957 will be the focus of the discussion, although, as previously, connections will be made between Chomsky's work and that of both his predecessors and his contemporaries. To this end, in section 5.2 Chomsky's rejection of stochastic grammars is considered as part of his assertion that syntax can be studied autonomously. In section 5.3 his redefinition of syntactic research is assessed, particularly the recommended shift away from discovery procedures and towards evaluation procedures. Since certain of the arguments that caused Chomsky to reconsider the role of discovery procedures in linguistic research were initially articulated by Goodman and Quine, it is necessary to explore the influence of constructional system theory upon the approach to syntactic analysis outlined in LSLT and Syntactic Structures (hereafter SS), and this is achieved in section 5.4 where it is shown that Chomsky's definition of a linguistic level is derived from constructional system theory. Given the name of the syntactic theory discussed in this book, ‘Transformational Generative Grammar’, it is necessary to discuss both the concept of ‘transformation’ and the process of ‘generation’. Accordingly, the complex evolution of grammatical transformations in syntactic theory is traced in section 5.5, while in section 5.6 the generative role of recursive definitions in TGG is considered.
The formal sciences, particularly mathematics, have had a profound influence on the development of linguistics. This insightful overview looks at techniques that were introduced in the fields of mathematics, logic and philosophy during the twentieth century, and explores their effect on the work of various linguists. In particular, it discusses the 'foundations crisis' that destabilised mathematics at the start of the twentieth century, the numerous related movements which sought to respond to this crisis, and how they influenced the development of syntactic theory in the 1950s. The book concludes by discussing the resulting major consequences for syntactic theory, and provides a detailed reassessment of Chomsky's early work at the advent of Generative Grammar. Informative and revealing, this book will be invaluable to all those working in formal linguistics, in particular those interested in its history and development.
As indicated in the introduction, and as demonstrated in the subsequent chapters, this book manifestly constitutes an exercise in historiography, and the general purpose has been to reveal the nature and extent of the influence of the formal sciences upon the development of linguistic theory in the twentieth century, with the main emphasis falling upon the advent of TGG. At this stage, therefore, it is probably worth summarising the main issues considered, in order to review the central conclusions of the various intertwined investigations presented in the foregoing chapters.
One of the main tasks attempted in several sections of this book has been the re-evaluation of certain aspects of Bloomfield's work in the light of his interest in the foundations crisis and (specifically) in Formalism, aspects which appear to anticipate some of the preoccupations that obsessed mathematically minded linguists in the 1950s. In particular, it was suggested that Bloomfield's wellknown mistrust of semantic considerations in the study of natural languages may have been influenced by his knowledge of Hilbertian proof-theoretical techniques which (at least in their popularised form) recommend the avoidance of semantic considerations in (meta)mathematical proofs in favour of noncontentual syntactic manipulations. In general, recent research has neglected Bloomfield's knowledge of the foundational debates of the 1920s and 1930s, as well as his professional interest in the relationship between linguistics and mathematics.
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.
The emergence of Transformational Generative Grammar (TGG) in the 1950s is an event in the history of linguistics that has been recounted many times, in many different ways, by many different people, and since this book is primarily concerned with the development of TGG, some sort of apologia is required in order to justify retelling the same story yet again. Accordingly, it is hoped that this introduction will provide the requisite justification, and, in summary explanation, it can be stated at the outset that the main motivation for the particular narration offered here is dissatisfaction – specifically, dissatisfaction stemming from the conviction that none of the existing versions of the TGG narrative provide sufficient information concerning the influence of contemporaneous advances in the formal sciences upon the development of linguistic theory in the twentieth century. If indeed it is the case that this aspect of TGG history has been neglected in the past, then this neglect is certainly surprising, since the earliest proponents of TGG have never disguised the fact that the theory derived considerable inspiration from the formal sciences. For instance, in 1995 (to consider just one example) Chomsky stated explicitly that ‘[g]enerative grammar can be regarded as a kind of confluence of long-forgotten concerns of the study of language and mind, and new understanding provided by the formal sciences’ (Chomsky 1995: 4), and the scientific nature of TGG itself has often been noted over the years.
The main purpose of this chapter is to consider Chomsky's research from the years 1951–1955 in the light of the topics presented in the previous chapters, and, to renew the words of warning in the introduction, it is at this stage of the discussion that the convenient abbreviation ‘TGG’ ceases to be especially helpful. As indicated previously, the main problem is that, during this period, Chomsky explored a number of different approaches to syntactic theory and, though various aspects of these approaches were maintained and further developed, others were swiftly discarded. As a result, it is not possible simply to use the term ‘TGG’ with reference to Chomsky's work of the early 1950s as if it denoted a clear and consistently identifiable grammatical theory. Consequently, it is necessary either to accept that TGG must be viewed as a fluid concept that altered continually during this period, or else to avoid using the term altogether (whenever possible). In this chapter and the next the latter course is adopted, since it necessitates more specific reference to the various ideas that Chomsky explored during this period and so avoids confusion.
The main sections of this chapter focus upon the influences that shaped Chomsky's earliest work. The basic approach is to identify the presence of a particular influence, and then to trace its development as his research gradually matured during the 1950s.