ABSTRACT
We are interested in the analysis of language with special emphasis on syntax, semantics, reference, inference, truth; this analysis will be referred to as (general) logic. We begin with an informal discussion; more details will be given in subsequent chapters of Part 1 of this book. In particular we will discuss later theories which are certain collections of sentences in a language. We agree that nothing is available to us except language; in particular we need to analyze language using language. Disentangling this self-referential aspect of the analysis will soon be one of our main concerns. Mathematics itself will be defined in Part 2 of the book as a theory (called set theory) in a certain language; it will have no semantics, no reference, and no notion of truth. Note that in Part 1 mathematics (set theory) is not available yet so it cannot be used to analyze language; this makes the (general) logic of Part 1 of the book a pre-mathematical logic. Once mathematics is available through Part 2 one can revisit the discussion of pre-mathematical logic within mathematics. The resulting discussion is referred to as mathematical logic and will be briefly presented in Part 3 of the book. This “extreme formalist” way of organizing the field is not standard; cf the Introduction for a comparison with other approaches.
