ABSTRACT
Our scientific (including mathematical) knowledge is typically organised in the form of theories. Theories are characterised by sets of fundamental laws, or principles, or postulates, or axioms, from which ideally everything else held to be true is deduced as consequences, though, as we shall see, a famous theorem of Gödel shows that in most cases of interest this ideal can never be achieved. In this chapter we shall talk about the formalisation of theories in first-order languages and some of the celebrated theorems proved in this century which reveal surprising properties of these formalisations.
