ABSTRACT
We already superficially mentioned semantics. In this chapter we discuss, in some detail, the semantics of (object) languages. Semantics is the analysis of meaning. The concept of meaning can be controversial and it often involves recourse to either psychology or (some brand of) metaphysics. Here we adopt a minimalistic approach: the meaning of a sentence in a language will be defined as the totality of its available translations into other languages. This definition is somewhat unsatisfactory. Indeed we did not say what the meaning of a sentence is; we only specified what it does, which is to single out a collection of sentences in other languages. However this minimal definition of meaning will be more than enough for our purpose of developing mathematics. This being said we may forget, in what follows, about meaning and only care about translations.
