In his classical 1892 article On sense and denotation, Frege associates with each declarative sentence its denotation (truth value) and also its sense (meaning) “wherein the mode of presentation [of the denotation] is contained”. For example, 1+1=2 and there are infinitely many prime numbers are both true, but they mean different things - they are not synonymous. Frege [1892] has an extensive discussion of senses and their properties, including, for example, the claim that the same sense has different expressions in different languages or even in the same language; but he does not say what senses are or give an axiomatization of their theory which might make it possible to prove these claims. This has led to a large literature by philosophers of language and logicians on the subject, which is still today an active research topic. A plausible approach that has been discussed by many (including Michael Dummett) is suggested by the “wherein” quote above: in slogan form, the sense of a sentence is an algorithm which computes its denotation. Coupled with a rigorous definition of (abstract, possibly infnitary) algorithms, this leads to a rich theory of meaning and synonymy for suitably formalized fragments of natural language, including Richard Montague’s Language of Intensional Logic. My aim in this talk is to discuss with as few technicalities as possible how this program can be carried out and what it contributes to our understanding of some classical puzzles in the philosophy of language.