The study of logic underwent a profound rebirth at the turn of the twentieth century. While logicians were traditionally concerned with the correctness of reasoning in ordinary language, Frege introduced formal languages as the primary medium and objects of logical enquiry. The shift from ordinary language to artificial languages containing formal expressions elevated the study of mathematics and philosophy to a new level of rigour and marked the beginning of the computer age.

But what exactly are formal expressions? Although the ontological nature of mathematical objects, such as numbers, has been a central topic in philosophy since antiquity, a systematic study of the ontology of formal expressions is hitherto lacking in the literature.

The aim of this talk is threefold. First, I will show that within the last century, the study of formal languages underwent a "structuralist turn". I will then argue that recent attempts to make the structuralist view of formal languages explicit are flawed. Finally, I will show how the structuralist view can be stated correctly.