Are purely formal objects entities or concepts ?

In this paper, our purpose will be to question the ontological nature of the structural - or purely formal - entities which, according to the formalist point of view, are defined within an axiomatic system, rather than described by this system.

After a brief reminder of the famous debate between Hilbert and Frege (in a postmail exchange from December the 27th 1899 to January the 6th 1900), as well as of the intuitionistic stance, we will consider Edmund Husserl’s and the early Carnap’s positions. This will lead to a new evaluation of the relations between the notions of “object” and “givenness”, as well as a to a new consideration of the respective contributions of conceptual description and acquaintance in the process of identifying purely formal objects.