The one ring gives the wearer the power of what the wearer defines as power. Frodo turns invisible because for a hobbit not being noticed means safety. The ring tells Sam that he could plant as many Apple trees as he likes, even plastering whole middle earth.

In this moment the ring probably tells to Boromir that he could rebuild Gondor to old strength and he might be able to (before giving in to saurons influence).

First Incompleteness Theorem: “Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e. there are statements of the language of F which can neither be proved nor disproved in F.” (Raatikainen 2020)