A philosophical interpretation is the assignment of meanings to various concepts, symbols, or objects under consideration.
An aesthetic interpretation expresses an understanding of a work of art, a poem, performance, or piece of literature.
The formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation.
The aim of these attempts is to construct a formal system that will serve as a conceptual model of reality.
Predictions or other statements drawn from such a formal system mirror or map the real world only insofar as these scientific models are true.