To interpret some package P is for the interpreting subject S to I:
use S’ s reasons (or if you prefer, “premises,” “assumptions,” “beliefs,” “truths,” and even “tradition”) rS in the explanation of P.
In short,
interpretation is the explanation in terms of the beliefs of the interpreter.
Problem:
(a) belief is a claim made true by virtue of an attitude (x believes that p is true if x believes p) and does not entail the embedded thoughts (p). To explain by way of belief is not to explain by way of the facts (true thoughts).
(b) explanation by way of what one takes to be true violates validity as truth is neither necessary nor sufficient for validity.
(c) interpretation can only explain what one already believes, and will hence end up depicting what is alien as mysterious and sub-rational, but because of (b) this diagnosis is objectively mistaken.
For more on this, please see my intro to the Bloomsbury Research Handbook of Indian Ethics, and Hinduism: A Contemporary Investigation (especially chapter 4). Both explore the explore the problems with interpretation in contrast to explication especially in light of the challenge of understanding alien philosophy.
I also explore the historical roots of interpretation as an outcome of the linguistic account of thought, characteristic of what I call the West.
