A detailed discussion of so-called two truths is found in this linked PDF:
The question is raised: While in the later Sanskrit, Mahayana, literature it seems that the expression “two truths” is used, but is it actually called “two truths” in the Theravadin literature?
The above linked PDF is titled: THERAVADA VERSION OF THE TWO TRUTHS, but its author, the Ven Y. Karunadasa, also uses the expression in his essay “double truth,” which is a better fit for what is being talked about here.
Ven Karunadasa gives us this from the Anguttara Nikaya commentaries:
This seems to sum up the idea of double truth, as it is used in the Theravada, quite well.Herein references to living beings, gods, Brahma, etc., are sammuti-kathā [“relative truth”], whereas references to impermanence, suffering, egolessness, the aggregates of the empiric individuality, the spheres and elements of sense perception and mind-cognition, bases of mindfulness, right effort, etc., are paramattha-kathā ["highest truth"].
One who is capable of understanding and penetrating to the truth and hoisting the flag of Arahantship when the teaching is set out in terms of generally accepted conventions, to him the Buddha preaches the doctrine based on sammuti-kathā.
One who is capable of understanding and penetrating to the truth and hoisting the flag of Arahantship when the teaching is set out in terms of ultimate categories, to him the Buddha preaches the doctrine based on paramattha-kathā.
To one who is capable of awakening to the truth through sammuti-kathā , the teaching is not presented on the basis of paramattha-kathā, and conversely, to one who is capable of awakening to the truth through paramattha-kathā, the teaching is not presented on the basis of sammuti-kathā.
There is this simile on this matter: Just as a teacher of the three Vedas who is capable of explaining their meaning in different dialects might teach his pupils, adopting the particular dialect, which each pupil understands, even so the Buddha preaches the doctrine adopting, according to the suitability of the occasion, either the sammuti- or the paramattha-kathā.
It is by taking into consideration the ability of each individual to understand the Four Noble Truths, that the Buddha presents his teaching, either by way of sammuti, or by way of paramattha, or by way of both. Whatever the method adopted the purpose is the same, to show the way to Immortality through the analysis of mental and physical phenomena. AA. Vol. I, pp.54-55
This can be illustrated by using two extreme examples from the suttas.
Dhp 157. If one [atta] holds oneself dear, one should diligently watch oneself. Let the wise man keep vigil during any of the three watches of the night.
158. One should first establish oneself in what is proper; then only should one instruct others. Thus the wise man will not be reproached.
160. One [atta] truly is the protector of oneself [attano]; who else could the protector be? With oneself fully controlled, one gains a mastery that is hard to gain.
"Monks, I will teach you the all. And what is the all? The eye and forms, the ear and sounds the nose and odors, the tongue and tastes, the body and touch, the mind and mental phenomena. This is called the all. If anyone, monks, should speak thus: ' Having rejected this all, I shall make known another all' - that would be a mere empty boast." SN IV 15.
"And which All is a phenomenon to be abandoned? The eye is to be abandoned. Forms are to be abandoned. Consciousness at the eye is to be abandoned. Contact at the eye is to be abandoned. And whatever there is that arises in dependence on contact at the eye — experienced as pleasure, pain or neither-pleasure-nor-pain — that too is to be abandoned. SN IV 15
What the double truth notion is doing drawing out the implication in the suttas of two different ways of talking about practice. In other words, there are not a literal two and distinct truths; rather, there are two general ways of talking about the same path to practice that leads to the same liberation. Understanding such a distinction would help one not read into the conventional use of language implications that are not there, and help keep a balance in reading the “ultimate” use of language.