The Buddha's teaching of the DharmaSatyadvaya (the two truths) is absolutely central to an understanding of Mādhyamikan Buddhism. They are:
Is based on two truths:
A truth of worldly convention
And an ultimate truth.
Those who do not understand
The distinction drawn between these two truths
Do not understand
The Buddha's profound truth.
Without a foundation in the conventional truth,
The significance of the ultimate truth cannot be taught.
Without understanding the significance of the ultimate,
Liberation is not achieved.
Nāgārjuna, Mūlamadhyamakakārikā (XXIV: 8-10)
Samvrti-satya: The conventional, or worldly, truth which applies to the everyday world of distinct phenomena and their relationships. This includes everything from the quark to human consciousness. It is designated conventional in that this individuated world is dependent on human dispositions and collective interests.
Paramārtha-satya: The ultimate, or sublime, truth which applies to reality in the absence of conventions, i.e., śūnyatā. Ultimate truth is deemed inexpressible in the sense that, in the absence of convention, there is no candidate for metaphysical-strength predication, including the ascription of existence/non-existence itself. Significantly, both conventional and ultimate truth has the same consequence – nothing can be said to exist by virtue of its own essence.
The general conception of two levels of truth is prevalent in Indian philosophy and can be traced to the Upanishads. To my knowledge, its prevalence in India is matched in scale by its absence in western philosophy. As such, some unfortunate misunderstandings can occur when a western philosopher hears of the two truths.
One major western misunderstanding of the satyadvaya which springs to mind would be to read in an appearance/reality distinction where paramārtha is the reality behind the samvrti appearance. This mistake would follow naturally from the assumption that śūnyatā is some kind of substance-in-itself which has been hitherto concealed by convention and/or faulty perception. This is not consistent with the Mādhyamikan rendering of the satyadvaya which asserts the ontic identity of conventional phenomena and the emptiness of śūnya whilst maintaining an epistemologically significant distinction between the two truths. The subtletly of this position and its consequences upon an understanding of the whole of Nāgārjuna's philosophy is expressed in the famous section from the Mūlamadhyamakakārikā:
By a misperception of emptiness
A person of little intelligence is destroyed.
Like a snake incorrectly seized
Or like a spell incorrectly cast.
Nāgārjuna, Mūlamadhyamakakārikā (XXIV: 11)
So, how should one cast this spell? I can't put it better than Jay Garfield does, so I won't:
Nāgārjuna establishes a critical three-way relationship between emptiness, dependent origination and verbal convention, and asserts that this relation itself is the Middle Way toward which his entire philosophical system is aimed. . . .Nāgārjuna is asserting that the dependently arisen is emptiness. Emptiness and the phenomenal world are not two distinct things. They are, rather, two characterizations of the same thing. To say of something that it is dependently co-arisen is to say that it is empty. To say of something that it is empty is another way of saying that it arises dependently.
Moreover, whatever is dependently co-arisen is verbally established. That is, the identity of any dependently arisen thing depends upon verbal conventions. To say of a thing that it is dependently arisen is to say that its identity as a single entity is nothing more than its being the referent of a word. The thing itself, apart from conventions of individuation, has no identity. To say of a thing that its identity is a merely verbal fact about it is to say that it is empty. To view emptiness in this way is to see it neither as an entity nor as unreal - it is to see it as conventionally real.
(Garfield, The Fundamental Wisdom of the Middle Way, p304-305)
I will return to the satyadvaya in due course, particularly with respect to understanding Robert Pirsig's Metaphysics of Quality in a non-dualistic way.