(9.106) (Other schools) “Well then, it follows that phenomena cannot exist even conventionally,
In which case your presentation of the two truths is invalid.
Moreover, if conventional truths are merely imputed by mistaken minds,
How can living beings pass beyond sorrow even nominally?”

Once again, it is important that we fully internalize the doubts and questions raised by the other schools and realize that we ourselves have these same doubts and questions. Only when we do this will we appreciate the prasangika refutation. First, the other schools say that if the prasangikas are correct, then phenomena cannot exist even conventionally and therefore there is no such thing as the two truths. Buddha explained the two truths: ultimate truth and conventional truth. All Buddhist schools agree there is ultimate truth and conventional truth. Where they differ is in the meaning of these terms. The other schools are saying if things do not exist inherently then things do not exist at all, so to say things do not exist inherently is to say there are no conventional truths, and thus there can be no presentation of the two truths.

Additionally, the other schools say if there are no conventional truths, then it is impossible for beings to attain enlightenment because we do so in dependence upon conventional truths. If conventional truths are mistaken, then how can they produce an unmistaken mind? A mistaken cause cannot create an unmistaken effect.

(9.107) According to our system, to exist conventionally
Does not mean to be imputed by a mind grasping at true existence.
A conventional truth, such as body, is imputed by a valid conceptual mind having perceived a valid basis of imputation.
Without such imputation by a valid mind, there would be no conventional truths.

The Prasangikas answer this doubt by saying they do not deny the existence of conventional truths, they deny the conventional truths as understood by the lower schools. The lower schools all grasp at conventional truths as existing inherently or existing truly. It is this form of conventional truth that the Prasangikas negate.

The conventional truth that the Prasangikas assert is a valid conceptual imputation upon a valid basis of imputation. For example, a forest is a mere imputation by mind, a label, that we impute upon a collection of trees. An army is a mere name imputed by mind upon a collection of soldiers. The forest and the army are by nature mere projections or imputations by mind, but they are valid imputations because they are imputed upon a valid basis of imputation for that object. For an imputation to be valid the basis of imputation has to conventionally correspond with the nature, aspect, and function of the object being imputed as understood in society. For example, a tennis racquet can strain the water out of spaghetti, but it is not a valid basis of imputation for imputing a spaghetti strainer. While the function is accomplished, the nature and aspect do not correspond to conventional understandings.

(9.108) The imputing mind and the object imputed
Are established in mutual dependence upon each other.
Each distinct phenomenon is posited by an analytical mind
According to what is validly known in the world.

How are conventional truths established?  As explained above, they need to have a conventionally valid nature, aspect, and function.  Nature generally refers to what the object is made of, or its uncommon characteristic.  For example, the nature of a gold coin is the gold itself.  According to the Tantra Prasangika view, the conventional nature of all objects is mind and the ultimate nature of the object is the emptiness of the object, or the emptiness of the mind.  Aspect refers to the form that the object takes, for example, the gold in the shape or aspect of a coin.  Function refers to what it does, what it accomplishes.  In the case of a gold coin, we can use it to buy things.  Nature, aspect, and function are what constitute a valid basis of imputation.  It is just convention to call things with different natures, aspects and functions different names.  The only thing negated by emptiness is its mode of existing independent of the mind.  It is just an object of mind, nothing more.

Here Shantideva also emphasizes that objects and the minds that know them arise in mutual dependence upon one another.  This is central to the Prasangika understanding of emptiness. All Buddhist schools agree all existent things are knowable by mind. To say there is something that is not knowable by mind is to say that Buddha is not omniscient. The lower schools believe that there are objects that exist from their own side independently of mind and that there are minds that exist from their own side independently of their objects. This corresponds with our normal way of thinking about things. We think objects exist out there and our mind, existing separately from those objects, knows them. Our mind has no role in the creation of the objects, we simply know what is there.

The Prasangikas, in contrast, say that mind and its object arise in mutual dependence upon one another.  They say it is impossible to have a mind without an object known to that mind, and it is impossible to have an object without a mind that knows it. Thinking deeply about the dependent relationship between object and mind reveals the lack of inherent existence of both the mind and the objects known to mind. Truly existent minds and truly existent objects exist independently of all other phenomena. If they exist independently then how can they enter into a relationship with one another?  If they have a relationship with one another, then there must be some sort of dependent relationship between them. We can even say that the definition of a truly existent object is an object that can exist without being known by mind. And the definition of a truly existent mind is one that could exist without an object being known by that mind. But such things are clearly impossible and have never been seen. Simply understanding the dependent relationship between mind and its object reveals the emptiness of both.

But this then begs the question how do the pairs of mind and object arise in dependence upon one another?  Do they simply arise out of nothingness without a cause? We will get into the answers to these questions when we look at the logic of the Vajra Thunderbolt. The short answer is when a karmic seed ripens, it produces the subject-object pair simultaneously. The quality of the previous mind determines the quality of the karma that gets activated. So we have a self-perpetuateing cycle in which mind activates karma, and karma produces subject-object pairs.