Does the absence of the son of a barren woman truly exist? In Je Tsongkhapa's, Great Treatise on the Stages of the Path Volume 3 pages 343-344 we have this:


  Therefore, as I explained before, the sword of reasoning cuts through
  phenomena, revealing that they lack even a shred of the two selves,
  and brings forth certainty about selflessness. So if a thing possessed
  of the two selves does not exist, then how could the non- existence
  which is its negation be established in reality? The con- ception that
  the nonexistence that is the absence of the son of a barren woman
  really exists must be based on the observation of a barren woman and
  her son. If those two are never observed, then no one thinks to
  construct the expression, “The nonexistence of the son of a barren
  woman truly exists.” In the same way, when you see no truly existent
  thing anywhere at all, you also do not give rise to the conception
  that the nonexistence of that truly existent thing is something truly
  existent. Therefore, you stop all thoughts conceiving of signs,
  because if a thought conceives of true existence, it must be a thought
  that conceives of the true existence of either an existent or a
  nonexistent. So if the larger category is negated, then the
  subcategory is negated. This is what KamalaŸıla’s Stages of Meditation
  says.


The context of this passage is a debate on how to generate the direct perception of emptiness. To my understanding, Je Tsongkhapa is refuting the notion that the Path of Seeing can be attained by eliminating all conceptual thought after one has used reason (ie., conceptual thought) to thoroughly conceive of the truth of emptiness.

The above passage to me seems to be saying that we have to use analysis/reason/conceptual thought during meditation to establish that, "the nonexistence that is the absence of the son of a barren woman really exists." In other words, that emptiness (the nonexistence or negation of the existence of the son of a barren woman) truly exists is the conclusion of analysis directed at the ultimate. Is this so?

However, right after that it says to enter into signlessness you have to stop all thoughts (emphasis in the original) of true existence ie., even the true existence of emptiness.

I'm confused. Is emptiness a true existent (ie., not mistaken with regards to its appearing object)? I think it is. However, in order to enter signlessness do we have to stop thinking this?

What is the correct interpretation of this passage?

I think Je Tsongkhapa must be using "true existence" or "real" existence synonymously here with inherent existence rather than the alternative defintion of, "non-mistaken with regard to its appearing object."

Why? In the very next passage he says this:


  Thus, to achieve the nonconceptual sublime wisdom, you alter- nate (1)
  developing certainty, profound certainty, that there is not even a
  particle of true existence in any thing or non-thing whatso- ever, and
  (2) stabilizing your mind on the conclusion thereby reached. You
  cannot achieve such wisdom by simply constricting mental activity
  without any analysis of an object, because this ap- proach does not
  make it possible to eliminate the conception of true existence. This
  is because it is merely not thinking of true existence; it is not
  knowledge of the absence of true existence. In the same way, it is
  merely not thinking of a self, but is not knowledge of the lack of
  self, so cultivating it does not stop the conception of self. There-
  fore, you must distinguish between (1) not thinking about true exist-
  ence or the existence of the two selves, and (2) knowing the lack of
  true existence or the nonexistence of the two selves. Remember this
  critical point.


Thus, I think he must be using 'true existence' synonymously with inherent existence.
No, it does not. 

One nice book on the topic that I encountered is Mario D'Amato's translation of Madhyāntavibhāga and its Vasubandhu’s commentary. In addition to providing an excellent translation, Prof. D'Amato does an awesome job retelling both texts in his own words, elaborating and clarifying the meaning. Another solid book on the topic is Mahāmudrā, The Moonlight, by Dagpo Tashi Namgyal.

Both books discuss the enlightened mind's perspective, particularly emptiness and signlessness.

In general, it is my understanding that emptiness refers to the fact that all conceptualized representations whatsoever are mere schematic models of the ontological reality and that signlessness refers broadly to the direct experience of reality beyond conceptualized representation, and specifically to direct ("intuitive") experience of emptiness thereof.

In Mahayana Buddhism there are many ways of inducing direct experience of reality beyond conceptualized representation -- most of them involve overwhelming or exhausting the discursive (conceptual) mind one way or another. The methods range from sleep deprivation, to teacher making sudden loud noise during student's meditation session, to koans, to analytical methods. The latter are particularly popular with Madhyamaka and Gelug students inclined towards intellectual speculation.

One particular pattern of demonstration involves showing the limits of basic descriptive constructs that pertain to "entity" - by deconstructing their underlying assumptions - which at that moment leaves the student with more or less clear idea of emptiness in their mind. However, in reality, the student is actually grasping onto the "sign" of emptiness (i.e. the handle of the abstraction) while mistakenly assuming to be experiencing the emptiness itself. 

So the next step in the demonstration necessarily involves some sort of analytical debunking of the concept of emptiness itself, which hopefully leaves the student with no conceptual ground to stand on. The resulting experience of being "lost" is a door into signlessness. 

In this passage, Tsongkhapa uses one particular technique for the second step of the demonstration, the debunking of the concept of emptiness. This particular technique employs simple logic that exploits the dependency between negation and negandum. If negandum does not exist, it says, how can its negation have any existence? The traditional example of a son of a barren woman is an example of a negandum. This impossible son metaphorically stands in for the svabhava of entities -- the intrinsic nature whose emptiness was demonstrated on step 1. This emptiness of the intrinsic nature of all phenomena (including all objects as well as the perceiving subject, "the two selves") is metaphorically compared with the non-existence of the son of a barren woman. The author says: if the son (the intrinsic nature) does not exist, how can its negation (the empty nature) not be a mere figure of speech? The purpose of this passage is not to discuss the intricacies of the notion of "existence" vs "true existence" vs "intrinsic existence" etc. - but to simply knock the concept of emptiness from under the student's feet.

Once the student lets go of the sign of emptiness and enters signlessness, he or she can hopefully see the emptiness of everything directly. This seeing involves actual direct and clear understanding of the limits of conceptual mind and the profound contrast between all models and reality. Hence in the next passage Tsongkhapa comments on the resulting state of "nonconceptual sublime wisdom", "developing profound certainty, that there is not even a particle of true existence in any thing whatsover", "eliminating the conception of true existence", "knowledge of the absence of true existence" and "knowledge of the lack of self".