Very good summary by Jared K Jones
To pull this out of a subthread from a different forum. My main teacher has an extensive background in the Zen tradition of Dogen (about 50 years), as well as 30 years in the Gelugpa and Tibetan Tantric traditions. So, what's the difference between Chittamatra and Madhyamika?
Within the Mahayana traditions of Asia, they are dominated by the writings of two main schools of thought - both originating in the Suttas and Sutras, but fully fleshed out in the 1st and 2nd century - Chittamatra and Madhyamika.
Chittamatra was enumerated by Vasubandhu, Asanga, Dignaga, and others and the Madhyamika was enumerated by Nagarjuna, Bhavaviveka, Buddhapalita, Chandrakirti, and others. Wikipedia has a pretty good record of the dates and major works of these yogi-scholars if you'd like to read their works.
Chittamatra said that the best method for getting at Emptiness (Sunyata) was to realize the conventional nature of mind: the non-duality of ”everything that appears in perception” with “the six senses.” In other words, the notion and direct perception that a sound, for example, only occurs when a valid basis (vibration in the air) meets a functioning organ (ear), and that gives rise to a consciousness (sound-consciousness).
The object, sense organ, and mind form one inseparable system. If you take away any component in the system, then nothing happens - no minds, no organs, and no objects. Hence, when a tree falls in the forest, no sound occurs if no ear organ and no sound-consciousness are present. Also, the mind is the aspect of reality providing identity, characteristics, and relationships to objects. So, mind plays a central creative role in your experience.
Like that, the early writers and commentators of Chittamatra said that it is okay to see mind (Awareness) as self-existent for a while because you are deconstructing everything else that appears. You are seeing the emptiness of all appearances.
At some point, seeing that all appearances are empty, you will also see that "that to which appearances appear" is also empty. The emptiness of awareness is your tathagatagarbha, your true nature, your Buddha nature, and the “face before you were born.” This is not mystical, nor paradoxical. It’s simply applying emptiness to the creative center of all experience: mind, cognition, awareness, knowing, or consciousness.
Ven. Dignaga uses various types of introspective-epistemological analysis to help get at emptiness. For example, he famously introduced the idea of Universals Vs. Specifics to the Buddhist discourse:
1. A word is a "Universal" because it applies to a universal category of things: "cow."
2. A specific instance of "cow" looks nothing like any other cow. When you look closely, each perception is utterly unique.
3. Not only that, what appears to your senses is constantly changing from moment to moment, so it can't even be called "self-similar" from one moment to the next (much less similar to other cows).
4. Further, you can't explain or make known the color of an orange to a blind man. Perceptions are actually utterly ineffable. What you perceive cannot be put into words.
5. Therefore, all language is inferential. The word and object have no fixed relationship. Words are learned and have an ambiguous relationship with objects of experience.
6. The word does not resemble nor infuse the perception with any new properties when applied to the perception. For example, the "chair" of a company does not resemble a chair nor is he or she infused with "chairness" when validly called a chair.
7. Words do not make know either specific instances nor universal categories. When you say "chair" you do not become aware of all chairs in the universe, nor do you become aware of all of the properties of any specific object.
8. Based upon all of this, how could the current object of perception be a chair or a cow in and of itself? Look at it - it's just the useful or utilitarian play of mind: we call an utterly unique, ineffable, unbounded, and constantly changing set of phenomena “a table” for a practical purpose - holding up our coffee mug.
Because objects aren't self-established, the subject also isn't self-established. The knower doesn't exist without the known. Awareness is always "awareness of" and never just "awareness." Therefore, consciousness is also interdependently arisen and empty of inherent existence. However, if you stop the process of non-dual inquiry too soon, you will arrive at an "Awareness-All-There-Isness" or a "Mind-Only" position. So, this is a big danger within the Chittamatra approach.
You see this error in the writings of many Zen adepts. The “Big Self,” the “Real Self,” ”You are the drop experiencing itself as the Ocean,” and “the Oneness” are nothing other than falling into the trap that Awareness gives rise to the universe, and therefore, Mind is all that exists. You are just making “I/mine” more subtle, without removing ignorance from the root. However, there is less chance of becoming a Nihilist with this approach.
Madhyamika comes in two main flavors - Svatantrika and Prasangika. Their pedagogies for getting at Emptiness/Sunyata involve logically deconstructing the various components or arrangements of phenomenon: parts-whole, one-many, cause-effect, and so on. The Svatantrika mainly uses syllogisms (If A = B then C) and posits that phenomena have "characteristic marks" or defining features prior to mental designation - i.e. dependent designation or prajñaptir upādāya.
Prasangika uses mainly reductio ad absurdum (logical consequences) to show that holding essentialist viewpoints always leads to logical impossibilities. For example, if you think the tree is permanent, then it must be unchanging. If it’s unchanging, then it can’t interact with light and appear to your eye consciousness. Therefore, if trees were permanent, they would be invisible.
Prasangikas also refute that phenomena have any defining features, properties, or characteristics whatsoever - they are utterly empty of self, at all levels. The most famous of the reductio-consequentialist masters is Ven. Nagarjuna. His most well-known quote is found at the beginning of the Mulamadyamikakarika - the Four Diamond Slivers (Nagarjuna's Tetralemma):
"Not from self,
Not from other,
Not from both,
Not without a cause (neither),
Does anything, anywhere, whatever arise."
He then goes on to extensively refute each of the four ways something might inherently arise by using the absurd logical consequences for each mode of inherent cause-and-effect: self, other, both, and neither. To take a practical example of how the Prasangika approach works, look at the below:
1. The chair is not something which pervades.
2. The chair is not among.
3. The chair is not the collection.
4. The chair is not outside the chair.
>If the chair pervades all the parts of the object, then we should have as many chairs as there are parts. If we cut it in half, we should have two chairs. This contradicts ordinary perception, so the thesis fails.
>If the chair is among the parts of the chair, we should be able to eliminate all the other parts and still have a chair. This contradicts ordinary perception, so the thesis fails.
>If the chair was all these parts collected together, then there could only be one chair in the world. Not only that, if it lost even a single atom, the chair should go out of existence. This contradicts ordinary perception, so the thesis fails.
>If the chair were outside the chair, then chairs should pop into and out of existence all over the place without reason and without relying upon parts. This contradicts ordinary perception, so the thesis fails. Like that, consequences are presented as refutations.
Prasangika posits full emptiness, in which all phenomena are empty of self at all possible levels: no inherent characteristics, no inherent absences, no inherent awareness, etc. To find a corollary in the Suttas, look up the Suñña Sutta. This is not unique to the Mahayana nor a fabrication of the minds of later Mahayana thinkers:
Like that, Madhyamika does not rely on recognizing the conventional nature of mind to give practitioners access to emptiness, and it does not have the danger of "Mind-Only" essentialism. On the other hand, it has a heavier danger of ontological, functional, and teleological Nihilism: you may wrongly decide that nothing exists; if you think things exist, you might wrongly think they exist but do not have any function; if they exist and function, you might wrongly feel they have no meaning or purpose.
You see this with many bad Tibetan Buddhists who turn emptiness into post-modernism or moral relativism, and then makes statements like, “Buddhism means you hold no views whatsoever, and you get to ‘skillfully’ do whatever you want. Nothing matters.” I see this a lot within bad Dzogchen, especially on the internet. This destroys the path and is vigorously refuted by all the great masters. This is a big danger with the Madhyamika approach, but there is less chance of becoming a Mind-Only essentialist.