There can be a determinate perception of things that are “blue,” but Udayana’s analysis finds that a determinate perception of blue presupposes indeterminate awareness of blue.
And Nishida would further say that the indeterminate awareness of blue presupposes the pure experience of "blue" (I put quotes around to emphasize that this is prior to our conceptualizing that it is blue).
In other words, if we would try to challenge the reality of self-awareness in this way, by reducing it to an object-less cognition generated by subconscious impressions, in a similar fashion we would challenge the reality of the color blue.
Nishida would say that our direct experience of color is "objectless" in the sense that it is prior to the subject-object duality. Before we say "I see blue" and thereby introduce the subject ("I") and the object ("blue"), there is simply the direct experience of "seeing blue" (but prior to conceptualizing that it is blue). In his maiden word, An Inquiry into the Good (1911), he actually refers to the experience of seeing color as an example of what he calls "pure experience": "The moment of seeing a color or hearing a sound, for example, is prior not only to the thought that the color or sound is the activity of an external object or that one is sensing it, but also to the judgment of what the color or sound might be." (p. 3)
It is not an “objectless cognition which is beginningless and is generated by a beginningless urge”
What is the nature of this "objectless cognition"? I am wondering how this relates to what Nishida refers to as pure experience (see my previous comments). Perhaps it is a kind of objectless perception but what does "beginningless and generated by a beginningless urge" mean here?
If the Buddhists admit that the objects of indeterminate perceptions are real, then they must concede that the self is such an object, too.
Why say that indeterminate perception has an object at all? Or if we grant that there is this kind of perception prior to conceptualization, could we admit that there is an even more direct kind of experience (not sure if we should call it "perception" since this word may suggest an object that is being perceived) that is prior to the subject-object duality?
Udayana introduces the idea of “indeterminate perception” in order to argue that the self is perceived much in the way that other categories of things are perceived. In Sanskrit the basis for this claim is the concept of nirvikalpaka, “in the raw,” where indeterminate perception grasps a qualifier of something prior to forming a robust conceptual deployment and organization of it and does not require a ‘mark’ since its object is perceived directly.
This reminds me of Nishida Kitarō's idea of pure experience which is the direct experience prior to the subject-object dichotomy. In the direct experience, say of hearing the sound of the bell, there is neither the subject ("I") nor the object ("the bell"). Rather, there is simply "ringing bell". But saying that is already not accurate since we are introducing a concept already. Pure experience is a very concrete and rich experience, but it cannot be grasped conceptually. This seems to come close to what you call "indeterminate perception" except that Nishida would refrain from saying that there is even an "object" that is being perceived at all here.
Udayana’s objective was to determine how the self might be known despite granting that it cannot be experienced empirically.
Nishida Kitarō, the founder of the Kyoto School philosophy, had a similar concern. According to Nishida, the self can be known empirically, namely as an object of our cognition, but this self is not the original self. In his words, it is the "known" but not the "knower". The problem for him was that most Western philosophers before him were concerned with the "known" or the self as an object and not the self as the subject. His main concern was to identify the self as the subject. But for him, the "knower" ultimately cannot even be called a "subject" since the non-objectifiable self cannot be predicated either. He eventually comes to conceptualize this self by reversing Aristotle's definition of hypokeimenon as that which is subject but never predicate. For Nishida, the self (or consciousness; these refer to the same thing for him) in its original form is "that which is predicate but never subject". I feel that this might be similar to Udayana's "indeterminate perception". Since it is never a predicate, we cannot say "what" it is, but, according to Nishida, this self is the ground of all our knowledge. Coming from the Zen Buddhist tradition, Nishida called this self "absolute nothingness" since it is absolutely no-thing (not an object). I wonder what Udayana would say of this. Also, I'm not sure what "objectless cognition" means here and how that relates to the non-objectifiable self that Nishida speaks of.
‘self-awareness’
I presume that you put "self-awareness" in single quotes here to underline the unique way in which one becomes aware of the self according to Udayana. Is there a specific term for this in Sanskrit that Udayana uses or is it a general term that he uses? And what are the connotations of this word? In the Kyoto School tradition, "jikaku" (自覚) is the specific term they use to refer to self-awareness. The word is originally a Buddhist word meaning "self-awakening" (which is what the two Chinese characters literally mean) and it is also used in ordinary speech today to refer to one's self-understanding of one's roles in a social context. The Kyoto School philosophers give the word jikaku a novel philosophical meaning but its meaning is also related to the original Buddhist sense and the way it is used in ordinary speech. We must be careful when translating jikaku to self-awareness since the English word does not carry the same connotation. I am wondering if a similar care should be given to the Sanskrit word for self-awareness.
According to Nyāya, mokṣa, or liberation from rebirth, or apavarga, the final liberation or beatitude, is the soteriological aim of all philosophical endeavors
Do you mean that the Nyāya tradition understood their philosophical aim to be soteriological or that they believed that any philosophical endeavor should have such a soteriological aim? Also, did the Nyāya tradition have other philosophical aims apart from the soteriological one? I'm also curious to know how one should understand this soteriological aim and their emphasis on logic and epistemology. In what way does this emphasis assist the liberation from rebirth?
These are the kinds of questions that guided the public and intellectual debates of Udayana and his peers.
I'm wondering what "the public" here refers to and how it differs from "the intellectuals". The questions you raise seem to be quite intellectual and theoretical. Was the general public interested in such questions and if so, what motivated such questioning? This point also relates to what "philosophizing" meant for Udayana and his peers (as well as for the Nyāya tradition more generally). Was "philosophy" an academic/scholarly endeavor isolated from everyday practical life or was it more continuous with it?