SUMMARY (TL;DR)
The mind is a reflexive entity, i.e., it can look at and analyse itself.
Yet, what if there are multiple levels in the mind, ranging from grossest to gross to subtle to subtlest?
To observe and analyse one level, attention has to reach a level subtler and also causal to that level. Or, awareness has to become subtler.
Reflexivity in this sense does not exist for the ātma since, by definition, it is pure (no impurities => zero distinct or separate parts), simple (or indivisible), and absolutely subtle.
This explains very simply why such a thing, the ātma, cannot become an object or observed.
META
"Meta" started out meaning "after". So meta-physics, which now connotes knowledge "above" or "about" (physical) knowledge, initially referred to Aristotelian books or texts that came after his texts on physics.
The currently popular connotation, with reference to a set of activities, means a more abstract level of activities describing or manipulating them. For example, counting or arithmetic, when abstracted becomes algebra. That is, 1-2-3-4 or 8-9-10-11 or even 10005, 10006, 10007, 10008, can all be expressed algebraically, and more generally, as n, n+1, n+2, n+3.
Why abstract or generalise? A variety of reasons. For easier manipulation. For coming up with a single solution to a similar set of problems. For concise representation of a pattern. For easier learning and teaching.
Layers of abstraction and generalization build over the years, followed by reduction of layers as people return to the underlying physical or actual data and find out simpler patterns and simpler representation.
This analysis may also be considered meta with respect to meta itself!
SAT-KĀRYA-VĀDA
sat-kārya-vāda is a simple idea with an overemphasis on subtle implications that has overwhelmed its simplicity. E.g., a clay pot. Going from physical cause to effect is from clay to clay pot. Looked at differently, a clay pot is imbued with clay even after it is made. Or clay is still present in a clay pot, though baked and no longer a ooey-gooey mass.
A subtler, though still obvious, implication is that all things made of clay contain clay. A not-so-obvious implication is that all clay things can be returned to their initial ooey-gooey state. Similarly for gold articles being meltable back into an unformed gold mass.
A subtler implication is that since all known clay vase forms came from clay, all forms of clay vases made till now, and those yet to be made, exist in clay. This, though, is obvious from the name "clay article" meaning made of clay.
(So far, so good, obvious and commonsensical.
But what if this is extended to organic products? Does every sort of organism exist in some general, undifferentiated, mass - or maybe soup - of organic matter? Or are there only certain organisms that can be produced, or better, that can evolve or manifest from that mass? How subtle should that mass be and how few elements need there be in that mass?
And an even more intriguing idea. What if all organic and inorganic things can manifest or evolve from a single mass? Isn't this the idea of the singularity underlying the Big Bang? Or that there were less than a handful of particles or energy fields then?)
This much as background.
REFLEXIVITY
Now, consider reflexivity. This is a "meta" activity in which one looks, analyses, judges, etc. oneself or one's actions or thoughts. Confusion about actions - what to do or say, or how to solve a problem, i.e., how to think - arises when reflexive (inward and circular or looping) activities are mixed up with actually doing the actions.
(Thus, one may decide what to do to achieve a goal. Then one must execute one's decision or plan. And after execution, check if the goal has been reached. Then, even if execution is not according to plan, reaching the goal may be enough, while how the goal was reached may not be important. If the goal is long-term, say many months or years, one may set interim goals, and stay on plan by checking every so often that they are being met.)
META and SAT-KĀRYA-VĀDA
What is the connection between meta and sat-kārya-vāda?
Consider algebra - it is at a subtler level of thinking than arithmetic. Thus meta. And if one does some assessment or monitoring or scoring of one's own arithmetic or algebraic activity, including thinking of oneself as the doer, that activity becomes both reflexive as well as meta.
Now, consider the idea that arithmetic does not evolve into algebra as a meta activity, but instead that algebraic patterns, or an algebraic level of thinking, is a necessary precursor to understanding arithmetic patterns. This somewhat convoluted and back-to-front idea can be associated with the sat-kārya-vāda notion that just as physical effects come from physical causes, so do non-physical or mental effects from mental causes.
Please note that in Sāṁkhya-Yoga, mind and mental are also material, and mental activity is not the same as conscious activity. Thus, mind, and even intellect and ego, may be considered mechanically and algorithmically.
Putting them together, there are levels of thinking or mental levels which go from grosser to subtler as one goes from the outer physical world to mental inner world. One level is subtler than another if it is the cause of the other. Or if the other level manifests from the first. Subtler or meta activity occurs when attention shifts from one actual material - though mental - level to its causal level. It seems reasonable to assume that attention can also jump to non-sequential, yet ancestral, causal levels, perhaps to even the subtlest root causal level.
SUBJECT-OBJECT AWARENESS FOR ĀTMA
Two more points.
Consider this sentence: "I throw the ball". "I" is the subject, the ball is the object, and there is an action "throwing" by the subject "I" upon the object. The awareness of subject, object, and action is a meta activity, and from the reasoning above, at a subtler level than the physical or mental activity.
Now, if the highest or subtlest mental level or activity is reached, can there be any meta activity? An activity above the highest?
So all this reasoning was to get to a simple idea - there is no meta level for the higher self - ātma or puruṣa. Since, by definition, it is the subtlest level of a living being.
From an advaitic point of view, ātma (= brahman) is subtler than the mind. It cannot have awareness of itself as either subject or object as, being without parts or levels, there is no part or level to know another. And it just is, or there is only being, no doing.
From a Sāṁkhya-Yoga perspective, it is even simpler. All activity, including mental, physical, meta, etc. occurs in prakṛti. Puruṣa has no mental activity since it is eternally separate from prakṛti, even while illuminating its activities. And being partless and without levels like the ātma, again, there is no subject awareness.
