Is there anything like discriminating intellect in Buddhism?

Buddhism teaches.

1)Internal - I suppose this is the subject

2)External - I suppose this is the object

3)Internal External

As far as I am aware the Buddhist meditation doesn’t focus on discrimination between observer and observed. We focus on the element which is causing stress. We can focus feelings , perception , form , choices and consciousness.... we do not indulge in any meditation which develops any idea of self (observer) We can also focus on awakening factors ... we can meditate on love ,joy , ashubh , equanimity , impermanence etc but there is no room for self indulgence ....

Theravadin interpretation of the Sutta is that 4 aggregates are conjoined and 4 aggregates have objects. One aggregate is without an object. I leave it up to you to figure out which these are, answers here https://suttacentral.net/vb1/en/thittila

Consider this

Suppose you see a wooden house. Here you objectify & think about what is thought of as 'the seen' as 'a house'. The house is here a 'seen object' iow it's an object of perception.

• The house is not without a wall

• the wall is not the house.

• The wall is not without wood

• the wood is not the wall.

• The wood is not without a carbon atom

• the carbon atom is not the wood

• The atom is not without an electron

• the electron is not the atom

• The electron is not without observed properties

• the observed properties of an electron are not the electron

• The observed properties are not without observation

• observation is not the observed property

• The observation is not without that which observes

• that which observes is not without observation

• The observation is not without an object of observation

That which observes is here likewise an object of thought-based-perception, 'the cognized[thought] is objectified & thought about as 'that which observes' iow it likewise is an object of perception seen with intellect.

"Monks, I will teach you the All. Listen & pay close attention. I will speak."

"As you say, lord," the monks responded.

The Blessed One said, "What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. [1] Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range."

Discernment As he was sitting there, he said to Ven. Sariputta, "Friend, 'One of poor discernment, one of poor discernment': Thus is it said. To what extent is one said to be 'one of poor discernment'?"

"'One doesn't discern, one doesn't discern': Thus, friend, one is said to be 'one of poor discernment.' And what doesn't one discern? One doesn't discern, 'This is stress.' One doesn't discern, 'This is the origination of stress.' One doesn't discern, 'This is the cessation of stress.' One doesn't discern, 'This is the practice leading to the cessation of stress.' 'One doesn't discern, one doesn't discern': Thus one is said to be 'one of poor discernment.'"

Saying, "Very good, friend," Ven. Maha Kotthita — delighting in & approving of Ven. Sariputta's statement — asked him a further question: "Discerning, discerning': Thus is it said. To what extent, friend, is one said to be 'discerning'?"

"'One discerns, one discerns': Thus, friend, one is said to be 'discerning.' And what does one discern? One discerns, 'This is stress.' One discerns, 'This is the origination of stress.' One discerns, 'This is the cessation of stress.' One discerns, 'This is the practice leading to the cessation of stress.' 'One discerns, one discerns': Thus one is said to be 'discerning.'"

Consciousness "'Consciousness, consciousness': Thus is it said. To what extent, friend, is it said to be 'consciousness'?"

"'It cognizes, it cognizes': Thus, friend, it is said to be 'consciousness.' And what does it cognize? It cognizes 'pleasant.' It cognizes 'painful.' It cognizes 'neither painful nor pleasant.' 'It cognizes, it cognizes': Thus it is said to be 'consciousness.'"

"Discernment & consciousness, friend: Are these qualities conjoined or disjoined? Is it possible, having separated them one from the other, to delineate the difference between them?"

"Discernment & consciousness are conjoined, friend, not disjoined. It's not possible, having separated them one from the other, to delineate the difference between them. For what one discerns, that one cognizes. What one cognizes, that one discerns. Therefore these qualities are conjoined, not disjoined, and it is not possible, having separated them one from another, to delineate the difference between them."

"Discernment & consciousness, friend: What is the difference between these qualities that are conjoined, not disjoined?"

"Discernment & consciousness, friend: Of these qualities that are conjoined, not disjoined, discernment is to be developed, consciousness is to be fully comprehended."[1]

Feeling "'Feeling, feeling': Thus is it said. To what extent, friend, is it said to be 'feeling'?"

"'It feels, it feels': Thus, friend, it is said to be 'feeling.' And what does it feel? It feels pleasure. It feels pain. It feels neither pleasure nor pain. 'It feels, it feels': Thus it is said to be 'feeling.'"

Perception "'Perception, perception': Thus is it said. To what extent, friend, is it said to be 'perception'?"

"'It perceives, it perceives': Thus, friend, it is said to be 'perception.' And what does it perceive? It perceives blue. It perceives yellow. It perceives red. It perceives white. 'It perceives, it perceives': Thus it is said to be 'perception.'"

"Feeling, perception, & consciousness, friend: Are these qualities conjoined or disjoined? Is it possible, having separated them one from another, to delineate the difference among them?"

"Feeling, perception, & consciousness are conjoined, friend, not disjoined. It is not possible, having separated them one from another, to delineate the difference among them. For what one feels, that one perceives. What one perceives, that one cognizes. Therefore these qualities are conjoined, not disjoined, and it is not possible, having separated them one from another, to delineate the difference among them."

"What do you think, Anuradha: Do you regard form as the Tathagata?"

"No, lord."

"Do you regard feeling as the Tathagata?"

"No, lord."

"Do you regard perception as the Tathagata?"

"No, lord."

"Do you regard fabrications as the Tathagata?"

"No, lord."

"Do you regard consciousness as the Tathagata?"

"No, lord."

"What do you think, Anuradha: Do you regard the Tathagata as being in form?... Elsewhere than form?... In feeling?... Elsewhere than feeling?... In perception?... Elsewhere than perception?... In fabrications?... Elsewhere than fabrications?... In consciousness?... Elsewhere than consciousness?"

"No, lord."

"What do you think: Do you regard the Tathagata as form-feeling-perception-fabrications-consciousness?"

"No, lord."

"Do you regard the Tathagata as that which is without form, without feeling, without perception, without fabrications, without consciousness?"

"No, lord."

"And so, Anuradha — when you can't pin down the Tathagata as a truth or reality even in the present life — is it proper for you to declare, 'Friends, the Tathagata — the supreme man, the superlative man, attainer of the superlative attainment — being described, is described otherwise than with these four positions: The Tathagata exists after death, does not exist after death, both does & does not exist after death, neither exists nor does not exist after death'?"

"No, lord."

"Very good, Anuradha. Very good. Both formerly & now, it is only stress that I describe, and the cessation of stress."

Ven. Maha Kotthita went to Ven. Sariputta and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there, he said to Ven. Sariputta, "With the remainderless stopping & fading of the six contact-media [vision, hearing, smell, taste, touch, & intellection] is it the case that there is anything else?"

[Sariputta:] "Don't say that, my friend."

[Maha Kotthita:] "With the remainderless stopping & fading of the six contact-media, is it the case that there is not anything else?"

[Sariputta:] "Don't say that, my friend."

[Maha Kotthita:] "...is it the case that there both is & is not anything else?"

[Sariputta:] "Don't say that, my friend."

[Maha Kotthita:] "...is it the case that there neither is nor is not anything else?"

[Sariputta:] "Don't say that, my friend."

[Maha Kotthita:] "Being asked if, with the remainderless stopping & fading of the six contact-media, there is anything else, you say, 'Don't say that, my friend.' Being asked if ... there is not anything else ... there both is & is not anything else ... there neither is nor is not anything else, you say, 'Don't say that, my friend.' Now, how is the meaning of your words to be understood?"

[Sariputta:] "The statement, 'With the remainderless stopping & fading of the six contact-media [vision, hearing, smell, taste, touch, & intellection] is it the case that there is anything else?' objectifies non-objectification.[1] The statement, '... is it the case that there is not anything else ... is it the case that there both is & is not anything else ... is it the case that there neither is nor is not anything else?' objectifies non-objectification. However far the six contact-media go, that is how far objectification goes. However far objectification goes, that is how far the six contact media go. With the remainderless fading & stopping of the six contact-media, there comes to be the stopping, the allaying of objectification.

Bāhiya, you should train yourself thus: In reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. That is how you should train yourself. When for you there will be only the seen in reference to the seen, only the heard in reference to the heard, only the sensed in reference to the sensed, only the cognized in reference to the cognized, then, Bāhiya, there is no you in connection with that. When there is no you in connection with that, there is no you there. When there is no you there, you are neither here nor yonder nor between the two. This, just this, is the end of stress."

Regarding "subject" and "object", the Buddha acknowledges these perceptions as:

MN146:6.27: ‘So these six interior sense fields are impermanent.’”
MN146:7.27: ‘So these six exterior sense fields are impermanent.’”

The Buddha also declares that for spiritual growth, it is important to understand that:

MN146:7.20: “But if they're impermanent, are they suffering or happiness?”
MN146:7.21: “Suffering, sir.”

care to explain how 'witnessing the present moment awareness' is any different than Mindfulness of the present moment that we as Buddhist practice.

It may be that "witnessing" might be taken to imply the existence of "a witness" or "the witness", which is then reified or even deified (i.e. identified with Atman or Brahman or something like that).

Perhaps that's similar to the "I think therefore I am" kind of idea.

Whereas I think that, conversely, Buddhism talks about mindfulness or awareness, skillfulness or unskillfulness -- that these qualities exist, and that they can and should be distinguished -- while still being careful not to identify or promote the idea of a "subject" or self.

In the Theravada traditions, I understand this be a reference to the enlightenment factor of investigation (dhammavicaya-bhojjanga).

In the field of dhamma, discrimination comes about by the very act of investigation, and what is discriminated is then known as arising in dependence on other factors and that, globally, those factors harbour three definitive characteristics: transience, unsatisfaction and not-self. This is understood through what he calls the contents of consciousness but what I would call the six-sense consciousnesses - sometimes enumerated as 8 or 9 consciousnesses to include mānas-vijñāna and mano-vijñāna. I think the ninth consciousness is seen as nirvana.

With regard to the consciousness or awareness aspect (possibly nirvana) I suggest reading the fascinating answers to this very interesting question: What is the invisible consciousness or consciousness without surface?.

It is only by investigating (and discriminating) the six-senses in this way that they are broken down by wisdom-understanding leaving behind a deeper understanding of reality; what you might call consciousness or awareness. I cannot see this as a cultivation. Nothing is cultivated. It is just that complications and their disturbances were removed to reveal the simplicity that had always been present.