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User10552, the answer to your question is not found in the Sutta Pitaka – the first basket. You will have to look into the third basket - the Abhidhamma Pitaka – for the answer. To get a proper understanding of the different type of Saṅkhāras, and of other kinds of paticca samuppada (PS), you will have to study the third basket of the Tipitaka. In the Abhidhamma Pitaka, there is a special ‘vibhanga’ for PS, where it is explained in detail.
In reading the Attakārī Sutta, you are now aware of the fact that we all make choices all the time and act on intentions all the time. In this sense, the word ‘Sankhara’ would mean everything that we do to live in this world. That would include breathing, walking, eating, that even an Arahant has to engage in until Parinibbana. Some sankhara arise from alobha, adosa, or amoha as a root cause. The other set of sankhara arise from lobha, dosa, or moha as a root cause. This is where it is important to know the difference between sankhara and abhisankhara.
In the Sutta Pitaka – the first basket – the PS that ordinary people are subjected to is explained, but not the PS that an enlightened being would experience. Akusala-mula PS describes the PS process for normal humans (Anariyas), who are trapped in the sansaric journey. When one becomes an Arahant, since there is no more rebirth, all kamma seeds that do not get to come to fruition before the death of an Arahant become ineffective in producing a rebirth: Because an Arahant has removed avijja, the “akusala-mula paticca samuppada cycle” becomes ineffective and thus “bhava paccaya jati” does not get to initiate a new birth.
The Vibhanga describes the Kusala-mula version of PS for Ariyas. An Ariya would not commit the worst kinds of akusala. His avijja is less potent, because it is well below the moha stage for an Anariya (normal human). The sankhara done with this type of less potent avijja does not become a cause for extending sansara; it is just sankhara. In kusala-mula PS, tanha does not arise because of vedana. With kusala-mula as condition, one accumulates punnabhi sankhara. With punnabhi sankhara as condition, a punnabhi vinnana arises. This punnabhi vinnana is accumulated as kamma bhava and could lead to corresponding “good” namarupa.
At death, the kusala-mula vinnana prevents a birth in the lower four realms for a Sotapanna, and a birth in the kamaloka is avoided for an Anagami. The sansaric process or the rebirth process is fueled by abhisankhara for normal humans, as they are with lobha (greed), dosa (hate), moha (delusion). What they acquire is apunnabhi sankhara, as opposed to punnabhi sankhara. Thus Sankhara = san + kära = actions done while in existence, and they can be either good or immoral. Abhi sankhara = “Abhi” + sankära = strong/repeated actions for prolonging rebirth process, the kind that normal human beings do.
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At the link of sensation you react due to ignorance.
Sensations are 3 types which are pleasant, unpleasant, and neutral. Pleasant sensations lead to craving, unpleasant lead to aversive and neutral there is still ignorance. In craving and aversion also here is ignorance. When ignorance is absent you maintain equanimity towards the sensations seeing their impermanence.
The unwholesome / wholesome roots lead to volition followed by action. Removing the roots both wholesome and unwholesome removes condition for future existence and experience.
The choice you have is when there is sensation you can react with craving, aversion and ignorance or be equanimous knowing impermanence.
Volition always arise due to a stimuli. This is the contact - feeling part of Dependent Arising.
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Is this topic a variant of the Brahmana Sutta?
The Brahamana sutta asks, "How can you desire to end desire?"
You seem to be asking, "How can you have the volition to end ignorance when you're ignorant?"
Presumably the "opposite" of ignorance (and of volition based on ignorance) are right view (and right intention etc. based on right view).
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On Tevijjavacchagotta Sutta the Buddha said that in the last ninety-one aeons, no fatalist who denies the power of volitional acts, has ever gone to heaven, except one, who happened to follow the doctrine of kamma and of morally effective deeds.
OK, if that is the case. I have not read this sutta.
How does this power of volitional act or volitional act happen with in the frame work of Pratītyasamutpāda?
It happens at the 4th condition. It will also arise with craving. Why don't you read the Pali suttas?
Feeling, perception, volition, contact and attention — these are called mentality (nama).
SN 12.2; MN 9
When the nutriment of volition is comprehended, the three forms of craving [for sensuality, for becoming, and for non-becoming] are comprehended.
SN 12.63
My intention is not to discuss about non-self rather about the volitional act done by the self-doer as explained in Attakārī Sutta.
O.K.
Also not so much about the change or motion, the being stepping forward or backward, but the volition or intention that brought about the change.
Sure.
Pratītyasamutpāda states that everything except Nirvana are conditioned,
It does not. Paticcasamuppada described the 12 conditions for the arising of sorrow, lamentation, pain, grief & despair.
and from ignorance (Avijjā) comes mental formations (Saṅkhāra) which includes volition.
'Sankhara' does not include 'volition' because the 'sankhara' are non-volitional since they arise from ignorance. 'Sankhara' are defined as the 'body, verbal & mind conditioner', which are defined in MN 44 as the breathing in & out; initial & discursive thought; and perception & feeling. This does not include volition.
For example, when you try to meditate & all of those discursive thoughts are spinning out of control in your head (which also make your breathing agitated), this is 'sankhara' in Paticcasamuppada. This obviously is not 'volition' since you are not 'choosing' to have these out-of-control thoughts.
Volition occurs at the 4th condition, nama-rupa (and also at the 8th condition, craving).
So if every mental formation is conditioned by ignorance including human volition (choice)
This is not true. Paticcasamuppada only describes when volition is tainted by ignorance. It does not describe when volition is guided by wisdom.
how come a being by choice, which is volition, which has ignorance at its base root out ignorance?
???
On the other hand, if volition (choice) is not conditioned by ignorance, then the beings choice is out side Pratītyasamutpāda which has ignorance at its starting point?
Correct. Paticcasamuppada is called "the wrong path" (SN 12.3). Paticcasamuppada does not describe wise or right intention/volition, which is the right path.
Similarly, if the answer is yes and no, this still implies that volition (choice) can be out side Pratītyasamutpāda?
Yes. Correct. Very good.
There are two types of volition: ignorant volition & wise volition.
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You have asked a very good question, I remembered if correctly it's in the Sutra of Perfect Enlightenment Maitreya Bodhisattva asked similar question: 以幻修幻 - how can if phenomenal world is illusory construct and the "I" is also illusory that a practitioner realize the Ultimate Truth? I remember the Buddha answered 以幻修真 - using the illusory to rid the illusion, as if using a wedge to get out another wedge stuck in the hole. Therefore, I think to give some help of your inquiry is to think of: your volition is to get over ignorance by choosing actions of not ignorant... You find that the action that is not ignorant is still an ignorant action... so on and so forth. Until you finally know the action that is not ignorant, that you are enlightened. It could be a long practice, or it could be a sudden realization. A bit like someone doing a difficult math equation, volition discerns the answers are not correct, over and over, that the working out incorrect answers are the footings to finally have the correct answer. Volition the ability to discern doesn't get hindered by ignorance, although ignorance prevented it from knowing the correct answer immediately. The Sutra has very good analogy full of wisdom far better than I presented here, I just recalled to make an answer in convenience. I hope I didn't misunderstand your question, and I'm not quite familiar with the terms and the Suttas mentioned in the OP.