# Paccaya; is the cause actually the effect? (proof by contrapositive in DN 15)

I was reading up on dependent origination. In DN 15, there is a very interesting use of logic in explaining some of the links of dependent origination (DO). Here’s an example:

“It was said: ‘With birth as condition there is aging and death.’ How that is so, Ānanda, should be understood in this way: If there were absolutely and utterly no birth of any kind anywhere—that is, of gods into the state of gods, of celestials into the state of celestials, of spirits, demons, human beings, quadrupeds, winged creatures, and reptiles, each into their own state—if there were no birth of beings of any sort into any state, then, in the complete absence of birth, with the cessation of birth, would aging and death be discerned?”

“Certainly not, venerable sir.”

“Therefore, Ānanda, this is the cause, source, origin, and condition for aging and death, namely, birth.

A classic method to prove P ⇒ Q is to assume ‘not Q’ and then arrive at ‘not P’, this is called proof by contrapositive. Here’s an example:

I didn’t hand in any paper for class, this implies I didn’t get a grade on the paper [for that class].
Proof:
Assume that I got a grade on that paper, then I must have handed it in or else it couldn’t have gotten graded.

So if the implication was false, the proof shows how this would contradict the (assumed to be true) premise [that I didn’t hand in any paper]. Therefore, (if you accept logic) the implication is seen to be valid.

The logical method used in DN 15 is almost a proof by contrapositive, only the first and last parts of each argument goes the wrong way. I.e. from the translation, it seems to me that the logic goes:

birth ⇒ aging and death
Why? Because 'no birth ⇒ no aging and death’
Therefore, birth ⇒ aging and death

Now, it would make me a lot happier if the Pali actually said:

aging and death ⇒ birth
Why? Because 'no birth ⇒ no aging and death’
Therefore, aging and death ⇒ birth

This would necessitate that “P-paccayā Q” means ‘P if Q’ which is equivalent to Q ⇒ P, the opposite of the P ⇒ Q implication that seems to be in the translation.

And also:

“Tasmātihānanda, eseva hetu etaṃ nidānaṃ esa samudayo esa paccayo jarāmaraṇassa, yadidaṃ jāti."

would mean “Therefore, Ānanda, this is the cause, source, origin, and condition implied by aging and death, namely, birth.”

Venerables @Sujato and @Brahmali, sorry for tagging you in another amateur pet-theory about Pali, but do you think the Pali allows for this sort of reading?

For dependent origination which also uses the “X-paccayā Y” construct this would mean that it should be thought about as:

Suffering, old age and death ⇒ birth ⇒ bhava ⇒ upādāna ⇒ feeling ⇒ contact ⇒ six sense media ⇒ nāmarūpa ⇒ consciousness ⇒ will ⇒ ignorance

Which means that one could start at one’s here-and-now experience of suffering and deduce the root cause for it in a logically sound way, using contrapositive proofs to get from one step to the next. This deduction would be logically equivalent to deducing dependent liberation, i.e. this DO-sequence is logically equivalent to ‘no ignorance ⇒ no will ⇒ … ⇒ no suffering, old age and death’.

In any case, I look forward to a swift rebuttal / valuable input / discussion

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Hi Erik

I’m glad somebody has finally noticed this oddity! I think I’ll give it a shot, since the 2 venerables are probably busy with other stuff.

This is in fact my favourite analysis of Dependant Origination. Let’s take the passage you cited, along with the Pali -

Jātipaccayā jarāmaraṇan’ti iti kho panetaṃ vuttaṃ, tadānanda, imināpetaṃ pariyāyena veditabbaṃ, yathā jātipaccayā jarāmaraṇaṃ. Jāti ca hi, ānanda, nābhavissa sabbena sabbaṃ sabbathā sabbaṃ kassaci kimhici, seyyathidaṃ— devānaṃ vā devattāya, gandhabbānaṃ vā gandhabbattāya, yakkhānaṃ vā yakkhattāya, bhūtānaṃ vā bhūtattāya, manussānaṃ vā manussattāya, catuppadānaṃ vā catuppadattāya, pakkhīnaṃ vā pakkhittāya, sarīsapānaṃ vā sarīsapattāya, tesaṃ tesañca hi, ānanda, sattānaṃ tadattāya jāti nābhavissa. Sabbaso jātiyā asati jātinirodhā api nu kho jarāmaraṇaṃ paññāyethā”ti? “No hetaṃ, bhante”.

It was said: ‘With birth as condition there is aging and death.’ How that is so, Ānanda, should be understood in this way: If there were absolutely and utterly no birth of any kind anywhere—that is, of gods into the state of gods, of celestials into the state of celestials, of spirits, demons, human beings, quadrupeds, winged creatures, and reptiles, each into their own state—if there were no birth of beings of any sort into any state, then, in the complete absence of birth, with the cessation of birth, would aging and death be discerned?”
“Certainly not, venerable sir.”

Take a look at the clause I’ve bolded. It’s the familiar existential locative absolute used in the Third Noble Truth, eg SN 12.50. So, here you have a clear example of the Buddha using the Third Noble Truth to establish the Second Noble Truth. So, you’re right that this is a Proof by Contrapositive, but see below for the logical analysis.

So, moving on to your scruples about the placement of the clauses. I would firstly mention Warder, who says at p.300 that clause order can be inverted for emphasis. Secondly, the invisible copula “hoti” (is) in the 2nd clause does not necessarily point to the present or even the future. It can point to the past as well.

Let’s see if there is clause inversion and a historical present used for the hoti in the 2nd clause.

While we have those pithy mnemonics for Dependant Origination in SN 12.1, the meaning of this list needs to be drawn out by the longer suttas such as DN 15. This is to avoid losing sight of the need to place all these teachings within the framework of the 4 Noble Truths.

One other sutta that makes explicit this framework is MN 38. Eg -

Bhikkhus, do you see: ‘This has come to be’ (bhūtamidaṃ)?”—“Yes, venerable sir.”—“Bhikkhus, do you see: ‘Its origination occurs with that as nutriment’?”—“Yes, venerable sir.”—“Bhikkhus, do you see: ‘With the cessation of that nutriment, what has come to be is subject to cessation’?”—“Yes, venerable sir.”

I’m sure you have little difficulty noticing the structure of the first 3 of the Four Noble Truths in this scheme. What follows next is interesting - a commentary by the Buddha on the SN 12.1 mnemonic (bolded), eg-

'With birth as condition, ageing and death’: so it was said. Now, bhikkhus, do ageing and death have birth as condition or not, or how do you take it in this case?”

This is then followed by a recapitulation of the mnemonic, expanded a little by the inclusion of the “imasmiṃ sati idaṃ hoti” formula of idappaccayatā -

Sādhu, bhikkhave. Iti kho, bhikkhave, tumhepi evaṃ vadetha, ahampi evaṃ vadāmi—imasmiṃ sati idaṃ hoti, imassuppādā idaṃ uppajjati, yadidaṃ— avijjāpaccayā saṅkhārā, …

Good, bhikkhus. So you say thus, and I also say thus: ‘When this exists, that comes to be;
with the arising of this, that arises.’ That is, with ignorance as condition, formations come to be …

This is where we now need to decides if the “hoti” in the formula is a historical present (ie past) or pertaining to the future. For me, what decides the issue is -

1. The Second Noble Truth is an explanation for how Suffering as the First Noble Truth is possible; and
2. The explicit use of bhūtamidaṃ is clearly pointing to suffering that already “has come to be”.

So, in this case, I would take the “hoti” to be a historical present, or at least referring to whatever has already come to be.

So, coming back to DN 15 passage above, you can express the Third Noble Truth like so -

If not-A, then not-B

where -A = A does not exist (taking A = birth)
-B = B does not come to be (taking B = ageing and death)

Now, applying the Proof by Contrapositive, “If not-A, then not-B” is logically equivalent to “If B, then A”.

Taking “If B, then A” to mean B = ageing and death, and A = birth, can you see any logical differerence between this proposition and the abovesaid DN 15 proof?

In the complete absence of birth, with the cessation of birth, would aging and death be discerned?

versus

If ageing and death is discerned, there was birth.

This could be the reason why Wijesekara suggests that we should translate the existential locative absolute “imasmiṃ sati” as “on condition that this exists”. So, instead of translating “jātiyā sati jarāmaraṇaṃ hoti” as “When there is birth, ageing and death comes to be”, the more precise interpretation that brings dependancy to the fore would be

On condition that birth exists, ageing and death comes to be.

Bearing in mind that the hoti/comes to be is referring to whatever is bhuta, I would say a better translation of hoti here would be “has come to be”.

Would you agree that the 2 propositions -

On condition that birth exists, ageing and death (has) comes to be

and

If ageing and death (has) comes to be, it is because of birth as condition

are logically equivalent?

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[Edit: I actually wrote a long post in reply to the points you are making @Sylvester, but then it hit me that the problem may be better phrased in terms of sufficient and necessary conditions. So please excuse me if it seems like I’m not replying to what you wrote, it just seems to me my premise has changed a bit ]

I just realized the problem actually goes away if we understand

‘Jātipaccayā jarāmaraṇan’
to mean
’Birth is a necessary condition for aging and death.’

This is logically equivalent to ‘aging and death ⇒ birth’. This is in contrast to ‘birth is a sufficient condition for aging and death’, because a sufficient condition leaves room for there to be other conditions in addition to birth, that cause aging and death.

In this light one could read parts of DN 15 as the Buddha teaching Ānanda what a logically necessary condition is. Here’s something it could potentially look like with this translation:

It was said: ‘Birth is a necessary condition for aging and death.’ How that is so, Ānanda, should be understood in this way: If there were absolutely and utterly no birth of any kind anywhere… would aging and death be discerned?”

“Certainly not, venerable sir.”

“Therefore, Ānanda, this is the necessary cause, source, origin, and condition for aging and death, namely, birth.

Since the Buddha’s teachings are big on cause and effect, this sort of refinement is actually quite nice, because this defines is a strict chain of causality that doesn’t leave room for other factors to cause the phenomena described in dependent origination.

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Agreed, but for me it comes down the ambiguity of the word ‘condition’; does it mean necessary condition or sufficient condition? It’s the ‘necessary condition’-interpretation that makes DN 15 logically correct, as far as I can see.

So, for example:

With birth as a necessary condition, aging and death has come to be.
or
If ageing and death has come to be, birth is the necessary condition for that.

I’d be happy with this!

Probably people read DN 15 and just assume implicitly that the conditions are necessary (in the logical sense) without thinking too much about it. I still think it’s worth being explicit about it :happy_nerd:

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Yes, here ‘paccaya’ means necessary, requisite condition:

http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.020.than.html

https://dhammawheel.com/viewtopic.php?f=23&t=5974

Just to clarify, in logic “A is necessary for B” is defined to mean “If B, then A”, or B ⇒ A

“A is sufficient for B” is defined to mean “If A, then B”, or A ⇒ B.

In the first case, B cannot live without A. In the second case, A is just one of possibly many things that guarantee B.

In dependent origination, this would be the difference between “old age and death cannot exist without birth” and “birth is one (of possibly many) things that creates old age and death.”

As far as I can tell this distinction isn’t explicitly brought up in the Dhammawheel thread.

I would still prefer “necessary” over “requisite” as a translation, but I agree that ‘requisite condition’ is better than just ‘condition’

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It seems to me that birth is both a necessary and a sufficient condition for old age and death. It is necessary because without birth there is no old age and death. It is sufficient because once you have birth you must also have old age and death.

The operation of the two kinds of conditions can be appreciated by considering the arising and the cessation sequences of dependent arising. For the arising sequence, sufficiency is the predominant form of conditioning: when there is birth, old age and death must follow. For the cessation sequence, necessity is the conditioning that applies: if there is no birth, there is no old age and death (that is, birth is a necessary condition for old age and death).

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I agree with you on birth bhante, but what about for example, feeling or delusion?

If feeling guarantees craving, how is it possible for an arahant make an end of craving during their lifetime?

If delusion guarantees will (saṅkhāra), how can the will stop for a non-arahant in 2nd jhana?

Or how can a non-arahant dwell in the cessation of perception and feeling, when delusion should guarantee saṅkhāras and [saṅkhāras should guarantee] consciousness?

Or a rebirth as a non-sentient being? How is it possible for a non-returner to be reborn in the pure abodes and have pari-nibbana (as a result of a rebirth) instead of old age, death and the entire mass of suffering?

If one drops the “creating” aspect of DO, there aren’t consequences like “are arahants made uncounscious?” because in this case it’s not that delusion creates consciousness, it’s the case that without delusion, the condition for creating the fuel for the next rebirth (as explained in DO) is gone.

This way DO doesn’t have to be tied to a specific number of births, and it’s not tempting to interpret it as moment-by-moment psychological thing, because here DO doesn’t have to account for all the world’s existing phenomena, it only has to account for how phenomena end. For example, DO could simply explain the mind of the arahant at the breakup of the five khandas.

Also, let me just say I’m not holding firmly to this view of DO, I just think it’s interesting to explore it for learning’s sake

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Yes, the link between feeling and craving would normally be regarded as one of necessity, not sufficiency. Or it could be argued that some degree of craving exists even for the arahant (it all depends on how we define craving), but in this case the link between craving and attachment (upādāna) is limited to necessity. Either way, it is clear that the factors of dependent origination are not always linked through sufficiency.

Well, this is just a temporary stopping, and I do not think this is enough to argue that sufficiency does not apply in this case. In fact a number of the links can be temporarily suspended in this way. The point, rather, as I see it, is that delusion eventually must give rise to willed activities, which in turn will keep saṃsāra rolling. In this sense delusion is a sufficient condition for willed activities.

Again, this is just temporary.

In this case you are an anāgāmī as a human, before you get reborn in the pure abodes. What happens once you get reborn there is not really part of the equation. Some of these pure abode devas reach parinibbāna soon after getting reborn, even while in the intermediate existence. Others seem to go through a number of rebirths within the pure abodes.

But how can you drop the creative aspect, when this is exactly what DO is about? DO is precisely a process of creation that describes how the five khandhas are kept going, especially from life to life. We need to interpret DO in a way that is true to this. So how do we do this? The simple answer is that consciousness in this life does not depend for its existence on saṅkhāra. Only at the point of rebirth does consciousness depend on saṅkhāra for its continuity. In fact, this shows how the single lifetime version (including the moment to moment version) of dependent origination cannot be correct, because this model does indeed imply that consciousness comes to an end as soon as the saṅkhāras cease. I could expand on this, but I will leave it at that for now.

The very name dependent origination means it must account for more than the ending of things. In fact dependent origination and dependent cessation have separate identities in the suttas.

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Not to be too fussy, but what about the case of babies who die in infancy. They experience birth and death, but not old age.

Yes, death is clearly enough to fulfil this link.

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Bhante, I can’t see how a temporary stopping is reconcilable with the idea of a sufficient condition, because the idea behind A being sufficient for B is that the existence of A guarantees that B is there too.

In fact, the only time the expression A ⇒ B is false is when A is true and B is false, so unless I have misunderstood the logic, if there is delusion and saṅkhāras can stop temporarily, delusion is by definition not sufficient for saṅkhāras.

Bhante, it’s not clear to me how the introduction of time affects the logical relationship between statements.

Bhante, aren’t you here describing saṅkhāra as a necessary but not sufficient condition for consciousness?

Because this is the understanding that to my mind is implied by the necessary-conditions-DO.

What about dependent origination accounting for how things don’t end, i.e. how things keep on going, and dependent cessation for how things end?

Maybe the word ‘creation’ is just a bit ambiguous? In my mind, there is a difference between a theory of (world) creation and a theory of ‘why the heck am I still being reborn?’

For example, in this human reality our form khandas rely on the laws of physics, quantum mechanics, laws of chemistry, atoms, electrons etc. Dependent origination doesn’t say anything about this or explain this – it doesn’t explain how heavy elements are created through cycles of supernovas or anything like that.

This is what I think of when I think of creation; how the content of existence comes to be. But this might just be because of the fuzziness of word meanings.

Coincidentally, have you ever considered translating DO as “why the heck do we keep getting reborn? ” it could be a good title for a book!

Well, to be honest, I don’t know much about formal logic, and so you may well be talking with the wrong person. I am just trying to apply common sense, while being all too aware that common sense is not always reliable. Anyway, I am happy to continue this exchange for now, not least because I might learn something.

I am really out of my depth here, but having perused a couple of articles on Wikipedia I am wondering if there is a difference between sufficiency/necessity as used in logic and the same as used in causality. Here is what Wikipedia has to say about necessary and sufficient causes in its article on Causality:

Necessary causes
If x is a necessary cause of y, then the presence of y necessarily implies the prior occurrence of x. The presence of x, however, does not imply that y will occur.

Sufficient causes
If x is a sufficient cause of y, then the presence of x necessarily implies the subsequent occurrence of y. However, another cause z may alternatively cause y. Thus the presence of y does not imply the prior occurrence of x.

And here is an extract from the Wikipedia article on Necessity and Sufficiency (in formal logic):

Necessity:
The assertion that Q is necessary for P is colloquially equivalent to “P cannot be true unless Q is true” or “if Q is false, then P is false”. By contraposition, this is the same thing as “whenever P is true, so is Q”. The logical relation between them is expressed as “if P, then Q” and denoted “P ⇒ Q” (P implies Q). It may also be expressed as any of “P only if Q”, “Q, if P”, Q whenever P", and “Q when P”. One often finds, in mathematical prose for instance, several necessary conditions that, taken together, constitute a sufficient condition …

Sufficiency:
If P is sufficient for Q, then knowing P to be true is adequate grounds to conclude that Q is true; however, knowing P to be false does not meet a minimal need to conclude that Q is false.

The logical relation is expressed as “if P, then Q” or “P ⇒ Q”. This can also be expressed as “P only if Q” or “P implies Q”. Several sufficient conditions may, taken together, constitute a single necessary condition …

And from the Stanford Encyclopedia of Philosophy, under Necessary and Sufficient Conditions, we have the following in regard to “directional” (i.e. causal) conditioning:

In general, if explanation is directional, it may not seem surprising that when A explains B, it is not usually the case that B, or its negation, is in turn an explanation of A (or its negation). John’s winning the race explains our celebration, but our failure to celebrate is not (normally) a plausible explanation of his failure to win. Lambert’s presence may explain why the seminar was such a great success, but a boring seminar is not—in any normal set of circumstances—a reason why Lambert is not at it. This result undermines the usual understanding that if A is a sufficient condition of B, it will typically be the case that B is a necessary condition for A, and the falsity of B a sufficient condition for the falsity of A.

What you are describing as a sufficient cause seems to me to be related to logic, not causality. In other words, you seem to be describing a structural principle whereby the existence of one thing guarantees the existence of something else. In causality, however, we are often dealing with ephemeral phenomena that have an effect over time (the Wikipedia article speaks of prior and subsequent occurrences). The best example of this from dependent origination is probably the link between birth and death (let’s leave out old age for simplicity’s sake). Birth is a time limited event, not a continuous process. But once birth has happened, death is guaranteed to ensue. Birth is not present when death happens, yet it is sufficient (and necessary) for death.

If there are saṅkhāras, then there will be consciousness. This shows the sufficiency of saṅkhāras. (If saṅkhāras were merely necessary, this would not guarantee the continuation of consciousness.) If there are no saṅkhāras, then there is no consciousness. This shows the necessity of saṅkhāras. (If saṅkhāras were merely sufficient, then the end of saṅkhāra would not guarantee the end of consciousness.) At the point of death, saṅkhāra is both a necessary and sufficient condition for the continuation of consciousness. (And by the way, during a particular life time, name-and-form is the sufficient and necessary condition for consciousness.)

Well, yes. I think we can agree on this.

But the “content of existence” is first and foremost experience itself. In other words, the most basic thing we can say about existence is that there is experience. Everything else is derived from that. And dependent origination shows us how experience keeps on going.

We have a rule at Bodhinyana Monastery that the one who has the idea must do the work!

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The relationship between logic and causality seems to go pretty deep into philosophy, so we probably shouldn’t venture into that

I found this post on Quora about “logical and causal necessity”, here’s a quote:

For example, we know that clouds (plus other conditions) cause rain. So the causal direction is clouds → rain. However, the correct logical inference is rain → clouds (if it is raining, then it is cloudy).

I think it boils down to the fuzziness of the language of causation. It seems to me that in DN 15, the Buddha may be actually teaching an understanding of causality that is the same as in modern science.

Looking at the text, it’s “‘Jātipaccayā jarāmaraṇan’ti” and then the Buddha explains how to understand it, by providing the proper logical inference that can be drawn from the causal relationships.

Or perhaps just pointing out the relevant logical inference (how something ending leads to something else ending) without going into what can be inferred.

So we could make a distinction between the causal direction and the logical inferences one can (should?) make based on causal direction. What do you think?

[quote=“brahmali, post:14, topic:5726”]
If there are saṅkhāras, then there will be consciousness. This shows the sufficiency of saṅkhāras. (If saṅkhāras were merely necessary, this would not guarantee the continuation of consciousness.) If there are no saṅkhāras, then there is no consciousness. This shows the necessity of saṅkhāras. (If saṅkhāras were merely sufficient, then the end of saṅkhāra would not guarantee the end of consciousness.) At the point of death, saṅkhāra is both a necessary and sufficient condition for the continuation of consciousness. (And by the way, during a particular life time, name-and-form is the sufficient and necessary condition for consciousness.)[/quote]
If we put aside sufficient and necessary for a bit, we could say that saṅkhāras cause consciousness, and that the salient logical inference to draw from that is that the end of saṅkhāras guarantees the end of consciousness.

This way, we don’t have to go too much into the relationship between language, logic, causality and reality, etc. which I think is probably more in line with the Buddha’s teaching style when I think about it.

I guess I mean this in the sense that “having a TV” doesn’t explain how the TV shows (the content) are created or how the TV works, but it does explain how I keep watching TV. In particular, if I throw out my TV, I won’t experience its content anymore.

Does that mean content is still being creating even if I don’t have a TV? I think I don’t have to take any position on that, because it’s not strictly relevant to my problem; it doesn’t affect whether or not I can throw out my TV.

The TV could stand for consciousness and nama-rupa for example.

I do not want to interrupt this good discussion; however, I would like to add some thoughts into this topic and hope that we may find something useful…

My English is bad, so I cannot be precise with my wordings. However, you can just take the ideas.

“With feeling as condition, craving comes to be”

To me, this statement means with enough level/amount/intensity…to that feeling, the corresponding craving comes to be.

Just as if there is enough water to overflow a cup, and we keep pouring water into that cup, then overflow will come to be with no exception. However, if there is not enough water, or we do not continue pouring water into that cup until it overflows, then overflow will not come to be.

Just as, bhikkhus, when rain pours down in thick droplets on a mountain top, the water flows down along the slope and fills the cleft, gullies, and creeks; these being full fill up the pools; these being full fill up the lakes; these being full fill up the streams; these being full fill up the rivers; and these being full fill up the great ocean; so too, with ignorance as proximate cause, volitional formations come to be; with volitional formations as proximate cause, consciousness … with liberation as proximate cause, the knowledge of destruction. (SN 12.23)

All dependently arisen phenomena are impermanent, conditioned, dependently arisen, subject to destruction, vanishing, fading away, and cessation (SN 12.20). By nature, after they arise, they must cease by themselves. Therefore, when a feeling arose, that feeling must cease by itself. We do not need to do anything to make that happen.

However, when a feeling arose, by ignorance we pay inappropriate attention to it and continue generating more and more feeling of that kind (This is the effect of the loop-back between name-and-form and consciousness). When there is enough feeling of that kind, it now can be used as a condition for craving comes to be, and craving must come.

For an arahant, when a feeling arose, he does not pay inappropriate attention to it. He does not generate any more feeling of that kind (the loop-back is cut). That feeling will cease by itself; therefore, there is not enough level/intensity of that kind of feeling so it cannot be used as condition for the corresponding craving comes to be. In other words, the feeling that can be used as condition for craving does not exist for the arahant.

Each dependently arisen phenomenon may have different sufficient level/intensity to be used as a condition for the next dependently arisen phenomenon. When birth arose, it right away fulfilled as a condition for dukkha comes to be.

That’s how I understand DO.

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Not paying attention to unwholesome phenomena won’t get rid of them necessarily. See the vitakkasantana sutta for a few other methods used by the Buddha and his disciples.

Defilements cease but they arise again and again as other propagating factors like ignorance (avijja) are still present.

The Four Right efforts must be used to remove defilements.

With metta

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Agree. that’s what a practitioner should do. However, I am here referring to an arahant who has cut off ignorance and has made an end of suffering. Moreover, I said that he does not pay inappropriate attention. In the same sutta that you mention (vitakkasantana sutta MN 20), the arahant can “think whatever thought he wishes to think and he will not think any thought that he does not wish to think”. This is how he can cut off the loop-back.

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Ok, let’s have look at how conditionality is explained in DN 15 (Ven. Bodhi’s translation):

‘Jātipaccayā jarāmaraṇan’ti iti kho panetaṃ vuttaṃ, tadānanda, imināpetaṃ pariyāyena veditabbaṃ, yathā jātipaccayā jarāmaraṇaṃ. Jāti ca hi, ānanda, nābhavissa sabbena sabbaṃ sabbathā sabbaṃ kassaci kimhici, seyyathidaṃ— devānaṃ vā devattāya, gandhabbānaṃ vā gandhabbattāya, yakkhānaṃ vā yakkhattāya, bhūtānaṃ vā bhūtattāya, manussānaṃ vā manussattāya, catuppadānaṃ vā catuppadattāya, pakkhīnaṃ vā pakkhittāya, sarīsapānaṃ vā sarīsapattāya, tesaṃ tesañca hi, ānanda, sattānaṃ tadattāya jāti nābhavissa. Sabbaso jātiyā asati jātinirodhā api nu kho jarāmaraṇaṃ paññāyethā”ti?
“No hetaṃ, bhante”.
“Tasmātihānanda, eseva hetu etaṃ nidānaṃ esa samudayo esa paccayo jarāmaraṇassa, yadidaṃ jāti.

“It was said: ‘With birth as condition there is aging and death.’ How that is so, Ānanda, should be understood in this way: If there were absolutely and utterly no birth of any kind anywhere—that is, of gods into the state of gods, of celestials into the state of celestials, of spirits, demons, human beings, quadrupeds, winged creatures, and reptiles, each into their own state—if there were no birth of beings of any sort into any state, then, in the complete absence of birth, with the cessation of birth, would aging and death be discerned?”
“Certainly not, venerable sir.”
“Therefore, Ānanda, this is the cause, source, origin, and condition for aging and death, namely, birth.

So, yes, here birth is given as a necessary condition for death: without birth, there is no death. And I agree with you, it does not follow from this that birth is a sufficient condition for death. I am not sure, however, if DN 15 is meant as an exhaustive treatment of causality in dependent origination. I would suggest the point of DN 15, rather, is to focus on the ending of suffering, as seems to be implied by the opening statement of the sutta.

To fully understand the conditionality that applies in DO we need to take a broader look at the suttas. I believe the best place to start is with the abstract principle of conditionality, which invariably is followed by the standard set of twelve links. It reads as follows in Ven. Bodhi’s translation:

Iti imasmiṃ sati idaṃ hoti, imassuppādā idaṃ uppajjati. Imasmiṃ asati idaṃ na hoti, imassa nirodhā idaṃ nirujjhati. (e.g. at SN 12.21)

When this exists, that comes to be; with the arising of this, that arises. When this does not exist, that does not come to be; with the cessation of this, that ceases.

Here we have, I think, an almost perfect match with sufficient and necessary conditionality. “When this exists, that comes to be; with the arising of this, that arises” shows sufficiency, whereas “with the cessation of this, that ceases; with the cessation of this, that ceases” shows necessity. If we are to take anything as the paradigm of conditionality that applies for DO, I would say this is it. It seems to me that DN 15 does not give the full story, but instead focuses on a particular aspect.

So I guess this means that the Buddha goes beyond causality as understood in modern science?

The abstract principle I have mentioned above is equally applicable here; in other words, both necessity and sufficiency applies.

[quote=“freedom, post:16, topic:5726”]
For an arahant, when a feeling arose, he does not pay inappropriate attention to it. He does not generate any more feeling of that kind (the loop-back is cut). That feeling will cease by itself; therefore, there is not enough level/intensity of that kind of feeling so it cannot be used as condition for the corresponding craving comes to be.[/quote]

It is not the intensity of the feeling that matters, but only how you relate to it. If you understand it in the right way, you will never crave for it regardless of its intensity. It is the insight of the arahant that matters.

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It just came to mind that dependent cessation guarantees the necessity of each link of DO in any case. I.e. if dependent cessation is assumed to be true, the necessity of each link in DO is just a logically equivalent statement.

So DO is at least a chain of necessity relations. But of course, there could also be links where there is sufficiency in addition to necessity.

Bhante, is there any link in DO where you see lack of sufficiency causing problems in the suttas?

It seems to me that one could interpret this abstract definition to show causal direction and logical necessity. For example, delusion is there before the volition, and the volition comes before consciousness etc.

It also depends on what one takes sufficient to mean in terms of causation. The way I understand sufficient is a 100% guarantee for a co-existing phenomena. E.g. feeling 100% guarantees there is craving. This creates an obvious conflict with the arahant for example.

You could say that sufficient means a guarantee but with exceptions. But then isn’t it better to say “in general feeling means craving, with some exceptions”, and then leave sufficient to retain a strict meaning?

And looking at DN 15:

[No birth means no aging and death]

“Therefore, Ānanda, this is the cause, source, origin, and condition for aging and death, namely, birth.

It seems to me that what is being said is almost that necessity is what it means for something to be a cause, source, origin and condition.

The intensity that I referred is the total weight/amount of all feelings of that kind (or just one) at that moment. This intensity is increasing if those same kind feelings are continuously fed to the system. When the intensity reaches certain level, next step (craving) will come with no exception.

Just as if one is getting angry about an issue. At first, the intensity of this anger is not enough for one to crave for violent or inappropriate action. However, if one keeps engaging with that issue, the intensity of that anger will increase up to the point that one will crave for violent or inappropriate action.

When one saw a beautiful flower, pleasant feeling arose. However, this does not mean that one must crave for that flower at the first sight.

When one saw a beautiful flower, pleasant feeling arose and one keeps thinking about that flower (or the pleasant feeling that one experienced) or/and intentionally seeing that flower again and again, then up to some point craving will come.

When a person with no wisdom saw a beautiful flower, pleasant feeling arose but he has no time to think about that flower or that pleasant feeling then craving may not come.

Intensity of the feeling and how we relate to it may have direct relationship. Depend on how we relate to the feeling, it will increase or decrease. However, there are some levels of intensity that even we have wisdom or how hard we have tried to properly relate to it, it is hard or impossible for us to ignore or decrease it (as in case of venerable Channa used the knife in SN 35.87)

“Friend Sāriputta, I am not bearing up, I am not getting better. Strong painful feelings are increasing in me, not subsiding, and their increase, not their subsiding, is to be discerned. Just as if a strong man were to split my head open with a sharp sword, so too violent winds cut through my head. I am not bearing up…. Just as if a strong man were to tighten a tough leather strap around my head as a headband, so too there are violent pains in my head. I am not bearing up…. Just as if a skilled butcher or his apprentice were to carve up an ox’s belly with a sharp butcher’s knife, so too violent winds are carving up my belly. I am not bearing up…. Just as if two strong men were to seize a weaker man by both arms and roast him over a pit of hot coals, so too there is a violent burning in my body. I am not bearing up, I am not getting better. Strong painful feelings are increasing in me, not subsiding, and their increase, not their subsiding, is to be discerned. I will use the knife, friend Sāriputta, I have no desire to live.” SN 35.87

If the intensity of the painful feelings does not matter, then Ven. Channa does not need to use the knife since he is the one who has right understanding and insight. However, in this case, the intensity has reached its level, so craving to end that life has come no matter what Ven. Sariputa and Ven. Mahacunda have tried to persuade him.

That’s how I understand.