user8157: Are the Pali words "cause" ("hetu'), "condition" ("paccaya"), "nutriment" ("ahara") and "root" ("mula") always synonyms? 

user10100: Paccaya/hetu/āhāra = Whole Condition (Lead&Supporting Condition) in paṭiccasamuppāda.
Mūla = Lead Condition/Root Condition in paṭiccasamuppāda.
Mūla = "Root" in pāli language. Life is similar  to a tree, lobha&dosa&moha&whole unwholesome are the seed & root of life. When you want to kill this tree you have to destroy whole seed&root. Because if you destroy just the top of tree, new trees can grow up again and again by the left seeds&roots. This is the reason which pali often use mūla as Lead Condition. See the quote sutta below for more explanation.
HetuPaccaya is used by sāriputta-mahāsāvaka in paṭṭhāna-abhidhammapiṭaka because he have to avoid to conflict mūla with Sutta Pitaka Vol 4 : Sutta. Ma. Mū.  {285.1} (English translation). if he use mūla in this context instead of hetu, all other unwholesome saṅkhāra can't be mūla, so paṭṭhāna will conflict with that sutta. That's the reason why sāriputta chose hetu instead of mūla for paṭṭhāna.
Paccaya/hetu/āhāra = Whole Condition (Lead&Supporting Condition)
Playing as lead condition in paṭiccasamuppāda

Tasmātihānanda  eseva  hetu  etaṃ  nidānaṃ  esa  samudayo esa paccayo
upādānassa yadidaṃ taṇhā. --Sutta Pitaka Vol 2 : Sutta. Tī. Ma. {58.3} / (English translation)

Playing as supporting condition in paṭiccasamuppāda

tasmātihānanda eseva   hetu   etaṃ  nidānaṃ  esa  samudayo  esa  paccayo  vedanāya yadidaṃ phasso.  --Sutta Pitaka Vol 2 : Sutta. Tī. Ma. {58.3} / (English translation)
Kavaḷīkāro āhāro oḷāriko vā sukhumo vā phasso dutiyo manosañcetanā tatiyā viññāṇaṃ catutthaṃ . ime kho bhikkhave cattāro āhārā bhūtānaṃ vā sattānaṃ ṭhitiyā sambhavesīnaṃ vā anuggahāyāti. --Sutta Pitaka Vol 8 : Sutta. Saṃ. Ni. [31] / (English translation)

Mula = Lead Condition/Root Condition

{79.7}   Katamo   ca   sīha   pariyāyo   yena   maṃ  pariyāyena sammā    vadamāno    vadeyya   tapassī   samaṇo   gotamo   tapassitāya
dhammaṃ   deseti   tena   ca   sāvake   vinetīti   .   tapanīyāhaṃ
sīha pāpake     akusale     dhamme    vadāmi    kāyaduccaritaṃ
vacīduccaritaṃ manoduccaritaṃ     yassa    kho    sīha    tapanīyā
pāpakā    akusalā Dhammā     pahīnā    ucchinnamūlā    tālāvatthukatā
anabhāvaṃ    katā āyatiṃ     anuppādadhammā     tamahaṃ    tapassīti
vadāmi    tathāgatassa kho   sīha   tapanīyā   pāpakā   akusalā
dhammā   pahīnā  ucchinnamūlā tālāvatthukatā    anabhāvaṃ   katā
āyatiṃ   anuppādadhammā   ayaṃ   kho sīha   pariyāyo  yena  maṃ
pariyāyena  sammā  vadamāno  vadeyya  tapassī samaṇo gotamo
tapassitāya dhammaṃ deseti tena ca sāvake vinetīti.
{79.8}  Katamo  ca  sīha  pariyāyo  yena  maṃ  pariyāyena  sammā vadamāno   vadeyya   apagabbho   samaṇo   gotamo   apagabbhatāya
dhammaṃ deseti  tena  ca  sāvake  vinetīti  .  yassa kho sīha āyatiṃ
gabbhaseyyā punabbhavābhinibbatti    pahīnā    ucchinnamūlā
tālāvatthukatā    anabhāvaṃ katā   āyatiṃ   anuppādadhammā   tamahaṃ
apagabbhoti   vadāmi  tathāgatassa kho   sīha   āyatiṃ   gabbhaseyyā
punabbhavābhinibbatti  pahīnā  ucchinnamūlā tālāvatthukatā   anabhāvaṃ
katā   āyatiṃ  anuppādadhammā  ayaṃ  kho  sīha pariyāyo   yena   maṃ
pariyāyena  sammā  vadamāno  vadeyya  apagabbho samaṇo gotamo
apagabbhatāya dhammaṃ deseti tena ca sāvake vinetīti. -- Sutta Pitaka Vol 4 : Sutta. Ma. Mū.  {285.1} / (English translation)


user8044: The Pali words "cause" ("hetu') is NOT a synonym of "condition" ("paccaya"). To explain this, let me take the example in paticca samuppada (PS). The PS cycle that describes the “cause and effect” in Buddha Dhamma starts as: “avijja paccaya sankhara, sankhara paccaya vinnana, vinnana paccaya nama rupa, nama rupa paccaya salayatana,….”.
One may tend to think that “avijja paccaya sankhara” means “avijja causes sankhara” or “ignorance causes one to acts that generate bad kamma”, but it is not so. All of us ordinay people have avijja, but that does not mean that we always act accordingly. Most of the time we act appropriately or morally. However, if avijja is there, it is likely that at times one will act with avijja and do inappropriate or immoral things.
Thus PS does not refer to a “direct link”. Any effect must have a cause. But there can be possible causes without leading to any effects. Otherwise, Nibbana would not be possible. For causes to bring about corresponding effects, suitable conditions must be present. That is what ‘paccaya’ means.
Similarly the Pali words "nutriment" ("ahara") is NOT a synonym of "root" ("mula"). In Pali language, “mula” is a root, so that “mūlika héthu” means “root causes”. To explain this, let me take the example of a tree. The roots (mūlika hetu) are critical for the tree’s survival, but the “patta” also plays an important role for the tree’s growth. The “patta” are essential for the tree’s survival, just as the roots of the tree are. One could kill a tree simply by a process called “girdling” where those phloem cells are removed. Girdling, also called ring-barking is the complete removal of a strip of bark. from around the entire circumference of either a branch or trunk of a woody plant. Girdling results in the death of the area above the girdle over time. A branch completely girdled will fail and when the main trunk of a tree is girdled, the entire tree will die.
So, the tree’s survival depends on not only its roots, but also its “patta” containing those critical phloem cells. Thus, CONDITIONS are as important as ROOT CAUSES, and both these taken together is "nutriment" ("ahara") for the tree. 

8157: <p>Are the Pali words "cause" ("hetu'), "condition" ("paccaya"), "nutriment" ("ahara") and "root" ("mula") always synonyms? </p>
 10100: <p><strong>Paccaya/hetu/āhāra</strong> = Whole Condition (Lead&amp;Supporting Condition) in paṭiccasamuppāda.</p>
<p><strong>Mūla</strong> = Lead Condition/Root Condition in paṭiccasamuppāda.</p>
<p><strong>Mūla = &quot;Root&quot; in pāli language.</strong> Life is similar  to a tree, <strong>lobha&amp;dosa&amp;moha&amp;whole unwholesome</strong> are the seed &amp; root of life. When you want to kill this tree you have to destroy whole seed&amp;root. Because if you destroy just the top of tree, new trees can grow up again and again by the left seeds&amp;roots. This is the reason which pali often use mūla as Lead Condition. <strong>See the quote sutta below for more explanation.</strong></p>
<p><strong>HetuPaccaya is used by sāriputta-mahāsāvaka</strong> in paṭṭhāna-abhidhammapiṭaka because he have to avoid to conflict mūla with Sutta Pitaka Vol 4 : Sutta. Ma. Mū.  <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=12&amp;A=5620" rel="nofollow noreferrer">{285.1}</a>  <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=12&amp;A=5620&amp;eng=accesstoinsight_than" rel="nofollow noreferrer">(English translation)</a>. if he use mūla in this context instead of hetu, all other unwholesome saṅkhāra can't be mūla, so paṭṭhāna will conflict with that sutta. That's the reason why sāriputta chose hetu instead of mūla for paṭṭhāna.</p>
<h2>Paccaya/hetu/āhāra = Whole Condition (Lead&amp;Supporting Condition)</h2>
<p><strong>Playing as lead condition in paṭiccasamuppāda</strong></p>
<blockquote>
<p>Tasmātihānanda  eseva  hetu  etaṃ  nidānaṃ  esa  samudayo esa paccayo
upādānassa yadidaṃ taṇhā. --Sutta Pitaka Vol 2 : <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=10&amp;A=1421" rel="nofollow noreferrer">Sutta. Tī. Ma. {58.3}</a> / <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=10&amp;A=1520&amp;eng=accesstoinsight_than" rel="nofollow noreferrer">(English translation)</a></p>
</blockquote>
<p><strong>Playing as supporting condition in paṭiccasamuppāda</strong></p>
<blockquote>
<p>tasmātihānanda eseva   hetu   etaṃ  nidānaṃ  esa  samudayo  esa  paccayo  vedanāya yadidaṃ phasso.  --Sutta Pitaka Vol 2 : <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=10&amp;A=1520" rel="nofollow noreferrer">Sutta. Tī. Ma. {58.3}</a> / <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=10&amp;A=1520&amp;eng=accesstoinsight_than" rel="nofollow noreferrer">(English translation)</a></p>
<p>Kavaḷīkāro āhāro oḷāriko vā sukhumo vā phasso dutiyo manosañcetanā tatiyā viññāṇaṃ catutthaṃ . ime kho bhikkhave cattāro āhārā bhūtānaṃ vā sattānaṃ ṭhitiyā sambhavesīnaṃ vā anuggahāyāti. --Sutta Pitaka Vol 8 : <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=16&amp;A=301" rel="nofollow noreferrer">Sutta. Saṃ. Ni. [31]</a> / <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=16&amp;A=301&amp;eng=accesstoinsight_than" rel="nofollow noreferrer">(English translation)</a></p>
</blockquote>
<h2>Mula = Lead Condition/Root Condition</h2>
<blockquote>
<p>{79.7}   Katamo   ca   sīha   pariyāyo   yena   maṃ  pariyāyena sammā    vadamāno    vadeyya   tapassī   samaṇo   gotamo   tapassitāya
dhammaṃ   deseti   tena   ca   sāvake   vinetīti   .   tapanīyāhaṃ<br />
sīha pāpake     akusale     dhamme    vadāmi    kāyaduccaritaṃ<br />
vacīduccaritaṃ manoduccaritaṃ     yassa    kho    sīha    tapanīyā<br />
pāpakā    akusalā Dhammā     pahīnā    ucchinnamūlā    tālāvatthukatā
anabhāvaṃ    katā āyatiṃ     anuppādadhammā     tamahaṃ    tapassīti<br />
vadāmi    tathāgatassa kho   sīha   tapanīyā   pāpakā   akusalā<br />
dhammā   pahīnā  <strong>ucchinnamūlā tālāvatthukatā</strong>    anabhāvaṃ   katā<br />
āyatiṃ   anuppādadhammā   ayaṃ   kho sīha   pariyāyo  yena  maṃ
pariyāyena  sammā  vadamāno  vadeyya  tapassī samaṇo gotamo
tapassitāya dhammaṃ deseti tena ca sāvake vinetīti.</p>
<p>{79.8}  Katamo  ca  sīha  pariyāyo  yena  maṃ  pariyāyena  sammā vadamāno   vadeyya   apagabbho   samaṇo   gotamo   apagabbhatāya<br />
dhammaṃ deseti  tena  ca  sāvake  vinetīti  .  yassa kho sīha āyatiṃ
gabbhaseyyā punabbhavābhinibbatti    pahīnā    ucchinnamūlā<br />
tālāvatthukatā    anabhāvaṃ katā   āyatiṃ   anuppādadhammā   tamahaṃ<br />
apagabbhoti   vadāmi  tathāgatassa kho   sīha   āyatiṃ   gabbhaseyyā
punabbhavābhinibbatti  pahīnā  ucchinnamūlā tālāvatthukatā   anabhāvaṃ
katā   āyatiṃ  anuppādadhammā  ayaṃ  kho  sīha pariyāyo   yena   maṃ<br />
pariyāyena  sammā  vadamāno  vadeyya  apagabbho samaṇo gotamo
apagabbhatāya dhammaṃ deseti tena ca sāvake vinetīti. -- Sutta Pitaka Vol 4 : Sutta. Ma. Mū.  <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=12&amp;A=5620" rel="nofollow noreferrer">{285.1}</a> / <a href="http://www.84000.org/tipitaka/read/roman_read.php?B=12&amp;A=5620&amp;eng=accesstoinsight_than" rel="nofollow noreferrer">(English translation)</a></p>
</blockquote>
 8044: <p>The Pali words "cause" ("hetu') is NOT a synonym of "condition" ("paccaya"). To explain this, let me take the example in paticca samuppada (PS). The PS cycle that describes the “cause and effect” in Buddha Dhamma starts as: “avijja paccaya sankhara, sankhara paccaya vinnana, vinnana paccaya nama rupa, nama rupa paccaya salayatana,….”.</p>

<p>One may tend to think that “avijja paccaya sankhara” means “avijja causes sankhara” or “ignorance causes one to acts that generate bad kamma”, but it is not so. All of us ordinay people have avijja, but that does not mean that we always act accordingly. Most of the time we act appropriately or morally. However, if avijja is there, it is likely that at times one will act with avijja and do inappropriate or immoral things.</p>

<p>Thus PS does not refer to a “direct link”. Any effect must have a cause. But there can be possible causes without leading to any effects. Otherwise, Nibbana would not be possible. For causes to bring about corresponding effects, suitable conditions must be present. That is what ‘paccaya’ means.</p>

<p>Similarly the Pali words "nutriment" ("ahara") is NOT a synonym of "root" ("mula"). In Pali language, “mula” is a root, so that “mūlika héthu” means “root causes”. To explain this, let me take the example of a tree. The roots (mūlika hetu) are critical for the tree’s survival, but the “patta” also plays an important role for the tree’s growth. The “patta” are essential for the tree’s survival, just as the roots of the tree are. One could kill a tree simply by a process called “girdling” where those phloem cells are removed. Girdling, also called ring-barking is the complete removal of a strip of bark. from around the entire circumference of either a branch or trunk of a woody plant. Girdling results in the death of the area above the girdle over time. A branch completely girdled will fail and when the main trunk of a tree is girdled, the entire tree will die.</p>

<p>So, the tree’s survival depends on not only its roots, but also its “patta” containing those critical phloem cells. Thus, CONDITIONS are as important as ROOT CAUSES, and both these taken together is "nutriment" ("ahara") for the tree. </p>
