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