You’ve cast a presumption that is not in alignment with my motivational intention. I am attempting to work out the reasoning as to why Yeshe is seeking this knowledge.
I am listening so I can tailor a response crafted to OP.
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Hello @dhammapala. Thanks for asking. I’m trying to understand the structure of the Buddha’s ways of knowing in order to hopefully better understand the knowledge itself. By ways of knowing, I mean exactly what the Buddha did and did not consider a valid way of knowing something. It is my hope that in understanding the logical arguments that the Buddha made - and specifically what rules of inference and what principles of logic/thought - that the Buddha deemed valid (and what he might have deemed invalid), that I’ll better understand the Buddha’s teaching: the sacred dhamma.
My original introduction to Buddhism was through reading the words of the Buddha as compiled in the Pali canon. While I have since gone on to study Tibetan Buddhism, my heart has continuously brought me back to the Pali canon as a foundation for my own (limited) understanding. I hope this explains the knowledge that I’m seeking and the motivation for that seeking. 
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Fair enough, I apologise! I am a little cranky today it seems 
Alright. We got another one: AN 3.105 Dutiyaassādasutta
“Mendicants, if there were no gratification in the world, sentient beings wouldn’t be aroused by it. But because there is gratification in the world, sentient beings are aroused by it.
If the world had no drawback, sentient beings wouldn’t grow disillusioned with it. But since the world has a drawback, sentient beings do grow disillusioned with it.
If there were no escape from the world, sentient beings wouldn’t escape from it. But since there is an escape from the world, sentient beings do escape from it.
Thanks for the information Yeshe. Urgency (samvega) and need to uproot immense pain, stress, dissatisfaction, worry and suffering because of having difficulty coming to terms with being born and all that comes with birth leads to a relentless non-stop process of seeking where one exhausts all avenues until the realisation that releases one from dukkha arises.
Dharma always comes with sound reasoning, concordant premises and when tested can be discerned to be actual for oneself in relationship to ones life situation. It’s effects are immediately felt, relieving. It is both ‘means and ends’ that leads to the desired effect I.e. ‘the uprooting of dukkha’.
Uprooting is a process and not a gigantic spectacular event. This capacity grows as ones practice begins to get gain momentum and one becomes better in identifying views that are not in align with the middle way/wrong views that one may harbour and through maintaining calm in mind-body - consciously noticing the seeds of stress as they arise in the physical/mental stress and then releasing them. This matures and ripens. It is then up to the Noble aspirant to discern that which further perpetuates stress and then that which leads to its cessation. The themes are general and can also be unique to each individual & their conditioning factors.
To summarise, I would suggest that one reaches the goal through exhausting all other possibilities. The North Star Guiding principle of working to resolve to live a life at peace, at ease, well, and free from suffering must be set as this is what one continually realigns with when one stumbles.
Ultimately, it is suffering which gives rise to that urgency and the need to uproot it.
No Pali Canon reference that I can recollect but I can share some of my remarkings on the middle between extremes. I will share what I speak in hopes that there may be a golden nugget in there somewhere for you.
The included middle between the ideas of annihilationism and eternalism is the present flow of nowness.
Wrong: There is a self.
Wrong: There is not a self.
Right (in alignment with middle way, causation): when contact is made between the myriad varying aggregate factors (mating pair, formation of elemental body, endowed with 5 senses and cognised of via 5 aggregates) then a sense of self born of the feeling of aliveness comes to be. Notice the attention to specificity.
Wrong: a life span is finite.
Wrong: a life span is infinite.
Right: a life span is conditional.
Instead of taking these wrong statements on a given, because of urgency, one observes how things come to be through the lens of causation and conditionality. When this mental formation arises, this unhelpful sensation arises in both mind and body. When I let go of this mental formation, this unhelpful sensation ceases. It is necessary to see the interrelationships between the arising of things in general but most importantly the specific mechanisms by which one experiences stress in mind-body and examining exactly that by which it is caused. It is seeing these interrelationships that is the middle way which frees from the bondage of extreme thinking.
We can look at the aggregates of feeling and mental abstraction here. In the untrained mind, lacking both calm as well as insight (into the mechanisms of ones make up and the four foundations of mindfulness) - one can become impressioned upon by external happenings as well as internal whims, emotions, and feelings. Sometimes a feeling can give rise to a thought which can then further perpetuate the unhelpful feeling. Sometimes a thought can give rise to a thought which gives rise to an unhelpful feeling. This creates vicious cycles that can be hard to snap out of.
This is where the conscious practice of learning to remain calm comes in. This is samatha. And vipasanna in its core crucible is just insight.
I wish that this is of some usage to you. Many thanks for the rich response as it supported in helping craft a tailored response. I don’t think the middle can ever truly be excluded when it comes to the Noble One’s. ; )
And another one: Iti 42 Sukkadhammasutta
“These two bright things, mendicants, protect the world. What two? Conscience and prudence. If these two bright things did not protect the world, there would be no recognition of the status of mother, aunts, or wives and partners of teachers and respected people. The world would become dissolute, like goats and sheep, chickens and pigs, and dogs and jackals. But because the two bright things protect the world, there is recognition of the status of mother, aunts, and wives and partners of teachers and respected people.”
Hmm, those don’t seem to be indirect proofs at all, but rather tautologies.
All good in the Buddhahood.
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You’re welcome, but your reply is not associated with the question from what I can discern. I’m looking for something specific as outlined in the question, not general advice nor summary of unrelated topics.
It seems to me you can replace “escape from the world” in AN 3.105 with the “unborn” in Iti 43 then it does not got the problem with triple negation?
I do not think the historical Buddha would have consciously employed this LEM notion, hence why I was compelled to let out that splurge. The middle is never excluded. The middle is the means by which sense is made between extremes.
There is unborn,
There is the born,
Then there is that which is giving rise and producing each term which is that which works to understand what it names the born and the unborn, the conditioned and the conditioned.
When this is, that is, when that is not, this ceases. That shoots right down the middle of “if this is not true, then that is true”. (Please correct me if I have misunderstood LEM?) The Buddha always lays it out very methodologically and with image, simile, or metaphor. In a way, this is seeing the mechanism by which something is rendered true or false by examining X-premises and relationships between variables.
Also, maybe you or someone else can explain this triple negation in a more “intuitive” way?
From this diagram below, it’s not clear that ¬¬¬P → ¬P if you do NOT exclude the middle.
This does not look like an existence proof, but rather noting a dependent relationship. The structure looks like:
- There is P.
- Assume ¬P.
- Consequence A would not be evident.
- But because P is true.
- Consequence A is evident.
Again, it isn’t a proof that P is true, but rather it is noting a dependent relationship of P and its logical consequence and ¬P and its logical consequence.
An indirect proof would look like:
- There is P.
- Assume ¬P.
- This consequence would be evident.
- This consequence is not evident.
- Therefore P is true.
The Buddha does not assert this. At least not in this translation. The Buddha in this teaching is illustrating a dependent relationship: between conscious and prudence and the recognition of the status of mother, etc. He asserts the existence of conscious and prudence, but he does not say that his knowledge of conscious and prudence is formed via an indirect proof.
Request for future examples: to aid future analysis of suttas you think imply indirect proof, if you could kindly draw out what you think the logical structure is and how it fits the shape of an indirect proof I’d greatly appreciate it.
Ah, I understand now what you were attempting to say. Please note: there is quite a big difference by what is meant by the formal logical notion of the Principle of the Excluded Middle (LEM) and what the Buddha meant by the “Middle Way” or at least it is not at all clear that there is any kind of one-to-one relationship between these two very different notions in their two very different contexts. One is a highly technical jargon having to do with formal logic and the other has to do with dhamma which is not rendered in a language easily amenable to translation into formal logical statements. In other words, even if we could reliably translate dhamma into the language of formal logical statements, it is not at all clear that the “Middle Way” is synonymous or even analogous to LEM.
Were it true that the Buddha never used LEM in his logical arguments, then it would be a nice slogan to say that this represents the “Middle Way” but that would be just that - a slogan 
Alright. Let’s see below:
The proposition to be proved is P. (which is: “These two bright things, mendicants, protect the world”)
Assume ¬P. (which is: “If these two bright things did not protect the world”)
Derive falsehood (which is: “The world would become dissolute, like goats and sheep, chickens and pigs, and dogs and jackals”)
Conclude P. (which is: “These two bright things, mendicants, protect the world”)
Ha, brilliant!
It is time for me to retire to rest. I wish you the best on your quest.
Thanks for the chat.
But he doesn’t say, “but because we don’t see a dissolute world, like goats and sheep, chickens and pigs, and dogs and jackals, therefore we conclude these two bright things, mendicants, protect the world.”
He also doesn’t say, “but because we see recognition of the status of mother, etc, therefore we conclude these two bring things, mendicants, protect the world.”
What he does say is, “but because these two bright things, mendicants, protect the world, there is…”
See the difference?
But do we see that situation?
But don’t we see that situation?
Not sure what you’re trying to get at? Can you expand or clarify?
Again, I’m not sure what you are asking or trying to get at… Are you asking if we can/should make a logical inference based on what we see? Or under what system of logic we should use? Or under what system of logic the Buddha used?
I’m focused in this OP on one thing: to see if anybody can find an unambiguous case of the Buddha using LEM or non-constructivist logic in a sutta to draw an indirect proof of knowledge of something. What I see above doesn’t fit the case.