I think Priest is interesting, and first degre entailment is interesting, I just think theres no reason to believe that anything other than “common sense logic” was at play in the undeclared points, they seem to be pre-buddhist, in DN2 they are associated with Sañjaya Belaṭṭhiputta and cover a range of different questions, none of which seem to me to require any other truth values than true or flase, at least if the 3rd and 4th options, where they occur, are treated merologically, which seems to me to agin be perfectly commonsensical.
As I see now, I object to both statements.
As I see, they do involve the use of LEM for “proof by contradiction”. Both “proof by contradiction” and “refutation by contradiction” use “law of non-contradiction”.
In the highlight part below, it’s the “double elimination negation” that makes the distinction between “proof by contradiction” and “refutation by contradiction”.
Intuitionistic logic excludes both “double elimination negation” and “LEM”, that’s why it’s compatible only with “refutation by contradiction” through “law of noncontradiction” that still holds in intuitionistic logic.
Those examples in Iti 43, Iti 42, , AN 3.105, AN 10.76 are “proof by contradiction”. They are not “refutation by contradiction”. As highlighted in the image: “Proof by contradiction is equivalent to the law of the excluded middle”. So, they do involve LEM.
As I see, it is instead: “Mapping them onto intuitionistic logic would entail the undesirable outcome to the 1st Noble Truth by claiming "to prove dukkha is the same as to prove 1=0"”
Thank you, that is very clarifying. I appreciate the time you took to explain as well. What is remarkable to me is it seems we are echoing a various famous debate in Madhyamaka buddhism: the Svātantrika–Prāsaṅgika distinction. Huge compendiums of commentary in the Tibetan Buddhist tradition are devoted to this very topic. Many modern western books have been written about it. In this famous debate, the jargon goes by slightly different technical names. The proof by contradiction is called “affirming negation” or “implicative negation.” The refutation by contradiction is called “non-affirming negation” or “non-implicative negation.”
A simple way to understand the Prasaṅgika argument is that by using proof by contradiction aka indirect proof this is what was meant by the Buddha of “holding a view.” On the other hand the Svatantrika believed that by denying proof by contradiction the Prasaṅgika was annihilitionist. This is a simplistic or very brief summary, but I think it gets to the heart of the matter.
What’s amazing is we seem to be echoing that debate based soley on sutta from the Pali canon and using analysis from modern mathematical/logical formalisms. What’s more the controversy of whether sunyata represents just the selflessness of persons or both the selflessness of persons and selflessness of phenomena is orthogonal to this debate.
You seem to be taking the Svatantrika side of the argument while I am taking the Prasaṅgika. Another striking feature here is a meta-level debate that occurred in this famous debate: the two sides argued over whether the distinction was meaningful. The Prasaṅgika side said the distinction was meaningful and that the Svatantrika side’s error was enough to destroy “the Middle Way.” The Svatantrika side claimed that the Prasaṅgika understanding was tantamount to annihilationism. Perhaps I was too quick to dismiss the connection between Madhyamaka and LEM as just a mere slogan.
Hi. Are you suggesting the OP’s definition of LEM was inaccurate, similar to how I also questioned it? It can be difficult for some to comprehend these linguistics.
Hi. How is this related to the Pali Suttas and other Early Buddhist texts?
In reading some Pali Suttas, it was clear to me the Buddha held views, particularly, ‘Right View’, despite the Buddha did not clinging to any views.
In reading the the Pali Suttas, I found the word ‘annihilitionist’ used in ways about views about self. Such as in Brahmajāla Sutta, ‘annihilitionist’ was talked about as the view a self is annihilated at death. And in Acela Sutta, it read as though ‘annihilitionist’ is attributing suffering to another self, possibly such as blaming others for one’s own self-made suffering.
Hi. I do not wish to sound rude but to me it looks like most people here are struggling to follow this topic. I cannot sense any “we” interacting in any debate, at this stage.
Hi. I currently cannot see this is occurring.
In reading Pali Suttas, it reads like there is no “persons” that are selfless. The Pali Suttas say all phenomena are selfless, therefore there is no “person” to be selfless, because what only exists is selfless phenomena. The five aggregates are selfless phenomena ignorantly taken to be a “person” but there is no person. There is only the five aggregates. I did read the word “person” used frequently in the Pali Suttas I read however this word “person” read as though it is just conventional language. As an example, I remember reading one sutta that said of the Buddha: there is one person that arises in the world for the benefit of the many. Obviously, the Buddha is not a real person. The word “person” must just be used here in a very worldly or conventional way. It would probably sound very strange to say: there is one set of five aggregates that arises in the world for the benefit of the many.
I now read Wikipedia: According to Tsongkhapa, Prāsaṅgika asserts that all phenomena are empty of inherent existence or essence, because they are dependently co-arisen with mental imputation. All phenomenon in all possible worlds lack inherent existence and come into existence relative to a designating consciousness which co-arises with that phenomena.
These ideas sound unfamiliar to the Pali Suttas I have read, where the primary subject matter was how suffering originates and how suffering ends. The ending of suffering is described as the ending of craving and not the ending of mental imputation. Setting the Wheel of Dhamma in Motion: And this, monks, is the noble truth of the cessation of stress: the remainderless fading & cessation, renunciation, relinquishment, release, & letting go of that very craving.
If all phenomena are empty of inherent existence or essence it must be the case the assertions of Tsongkhapa & Prāsaṅgika are also empty of inherent existence or essence therefore those empty assertions without essence of Tsongkhapa & Prāsaṅgika mean nothing. This being the case, it is easy to empathize with how the Svatantrika side claimed that the Prasaṅgika understanding was tantamount to annihilationism.
The Middle Way is the Noble Eightfold Path. Setting the Wheel of Dhamma in Motion: Precisely this Noble Eightfold Path: right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration. This is the middle way realized by the Tathagata.
What could be a good subject for debate is if the Indian logistician philosopher Nagarjuna understood or misunderstood the Kaccayanagotta Sutta?
I’ll let Clarity answer that, but in the meantime I wonder if this video might be helpful. There are other videos that also describe intuitionistic logic on youtube, but the one above seems to do a good job IMHO. Just a note: “intuitionistic” is a really unfortunate name that has to do with the particular historical way that this logic came about and much less to do with the actual content. That’s why I prefer to call it constructive logic.
In so far as the disagreement between Clarity and myself about the specific interpretation of the Pali Suttas discussed above echoes a previous debate, but I wish this Q&A to stay focused on the Pali canon suttas and LEM. Thanks for pointing out the digression.
Not surprising given the formalisms of logic discussed. They are deep subjects in themselves full of unknown jargon to those who have not studied modern logic. I posted a link to a video above hoping it might help. There are a lot of good resources on the web if you wish to learn more about the modern logical formalisms mentioned in this thread. When I said “we” were echoing a debate in a different context in the previous comment it was specifically meant to refer to Clarity and myself.
The cleansed one has no formulated view
Dhonassa hi natthi kuhiñci loke,
at all in the world about the different realms.
Pakappitā diṭṭhi bhavābhavesu;
Having given up illusion and conceit,
Māyañca mānañca pahāya dhono,
by what path would they go? They are not involved.
Sa kena gaccheyya anūpayo so.
Snp4.3
One here who has no wish for either end—
Yassūbhayante paṇidhīdha natthi,
for any form of existence in this life or the next—
Bhavābhavāya idha vā huraṁ vā;
has adopted no dogma at all
Nivesanā tassa na santi keci,
after judging among the teachings.
Dhammesu niccheyya samuggahītaṁ.
For them not even the tiniest idea is formulated here
Tassīdha diṭṭhe va sute mute vā,
regarding what is seen, heard, or thought.
Pakappitā natthi aṇūpi saññā;
That brahmin does not grasp any view—
Taṁ brāhmaṇaṁ diṭṭhimanādiyānaṁ,
how could anyone in this world judge them?
Snp4.5
“But does Master Gotama have any convictions at all?”
“Atthi pana bhoto gotamassa kiñci diṭṭhigatan”ti?
“The Realized One has done away with convictions.
“Diṭṭhigatanti kho, vaccha, apanītametaṁ tathāgatassa.
MN72
Did you just miss those in your sutta study @Dunlop?
Thank you. I may not be as well read as you. I have not read this Snp.
The link provided is amazing. It includes Pali that says: pakappita past participle 1. considered; designed; arranged; thought over. This does not negate the Right View of the Buddha. Pakappita reads as though it is thought created invented view, including views using worldly logic, such as LEM. It does not read it is Right View according to reality. Maha-cattarisaka Sutta Thus the learner is endowed with eight factors, and the arahant with ten. A Buddha, an Arahant, has Right View.
This apparent error attempting to use Snp 4.3 to say the Buddha had no Right View is sufficient to support the Right View a Buddha has Right View. Snp 4.3 says That brahmin does not grasp any view. A Buddha has Right View, which is not a formulated view and also not grasped. 
Does diṭṭhigatan mean “convinctions”? This reads very strange. I am sure a Buddha has convictions. The link says diṭṭhigatan means a (false) view, a theory. I might stick to my Access To Insight Suttas.
The verse is relevant to the topic. This verse indicates LEM is an example of formulated view. This verse shows the Buddha did not & could not rely on LEM. The Kalama Sutta says to not rely on logic.