Would a true Buddhist engage in the No True Scotsman fallacy?

First, be careful with the word logic. It is easy to see oneself as ''logical'', but for anybody who does not want to pass for a boob, there is no relevance in using the word logical, before any learning about formal logic and natural logic, typically by talking to logicians.

Second, only rationalists claim that logics matter and they fantasize that some of the products of their imagination connect them to ''true reality'' which is some fantasy of going beyond ''appearances'' and ''emotional biases'' and that the various logics is a way to ''communicate clearly'' and a way of ''justifiable knowledge'' which would be a realization one of their deepest fantasy of labeling as knowledge something that is something else that the consciousness of whatever ''objects'' (to speak like the realists) is felt through the 5 senses. This is for the ''secular'' rationalists. For the ''religious'' rationalists, the ''justifiable knowledge'' also include the scriptures that they claim ''are true'' or, let's say, ''are authentic, meaning authoritative'' or ''not altered'' by bad people. In natural languages, their fantasy of ''arguments'', inside a ''debate'' are there to ''support a thesis'' and they claim that, somehow, the adversaries are supposed to changed side once they ''understand the arguments''. When they do not like a statement qualified as an argument, they are quick to label the statement as ''fallacious''. All those quoted words are theirs and mean absolutely nothing.

Third, since you care about what rationalists do and that those people write books, you ''learn'' (to speak like a them) that the various indian buddhisms that you have today have been created by indian puthujjanas, then later on taken by the chinese and the tibetans who created the Mahayana and the vajrayana whose followers -- being puthujjanas -- are bound to love to use bad words to express their bad ideas. The buddha did not create any buddhism. IT is the puthujjanas who created buddhism as their natural tendencies to fantasize a system out of any doctrine they hear or read. Some of those people go even further and try to create, or rather mix, their system with the organization of people, which is typically called a society. Those people love to fantasize that the buddha would worry, or even worse, would agree with their views about some current social issues. Yet, Typically, the only system created by the buddha is the called the vinaya.

Now puthujjanas love to fantasize about what a ''true something'' would be, like you who want to follow your natural tendency of puthujjanas to fantasize about ''what is a true buddhist'', you could say it is the one who at least follows the 5 precepts, but most people are not able to follow those for more than a few days or weeks. You can even be more severe on your ''criteria'' (as if you -- as a puthujjana -- are able to discriminate among people) declare that such a person would be someone who has sati and restrain the senses all day long like a good fortress, day after day avoiding ''the 3 poisons'' of ignorance of the right view, of the path, of the 8 fold path, and, of course, of the lack of engaging in the ''middle way'' which is the presence of aversion and avidity towards the pleasures and pains, (by enjoying the senses or being such an ascetic that even the joy of the jhanas would be seen as inappropriate), like mentioned here https://www.accesstoinsight.org/tipitaka/an/an07/an07.063.than.html . In one word, a true buddhist is a student of the buddha.

No true Scotsman would do such a thing.

The statement above assumes existence of two kinds of Scotsman ,true Scotsman and untrue Scotsman. It assumes people are struggling to be called true Scotsman. True Scotsman is a highly coveted title. The statement silently encourages the person be a true Scotsman. Applying that to Buddhist Sangha, it perfectly makes sense. The statement appeals to conscience. I think the statement can be used to make a valid and wise appeal to both true Scotsman and true Buddhist.

The "Scotsman" type of generalisation consists of trying to formulate a rule which links two pre-existing definitions. In the example you referenced ...

• Person A: "No Scotsman puts sugar on his porridge."
• Person B: "But my uncle Angus is a Scotsman and he puts sugar on his porridge."
• Person A: "Ah yes, but no true Scotsman puts sugar on his porridge."

... there's a pre-existing definition of what "a Scotsman" is, and there's a pre-existing definition of what "porridge" and "sugar" are.

I get the impression that Buddhist dhamma avoids this, by (explicitly or implicitly) inventing new definitions or redefining existing definitions. And so for example when Buddhist dhamma talks about kamma or etc. you can't assume that's a new statement about a predefined already-well-known thing, instead it may be a new definition. Thus, to learn dhamma you need to learn (to understand) new definitions of existing words: what does "dukkha" mean when that occurs in Buddhist dhama, for example? What is considered "skilful" versus "unskilful", and so on?

I think there's an obvious example of that in the Dhammapada, e.g. in the last chapter -- the following is an example of a statement that might seem like the "no true Scotsman" fallacy:

• "Holy men don't get angry."
• "But uncle Angus is holy -- you can tell he's holy, by his matted hair -- and he gets angry."
• "Well Uncle Angus isn't truly holy then."

... but the Dhammapada is quite clearly intending to redefine holiness:

• 393. Not by matted hair, nor by lineage, nor by birth does one become a holy man. But he in whom truth and righteousness exist — he is pure, he is a holy man.
• 400. He who is free from anger, is devout, virtuous, without craving, self-subdued and bears his final body — him do I call a holy man.

See also Sat-Dharma: Buddhism is an (arguably successful) attempt to invent new generalisations which are always true.

I think that Buddhists (even true Buddhists -- who would I be to call anyone a fake Buddhist?) are inclined sometimes to test the limits of these generalisations, for example I've seen questions like:

• If dharma is meant to be evident and here-and-now, then what about the doctrine of "rebirth"?
• If lying is breaking a precept, what about a white lie told to save someone's life from a villain?

Perhaps this question is another example: trying to define (and assert) what a "true Buddhist" is.

I'm sure the Buddha would not have approved of such illogical argumentation

Also I somewhat doubt that the Buddha was a slave to logic -- "Do I exist, or don't I?", or, "Does a dog have Buddha-nature, or not?".

It wouldn't surprise me if logic can be viewed as a example of "skilful means".

It's somewhat up to the audience to make sense of what's being said.

And I think that Buddhism isn't necessarily about making well-defined, legalistic statements of a type that can be tested and disproven; it's not like, "here is a picture", where you might ask, "does this picture match a photograph in every detail: or is the picture wrong?" It's more about providing frames of reference, compass directions, doctrine to help evaluate, structure, classify, and make sense of experience -- this answer is an example of de-emphasising the supremacy of the logical/rational (calling it "fruitless quasi-intellectual speculation").

Do you believe there is one true meaning of dukkha that is valid for all Buddhist dhama?

I'm not sure whether it's that ("one true meaning of dukkha") or the opposite.

• For a start, they say there's no single English-language word that's a worthy translation ("suffering? unsatisfactoriness? stress") -- so instead, for an anglophone, it's a new word to be learned (with a meaning of its own).
• It seems to be defined (in the first noble truth), or maybe the 1NT is merely using it (as a then-well-known word) to characterise other experiences

• It seems to be broad or all-encompassing, for example:

  "Both formerly and now, monks, I declare only stress and the cessation of stress."

  and:

  sabbe saṅkhārā dukkhā

This sounds like Buddhism as a form of perfected dogmatism... you really think that's what it is about?

Google defines "dogmatism" as ...

the tendency to lay down principles as undeniably true, without consideration of evidence

... so no, I don't think that (though I suppose I'm more willing than some are, to consider dogma).

I see it as more of a science, e.g. it identifies experienced characteristics of things, and makes generalisations about relationships between things and between characteristics.

Part of what I find welcoming (about the dhamma as explained in the suttas) is that it claims to be "inviting inspection":

Svakkhato Bhagavata dhammo sanditthiko akaliko ehipassiko opanayiko paccattam vedittabbo vinnuhiti

... and, "good in the beginning".

It's more useful (practical, beneficial, applicable) than some other forms of science.

In particular I see it as a set of (personally) useful (helpful) collection of tools (observations, views), rather than an abstract (impersonal, only-theoretical) set of dogma.

Note that in science it's alright to use logic to predict reality -- that's not called "dogma", it's called a "(working) hypothesis" (see also "faith" -- Andrei's answer maybe suggests that "dogma" is more a character of later forms of Buddhism).

And there's another sense in which it's not dogmatic: i.e. it allows for two forms of right view (mundane and supramundane).

can you give an example of the virtues of illogic

Here's a strawman example:

"Either you love me, and you'll let me skip going to school and stay home; or, you hate me."

I think that's a fictional example or illustration of childish logic, which an adult needn't accept.

SN 7.2 is a sutta about not accepting an insult. I think that in a similar way the Buddha wouldn't necessarily accept someone's logic: for example, "either practice austerities and self-mortification, or backslide into abundance" (instead of which, the Buddha taught a Middle Way).

Logic (as I understand it -- I was taught maths rather than logic or philosophy) is no better than its premises (its axioms); and tends towards black-or-white statements ("Are you logical, or illogical?"); and a closed system of logic is somewhat incomplete.

Other examples of what you called "illogic", and which I'd prefer to call "not constrained by logic":

• The unanswered questions
• The paragraphs which describe A thicket of wrong views
• More generally, views and "attachment to views" can be a type of hindrance or fetter (partly because that becomes a cause of disputes; see also the simile of dhamma as a raft)

Identifying and avoiding the "thicket of views" and characterising it as a "fetter" is an impressive and useful achievement IMO (and an example of not being a slave to logic) -- comparable to cutting the Gordian knot (except kinder and everything).

Finally my personal opinion is that the Buddha described as trackless needn't care to be constrained by logic. Not that the dhamma is self-contradictory, but I once read the following aphorism described as a prière païenne ...

Faites que je me contredise souvent : afin d'être simple et vrai.

... which says that if you have a choice between saying something logically self-consistent, versus saying what's simple and true, prefer the latter.

Also my physics teacher for example taught me to see "first and second order approximations" as useful (practical, admirable, true, and appropriate), rather than as inaccurate.