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:
- 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.
- 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.
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.