I understand your logic, but I disagree. The first version is never right. The naming context is clearly the school boards within Montreal. “Montreal” therefore represents the larger set, and the “English” modifier increases the specificity and should be closer to the noun. This also comports with the article that @Colibri linked, where “Montreal” can be associated with the “physical quality” attribute, and “English” with the “origin or religion” attribute. In the given order in which adjectives should appear, the former comes well before the latter.
I agree that the second one sounds much more natural.
Someone who considers “Montreal” to be just part of the unitary phrase “Montreal-School-Board” would naturally say “English Montreal-School-Board” though (this is analogous to what Tolkien did: as a child he referred to a “green, great dragon,” and was told that that was incorrect - so he invented something called a “Great dragon” - so that he could reasonably refer to a “green Great dragon”)
The most interesting thing here is that it illustrates that there are loads of rules in English that we “know” but cannot articulate. It is one of the things that makes linguistics hard, but also interesting.
Every native speaker of English will know the difference between French teacher and French teacher or between the Brown building and the brown building (even if I hadn’t capitalized the first one).
Agreed. Those unspoken, unacknowledged rules are fascinating. Any native speaker can sense the various meanings of “I didn’t say you stole the money” depending on which word was stressed - but no one teaches that explicitly (I count at least 6 different meanings, but I might be missing one).
It also occurs to me that the “English Montreal School Board” thing may not be entirely the result of a pointy-headed bureaucrat whose native language was not English, or who failed to get the assistance of someone who knew better. In the current zeitgeist of contemporary Quebec it may have been quite deliberate, the “English” modifier being placed first because the board being non-French is considered its most important determining characteristic. In that sense it rises from the status of “origin or religion” to the more dominant status of “opinion or observation”, in the manner, say, of a derogatory adjective which would be high in the order of precedence. If this awkward construction is read as “English” being a modifier of “Montreal”, thus “a school board serving only English Montreal” (instead of the general population of Montreal), well, so much the better, n’est-ce pas? Note that none of the other Montreal area school boards have any language modifier in their names, only the “English” one.
Just so it doesn’t get ignored, “The” has similar rules except that it is only the pronunciation that changes and not the spelling. “Thuh” before consonants and “Thee” before vowels. Since it is entirely verbal, it doesn’t get near the attention.
“Thee Ohio State University is thuh home of thuh Buckeyes.”
Although interestingly, this distinction is not universal among the various regional accents even in America. This was discussed in a previous thread as an aside. In my northern Utah accent both are pronounced the same as “thuh” and not “thee”.
I don’t remember which other regions also did not distinguish between the two and I forgot British English was discussed or not.
Speaking of the difference between British and American English, the teachers at my last school almost came to blows over the question if the toy plastic bricks made by the Lego company were to be made plural or kept singular for a speech contest. “Lego” or “Legos”.
Or, as a linguistics professor one told our class, “Every white house is not the White House.”
Does that mean “Every one is not” or “not every one is”? (“For every white house x, x is not the White House” vs “There exists at least one white house x such that x is not the White House”)
And that’s another situation, at least in my dialect, of “the” being pronounced as “thee” – when used as an emphatic. I also remember hearing about a decade ago on some radio program that linguists also found a lot of people pronounced it as “thee” in – I can’t remember the term for it – but hesitated speech, something like “Dad’s out back replacing theeeee … whaddaya call em? Rotors.”
A classic that’s been used in the past to illustrate the inherent difficulties of automatic translation systems is “Time flies like an arrow”. It has an obvious and unambiguous meaning to a native English speaker, but if you open your mind and think outside the box in strictly literal terms, it has numerous nonsensical meanings that are all grammatically and semantically correct. Along the same lines, an actual result of early English-to-Russian machine translation efforts involving the old adage, “the spirit is willing but the flesh is weak” came out in Russian as something akin to “the liquor is still good but the meat has gone bad”. 
fruit flies like a banana.
Out of sight, out of mind= Invisible idiot.
Yes, ‘a lego’ sounds as weird to me as ‘a software’, though I have encountered both constructions several times online.
According to the Lego company themselves, “Legos” is not the preferred construction (heh) anyway. They prefer “Lego” to be used strictly as a modifier, as in “Lego bricks.” The company never uses “Lego” or “Legos” as the noun, either singular or plural.
Not that the manufacturer’s preference has any enforcement weight over colloquial usage. Just a note.
There’s probably a strategic rather than linguistic reason for this. I would think that the usage of “Lego” as a noun carries a greater risk of it becoming genericised, by applying that noun to any interlocking toy bricks, not just those of the Lego brand. If you’re worried about genericisation (because it might lead to a loss of trademark protection in the longer run), then you’d want to promote the attributive usage.
The problem with that argument is that probably both things are true - there’s a French and an English school board within Montreal, and many Canadian local governments have an English school board.
I’m not a native speaker, but I agree that “Montreal English School Board” sounds much more natural (it would be the same in my native German). The only point I could see for “English Montreal School Board” would be if “Montreal School Board” had already been a set phrase before the introduction of the English aspect into it. Suppose the Montreal School Board has been in existence for a long time, and people routinely refer to it - possibly even to “the MSB” in abbreviation, and to stay in line with the topic of this thread, someone sitting on the MSB would be “an MSB member”. Suppose that now, after a long and established existence of the MSB, it is decided to split its responsibilities among two new boards, one in charge of English schools and one in charge of French schools. Then I could see why people would start speaking of “the English MSB”, or, spelt out, “the English Montreal School Board”. But if you were to set up such a body from scratch, it would feel much more natural to call it the Montreal English School Board.
I agree with this analysis.
Or, “Every white house, except one, is not the White House.”
“I didn’t say you stole the money” (implication - someone else said it)
“I didn’t say you stole the money” (simple denial)
“I didn’t say you stole the money” (I sure implied it though)
“I didn’t say you stole the money” (I said Tom did it)
“I didn’t say you stole the money” (I don’t know where you put the money, but I’m sure it’s safe and that you aren’t keeping it for yourself)
“I didn’t say you stole the money” (you stole something - just not the money)
“I didn’t say you stole the money ” (you stole some money, just not the dime we’re we discussing)
I teach a simpler example of “I love you.” that had three separate implications depending on the stressed word.