Without reading the thread:
Next Saturday means “Saturday of next week” to me. At least in theory. In practice I try to always use the longer construction because it is less ambiguous; some people use “next Saturday” to mean “the next day that is Saturday, regardless of what week it is.”
What is this “weekend” of which you speak?
That’s Friday (the 7th), Friday week (the 14th) and Friday fortnight (the 21st).
My Dad once told me there would be a party “Next Saturday”. He meant the upcoming Saturday.
When the confusion arose, I asked why he used the word next. Had he said “There is a party on Saturday” I would assume it means the one coming up, and not that we would be traveling backward in time to some other Saturday, it would be the next day called Saturday.
An event on Saturday means the one coming up, because time is linear. “Next Saturday” contains a modifier to tell you that it isn’t the Saturday you would just use the word “Saturday” for, but it’s the next one.
Saying “Next Saturday” to mean the upcoming one is misleading. If you just say the event is on Saturday, it’s clear to all that it is not in the far future or in the past. “Next Saturday” means “The Saturday after the one I would just call Saturday”, hence the next modifier.
The statement “Next Saturday” is basically an ambiguously shortened statement:
It could be the shortened form of “The next Saturday to occur after today.”
It could also be the shortened form of “The next Saturday to occur after the next Saturday to occur after today.”
Assuming that the recipient of your comment knows what the actual day of the week is (and this assumption might very well be mistaken) and that you also know what the actual day of the week is (and this assumption might also be mistaken), then the following are likely scenarios:
A) If today is Sunday, Monday or Tuesday then many (perhaps most) people will assume you are shortening statement 1.
B) If today is Wednesday, Thursday or Friday, many (perhaps most) people will assume you are shortening statement 2.
C) If today is Saturday, almost every person will assume you are shortening statement 1.
So, in my opinion, it is best to clarify the “Next Saturday” statement. I also feel that the burden to clarify falls equally on all parties when the statement “Next Saturday” is used.
Some folks feel very strongly that their method of shortening (always 1 or always 2) is the correct and only proper method. These folks often feel that the recipient of their shortened statement is “dense” if they disagree. It might be “uncomfortable” clarifying with these folks, but should still be done.
So, to me, saying “Next Saturday” is like telling someone that “there are two groups of items, totaling six items.” This statement could, of course, mean there are two groups each consisting of 3 items. It could also mean that there are two groups, one consisting of 2 items and the other consisting of 4 items. (Let’s not even try to cover the people that think groups can consist of one item. [Or the people that believe the ‘totaling’ could be applied to the individual group quantities which means there are 2 groups of 6, obviously]) :^)
And then, holding that it really “should” be clear to all what is meant, because (pick i or ii):
i) The “norm” is to assume that groups are “differently sized” unless it is clearly stated that they are “identically sized”.
ii) The “norm” is to assume that the groups are “identically sized”, unless it is clearly stated that they are “differently sized”.
Just my two cents…
I always say “the first Saturday that one would encounter travelling forward in time from this moment”. 