At what point does next Tuesday mean
the next Tuesday that will come to pass
and no longer
the Tuesday after the Tuesday that will come to pass?
And, when does the meaning switch back?
To me, “next Tuesday” means the Tuesday that comes next week. For example, on Monday, October 11 and Wednesday, October 13, “next Tuesday” means October 19. Whereas on Monday, October 18, “next Tuesday” means October 26. “This Tuesday” refers to the Tuesday that comes this week, which on Wednesday would refer to yesterday, and on Monday refers to tomorrow. Similarly, “Last Tuesday” is the Tuesday that came last week. Without any descriptors, day names by themselves mean the next such day in the future unless used in the past tense. “He will do it on Tuesday” means the next time there is a Tuesday, which on Monday would mean “tomorrow” but on Wednesday would mean the following Tuesday. In the past tense, day names mean the last such day which occurred. “He did it on Tuesday” means the most recent day that was a Tuesday.
Not everyone may agree with this analysis, but in my experience this is what most people mean when they use “this”, “last”, and “next” with day names.
This clearly has no definitive answer - usage varies between speakers. To me, "next Tuesday" means (strictly) the next instance of a Tuesday, although I just wouldn't use it on Sunday or Monday (preferring the day after tomorrow/tomorrow or an unqualified "Tuesday", which generally refers to the current week, past or present). However, I accept that this is personal and that others may sometimes mean "the next Tuesday but one", bizarre as that may seem.
This assumes that I know what day it is, which cannot always be relied on.
My preferred use is to specify "this coming Tuesday" or "the Tuesday after next" when I talk about days, specifically because of the ambiguity of what "next Tuesday" could be.
That's just my preference, though.
My answer to another question making a similar inquiry about using the phrase "next week"—
The issue isn't as definitive as you might think. Ultimately, it comes down to what interpretation of "next" you consider to be correct. For example, the American Heritage Dictionary (4th ed) defines 'next' simply as
Immediately following, as in time, order, or sequence
Following this definition, "next weekend" will always mean the weekend with the start date in closes proximity in time. If the phrase is used during a weekend, of course, you'd be referring to the weekend following the one you are currently experiencing.
However, the issue gets more complicated if you look to other definitions. The Oxford American Dictionary has a specific definition for 'next' when used in the context of time:
(of a day of the week) nearest (or the nearest but one) after the present : not this Wednesday, next Wednesday
Here, we're given the choice: it can either mean the weekend with the closest start date, or the following one (as specified by the parenthetical addition or the nearest but one).
This definition has come about mostly because of usage development. Many words and phrases in the english dictionary have meanings contrary to their technical definitions, and yet are still used commonly and considered valid. Thus, while technically "next" implies immediate sequence, it is used in other ways (which dictionaries like the OAD have accommodated for validity), so it's really a matter of personal preference. For example, it is unlikely that I will even use the phrase "next weekend" during the week, because some people might be confused as to what I am referring to. Instead, I will say "this weekend," unless it is currently the weekend, in which case I will say "next weekend."
"next-Tuesday" would be better said as "Tuesday of next week". Thus, the answer to your question would be "on Tuesday".
There are several possibilities:
Some people switch meanings on Tuesday. For example, they mean (1) on Sunday and Monday, but (2) from Wednesday onwards.
Occasionally, I've heard people talking who have different understanding of the terms, but who happen to come to the same conclusion about the date of an appointment!
And then there's "Last Tuesday"... but let's not get started on that one!
All in all, unless you know that you speak the same "calendar language" as someone else (and it isn't always obvious) your best bet is to:
I know someone who would confuse it even further with the usage "Tuesday first" meaning the first Tuesday after today - where most people would interpret that as meaning a Tuesday which landed on the 1st of a month.