When I say "next Tuesday" I mean the Tuesday of next week. So if today's Monday, I don't mean tomorrow. Similarly, if I say "next Saturday", I mean the Saturday of next week. On Monday, I don't mean the day five days from now, I mean the day twelve days from now. I've found that this is not true of everyone, and that there's quite a split in how people perceive this usage. It seems the two main interpretations are "the next X that occurs" and "the X of next week". So to some people, saying "next Saturday" means "the next Saturday that occurs" which may often be the Saturday of this week. On the other hand, to people like me, "next Saturday" always means the Saturday of next week; using the word "next" cannot refer to any day this week. Needless to say, this causes problems.
The OED gives us, under the entry for "next":
Applied (without preceding the) to days of the week, with either the current day or (in later use; orig. Sc.) the current week as the implicit point of reference.
Thus (for example) next Friday may mean ‘the soonest Friday after today’ or ‘the Friday of the coming week’. The latter may be indicated contextually, e.g. by contrast with this, but it is not always clear which meaning is intended.
So the key question here is what kind of scope "next" has (here I don't really mean semantic scope so much as temporal scope). For some people, the frame of reference is the day, for some the week. It seems the key distinction is that last sentence from the OED quote: people who distinguish "this Friday", "next Friday" are going to use the week as the frame of reference, whereas for someone who doesn't use "this X" for days of the week isn't going to have any kind of week association with the word "next"; it will mean what it means in ordinary speech, i.e., the next X that occurs, without any intervening time.
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