At least two or more
Is the “or more” bit above ever not redundant? Seems absolutely redundant to me, but it gets about 170 million Google hits, and many from government sites and university sites.
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"...at least two or more..." is a frequently used pleonasm. So are "...at least two, or more..." and "..., at least, two or more ...". Two or more or at least two are the non-redundant equivalent sub-phrases.
However, a Google search for "at least two or more" can also yield this:
But here's the catch---when you bring up Free Transform, at least two (or, more likely, all four) of the handles that you need to resize the image are out of reach.
[The Photoshop Elements 13 Book for Digital Photographers, p. 118], emphasis mine
Why is "at least two or more" popular, despite its shortcomings? A few ideas.
Pleonasms have their uses. If it is vital that the text be understood correctly, even if only scanned in haste, then the formulation in question can be a preferred choice. Utility takes the better of logic.
Related to that, while "two or more" seems clear, people may have some trouble realizing what "at least two" means.
It is conceivable that the expected number or amount is much more than two; in that case, "at least two or more" can be uttered to mean "at least two, or much more". Ideally one would desire a phrasing that elides the numeral "two" altogether.
In spoken language, "at least two or more" can happen easily; one cannot take back what has already been said.
Interestingly, the collocation "at least two or three" is also quite popular, while not a bit less embarrassing from the strictly logical viewpoint. Of course, the collocation two or three can be conveniently used to convey a small but indefinite number.
The movie is worth seeing at least two or three times.
On a related note, we find the following in the New Testament (Matthew 18:20): "For where two or three are gathered together in my name, there am I in the midst of them." Two or three. Does that cover four or more? Again, from a logical viewpoint, yes: if there are four, then there are also three, and two. Why then say "two or three", where merely "two" would have been sufficient? But then, can two actually gather?
While "at least two or three" gives about 32m hits, "at least three or four" gives about 1m. (I cannot resist quoting this:
The Advanced Math Placement Test (MPT-A) is directed toward students who have taken at least three or four years of high school math and who wish to enroll in Calculus. It covers Intermediate Algebra and Pre-Calculus I and II.
[Mathematics placement test, University of Washington, Seattle]; emphasis mine)
Next, "at least six or seven" 174k; "at least eleven or twelve" 6.5k; etc. What is perhaps apparent here is that as the numbers zoom out to amounts indistinguishable by a quick glance (as one cannot, perhaps, tell apart a flock of twelve sheep from that of thirteen), people do not even bother to mention two separate values; it is less and less important how many items exactly are involved.
The trichotomy one / two / many (more than two) is/was ingrained in many European languages via their grammatical numbers (singular/dual/plural). This is how we count.
I suppose it’s conceivable that there should be a situation in which I might want to indicate a requirement of “at least two or more” of something (for example, “Elements of this kind must be defined as requiring at least two or more attributes”), but I’m really stretching credibility here. I’m inclined to suggest that in upwards of 99.9% of those 170 million occurrences this usage will prove to be an inelegant redundancy.
The fact that this concept seems to be a bit difficult for some people to understand amply demonstrates the obscure nature of the stipulation!
The set of “things that require at least two or more of something” may be defined as the union of the set of “things that require two or more of something,” the set of “things that require three or more of something,” the set of “things that require four or more of something” and so on. An unusual thing to want to say, certainly, but not totally inconceivable (in the context, for example, of formal language schemes or similar constructs).
Is that perhaps a little clearer?