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Does that statement mean:
1.  There exists no thing that is ambiguous?
2.  "Nothing" is an ambiguous term?

You can probably tell from the context that #2 is intended, but it's not always that obvious.  It is important to distinguish the absence of anything from something in which nothing exists.  How about this statement:

Does that mean:
1.  No thing exists?
2.  "Nothing" is a term denoting a concept that exists?

In context or out of context, #1 is absurd; #2 is obviously correct.  This shows the difference between a term and the concept labeled by the term.  Does that mean the term exists, but the concept doesn't?  No.  The concept also exists.  If it didn't we couldn't identify it as a concept.  Does that mean the concept exists, but the thing represented by the concept doesn't?  No.  The thing also exists.  If it didn't we couldn't identify it as a thing.  How long do you want to chase your tail?

See what's going on here?  It doesn't matter what you call it - nothing, absence, null set - doesn't matter.  As soon as you refer to it, it becomes something referred to.  Something, get it?

This is why the Indians took so long to figure out that zero is a legitimate integer.  It's also why Aristotle could formulate a perfectly consistent logic system without a null set.  Thanks to George Boole and his Boolean logic we have the null set, without which our computers couldn't operate.