Priest (top of page 3 in the PDF above, numbered page 199) suggests an example:

I thought of something I would like to buy you for Christmas, but I couldn't get it because it doesn't exist.

In symbols:

∃ x, (I thought of x) & (I would like to buy you x for Christmas) & [(I couldn't get x) ∵ (x doesn't exist)].

Turning this back into English:

For some x, I thought of x, I would like to buy you x for Christmas, and I couldn't get x because x doesn't exist.

But not this:

There exists x such that I thought of x, I would like to buy you x for Christmas, and I couldn't get x because x doesn't exist.

One could rescue this by claiming that x exists in the speaker's past thoughts but not in reality, or something like that. But then an uncountable ordinal may also exist in the thoughts of mathematicians without existing in reality.