I can't think of a situation where I would accept one but not the other of "there exists x such that ---" and "for some x ---". Do you have an example?
Godel has a very interesting paper about syntax for intuitionism, where he introduces a new operator read "there exists constructively."
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 Chr
Update: Discussion has moved on to a new thread.
The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: