Should a stereo soundstage be 3D or 2D?


I read several people talking about a “3D” soundstage. The main purpose of stereo is to provide left-right separation between different sounds in a recording (a “wide” soundstage). I understand that when properly set up, there is also front-back separation (a “deep” soundstage). So there are certainly two dimensions. Where is the third? Will a stereo system provide up-down separation as well? What is the technical explanation?

Thanks for the help!
128x128saintsaens_op61
Thank for the helpful responses, everyone. @williewonka , I like your explanation of how the 3D soundstage provides a “sense of space”. That makes more sense than the speakers providing definite vertical separation. 
I have never been to a live performance (orchestra, acoustic etc) where I perceived front to back cues.

I imagine that any front to back cues that may exist in our systems and recordings has more to do how the recording session was mic'd.  But it is my opinion that is not how live music sounds.
@rodman99999 thanks for the Audio Check link! Just now, I did the LEDR test with my headphones, and I could hear the test tone move up in an arc, in addition to left to right. 
@jderimig

That is very true, thus the paradox of live vs recorded music. We are so far from replicating a live performance still, I think the only way we can ’think’ of doing so is with these spacial cues. And I am just as guilty of that. I want and need depth (sound coming from behind and in front of the speakers), height, width, etc. as for most of us it creates an illusion of space, a room, a ’soundstage’. When a recording wasn’t mic’d or engineered to offer that, it displeases me.

As you say, rarely in a live performance do those spacial cues exist. But the difference is that ’we are there’, we can perceive the space and separation with our eyes, whereas in reproduced audio, we only have our ears.

It is odd, but I think most of us strive for that ’3D’ imaging during playback.

Interesting, when I watch the Berlin Philharmonic live on my TV and system in 5 channel HT mode, I’m not as critical about those things (stereo imaging) as I’m also watching the performance, and as the sound is all around me, also not realistic. But none-the-less, enjoyable. Funny how I cannot listen to only music in that mode.
Perhaps the reason why some live concerts appear two dimensional is because of the two really large "walls" of speakers each side of the stage.

Even orchestral concerts are mic'd these days - but if you get in the right concert hall, you will definitely hear depth and height(i.e. sense of space) from a live performance.

The live recordings made in churches and smaller halls tend to exhibit more front to back and a greater sense of space. I have several tracks that excel in making you believe you are right there in the midst of things when played on a two channel system.

One of the better rock recordings that also provide the grandeur of the hall it was "supposed" to have been recorded in is "The Best of Supertramp". A fine example of studio sound engineering at its very best Dire straits also has some great live recording.

Regards - Steve