Why is it that...

If I ask a person "Does superman exist?" Most would answer "No".
And if I ask "Does the 5th symphony of Beethoven exist?" Most would answer "Yes".

If one was consequent as a person, shouldn't he either answer to both questions either "yes" or "no".

Both are products of somebody's fantasy. Now there are lots of philosophical discussions on the topic of "Is a fantasy something real and therefore exists".
But if you had a opinion on that in one way or the other way, then one should stay consequent and answer both questions on superman and Beethoven's symphony with either "yes" or "no".

Still to most people (also to me) it is natural to say that superman does not exist and beethoven's 5th symphony does exist.

Multiple definitions of "exist": people tend to assume you mean "does superman corporeally (currently or historically) exist" since (like with the 5th) asking if it conceptually exists is a no-brainer (as is physically, but less so as I will demonstrate soon); you are taking it as "does superman conceptually exist". I think this explanation creates the question, "can anything not conceptually exist when one asks if it conceptually exists"? No, imo:

Does blagla conceptually exist?
What is blagla?
The idea of red shoes floating in space.
Apparently it does now.

Think that covers it.

This is what I also thought about.

But then the word 'exist' and 'exist' are thus two different words.
Now I start to wonder if there is any language in this world that really has two different words to use for these two questions.

Adverbs/adjective exist for a reason.

Too much vocab makes learning a language a pain and creates unnecessarily high hurdles for new adopters. Merging two more common words via grammar makes sense pragmatically. There might be two English verbs that would work. "Live" would imply corporeal existence. I think here the problem is that there's going to be some ambiguity on the object of the verb which needs to be sorted out either by modifying the verb or the object with another term" "The idea of superman" or "conceptually exist". We don't usually ask if things conceptually exist, and I think the reason is it's likely due to the reasons I outlined above in my dialogue. Why create a verb to ask a question no one would ever ask?

It's late, so I might be off my rocker on this. Sleeping pills and such.

Uh, like DDNK said, it's impossible for a concept to not exist conceptually. Thus, having a verb for that would be utterly pointless.

Making the difference does not come from the verb, it comes from the subject. If you wanted people to have that in mind, ask "does the story of Superman exist".

By the way, it's actually not about material vs conceptual, it's about something else. Ask wether Beethooven's 3592785th symphony exists, and the 5th one suddenly looks very substantial, doesn't it.

Does this mean that you have a concept for the set of all sets that are members of themselves?

There's the problem. An entity called Superman does exist. The question is, in what capacity: as a fictitious construct or a living being?

The empty set.

people with properly functioning brains can differentiate between fantasy and reality.

Well, they may differentiate but a brain does not depict reality, the brain's perceptive regions will add to the information it receives from the sensory organs...and generally it will do so pending on the context of the received information. Roughly speaking your brain generates your reality.

Here is a nice little TED talk on the issue: http://www.ted.com/talks/beau_lotto_...ow_we_see.html

Classic example:

"Roughly speaking your brain generates your reality."
Well, it creates our phenomenological reality, which is based on reality but isn't 100% exact. We even have the capacity to understand how our brains trick us into seeing things that aren't actually there (or not see things that are there).

Sure, we should study and acknowledge the limitations of our brains, but going as far as implying that reality is subjective is just a simple equivocation and an abuse of the word "reality" (I'm not saying that you implied that, but there are schools of thought that do so and your statement can certainly be read that way).