i thought they said you could it was in the devstream not this last friday but the previous one to that 

i cant check it out atm but i recall them saying you would be able to build one from a contstructor or possibly they were toying with the idea Of buildin from a constructor

Ok I did build a constructor. It does not currently ask for a special purpose. Fun stuff. Will we be able to build starships from Starbases?

I think theres a bit of confusion here

shipyard -  ( planned for an upcoming alpha )

can be built from planet 

can possibly be built from constructor

Can build ships

can move 1 tile per turn while not building ships

starbase -

stationary  ( at least as far as i know)

can be built from constructors

has range effects on military/ economy/ culture

cannot build ships

You could on GC2 and I have not heard anything official that says it can't be done in GC3. The only restriction I have seen in GC3 to date is that a constructor, like any ship, has a range limit (variable based on how much life support is on the ship) and I have not, as yet, heard anything to make me believe this will change. And, since starbases can be used to extend your range, it is possible to build chains of starbases to give you access to the entire galaxy.

Only 5? Are you talking about on a tiny galaxy? On a small galaxy I have built as many as 15. And the support in build 0.20 is still quite primitive and simply there to prove the support mechanics. They have announced that the first Beta build will have almost all of the final release features in it. By reading between the lines in the tentative schedule posted by Frogboy, it looks like we will see much more for starbases in Alpha 3 later this month.