Lumens don't 'add.'
Here's 2 CFLs with a lux meter sensor within 2" of each.
Here's the meter reading one of the two CFLs as pictured above:
huh, they're almost exactly the same....
So, am I fucking retarded, is my lux meter fucking retarded, are my CFLs fucking retarded or is the science fucking retarded?
Note the glaring omission of the possibility that YOU could be fucking retarded...
So, as Dr Julius Sumner Miller would say-
WHY is it so?
Luminous intensity (in lumens) is a measure of brightness. Putting a lamp next to another makes it no brighter. The lux meter is reading the intensity of the brightest light source- it is not counting the number of photons.
Luminous intensity in parallel is a lot like voltage in parallel. You get the same voltage/luminous intensity but you can source more current/light more area at the same voltage/same luminous intensity. However, it's not possible to add luminous intensity in series as one can add voltages of batteries in series. If you want more luminous 'voltage' you have to get a higher 'luminous voltage' single source- aka a more intense light... like HID.
The lumen unit measures the energy of or 'push' behind the photons, not the quantity of them.
1x or 1,000,000x 1750 lumen CFLs over a certain area will yield 1750 lumens. You can cover more area at 1750lm with your million 1750lm CFLs, but none of the lights gets any brighter than 1750lm.