Maximum size drive for Mac OS X
SATA Controller

I had something similar happen to me and I seem to recall it was not so much the O/S as it was the controller in the drive caddy.

The drive is probably SATA 3 and the drive caddy is probably a SATA 2. And there are limitations to drive size in various versions of SATA. If you got a drive caddy with a SATA 3 controller (to USB) and plugged it into your Mac it would likely show all 4 TB.

Mac OS X Volume Limits

Your version of Mac OS X supports drive sizes up to ~8 EB (Exabytes). 

See this Apple technical note, Mac OS X: Mac OS Extended format (HFS Plus) volume and file limits.