The white one is always hot, the purple and black ones are neutral.
White and grey are neutral. The only exception should be if the wires are in a cable - e.g., a switch loop with white & black but no neutral has to use white for either hot or switched hot, neutral just isn't an option. If you had red and black then it could be some sort of "crazy setup with a cable". But purple isn't a typical wire-in-cable color, so I assume your wires are in conduit as described in Harper's answer.
Colored wires are NOT neutral. No exception there.
So that leaves two possibilities:
- You misunderstood the function of the wires
For example, the purple and black wires might be switched hot and appear dead until a switch is flipped. No current doesn't mean "neutral".
- The wires are connected in a very strange, possibly not code compliant, manner
In any case, figuring out where these wires are going is necessary before doing anything with the wires or replacing the wires. It is impossible to guess what someone else did. If everything is working and you open up a switch and everything looks "normal" then it is normally OK to swap things based on normal expectations. But when you start with capped wires with no known matching switch, you are just guessing. And guessing can be dangerous.
The first thing I would do is get a non-contact tester. They are not 100% reliable - nothing is. But they are generally safer for poking around unknown areas than a tester with open metal tips. Plus you can use it easily one-handed. Something like:
Then figure out what breaker controls the wires. You should find the tester showing voltage on at least one wire (based on your description, the white wire, but I suspect it may be different with a different type of tester) and when you turn off the right breaker you'll find no voltage on any of the wires. Turning off the breaker will be necessary for doing any work anyway, so you might as well figure that out first. Simply knowing what else is on the same circuit might provided clues as to where the wires go.
Then you need to figure out where the wires go. Once you figure that out, we may be able to help explain how it all works - or how the wires in this box should be connected to a light.