
MADRED: Yes, I'm sure you have. (he turns on four spotlights behind his desk) How many lights do you see there?
PICARD: I see four lights.
MADRED: No, there are five. Are you quite sure?
PICARD: There are four lights.
MADRED: Perhaps you're aware of the incision on your chest. While you were under the influence of our drugs, you were implanted with a small device. It's a remarkable invention. By entering commands in this PADD, I can produce pain in any part of your body at various levels of severity. Forgive me. I don't enjoy this but I must demonstrate. It will make everything clearer.
(Picard falls to his knees in agony)
MADRED: Surprising, isn't it? Most people feel at first that they can steel themselves against it but they're completely unprepared for the intensity of the pain. That was the lowest possible setting.
PICARD: I know nothing about Minos Korva.
MADRED: But I've told you that I believe you. I didn't ask you about Minos Korva. I asked how many lights you see.
PICARD: There are four lights.
MADRED: I don't understand how you can be so mistaken.
For the sake of argument we're going to assume there are indeed five lights. Now we just have to prove it. Why are there 5 lights?
Here are some ideas I can think of:
1) "Five" in Cardassian language means "Four" in ours
2) 1 light to them means 1 and 1/4th of a light to us. Then do 4*(5/4) = 5 lights
3) Some kind of anomaly is affecting the laws of logic causing the law of non-contradiction to allow 4 to equal 5 but 5 to not equal 4. It's similar to how the gambling devices in DS9 episode "Rivals" affected the laws of probability
4) There's a special characteristic about one of the lights which requires it to be counted twice
5) One of the lights is outside of the visible spectrum of Humans but perhaps not Cardassians
6) When he says "there" in "How many lights do you see there?", he's referring to the 4 lights above him plus some other light in the vicinity of what "there" means.