She would also kill Madoka if 1=2, by the principle of explosion. So what?
If Homura was going to kill Oriko because there are counter-factual worlds where Oriko kills Madoka, she would have already done it. She knows the answer to that question, she lived through it. We only care about things that are possible here and now in the world that actually exists. By the normal, common interpretation of "lie", it is not a lie for Oriko to say that she will never kill Madoka.
No, it only requires Oriko to be capable of making agreements and sticking to them. The tiny fraction of futures where it might actually be be better to kill Madoka is worth very little, she is perfectly capable of trading that away for something worth more to her. That would fulfill even an unreasonably strict definition of "lie", unless you're going to say that mind control also counts.
I'm not certain what you're saying, but it seems to me you're making a few important assumptions about how a theorical lie detector (we haven't even tried making) would work.
Unless I'm mistaken, the point of discussion is "why haven't we proposed interrogating Oriko under a lie detector?" with the assumptions that doing this
would help.
Not only do we not know whether we can make a Lie Detector, how would it work if we made one, whether Homura would trust in an interrogation with Oriko, whether the way the Detector would work help or
not...
Maybe Oriko would say "No, I will not kill Madoka", hold onto the specific doubt "what if it ever becomes necessary" (becomes then she would do it), the detector would detect
that, and Homu would kill Oriko.
Or maybe Oriko will truthfully say, with the Detector's confirmation, that she believes she won't ever kill Madoka. This gives us no guarantee that Homura will believe her.
That's kind of the deal breaker. There's no reason for Homura to believe out hypothetical Lie Detector. Beyond the fact Oriko could truthfully claim to not want to harm Madoka
and change her mind later, Homura will simply still distrust Oriko because she's Oriko. The Lie Detector won't change that.
There's many reasons why a Lie Detector might not help, and some why it might make things worse. I'd like to try making a Lie Detector (for different reasons), but it's not something we could bring up right now.
So don't ask her that. Instead, ask her if she has any intention of harming Madoka.
Oriko is completely capable of changing her mind.
She could say "no" today, and kill Madoka tomorrow.
The point of the Lie Detector is to help convince
Homura, isn't it? It won't work.
