Quote from kjkent1:
Pathetic definition, but I'll use it until you move the goalpost.
The court considers motive principally for the purpose of finding that a person had the intent to do an act/omission, which is an element in creating legal liability.
Motive is considered, based on what an objectively reasonable person would do under similar circumstances. Given enough circumstantial evidence, a trier of fact can find that it is beyond reasonable doubt that a certain motive is present.
As with every other issue, there is always the possibility that some alternative, which has not been excluded by the evidence, is actually the truth.
But, the court is not required to exclude every possibility. The burden of proof depends on the ulitmate issue at stake, and at worst case, proof beyond reasonable doubt is all that is required.
Of course, when it comes to you Z, there is no such thing as reasonable proof. There's only absolute proof. Either something is absolutely true, or Z get's to proclaim that it's false, if Z wants to. And if Z doesn't want to, then Z doesn't have to.
This works great for Z, because nothing can be proven absolutely, which means that Z can proclaim whatever he wants to proclaim as true or false whenever he wants to proclaim it.
What will now follow will be another proclamation by Z. Which I will leave stand, because I'm not gonna waste my time, with this for another second.