If you can find a solution it’s no longer a paradox. Paradoxes are defined† as un-answerable. Whoever created the paradox made a mistake and merely created something that looks like a paradox.
“Paradox” is just a word. There is nothing special about something being a paradox (except that paradoxes are cool to think about).
†That’s at least a common definition. That’s where I’m getting such crazy ideas like “paradoxes have no answer.” You are free to define “paradox” some other way. Be assured that it was never my intention to claim that the definition I used is in some sense the true definition. Definitions are all about communication (you need to agree on definitions in order to be able to talk to each other), not tools for finding the truth.
"Mistake" means there is a "right answer", a point of reference. What is that? Otherwise, your use of the concept "mistake" doesn't make sense.
> Paradoxes are defined as un-answerable
Yeah, of course we can define things ad-nauseam. That doesn't just make "reality" any more "real", it just helps us send men on the Moon, curing diseases or building atomic bombs.
If whoever created the paradox had the goal of creating a paradox (as commonly defined) and ends up with something that has an answer (i.e. with something that is not a paradox as commonly defined) that person has failed to achieve her or his goal of creating a paradox. It is likely that the reason for this failure is a mistake the person made while creating the paradox. Other explanations for such a failure are also possible.
That’s the ultra verbose version of that sentence. I can crank the verbosity up quite a bit still but I would rather not want to.
The point of reference you are asking about is the goal of creating a paradox. That was sort of implied but seem to be quite a fan of verbosity. It is, of course, possible that someone – for example – just stumbles upon something that looks like a paradox. The mistake would then be the identification as a paradox.
I’m not really sure what you are trying to tell me with your last point. You started trying to define paradoxes some other way as they are commonly defined. (Quote: “You take as a given that paradoxes are or at least should be ‘un-answerable’.” – thereby implying that according to you definition of “paradox”, the same can have answers.) I wouldn’t have brought definitions up otherwise.
I agree with you that merely defining doesn’t tell you much (maybe nothing) about the nature of reality and said as much. Definitions are for communication, no tool for finding truth. Those tools are the meat of science, not definitions.
“Paradox” is just a word. There is nothing special about something being a paradox (except that paradoxes are cool to think about).
†That’s at least a common definition. That’s where I’m getting such crazy ideas like “paradoxes have no answer.” You are free to define “paradox” some other way. Be assured that it was never my intention to claim that the definition I used is in some sense the true definition. Definitions are all about communication (you need to agree on definitions in order to be able to talk to each other), not tools for finding the truth.