When are we justified in saying something is possible or impossible?

I saw a clip with Matt Dilahunty yesterday in which he was telling a caller to his show that if somebody says something is possible, they have to demonstrate that it's possible just as somebody would have to demonstrate impossibility if they said something was impossible. My initial reaction was to disagree with him because it seemed to me the default position in most cases is that we should think something is possible until it is demonstrated to be impossible. I was thinking of logical possibility and impossibility at the time. Unless some scenario is contradictory, then it's logically possible. Logical possibility only requires that there not be any contradictions, so as long as no contradictions jump out at you, you're warranted in thinking it's possible. With that in mind, you shouldn't have to demonstrate possibility since to demonstrate possibility, you'd be required to demonstrate a universal negative--there are no contradictions. It seemed to me that as long as no contradictions presented themselves to you, that's all that's required for you to be justified in thinking something was possible.

That was my initial reaction. But there are different senses in which we say things are possible or impossible. Logical possibility/impossibility is just one of them. There's also physical possibility/impossibility. But when is something physically possible or impossible. At first, it would seem that something is physically impossible as long as the laws of nature allow for it and it doesn't violate any of the laws of nature. But consider the question of whether it's physically possible for me to outrun a healthy cheetah. That seems physically impossible, not becuase it violates any of the laws of nature, but because I lack the physical strength in my legs or whatever. I'm not sure how to characterize that. Maybe we could say something is physically possible as long as (1) it doesn't violate the laws of nature and (2) you have the physical conditions to bring it about. If there were just that first condition, then I would think physical possibility/impossibility would be just like logical possibility/impossibility as far as whether there's a default position or what that position is. But given that second condition, that woudl seem to place a higher burden of proof on somebody who claimed that somethign was physically impossible. You'd have to demonstrate or explain somehow why my legs are incapable of allowing me to outrun a healthy cheetah. After all, for all we know, there may be animals in the future that will be able to outrun cheetahs. Maybe gazelles already can sometimes.

Another difficulty with physical possibility/impossibility is that whereas we probably have the basic laws of logic nailed down (especially the law of non-contradiction which is the most important one when it comes to possibility and impossibility), the laws of nature are a bit more complicated. We don't know all the laws of nature, and the laws of nature we do know are only provisional. Take general relativity for example. It does a good job of explaining most things. But we know it can't be the whole pictures because it predicts singularities which are physically impossible. So we know it breaks down at some point and we need a new theory to explain those cases. General relativity is, at best, an approximation. Since we don't know all the laws of nature, it's harder to say whether things are physically possible or impossible. General relativity makes it seems like backward time travel is physically possible, but it may be physically impossible due to unknown laws of nature. (Nevermind whether it's logically possible.) So it seems like physical possibility would have to be demonstrated or justified in some way even if logically possibility doesn't.

There's a third kind of possibility--epistemic possibility. A thing is epistemically possible or impossible when it's possible or impossible for all we know. You could say that backward time travel is possible for all we know as long as there's no reason to think it's impossible. In that case, there doesn't seem to be a big burden of proof for somebody who claims it's possible. As long as there are no known laws of nature that prevent backward time travel, that's enough to say backward time travel is possible for all we know.

What do you think about all this? Do you think the claim that something is possible carries the same burden of proof as the claim that something is impossible? Does it depend on the kind of possibility we're talking about? In general, how would you go about showing that something is possible, whether logically or physically or in some other sense? Does it require demonstrating a universal negative--that there's nothing to make it impossible? Do you think there are ever default positions to certain questions in which we should assume one thing is true until it is shown to be otherwise?