I think you are led onto a false path partly by the typical problems with natural language that is woefully inadequate for rigorous reasoning.
"Can pigs fly" is a sentence with only three words, but all of them are ill-defined.
Can.
"Can" may mean "able to survive survive" (as in "can humans breathe helium") or "able to perform an act actively" (as in "can I lift a 100 pound weight"). This difference is crucial when we talk about whether pigs "can" fly: The active act is very impossible, but there is a finite chance that they survive flying through the air, depending on the altitude and the manner of landing. How we interpret "can" is connected to our interpretation of the next word, "fly".
Fly.
"Fly" generally only means that something is airborne. Among the possible ways to be airborne is flying by actuating wings, like a bird, or staying suspended on a ballistic trajectory, like a missile, or being suspended from the wind, like a kite. There is probably also a measure of time involved: "Jumping" is not "flying": We are in the air, but only briefly, and then we fall down. Competitions involving "flying" are very careful to define parameters like altitude and duration.
Flying like a cannonball or being lifted by wind is clearly conceivable with pigs. All kinds of objects have been lifted into the air — one of the interpretations of "fly" — by strong winds, among them cows and Dorothy in her house.
Pig.
Are we talking about the Domestic Pig, sus domestica? Or the she mammal suborder suina, a much larger group of animals of various sizes, including possible extinct species? I think none of them could fly actively, but I'm less sure about that than about the sus domestica with which I am reasonably familiar.
The main reason I'm asking is that a wider definition may include future species which may very well develop the ability to fly. Reptiles spawned a flying branch; why not pigs. If we ask whether there is a chance that any pig ever can fly, the answer is certainly yes. We cannot exclude such a development.
Discussion.
If we understand the question "naively", imagining a sus domestica attempting to perform powered flight on a calm day at sea level on a level surface, the possibility is clearly zero: It is impossible. But this is not the only way to understand this sentence. In order to get proper answers you need a clear definition of what you are asking. Part of being specific is whether you are asking about a future possibility (which is implied when we talk about probabilities) and whether you include the past. The past is only imperfectly known; the future is essentially unknown.