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There is quite a bit of fun in building a little web of questions and answers throughout StackExchange. (Let's call it an exercise in interdisciplinarity.)

"Molecular biologist Robin Holliday has written that the apparent lack of biological wheels argues against creationist or intelligent design accounts of the diversity of life—for, free of the limitations imposed by evolution, an intelligent creator would be expected to deploy wheels wherever they would be of use." (See Wikipedia.)

Now, that (let's call it A) didn't strike me as particularly strong argument, given that there are other (potential) explanations for the apparent lack of wheeled animals. One consists in the developmental and anatomical constraints (B), and another one consists in the disadvantages of wheels (C).

Therefore, I asked for an explanation on Biology SE and stipulated that I would like to see included in the answers what assumptions would be falsified once a wheeled animal would be discovered, hoping that that will produce thoughtful answers. However, perhaps I myself just didn't think about this enough.

In the meantime, however, it struck me that one can get a bit philosophical about this. In particular if one asks: How many correct explanations can there be for something not to exist? Must they be dependent? Must they be independent? Is an explanation the same thing as a reason? Etc. I vaguely recall that some philosophers like to discuss unicorns, and this seems related.

So, I ask you, can you please shed some light on the exact logical structure of this problem, as the use of formal logic seems appropriate?

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From a purely mathematical-logic point of view, if we take for granted that "not X" is true, then any implication of the form "if Y, then not X" is also true, regardless of what Y is - or whether Y is true or false.

So, if we take for granted that wheeled animals don't exist, then any argument will suffice to demonstrate the fact, and the argument will be valid.

If the question is, instead, about arguments leading to the conclusion that the existence of something is impossible... the situation becomes much more difficult. It's not at all clear that wheeled animals are an impossibility, for one thing. In fact, it seems hard to even relate such a question as the one you propose to this interpretation: the original argument assumed that the existence of wheeled animals was possible. If it isn't possible, there is no basis for the other argument.

Now, you may object to taking false Y as reasons for X, a known truth. This could be justified by a broader understanding of "reason", which requires that the reason be sufficient and necessary. In that case, any true Y will suffice, since Y iff X holds for true X in exactly the case that Y is also true.

To summarize, I guess what I'm getting at in a roundabout sort of way is that if we take for granted some claim, there's no difference between a reason, an explanation and a description. Only as long as the possibility exists that not X can there be reasons given supporting the likelihood, or even necessity, of X.

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