If it could be shown that some progeny could not be related to its parents through set theory, then common ancestry would be wrong. In the "common designer" argument, for example the arrangement and changes in DNA could be (are allowed to be) mixed up by either random patterns or patterns that violate set theory. This case has never been observed in nature.
However, the "common designer" idea itself could never be falsified because the first step in falsifying any designer is to specify the abilities and limits of the designer which is the exact opposite thing "common designer" proponents are trying to do.
However, the "common designer" idea itself could never be falsified because the first step in falsifying any designer is to specify the abilities and limits of the designer which is the exact opposite thing "common designer" proponents are trying to do.
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