(Meta note: the post itself is not really about teleology, that’s just an example. That said, here’s how the tentative answers we give for teleology in the post would apply to your question.)
Insofar as the beak was optimized to consume certain kinds of food, we should find that it’s unusually well-suited to those foods in multiple ways—for instance, not just that it’s big, but that it’s also the right shape for those foods. The more distinct unusual features can be explained by optimization toward the same purpose, the more evidence we have that optimization was applied toward that purpose.
On the other hand, if a large beak resulted from genetic drift or a single mutation which isn’t actually fit, then we would not expect other features of the beak (or the rest of the bird) to also look like they’re optimized for the same foods. (Note that this also applies to “features” at the genetic rather than phenotypic level: genetic drift or a single mutation would not produce a set of mutations which mostly look like they’ve been selected for the same criterion.)
A similar story applies to sexual selection: if a large beak is could have been selected for some foods or could have been selected for sexual purposes (or some combination of the two), then we should go look at other features of the beak/bird in order to whether those other features look like they’re optimized for the same foods.
(Meta note: the post itself is not really about teleology, that’s just an example. That said, here’s how the tentative answers we give for teleology in the post would apply to your question.)
Insofar as the beak was optimized to consume certain kinds of food, we should find that it’s unusually well-suited to those foods in multiple ways—for instance, not just that it’s big, but that it’s also the right shape for those foods. The more distinct unusual features can be explained by optimization toward the same purpose, the more evidence we have that optimization was applied toward that purpose.
On the other hand, if a large beak resulted from genetic drift or a single mutation which isn’t actually fit, then we would not expect other features of the beak (or the rest of the bird) to also look like they’re optimized for the same foods. (Note that this also applies to “features” at the genetic rather than phenotypic level: genetic drift or a single mutation would not produce a set of mutations which mostly look like they’ve been selected for the same criterion.)
A similar story applies to sexual selection: if a large beak is could have been selected for some foods or could have been selected for sexual purposes (or some combination of the two), then we should go look at other features of the beak/bird in order to whether those other features look like they’re optimized for the same foods.