Either way, let's say that mechanism was there. It doesn't seem like you have some way to disambiguate why certain empirical events are teleological and others are not. You can postulate that one presupposes a mind having an intention, but that seems to be appealing to some psychological state, not empirical events. — Marty
The human brain certainly has the necessary "mechanism" for inference : for putting 2 and 2 together and inferring 4. But even many animals have that innate ability. And, as noted in the discussion of predators, their application of the ability to predict the near future is self-serving. I'd call that Ego-Teleo-Logy. Tele- means "far", and -logy means "knowledge". So, it literally means knowledge far ahead of now --- specifically, knowledge that is pertinent to me, and to my purposes.
Apparently the human big brain allows us to extend our knowledge of future possibilities much farther into the future than other animals. But even so, such predictions seem to be limited by the Inverse Square Law of physics : the intensity (accuracy) of a prophecy gets weaker as the distance (in time) gets greater. So, human teleology is not very useful for anticipating events beyond a couple of weeks. The farther-off the event, the more general the picture. Beyond a few years, prophets and prognosticators are reduced to predicting history and tautologies.
So, Cosmic Teleology, in the sense of this thread, requires a Mind that is not limited by physical restrictions. But, that would also entail the power of intention : purposeful behavior that is self-serving. The OP was concerned with " the teleological paradox: the parts having purpose but the whole (apparently) lacking purpose." Hence, limited human teleology can only serve short-range purposes or intentions. Only a Cosmic Deity could accurately anticipate "empirical events" billions of years in the future. Consequently, our little short-range self-serving purposes can only overcome the paradox by somehow also serving the Greater Purpose of the Ultimate Teleologist --- with knowledge that is pertinent to all. Which is apparently what most religions are trying to do by simply sucking-up to (worshiping) the One Who Knows All. But, their scriptural guesses about the Ultimate Purpose are also limited by the Law of Illumination --- hence, the paradox.
