The first talk of this session was by Devin Henry, Western Ontario. Plato and Aristotle's accounts of teleology is seen in the light of the concept of optimization. In the Phaedo Socrates says that we need to inquire into what is the best way for things to be, a research program stemming from the idea that the universe was put together by a mind aiming at what is best (because that mind is supremely good). The universe is the way it is by necessity, because that is the best way for things to be. Finding that necessity explains a given phenomenon.
This idea is seen by the author as the ancestor of Aristotle's ideas on the subject, including that nature does nothing in vain. It also follows that being the best is in accordance to nature. However, there are important differences between Plato and Aristotle. For instance, Socrates makes his argument at the cosmological level, the good is the good of the whole cosmos, not of individuals (indeed, the other way around, individuals are for the good of the cosmos). Aristotle doesn't invoke a cosmological principle, what is good for the organism is good for it, not for the broader context of the cosmos.
A second difference is that Plato clearly speaks of an intelligent designer. While Aristotle's language is full of design talk, his personification of nature is only metaphorical, like Darwin's. Aristotle's form of teleology is seen in his analysis of why snakes do not have legs. Nature does nothing in vain while doing the best for the organism: if the length of a snake is a built in feature, and if no blooded animal can move with more than four points of leverage (as Aristotle thought), then having no legs is better than having some legs (as a centipede type solution wouldn’t work for bloodied animals).
Aristotle even criticized what today we would label a Panglossian view of the world: things are the best they can be, not the best they can conceived to be. (Again, close to the conception of constraints by modern biologists, the author citing the Gould & Lewontin paper on spandrels.) So Aristotle's concept of teleology is based on optimality, not perfection.
In his analysis of male testis, for instance, Aristotle claims that we need to understand the function of the organ in order to understand its form. Again, a remarkably modern sounding connection between form and function. Aristotle was aware that some species of animals (fish) don't have male testis, which means that testis cannot be essential for reproduction, and yet somehow have to make it better in the animals in which they are present. (Aristotle's specific explanation, that testis slow down sperm production, is not the correct one, of course, but the idea is still guiding functional biology today.)
The second talk was by Jeffrey McDonough, Harvard. A teleological explanation purports to explain something in terms of its outcome. In ancient and early medieval periods the range of teleological explanations was broad, including not just rational beings, but living beings more generally, and even features of the cosmos at large.
In Plato, as well as for Augustine and Aquinas, goodness is prior to being: the universe exists because it is good, it isn't good as one consequence of existing. So goodness figures into explanations of why things are. Also, in this view, teleological explanations are just as appropriate, if not better, than efficient explanations.
This ancient view, however, seemed to commit one to some sort of moral necessitarianism, where god simply has to do what is good, in contradiction with the classic Christian view of divine agency. In later medieval and early modern views, from Scotus to Boyle to Descartes, we see the concept of a libertarian will, where one could choose something that is not best. This means, however, that one can no longer explain what the agent does by considering the outcome. It is the will's efficient decision that becomes central to explanation.
This quickly led to philosophers giving up teleological explanations (final causes) for anything that is not a rational agent (god, angels, and human beings). Hence a mechanistic view of anything that is not a rational agent, a la Descartes.
In more modern times, Spinoza is considered the ultimate enemy of teleology and final causes, again, however, with the exception of rational agents. However, Spinoza was also a naturalist, and it becomes difficult to justify limiting teleology only to a particular subset of natural entities. Accordingly, for him there is no sharp distinction between rational and non rational agents. Spinoza also rejected the idea of objective goodness, which means that one cannot invoke goodness as explanatory. For Spinoza we do not strive toward certain things because we think them valuable, but on the contrary we think certain things valuable because we happen (by our nature) to want them.
Leibniz, on the other hand, presented himself as a strong defender of teleology, in important ways arching back to the Greeks. God here does things because they are good, but god has to consider total goodness, and so chooses whatever maximizes good overall, and may not necessarily be individually good. Leibniz therefore opens again himself to the problem of moral determinism (for finite agents) and moral necessitarianism (for god). Hence some of his compatibilist maneuvering when it comes to free will.
Overall, it seems to me that this session was badly titled, as neither talk (and particularly the second one!) had much to do with scientific explanations, certainly not in the modern sense of the term. Oh well.