In recent times, Aristotle is often criticized for holding back the progress of science for two thousand years. (As Armand Leroi argues in his book The Lagoon based on the research of scholars like David Balme, Allan Gotthelf, and James Lennox, this is rather wrongheaded, given that Aristotle founded the science of biology!) One of the ways Aristotle is alleged to have gone astray is in his "doctrine of the four causes" (especially, we're told, the so-called "final cause" which involves impossibilities like backward causation); although I'm always suspicious when someone attributes a "doctrine" to Aristotle, it's worth looking carefully at what Aristotle actually said instead of relying on shallow or antagonistic summaries.
First, even the term "cause" can be misleading, since in modern physical sciences it conjures up images of billiard balls and inclined planes. The Greek word here is αἰτία, which I prefer to translate as "ground": looking at things from the perspective of epistemology, we can ask ourselves about the grounds for explaining why something is the way it is.
Second, the names for the four cases (efficient, material, formal, and final) come from Latin, which always worries me because Latinate terminology often bakes in assumptions from Neo-Platonism and scholastic theology. Let's take them one by one. (I base much of what follows on the fine analysis by Monte Ransome Johnson in his book Aristotle on Teleology.)
The efficient cause maps most closely to our modern notion of causation. The term that Aristotle often uses is ὅθεν, literally "whence" or "from which". For Aristotle, this is the active entity that brings a thing into being or that makes a thing change. Typically this active entity is external to the "passive" entity that is made or changed: the parents make a baby, the builder makes a house, etc. However, the active entity can also be internal: the person who deliberates brings about their own actions. For details, see On Nature (the "Physics"), Book 2, Chapter 3.
The material cause brings to mind our modern theories of materialism, whether reductive or eliminative. Yet let's look at Aristotle's examples from the same book: a syllable is made up of letters, a living body is made up of liquids and solids, a plant or animal is made of its various organic parts (hand, eye, heart, etc.), and even a conclusion in logic is made up of its premises. Clearly, these grounds are not all material in the modern sense.
The formal cause is in Greek the εἶδος or what I prefer to translate as the "way of being" or identity of a thing. The strange technical phrase Aristotle uses is τὸ τί ἦν εἶναι or "what it has been to be a thing", which in Latin philosophy was translated as "essentia" (whence "essence" in English). One example from Aristotle is the musical octave: what it is to be the octave is to have a ratio of two to one. Similarly, the form of a house is the architectural plan according to which it was built. In biology, the εἶδος is a living being's βίος or way of life.
This brings us to the final cause. Many scholars have written books and articles on this topic, but in brief this is what Aristotle calls τὸ οὗ ἕνεκα or "that for the sake of which". Grammatically this phrase can be used with the dative case in the sense of the aim of something or with the genitive case in the sense of the beneficiary of something. For example, Aristotle says that the eye is for the sake of the activity of seeing (the "aim" or function or adaptive value of the eye is seeing); he also says that the activity of seeing is for the sake of the animal that sees because it is beneficial to have sight (e.g., to find food or avoid prey).
Here is a simple example that summarizes these different grounds for a given phenomenon. Think of a feast or a trip to your favorite restaurant: the thing that moves you to go (the "efficient cause") is hunger; the meal is made up out of food and drink (the "material cause"); the activity of eating and of course talking with other people is part of the human way of life (the "formal cause") since we are social animals who engage in discourse; and that for the sake of which you and your fellow revelers participate (the "final cause") has two aspects: the aim is living well (eudaimonia) and the beneficiaries are the people involved. With regard to the last two of these grounds, we can contrast the human way of eating with that of, say, a herd animal like cattle, who graze in the same field but don't have reason-and-speech (λόγος) and therefore eat together for the sake of living but not for the sake of living well (cf. Nicomachean Ethics 1170b11). Here the "formal cause" and "final cause" give different grounds for a similar phenomenon based on the natures of the beings who engage in the activity.
There's much more to say on this topic, of course, but this little outline at least gives a sense of the issues involved.
(By the way, I just finished reading the last book on my list for the research underlying Complete Yourself: Aristotle on Human Fulfillment; now I have only a few dozen individual scholarly articles to work through. I'm getting there...)
FOR FURTHER EXPLORATION
Peter Saint-Andre > Journal