This is a series working from the Penguin edition of Aristotle’s Metaphysics, translated by Hugh Lawson-Tancred.
In chapter two Aristotle addresses an important objection to the project of metaphysics, that is, there is an infinite series of causes. By implication, metaphysics can never adequately arrive at any kind of first cause. Aristotle begins by noting that matter if traced back through its causes eventually reaches a beginning point, so does change, and so does the goal of things when traced forward. Neither last things nor middle things are causes of a series. Last things do not cause because nothing follows them. Middle things, though they cause last things, are dependent on that which comes before them. Without this primary thing there can be no cause.
Aristotle also considers that not all things are caused in a linear series like this. Some things “bend back” (46) for mutual causality so as air causes water so water causes air. In this process, one thing is destroyed and the other is generated, then again. However, that from which water and/or air originated in the first place cannot be destroyed as it is eternal. Not only backwards, it is also eternal in that all things are done for its sake. If there are infinite causes then there can be no “good” at which all things aim. Neither would mind, which acts for the sake of limited things, exist. The next part is quite technical, but from what I understand Aristotle argues that because an infinity of causes has no beginning and thus also no end then tracing the series is impossible to do with a finite mind. Indeed, an infinite mathematical series cannot be known. But this knowledge is not necessary to cognition. Cognition, which is knowledge of causes, would be impossible if the causes were infinite.
I doubt I’ve done Aristotle the grace of understanding him before writing this post. Nonetheless, from what I do understand, there are some important assumptions here underlying his metaphysical project. Aristotle rejects the idea of any existing infinity: “And it is not possible for any infinite thing to exist; otherwise, infinity would not be infinite” (47). To me this is both poetically and logically valid. A truly infinite infinity must extend beyond existence itself. My confusion is with Aristotle’s invocation of an eternal first cause from which and to which all things go. There is probably some important distinction between eternity and infinity in the Greek of which I’m unaware, but initially I see little difference between an infinite series of causes and an eternal first cause. If this first cause is eternal, the source of all, and thus unlike any other cause we know then how can we be sure that it does not consist in an infinity of other causes, those obviously not open to human cognition!
Another assumption is that the source provides the end. But I wonder if it can be said that if the source produces something other to itself then is not that otherness, even if it is an otherness in the minimal sense, that there is something other than the eternal first cause, already the source of another end? Is it quite possible that this first cause is swallowed up in a teleology completely foreign to itself? It could be said that if this is the first cause then nothing foreign to itself could be its teleology because all that exists comes from it. However, this understanding of cause is very linear and assumes that nothing new can come about. That the caused thing is not the cause itself is the beginning of a last thing that differs from its first thing.