In the Second Way, many Thomists have used Aquinas’ argument in On Being and Essence as what he was getting at. See Chapter four, six paragraphs down: http://www.fordham.edu/halsall/basis/aquinas-esse.html

What he is arguing is that the properties that make a thing what it is and the existence of that thing are separate, but the thing cannot give itself existence (since it doesn’t exist), and so something else must give it existence. But then THAT thing must be the same. And so on down the line, and thus an essentially ordered series (or “per se” ordered, as Aquinas might say) which must terminate in something whose properties include existence itself and thus does not need to be sustained by anything else. So the Second Way is about a first sustaining cause, on the bottom level of reality, happening right now, without which nothing would exist at all.

Damned if I know if it works or not, but I do find it at least a fascinating angle to think about.

To make this work for the world as a whole, it would seem that you have to assume that the world is one big clockwork of essentially related efficient causes. Yet the world also contains accidentally related causes, which undermines the world-is-one-big-clockwork assumption. Even given that assumption, it means that when God creates the world he is not providing an essential, efficient cause but rather an accidental one—winding up the mechanism and then walking away. But that is a role that doesn’t require God: it could be handled by something natural.

At any rate, “essentially related efficient causes” don’t really exist (outside of our thoughts). The argument assumes this type of causation is real so that God is required. On the other hand, accidentally related causes seem to actually exist. Yet, since its allowable to have an infinite series of accidental causes, you don’t need God.

So I think my conclusions still stand.

You say:

The claim that unless there is a first cause of the series there can be no causality in the series, is one without any basis. Why should it be so?

From the book you quote:

There cannot be an infinite regress of (essentially related) efficient causes

The key term here is “essentially related”, which means a series where every member must be in place at all times, as opposed to “accidentally related”, where the previous member no longer has to be around for the next member to work (like a father having a son, who then has his own son, and so on).

Aquinas is arguing for a string of concurrent causes, like the gears of a clock, where each member of the series must be in place at all times. If the clock hands are moving, then there cannot be an infinite number of gears in the clock, because then there would be no motor and the clock would not work at all. The series has to terminate in something that is transmitting the motion down the line.

Aquinas agrees with you that accidentally related causes can in fact stretch to infinity. Here he uses the term “per se” to mean “essentially related”:

In efficient causes it is impossible to proceed to infinity “per se”–thus, there cannot be an infinite number of causes that are “per se” required for a certain effect; for instance, that a stone be moved by a stick, the stick by the hand, and so on to infinity. But it is not impossible to proceed to infinity “accidentally” as regards efficient causes…

Just thought I’d point that out…