Aquinas' Five Ways to demonstrate the existence of God are the epitome of meticulous logical demonstration of God's existence. Aquinas presents them in considerable detail in Summa Theologica and Summa Contra Gentiles, and discusses their implications extensively. They have never been refuted. They are each very strong arguments, and most contemporary philosophers (and many ancient ones as well) who attempt to refute them construct straw-arguments. There is much misunderstanding about what Aquinas actually argued, which often leads to faux-claims to have refuted one or another of the Ways.
The first three Ways are variations on the cosmological argument, which is, loosely speaking, a series of related arguments for God's existence based on the need for a First Cause of one sort or another. They differ in important ways, and approach the need for First Cause in different ways-- the Prime Mover of change (First Way), the First Efficient Cause (Second Way) and Necessary Existence (Third Way). I've posted on the First Way, and I'll work my way through each in time.
The Second Way, like the First Way, depends on the impossibility of infinite regress in an series of essentially ordered causes. Some definitions and observations are helpful:
1) A "series of causes" obviously means a series of things that cause each other in sequence. There are two broad categories of causal series as understood by classical philosophers. One is an accidentally ordered series, which means a series in which each prior cause need not continue to exist for the series to continue. A classical example is a series of fathers begetting sons who beget sons etc. Grandpa may have passed away, but his line continues. This is not the kind of causal series to which Aquinas refers.
The second kind of casual series is an essentially ordered series, in which each cause must continue to exist for the series to continue. The hammer-nail series is an essentially ordered series, in that each cause (the neuron firing, the nerve conducting, the muscle contracting, the hand moving the hammer, etc) must exist for the series to work. If the nerve is cut or the muscle paralyzed or the hammer slips out of the hand, the series stops, unlike the accidental series, in which prior causes (grandpa) can cease to exist and the series continues to work fine.
Aquinas refers only to essentially ordered series in the Second Way.
2) Causation in an essential series does not necessarily imply temporal progression. Causes are understood to be more or less simultaneous with effects. Thus, causes here and now in an essentially ordered series are give rise to effects here and now. This is of vital importance to the Second Way, because Aquinas demonstrates that God is necessary to cause the existence of things at every moment, and the argument has nothing to do with a beginning in time. The Second Way, like the First and Third Ways, have nothing to do with the Big Bang. It works just as well for an eternal universe as it does for one that is finite in the past. In case I wasn't clear (for you atheists), I'll reiterate:
Aquinas' Second Way has nothing to do with the Big Bang.
Therefore, attempts to refute it by claiming that quantum mechanics reveals that something can be created from nothing demonstrate not only abject stupidity about quantum mechanics (a quantum vacuum isn't "nothing"), but demonstrates abject stupidity about Aquinas' argument, which depends not at all on a temporal beginning of existence. Atheists beware.
3) Efficient cause refers to one of the Four Causes of Aristotle which are necessary to explain why something is the way it is (the other three are material, formal, and final). The efficient cause is sometimes called the moving cause or agent cause. The efficient cause is the thing that makes the cause happen. The efficient cause of a sculpture is the sculptor wielding his tools. The efficient cause of a window broken by a falling tree is the tree.
The Second Way proceeds as such:
1) There exist in the world an order of efficient causes. Some things give rise to other things. This is self-evident, as Aquinas says, revealed by the senses.
2) Some of these causes and effects are arranged in essential series (see above)
3) Nothing can cause itself. This is self-evident, of course, but some (Hume) have challenged it, asserting that we can just as easily take the universe itself as brute fact as we can accept God as First Cause. This argument fails, in Aquinas' analysis, because in order to "cause itself" an agent must contain the explanation for its own existence. To use Thomist terminology, an agent's essence (what it is) must contain its existence (that it is). Such an agent could not possibly not exist. But the universe is comprised of things that go in and out of existence on a regular basis, so neither the universe itself nor any of its members can be the First Cause.
4) In a series of efficient causes, the first cause gives rise to the intermediate causes which give rise to ultimate causes, etc. Without a first cause, there can be no intermediate or ultimate causes.
5) If the series of efficient causes were to go to infinite regress, there would be no first cause, which means there could be no intermediate and ultimate causes.
6) But intermediate and ultimate causes exist-- we observe them-- so infinite regress in a series of essentially ordered efficient causes is not possible, and there must be a First Cause.
7) That is God.
Note that Aquinas does not say that "everything has a cause", and thus the Second Way is immune to the idiotic "what caused God" retort (sorry, Richard Dawkins). Aquinas asserts that everything that begins to exist has a cause other than itself. Aquinas argues that everything that is a composite of distinct essence and existence (what it is as distinct from that it is) has a cause. An Agent in Whom essence is existence is prior to the chain of causation, because He (the Agent) contains the explanation for His own existence. In a sense, He is existence itself, and has no need for-- actually, cannot have-- a cause.
Existence Himself cannot have a cause (because any cause of existence would have to exist prior to existence). He can only be a cause.
Aside from the easily refutable Humean assertion that the universe itself is the First Cause noted above, Kant's objection is sometimes raised: the chain of causation to God extends beyond the phenomenal to the noumenal-- to the realm inaccessible to the human mind, and beyond what logic can demonstrate.
Kant's argument is perhaps the most cogent attempt to refute Aquinas, but it fails, utterly, for three reasons:
1) It depends on Kant's concept of noumenal, which is controversial.
2) There are many non-sensible things that exist (numbers, logical propositions, transcendentals such as truth, etc) that exist and can be understood using logic. Logical relations such as Aquinas uses in the Second Way can extend beyond the phenomenal.
3) If Kant's assertion that causation in the universe is ultimately beyond logical analysis, then the Principle of Sufficient Reason is demolished. The PSR is the principle that everything in the universe that exists has a reason for its existence. Nature is logical, so to speak. But if PSR is invalid, which it must be if Kant is right that efficient casual chains cannot extend to the noumenal, then all science and logic is destroyed. If the whole universe can exist without Cause, then anything in it can exist without Cause. Occam's razor prefers "mammals happened without cause" to "mammals evolved". Planets just popped into existence; human beings just are, without need to invoke evolution.
Rejection of First Cause in Aquinas' Second Way is rejection of all science and logic.
A perceptive reader might ask: how does Aquinas' Second Way differ from his First Way?
The Second Way (First Cause) differs from the First Way (Prime Mover) in that the First Way demonstrates that God is necessary for change in nature, whereas the Second Way demonstrates that God is necessary for all contingent things to exist at all.
They both demonstrate God's existence.
I'll post on the Third Way soon.