It is said that all philosophy begins in wonder; and Leibniz was surely right in insisting that the most fundamental thing to wonder at is why anything exists at all. “Why,” he asked, “is there something rather than nothing? This is the first question which should rightly be asked.” Even if it turns out to be unanswerable, the question is certainly reasonable. Everything that exists (from protozoa and poets to planets and parrots) has an explanation of its existence. It would be very strange indeed if, meanwhile, there were no ultimate explanation for the totality of things that comprise the universe.
However, in seeking ultimate explanations a philosophical riddle emerges—even if we constrain our focus to the ultimate explanation for the existence of a single thing. For we observe that all things owe their existence to some prior thing and we know that the series of causally interrelated things is either infinite or finite. But if the series is infinite, then there is no beginning to or explanation for it; and if the series is finite, then it must come to a stop at some first self-existent thing which, strangely, will not owe its existence to any prior thing. A number of different philosophers and thinkers in a number of different times and places have pondered this riddle and concluded to the necessity of an originating cause of everything in God. 
On superficial inspection, one might be tempted to object to the above line of reasoning as follows: If everything that exists needs an explanation, then God needs an explanation; and if God doesn’t need an explanation, then why does the universe need an explanation? The Cosmological Argument seems to come to grief on the child’s question, “Who created God?”
Leibniz attends to this issue by pointing out that all existent things can be classified into two broad types: contingent things and necessary things.
A “contingent thing” is the most familiar of the two: a thing whose existence is explained by, or contingent on, something external to itself and which could, in principle, have failed to exist. All manmade objects are like this. They owe their existence to whoever created them and it is conceivable that whoever created them could have failed to do so or chosen not to do so. We can easily conceive of a world in which Rembrandt did not paint The Night Watch or a world in which a particular teacup in your kitchen cupboard was not manufactured. You and I, likewise, are contingent: Our parents might never have met or might have chosen not to have children. And things in the natural world, too, such as starlings, sapphires and stars, seem to fall into the same category: It is plausible to think that the universe, having developed differently, could get along without them.
A “necessary thing,” by contrast, is a thing which exists by a necessity of its own nature in every possible world. Many philosophers think abstract objects (such as numbers, sets and propositions) exist in this way. The number 5, for example, is not brought into existence at a discrete moment in time by something external to itself: an integer between 4 and 6 just exists by logical necessity. Likewise “2 + 2” make “4” in every possible world. Unlike poets and paintings and planets, there is no possible world in which the truths of mathematics and logic do not obtain and so each contains within itself the reason for its own existence: It exists because its nonexistence is logically incoherent.
Leibniz formalised all this into his famous Principle of Sufficient Reason: Everything that exists has a sufficient reason for its existence, either in an external cause, or in the necessity of its own nature. This principle is widely recognized as powerful and intuitive. And is, moreover, the way every rational person already thinks—even in the most extraordinary of cases. Suppose that you saw an adult horse materialise out of thin air. You would first seek a physical cause (“It is the work of an illusionist”) or, failing that, a psychological cause, (“I am hallucinating”) or, failing that, a supernatural cause (“It is an act of God”). As a last resort, you might simply give up and admit that you don’t know the cause, whatever it is, but what you would never do is conclude that, “There is no cause.”
Unless it can be demonstrated that the Principle of Sufficient Reason is less plausible than its negation (unless it can be demonstrated that it is more plausible to believe that things can exist without a sufficient reason for their existence) we are rationally obligated to postulate a sufficient reason for the existence of the universe. The question arises whether, like an abstract object, the universe exists by a necessity of its own nature or whether, like a blackbird or a black hole, the reason for its existence is to be found in an external cause.
But very obviously the nonexistence of the universe is not logically impossible. One can coherently imagine our universe being reduced to the size of a full stop and there is no known metaphysical precept or rule of inference preventing us from subtracting from reality that remaining atom of space, matter and energy. The universe is contingent.
Here a skeptic, conceding the point, might be tempted to appeal to the eternality of the universe. For if the chain of causation recedes into the infinite past, then one might argue with Hume that for each and every state of the universe q there is a prior state p which caused it, and so on, ad infinitum, with no state being left without explanation. However, multiplying the number of contingent things, even to infinity, fails to solve the problem.
Leibniz himself anticipates this objection and, in response to it, asks us to imagine a book on geometry that was copied from an earlier book, which was copied from a still earlier book, and so on, to eternity past. “It is obvious,” he says, “that although we can explain a present copy of the book from the previous book from which it was copied, this will never lead us to a complete explanation, no matter how many books back we go.” Even given an infinite series of copies, we will always be left wondering why the contents of the geometry book duplicated in each copy exist to be copied; that is, we will still be left without a sufficient reason for the existence of the book.
Or imagine a man who has never seen a train before and arrives at a crossing as a long freight train is filing slowly past. Intrigued, he asks what is causing the train to move and is told that the boxcar before him is being pulled by the boxcar in front of it, which is being pulled by the boxcar in front of it, and so on, down the length of the train. It is obvious that we have not given the man a sufficient reason for the movement of the train and that his question will remain unanswered even if we tell him that the boxcars are connected together in a circle. Or that the whole universe is cluttered with slow-moving boxcars all intricately interconnected. Or even that there are infinitely many boxcars.
This analogy frames the problem in terms of a causal series but it can also be framed in terms of a simultaneity of causes. The rotation of meshing cogwheels in a watch cannot be explained without reference to a spring, even if there are infinitely many rotating cogwheels.
In The Coherence of Theism, Oxford professor of philosophy Richard Swinburne finds and precisely articulates the problem under discussion: A series of causes and effects sufficiently explains itself if and only if none of the causes is itself a member of the collection of effects. So: If the cause of a lamp lighting up is its being connected to a battery, and the cause of a second lamp lighting up is its being connected to a second battery, then the cause of the two lamps lighting up is accounted for—a principle that would hold even given infinite lamps and batteries. But this principle cannot account for cases where each event is both the effect of a preceding cause and the cause of a succeeding effect. For if A causes B which causes C which causes D, then, strictly speaking, the cause of D is not C but A. In short: An infinite series of causally concatenated events is like infinite number of glowing lamps all wired together in a vast network in which a battery is nowhere to be found. Appealing to an infinite regress of explanations and causes is finally no better than suggesting that, when it comes to the universe, there is no cause or explanation. Both responses violate the Principle of Sufficient Reason.
Schopenhauer aptly dubbed such reasoning a commission of, “the taxicab fallacy.” The Principle of Sufficient Reason is a lynchpin of rational thought for atheist and theist alike and all a proponent of the Cosmological Argument is doing is inviting us to follow it out to its ultimate logical consequence. An atheist, seeing where the Cosmological Argument is leading, cannot simply dismiss the Principle of Sufficient Reason like a hired hack because it has already taken him as far as he is willing to go.
We have seen that denying that there is an ultimate cause and explanation of the universe (either simpliciter, or by appealing to an infinite regress of causes and explanations) violates the Principle of Sufficient Reason. It follows that we are obligated, on pain of irrationality, to postulate a terminus to the series of causes and explanations. But why think that the terminus implicated is God or something like God?
Just as it is possible to make inferences about a writer or painter from his or her artistic output, so it is possible to make inferences about a cause from its effect. And what can we infer about the cause of the universe from its effect? We begin to answer this question by asking another: What is the universe? The universe is all existing space, time, matter and energy. And it follows by inferential necessity that the cause of the universe is an immaterial entity that lies beyond space and time.  Only two things fit this description: An abstract object and God. And abstract objects (the number 14, the set of all right triangles, etc.) are causally inert and so cannot possibly be capable of creating all of physical reality. The entity implicated by the Cosmological Argument is therefore God, or something like God: a Necessary Being that transcends physical reality and is of unimaginable intelligence and creative power.
 Ancient Greek philosophers developed the cosmological argument into clear form. Christian, Jewish, and Islamic traditions all know it. And it can be found in African, Buddhist and Hindu thought as well. It is, moreover, studied and defended by contemporary philosophers and remains influential—in some cases, surprisingly so. Alasdair MacIntyre, for example, is recognized as one of the most important Anglophone philosophers of the 20th century. He claims that he converted to Catholicism, “as a result of being convinced of Thomism while attempting to disabuse his students of its authenticity.” (Thomism being the philosophy of Thomas Aquinas of which three versions of the cosmological argument are an integral feature). And the philosopher Edward Feser tells a similar story.
 The Cosmological Argument is reducible to the proposition, If a contingent being exists, then a Necessary Being exists. Copleston argued that this is a logically necessary proposition but not, strictly speaking, an analytic proposition. And this is because it is logically necessary only given that there exists a contingent being, which has to be discovered by experience, and the proposition, A contingent being exists is not analytic. “Though once you know that there is a contingent being,” he emphasised, “it follows of necessity that there is a Necessary Being.”
[*] This is a shortened version of a longer discussion of the argument given here.