In my own studies, I have embraced a particular argument for God's existence that I find utterly convincing.  And any non-theist open to the evidence should have little difficulty coming to the same conclusion when brought into contact with it.  Here is how the argument goes:

Premise 1: Everything that Begins to Exist has a Cause for its Existence.

The first premise in the kalam argument claims to conform with the general uniform intuition that things just do not "pop" into existence uncaused. Nothing in nature or in the theoretical sciences have been able to push for an incredible belief that something can or did mysteriously "pop" into existence without the aid of a cause. Such a premise has usually gone on without much debate. It just seems to be a veridical reality that everything that exists has a cause for its existence, and if it does not then we would naturally begin to probe such a fantastic claim. It makes no sense to suppose that we can derive the first notion that everything which begins to exist has a cause via experience unless something non-experientially distinguished this notion to begin with. But even if one denies the a priori category of the causal principle, it still strongly appeals to the intuitions of even the most ardent skeptic. Natural philosopher and empiricist David Hume once made in a letter to John Stewart in 1754 an interesting admission:

    But allow me to tell you that I never asserted so absurd a Proposition as that anything

    might arise without a cause: I only maintain'd, that our Certainty of the Falshood of

    that Proposition proceeded neither from Intuition nor Demonstration; but from another Source.
 

This implies that even one who questions the validity of cause-effect relationships has to admit its veracity in order to remain rational in accepting it. I suppose that even empiricists unite on the most basic of beliefs when it comes to obvious truths such as this one. Therefore, without having to spend too much time and energy dealing with what could only be criticized in a philosophical vacuum and not in the real world, the premise that everything which begins to exist has a cause for its existence seems to be a well-established principle underscored by experience.

Premise 2: The Universe Began to Exist.

This premise is perhaps the most vital organ of the kalam cosmological argument and, if removed or refuted, would certainly put this argument into academic arrest. There would be no need to worry about a clearly intuitive notion that everything which begins to exist has a cause for its existence since the other leg of the argument would be undermined. This simple statement, yet one which has been the target of both philosophers and scientists, is the key to a sound deductive argument whose implication is to believe in an ultimate cause of the universe. Defenders of the kalam argument have split the support for the belief that the universe began to exist into two categories: (i) Philosophy shows that there cannot be an infinite regression of time since that would imply the absurd notion that an actually infinite number of things exists in the real world. (ii) Science shows us through the best astronomical model of the origin of the universe and through the Second Law of Thermodynamics that the universe began to exist. If at least one of these independent categories turns out to be true, then we have no rational choice but to concede the truth that the universe began to exist. So we will now take a closer look at four divisions of these two categories and why no rationally thinking person should reject them.

(A). It is impossible to have an actually infinite number of things. Zeno of Elea, born around 489 B.C., arguing against the Pythagoreans, asked us to imagine a race where Achilles and a tortoise are going to compete. Achilles, being the sportsman that he is, grants the tortoise a head start. But when Achilles begins his run after the tortoise has reached a certain distance then the supposition that a straight line on the racetrack has an infinite number of points promotes a paradox. Zeno shows that Achilles, in order to catch up to his opponent, must first arrive at the point where the tortoise was. In so doing, the tortoise naturally has advanced to another point on this racing line. Even if the tortoise only moves a relatively short distance, Achilles still has the task of reaching that point before proceeding any further. But, again, the tortoise has already moved on to another point on the line. On the surface, Achilles seems to be closing in on the tortoise, but since he must first traverse the same points already covered by the tortoise then he will never overtake his opponent. In order for Achilles to catch up to the tortoise he must approach those points already traveled by the tortoise. But when Achilles makes his move the tortoise is also moving toward additional points on the race line. And Achilles must reach those points before he can at least catch up to his opponent. But since the tortoise is obviously not going to stop but keep running, then Achilles still has the task of reaching those same points that the tortoise has already covered.

Therefore, if an actually infinite number of things really exists then such a number results in self-contradictory answers. Zeno's paradox shows that there cannot really be an actual infinite since this would imply that a lagging racer could never reach his winning opponent no matter how long he has and how slow the winner moves. These considerations rationally force us to suppose that an actual infinite is just an idea in the mind and not something that exists as a property in reality. Since time itself is a set of discrete members partitioned by seconds, days, years, and so on, then time must be a finite set of members. This means that the universe must have begun to exist.

(B). It is impossible to obtain an actually infinite number of things through successive addition. Analytic philosopher Bertrand Russell (1872-1970) believed that an actual infinite could be achieved through successive addition as long as the counter possessed an actually infinite number of years to accomplish it. In the example given in Sterne's novel, we have the example of Tristram Shandy. Sterne writes about Tristram Shandy as an extraordinarily slow individual committed to writing an autobiography. However, he is so slow that it takes him one year of writing in order to complete only one day of his personal history. This means that the most recent event that could be recorded is the day that occurred only one year ago. As Shandy writes an additional day, it takes him an additional year to completely write about the events of that day. Russell believes that an actual infinite can be achieved through successive addition only if Shandy has an infinite number of days to complete it. His argument is that given an infinite number of years to write plus the infinite number of days written about results in an infinite amount of time actually transpired. Thus, the amount of time to write (if obtained) would be equal to the amount of time given to write about. My observation of the matter seems to yield two problems with Russell's justification.

First, if we observe what is really going on in the paradox then it becomes apparent that it is logically unsolvable and not merely epistemologically unsolvable. When we see that for each day there are 365 subsequent days of writing, then I fail to see how Shandy "catches up" on the autobiography. Mere comparisons of infinite sets and subsets bespeak the paradox's lesson. It is precisely because an infinite proper subset equals an infinite set why successive addition fails to obtain. It appears, then, that we are discussing two different worlds: the finite and the infinite. So, if we uphold the principle of correspondence then it would appear that Tristram Shandy falls behind with each additional day he must write on. This makes the task unending.

Second, if we grant Russell's solution by granting immortality to Shandy, then it would appear that the problem is merely extended instead of solved. In other words, there is no reason to adhere to an actual infinite via successive addition by simply pushing back the length of the task to the time of the task. The question now becomes, "Will temporal segments of duration through successive addition arrive at an actual infinite?" Would we not still be dealing with successive addition to the infinite? At this point it would be absurd to respond by suggesting that such an achievement is based on finite time because the argument now concerns time itself. Therefore, it would be question-begging to merely extend the problem. These reasons constitute evidence as to why an actual infinite cannot truly be achieved by successive addition.

(C). Astronomical observations demonstrate that the universe began to exist. In 1929, Edwin Hubble made a remarkable discovery. During his examination of the light spectrum from various galaxies, he began to see an interesting pattern indicative of every galaxy he would observe: galaxies have redshift. This means that the light observed in the light spectrum of those galaxies is shifted toward the red end of the spectrum. When we match this observation with the so-called Doppler Effect (the rule that wavelengths, when they are "approaching" an observer, are shorter while wavelengths, when they are "receding" from an observer, are longer), we can ascertain that the galaxies are receding away equally from our earth (where our observers reside). This means that since all galaxies are receding away from us in all directions equally then, if we were to go back into time, we would eventually come to a point where all physical mass would be concentrated at a single point. This point is called the singularity. All technical calculations aside, astronomers and astrophysicists are confident that their calculations of the expansion rate of the universe and the distance of galaxies suggest that the universe must have begun to exist about 15 to 20 billion years ago. The physical evidence in this case points convincingly toward a universe whose age is marked in finite terms.

(D). The Second Law of Thermodynamics points to our universe as having begun to exist. Natural science has also been the friend of theism in many respects. Most interestingly, nature has been governed by laws that consistently operate and maintain the modus operandi of the interrelations between the natural world and causal principles. Natural laws serve to represent, under ideal conditions, how events are going to turn out given the sum of the particular event in question and the over-arching governing law. One of the best attested natural laws that so widely pervades the realm of science is the Second Law of Thermodynamics. Without this law we could not expect to take a warm bath or properly scent a house with air freshener. The Second Law entails two components of energy transfer: Temperature and Entropy. While temperature is a more familiar concept, entropy is more enigmatic since it is a term that is tossed about in various circumstances under different pretenses. Quite simply, entropy is a measure of the unavailability of some energy to do work. So the less energy that exists to do work, the more entropy there is in the closed system. In addition, the correlation between entropy and disorder is such that where entropy is increased, disorder is proportionally increased. In regard to high-temperature energy systems (should the system be isolated), heat energy would eventually spread out over time throughout the system it inhabits. Once the dispersion is complete (or equilibrium is reached) then the energy begins to minimize until the energy "runs out." For example, suppose we enter a room where a cup of coffee is sitting on the table. Knowing that coffee is originally brewed hot, we sip it to see if it has been sitting out for any period of time. Upon taking a sip should it taste cold, then we know that the coffee had been placed there some time ago. If the coffee tasted very hot, then we may surmise that the coffee had just been poured. But the fact that the coffee is either hot or cold tells us that, given the nature of coffee when it is made, it had an origin. The question about whether or not to apply the Second Law of Thermodynamics to the universe has been answered differently by a variety of astrophysicists. They maintain that the Second Law can only be applied to the universe if it is a closed system (i.e. a system where new energy is not being added by any outside source; this is not to be confused with the notion of a closed universe). So, in order to retain thermodynamic relationships within the universe it must first be understood that the universe is indeed a closed system, but more likely an open universe. Concerning the universe's fate, Dr. Beatrice Tinsley, in a Natural History Magazine article entitled "From Big Bang to Eternity", vividly describes its inevitable outcome:

    If the universe has a low density, its death will be cold. It will expand forever at a

    slower and slower rate. Galaxies will turn all of their gas into stars, and the stars

    will burn out. Our own sun will become a cold, dead remnant, floating among the

    corpses of other stars in an increasingly isolated Milky Way.
 

Theoretical physicist Paul Davies, in his book God and the New Physics, makes this argument:
 

    If the universe has a finite stock of order, and is changing irreversibly towards

    disorder - ultimately to thermodynamic equilibrium - two very deep inferences

    follow immediately. The first is that the universe will eventually die, wallowing,

    as it were, in its own entropy. This is known among physicists as the 'heat

    death' of the universe. The second is that the universe cannot have existed

    forever, otherwise it would have reached its equilibrium end state an infinite time

    ago. Conclusion: the universe did not always exist.
 

These observations about the Second Law of Thermodynamics when applied to our universe show how the universe must have begun at some point in history. It would be false to suppose that the universe existed infinitely and yet had not used up its energy. In addition, the fact that the universe is still moving toward a state of energy loss entails that the universe began to exist some finite time ago. As Davies explained, an infinitely old universe would already have reached a state of equilibrium. Therefore, the Second Law of Thermodynamics proves that the universe began to exist a finite time ago.

Premise 3: Therefore, the Universe has a Cause.

If it is true that the universe began to exist and that everything that begins to exist has a cause for its existence, then it follows inescapably that the universe has a cause. But how does this import into the question of God's existence? The answer is found in the nature of the cause itself. Consider that if the cause precedes the beginning of or resides apart from the physical universe then it seems rather obvious that the cause must be non-physical or incorporeal. Plato, in the development of his theory of the incorporeal Ideas and Forms, once noted that the presence or status of materiality implies spatial existence. But, as Frederick Copleston notes in volume one of A History of Philosophy, "[There is] no question of the Ideas being in a place, and, strictly speaking, they would be as much 'in' as 'out of' sensible things, for ex hypothesi they are incorporeal essences and incorporeal essences cannot be in a place." Since the incorporeality and non-spatiality of God apply then we may surmise further that this cause is not mutable either. Mutability requires extension in space and time in order for real and measurable change to occur (it should be quite obvious here that such change does not equivocate to mean the changing of one's mind as was evident with the angelic realm). Plato found agreement with Parmenides' concept of the incorporeal "One" because it too transcended physical space and time. Like Parmenides, Plato understood that matter implies change. But if this cause resides outside of physical space and differentiated time and is an incorporeal and unchangeable entity, then how do we conclude personality? We know that events do not spontaneously "pop" into existence for no reason at all. Nor is it true that the cause must be event causation. If a cause begins to obtain then it is because of a prior cause. But since we cannot regress back toward infinity then there must be something that decisively begins the causation process. Consider a pot of water sitting on a stove. In time the stove will eventually heat the water to a boil. Unless someone alters the temperature of the stove by either removing it or shutting it off then the water will boil indefinitely until it completely evaporates into the air. Simply put, a constant material cause will yield a constant effect. If the cause were eternal then the effect would be eternal as well since it would forever apply the same conditions that existed at every other point of the effect's existence. This can only mean that if the effect is temporal then the cause itself must be personal. A personal (or agential) cause freely brings into existence its intended effect at any time the cause so chooses. Of course if the personal cause were to cause something as grand as our universe then it must be both extremely intelligent (if not omniscient) and extremely powerful (if not omnipotent).

Therefore, the cause of the universe, having been established by both philosophical and scientific considerations, must be an uncaused, changeless, timeless, incorporeal, personal being with vast amounts of knowledge and power. This evidence (I believe) points conclusively to the existence of God.

For an unabridged and expanded study, see my "Theism and Contemporary Cosmology."