There is a certain deductive argument for the existence of God that is particularly more popular than others. Unlike other purely deductive arguments for God's existence, the Cosmological Argument is one which is readily used by the laity, albeit not under that name. Since the time of Saint Thomas Aquinas, it has been an established part of Catholic doctrine. In fact, there is a certain Catholic tradition which regards the existence of God as something which is deductively provable without reference to the Bible, church authorities, or faith. Instead, from mere recourse to logic alone, the doctrine states that we should be able to deduce God's existence. Several such deductive arguments were proposed by Augustine, Aquinas, Anselm, and other scholars from the medieval period, often drawing from earlier work (most notably Aristotle and Plato.) Later, inductive and/or abductive arguments joined the fray, including William Paley's 19th century divine watchmaker argument (which would lead to its modern incarnation as Intelligent Design.)
Here, I would like to discuss the Cosmological Argument I previously mentioned. This argument usually proceeds as follows:
1. The universe exists.
2. If (1) then the universe must have had a beginning.
3. Therefore, the universe must have had a beginning (modus ponens from premises (1) and (2)).
4. If (2) then the universe must have had a cause.
5. Therefore, if (1) then the universe must have had a cause (hypothetical syllogism from premises (2) and (3)).
6. If the universe had a cause, then God must exist.
7. Therefore, if (1) then God must exist (hypothetical syllogism from premises (5) and (6)).
8. Therefore, God exists (modus ponens from premises (1) and (7)).
The argument is usually shortened to merely stating that since someone must have created the universe, God must have done so -- thereby implying that God must exist. As one might state it, there should be an answer to the questions "who created the universe?" or "why is there something as opposed to nothing?"
There are a number of problems in this argument and each one is worthwhile to address. Since the argument is deductively valid, it must be the case that either the argument is sound or one of its premises fails. I will assume that premise (1) is true; I will reject solipsism a priori and hope that the reader does not find that too uncomfortable. Propositions (2), (4) and (6) are assertions, while the other propositions follow from (1), (2), (4) and (6) by the rules of standard syllogistic logic (following common academic philosophical practice, I will not try to refute standard logic here and will be assuming that the associated rules of inference are legitimate.) Thus, if I have a problem with the argument in the manner that I presented it, the problem(s) must stem from premises (2), (4) and/or (6).
First, I will consider premise (2) -- that if the universe exists, it must have had a beginning. Clearly, this proposition results from the intuition that all objects that exist must have had a beginning. That's actually too strong of a statement. Any one who accepts Platonism (about, say, the foundations of mathematics) would deny that all objects have had beginnings. To the Platonist, abstract objects did not have beginnings nor do they change with time, being as they are eternal and outside of time. Lest we put ourselves in the position of having to refute the Platonist position, we should weaken the claim that all objects have a beginning. Besides, if we did postulate that all objects must have had a beginning then we put ourselves in the position of having to deal with an infinite regress from the conclusion -- that is to say, if the universe must have had a beginning, why not God? And if something brought God into existence, then what brought that into existence? And so on.
Instead, we can go a safer route by merely claiming that all physical objects had a beginning. To establish that this statement is false, it would of course suffice to show that there exists at least one physical object which did not have a beginning.
Now, to show that all physical objects had a beginning can proceed in one of either two ways. Either we could show that it would result in a logical contradiction to hold that at least one physical object existed forever or we could examine every physical object that ever existed (or ever could exist) to determine whether it was brought into existence at some point. Since the latter is definitely impossible, we are stuck with the former. In the former case, it's unclear how one could ever construct an argument showing that it produced logical contradictions to postulate the existence of at-least one eternal physical object. It's certainly not clear to me how one could do so, but that one could is a situation I would be open to. Certainly, many theologians -- such as William Lane Craig -- argue that an eternally existing physical object is impossible. As far as I can tell, the only arguments Craig has to offer on this point result from confounding counter-intuitive properties with logically contradictory or impossible properties. Certainly, any eternally existing object would have some mighty strange properties merely by virtue of being an eternally existent object, but that is insufficient to justify the assertion that such things do not exist.
Nonetheless, a common interpretation of the universe's expansion is that the universe did, in fact, have a beginning. Perhaps the only way to proceed would be to reject the Catholic doctrine that the Cosmological Argument alone, without scientific investigation, is sufficient to prove the existence of God. That is to say, perhaps the way to proceed is to allow ourselves access to the scientific evidence that the Universe did have a beginning. From there, we simply modify the argument to begin with premise (3) (which we would presumably believe to be the case due to a prior examination of empirical evidence.) It is worth noting that this is not the only interpretation of the Universe's expansion. For instance, there could have been an infinite sequence of prior Universes to the Big Bang. Nonetheless, for the purposes of the present discussion, let us assume that the empirical evidence leads us, abductively, to the conclusion that the Universe had a beginning and that we should examine the proposed modified form of the argument:
1*. The best possible explanation for the available empirical evidence is that the universe had a beginning.
2*. If (1*) then the universe must have had a cause.
3*. Therefore, if (1*) then the universe must have had a cause (hypothetical syllogism from premises (1*) and (2*)).
4*. If the universe had a cause, then God must exist.
5*. Therefore, if (1*) then God must exist (hypothetical syllogism from premises (3*) and (4*)).
6*. Therefore, God exists (modus ponens from premises (1*) and (5*)).
Given that I am willing to assume (1*) to the be the case, at least for our present purposes, let's examine premise (2*). Premise (2*) tells us that since the universe had a beginning, it must have had a cause. The most common way of justifying this is to simply state that all effects have causes. The universe beginning is an effect, so it must have had a cause. However, to say that the universe beginning is an effect inherently begs the question. What we mean when we use the word effect is to denote a caused event (I believe this to be the definition of the word "effect"); i.e. effects are events that bare certain kinds of relations to antecedent events and/or conditions. A non-caused effect would really be a contradiction in terms; we really should be talking about events instead of effects. In that case, the justification for (2*) would state that all events must have causes and since the beginning of the universe is an event, it too must have had a cause.
Usually, lay people try to justify the proposal that all events must have causes by simply stating that all events they have ever seen had a cause. More sophisticated but philosophically naive individuals might state that all scientifically examined events had causes. Nonetheless, there are events in, say, quantum mechanics about which we are scientifically justified in calling non-caused. That an electron is observed at such-and-such a place at such-and-such a time is a fact for which there is no specific de facto explanation to be had nor any kind of identifiable antecedent cause that necessitates, by virtue of physical law, that it occurred. That's what we mean by "quantum randomness". It is inarguable that for large-scale, macroscopic objects, these kinds of effects are negligible, which is why we find these aspects of quantum mechanics so tremendously counterintuitive. Nonetheless, that they occur is extremely well-established. In fact, without delving too deeply into quantum mechanics, it should be briefly noted that violation of the so-called Bell Inequalities allows us to rule out a wide variety of alternative theories (technically speaking, any local hidden variables theory.) What I explicitly mean here is that even with further knowledge beyond our present scientific understanding, we will never find out that we were wrong and that there were localized, hidden effects that brought about the observation of the electron at that particular time and place. As with all scientific understandings, our present theory of quantum mechanics is contingent upon empirical evidence. Nonetheless it is mathematically provable that any theory which postulates localized hidden variables would be inconsistent with violations of the Bell Inequalities so that no future theory can or should include them.
However, let's suppose that we could give some kind of account of quantum mechanics that preserved some species of causation. Certainly, we are always free to postulate a non-local hidden variables theory or to generalize what we mean by saying that an event is caused. Perhaps what we need to do is to restrict what we mean by the word "event", with the implication that these things we call "non-caused events" are not really events at all (perhaps they are some species of epiphenomena, mere shadows of the "true" events, whatever that might mean.) To take a further example from quantum mechanics, when an atom radioactively decays, there were certain kinds of antecedent conditions that must have been fulfilled for that atom to decay. It must have been unstable, for example. Personally, I would say that there were some aspects of the atom's decay that were caused and others which were not. That the atom decayed at all is caused; we have an explanation for its occurrence that involves the instability of heavy nuclei. That this particular atom decayed at this particular time and at this particular place is a fact for which there is permitted no explanation. I would surmise this to be sufficient to establish the claim that non-caused events exist. Nonetheless, someone else might be sufficiently clever so as to defeat this understanding of quantum causation and to propose something else altogether which is still consistent with the empirical evidence.
Even though the counter argument from quantum mechanics would have been defeated, the assertion that all events have causes would hardly have been established. It's simply insufficient to conclude from the proposition that all observed events have causes to the conclusion that all possible events have causes. There's hardly anything logically problematic about the position that there exists at least one non-caused event.
Without arguing that there is something problematic with non-caused events, one can still try to establish that premise (2*) is true. The so-called Argument from Contingency tries to patch over this problem in the Cosmological Argument by asserting that there are two kinds of events -- contingent events and non-contingent events. Events in the former category are termed "contingent" because they did not have to be the case. It is then claimed that any contingent event must have had a cause for it to unfold in the manner that it did; counter-factually speaking, had event A not occurred, then event B, being contingent on A, would also not have occurred.
There is a subtle difference between a caused event and a contingent event. Contingent events are any events which could have happened differently but due to certain reasons (which may or may not be causal) happened in the way that they did. Most importantly, all contingent events have explanations for their occurrence. Caused events are those which were directly caused by other events. Clearly, there is overlap in the two cases, and how strongly that overlap is or where precisely the border between the two categories lies presumably depends on the account one gives of the nature of causation. Certainly, if the counter-factual account of causation is true, then all caused events are contingent events (but not necessarily vice versa.)
Nonetheless, the further claim is that if one traces back contingent events through the other events or facts upon which they depend, one will either be faced with an infinite regress or one will eventually come to a non-contingent thing (a non-contingent, and therefore logically necessitated, fact, event, or being). Unlike contingent things, something which is non-contingent is a thing whose existence is logically necessitated; i.e. had it not existed, a logical contradiction would have resulted. It has been argued that even if one is faced with the infinite regress, there still must be a non-contingent thing to explain the entire chain. As Catholic philosopher and theologian Frederick Copleston stated in his famous debate with Bertrand Russell on the existence of God:
"...I don't believe that the infinity of the series of events... if such an infinity could be proved, would be in the slightest degree relevant to the situation. If you add up chocolates you get chocolates after all and not a sheep. If you add up chocolates to infinity, you presumably get an infinite number of chocolates. So if you add up contingent beings to infinity, you still get contingent beings, not a Necessary Being. An infinite series of contingent beings will be, to my way of thinking, as unable to cause itself as one contingent being. However, you say, I think, that it is illegitimate to raise the question of what will explain the existence of any particular object."
The point here is that, since by construction, contingent events are incapable of necessitating their own existence, without postulating something that is non-contingent, we are never in a position to explain why there is something rather than nothing.
However, given that there is no reason to think a priori that the universe's existence must, by way of logical necessity, have an explanation, the Argument from Contingency simply fails. It could very well be that there is an explanation for the universe's existence. But since we don't know that there is, the Argument from Contingency at best establishes that either at least one non-contingent thing exists or there is no explanation at all for the universe's existence. Without further reasons, we cannot reject either of those two possibilities.
Having discussed the other premises ad nauseum, we lastly come to premise (4*). This is, perhaps, the weakest of the premises examined thus far. Premise (4*) states that if the universe had a cause, then God must exist. This premise is definitely weak; it seems to skip over a bit of logic. It would seem to imply that the only possible mechanism by which the universe could have come into existence would have been God's doing and would ignore all other conceivable (or non-conceivable) mechanisms of universe production. In fact, how a benign timeless and unchanging essence (the Catholic theological perception of God) could actually do any act is something which theologians have wrestled with presumably since there were theologians. It seems as though actions performed by such a being is simply an unintelligible and incoherent notion. But let's assume for the time being that we could find some solution to this or that the Catholics were really just overzealous in their definition of God. In that case, perhaps this Argument from Contingency business could clear things up for us.
As previously discussed, the Argument from Contingency claims that there must be a non-contingent (and therefore necessary) being responsible for the creation of the universe. Anselm's Ontological Argument attempts to establish that God exists because he is a necessary being. One might simply argue that since the Argument from Contingency establishes that the universe's Creator was necessary and non-contingent, and the Ontological Argument establishes that God is necessary and non-contingent, together they establish that God created the Universe. However, if the Ontological Argument were alone sufficient to establish the existence of God, then the Cosmological Argument would be unnecessary; the conclusion would already have been established. Combining the two arguments would be problematic, since one would then be proving the existence of God from the existence of God. It would be merely tautological in some sense.
This is to not even mention the severe problems that have been identified in the Ontological Argument itself. Consensus amongst modern academic philosophers is that the Ontological Argument is, at best, highly dubious (with a few scattered exceptions, most notably Alvin Plantinga at Notre Dame.) Since I have already established some of the failings in some of the other premises in the Cosmological Argument, bringing in the Ontological Argument to try to save premise (4*) doesn't really seem worthwhile. It would be something like trying to save the lives of starving children by giving them poisoned food; it doesn't really save a failing argument to introduce another failing argument.