Gottfried Leibniz famously asked the question, “Why is there something rather than nothing?”  Leibniz was asking why the universe exists rather than nothing at all? From this question, Leibniz developed a simple but powerful argument for the existence of God. I will introduce you to his argument and how answering his simple question gives us reason to believe that God exists.
There are three concepts we need to think through to understand Leibniz’s reasoning. These are Contingency, Necessity, and the Principle of Sufficient Reason.
Most of the objects that we can think of exist contingently. This means that their existence is contingent on factors outside of themselves. Think of a chair that owes its existence to the woodworker. If not for the woodworker, the chair would not exist. In this way, the chair exists contingently because its existence is contingent on the woodworker.
The opposite of contingent existence is necessary existence. In this case, the object does not owe its existence to anything but itself. Its existence is self-explanatory, rather than “other-explanatory.” William Lane Craig puts it this way, “According to [Leibniz] there are two kinds of being: necessary beings, which exist of their own nature and so have no external cause of their existence, and contingent beings, whose existence is accounted for by causal factors outside themselves.” 
The other concept that Leibniz’s argument uses is the Principle of Sufficient Reason. This is a logical principle that says that there is some sufficient reason or explanation for the existence of everything that exists. Nothing just exists without cause. If you are a parent and come home to find a smashed vase in your living room, you automatically assume that one of your children has broken the vase. The inference to some explanation for its being broken is automatic and obvious. If your child said, “I don’t know, it just happened,” you would demand a better answer because you know better. As Douglas Groothuis explains, everything exists for a reason, and the reason is either from within or from without. 
So how do we get to God?
Leibniz took these concepts of “necessity” and “contingency” and asked what sort of existence the universe has. Is the reason the universe exists found within the universe our outside of it? If the cause is not within the universe, it is outside of it. If the reason for the universe is outside the universe, then the reason is God.
The reason why the universe’s explanation must be God is found when we consider what is being explained. When we refer to the universe, we are talking about space, time, matter, and energy. Whatever stands as the explanation for these things must transcend them. Nothing can cause its own existence. So the cause for time, space, matter, and energy must be timeless, spaceless, and immaterial.
In addition to these attributes, the transcendent explanation must be uncaused and personal. Since to be caused is to be explained by another, a necessary being must be uncaused. If there were a cause for the transcendent cause, it would be contingent. There would be yet another explanation above it. So whatever stands as the necessary being that explains the existence of everything must be uncaused.
It must also be personal, as Craig explains, “The cause of the universe must (at least causally prior to the universe’s existence) transcend space and time and therefore cannot be physical or material. But there are only two kinds of things that could fall under such a description: either an abstract object (like a number) or else a mind (a soul, a self).”  Numbers do not cause anything (the number “5” never put $5 in my pocket). So by process of elimination, the cause of the universe must be a mind or soul.
So we see that Leibniz’s argument is subtle but powerful. As Craig explains, “I hope you begin to grasp the power of Leibniz’s argument. If successful, it proves the existence of a necessary, uncaused, timeless, spaceless, immaterial, personal Creator of the universe.” 
What if the universe caused itself?
Nothing can cause itself. Something must exist if it is going to cause anything. If something is going to cause itself, then it would need to pre-exist itself, which is absurd.
Some might argue that since the universe is not an object but a system of objects, the explanation can ultimately be found within the system. In the case of each object, its cause is located in another object. Still, through the network of objects, everything is ultimately explained.
Geisler explains the problem here, “To say [such a network could exist] is like arguing that one paratrooper whose chute did not open can hold up another whose chute did not open. And adding more paratroopers whose chutes do not open does not help the problem; it compounds it.”  In other words, we must have an ultimate explanation that is self-explained (necessary). We need a paratrooper whose chute is open and who does not rely on any other paratroopers to hold him up. With a universe of contingent objects, there must be a necessary object to ground them.
So why can’t the universe be the necessary object? There are at least two reasons that the universe cannot exist by necessity. First, the scientific consensus is that individual subatomic particles in the universe are not necessary beings. These subatomic particles could have been different or could have failed to exist. Since the universe is just a collection of these particles, the universe itself could also have been different or failed to exist. Craig explains, “No one thinks that every particle in the universe exists by a necessity of its own nature. It follows that neither does the universe composed of such particles exist by a necessity of its own nature.” 
Some might push back with the Composition Fallacy at this point, but this move would be wrongheaded. The Composition Fallacy points out that a collection does not necessarily possess all the individual objects’ attributes. So a brick wall is heavy even though individual bricks are light. The critic might say that the universe may not be contingent even if all of the objects within are contingent. Someone would be committing the Composition Fallacy to say otherwise, according to the critic.
However, when it comes to the composition fallacy, it is the “accidental” qualities of the object that may not translate rather than the “essential” qualities. Accidental attributes are those qualities that an item possesses, given the circumstances. So a brick happens to be light because it has been cut small. You could cut a brick the size of a house, and it would be heavy instead. So its weight is an “accidental” quality because it is not the essence or nature of the brick to be any particular weight. An essential quality of brick might be that it occupies space. If we strip away this quality, then whatever we discuss is no longer a brick at all but something else entirely. No matter how many bricks you might add, you will never reach a point that they no longer occupy space. When it comes to the universe, you never get a necessary universe regardless of how many contingent objects you add to it.
However, the most apparent knockdown argument against the universe existing by necessity is the universe’s beginning. If something can’t fail to exist, then it can never have come into existence. As Craig explains, “An essential property of a being that exists by a necessity of its own nature is that it be eternal, that is to say, without beginning or end. If the universe is not eternal, then it could fail to exist and so does not exist by a necessity of its own nature.” 
When we answer Leibniz’s original question, we are drawn to a being that must exist by the necessity of its own nature. When we look out and see a world full of contingent objects, and we consider what explains their existence, we must eventually come to an explanatory stopping point. We inevitably come to a self-explained explainer of everything that exists. This being is timeless, spaceless, immaterial, personal, and is the foundation for all reality. It is what we are referring to when we use the word “God,” and Leibniz’s argument gives us good reason to believe that he exists.
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 Douglas Groothuis, Christian Apologetics: A Comprehensive Case for Biblical Faith – Kindle (Downers Grove: InterVarsity Press, 2011), Ch 11, paragraph 2.
 William Lane Craig, Reasonable Faith: Christian Truth and Apologetics (Wheaton: Crossway Books, 2008), pg 107.
 Douglas Groothuis, Christian Apologetics: A Comprehensive Case for Biblical Faith – Kindle (Downers Grove: InterVarsity Press, 2011), Ch 11, The Principle of Sufficient Reason and the Existence of God.
 William Lane Craig, Reasonable Faith: Christian Truth and Apologetics (Wheaton: Crossway Books, 2008), pg 108.
 William Lane Craig, On Guard: Defending Your Faith With Reason and Precision – Kindle (Colorado Springs: David C. Cook, 2010), Ch 3, Another Argument for Premise 2: The Cause of the Universe: Abstract Object or Unembodied Mind?.
 Norman Geisler, Systematic Theology in One Volume (Bloomington: Bethany House Publishing, 2011), pg 24.
 ibid, pg 25.
 William Lane Craig, On Guard: Defending Your Faith With Reason and Precision – Kindle (Colorado Springs: David C. Cook, 2010), Ch 3, Atheist Alternative: The Universe Exists Necessarily!.
 William Lane Craig, Reasonable Faith: Christian Truth and Apologetics (Wheaton: Crossway Books, 2008), pg 111.