In regards to the present subject, we may sure ask ourselves, what is The Principle of Sufficient Reason (PSR)? Particularly, in matters of debate regarding the existence of God, the philosophy of Gottfried Leibniz, and the writings of predominant philosopher and apologist William Lane Craig, the principle of sufficient reason is an often brought up subject. Found within a historical context, German philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716) in his book On the Ultimate Origins of Things (1697) writes:
You may indeed suppose the world eternal; but as you suppose only a succession of states, in none of which do you find the sufficient reason, and as even any number of worlds does not in the least help you to account for them, it is evident that the reason must be sought elsewhere.
For in eternal things, even though there be no cause, there must be a reason which, for permanent things, is necessarily itself or essence; but for the series of changing things, if it be supposed that they succeed one another from all eternity, this reason is… the prevailing of inclinations which consist not in necessitating reasons, that is to say, reasons of an absolute and metaphysical necessity, the opposite of which involves a contradiction, but in inclining reasons. 
In short, Leibniz is suggesting that a collective set of finite objects requires and explanation of its existence that must be sought outside of itself. In other words, finite collective sets cannot be the explanation of their own existence. A finite collective set can be exemplified in terms of a limited number of coins, and not an unlimited. This line of reasoning can be schematized as such:
- (1) Everything that exists, has an explanation of its existence.
- (2) If the universe has an explanation of its existence, that explanation is God.
- (3) The universe exists.
- (4) Therefore, the universe has an explanation of its existence. (from 1, 3)
- (5) Therefore, the explanation of the existence of the universe is God. (from 2, 4).
Premise (1) is what is known as the Principle of Sufficient Reason. Namely (and simply), that any existing thing has an explanation of its existence. As William Lane Craig writes, “This premise is compatible with there being brute facts about the world. What it precludes is that there could exist things which just exist inexplicably. According to (1) 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.” 
In light of Craig’s analysis, Leibniz’s principle can otherwise be stated as:
- (1) Anything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. 
This line of argument has come to take it’s name most particularly as the Leibnizian Cosmological Argument, which serves as a rather deductive system as opposed to what I think is the more stronger cosmological argument, the Thomistic Cosmological Argument (an inductive version). Though I will not go in depth to the argument here, I have written in other places about an inductive version of the cosmological argument.
(IA) Philosophic Justification of PSR
Any alternative in a person’s denial of PSR requires justification. However, Crispin Wright and Bob Hale think that this can be done. According to their objection, the explanation of any physical state of affairs S must be found in a causally prior state of which affairs in which S does not exist. However, as they object, since a physically empty world couldn’t cause anything, the demand for an explanation of the universe becomes “absurd.”
The problem with Wright and Hale’s objection is that it begs the question in favor of atheism. For,
unless one assumes in advance that the nuniverse is all there is, there’s just no reason to think that the state of affairs causally prior to be a physical state of affairs. The explanation of why the universe exists could be some causally prior, nonphysical state of affairs. If one assumes that that’s impossible, then one is just begging the question in favor of atheism. 
(IB) Philosophical Justification of a Necessarily Existing Mind (NEM)
As Timothy O’Connor argues in his book Theism and Ultimate Explanation , the mere existence of contingent things leads us human beings to “ask the question (while waving one’s hands all about) “Why is there this – why, indeed, is there anything at all?”  O’Connor continues:
The reason that any contingent thing exists at all (and, in particular, the world of which we are part) is that it is a contingent causal consequence of an absolutely necessary being, a being which itself could not have failed to exist, since that it is is inseparable from what it is. 
However, what reason do we have to believe that the universe doesn’t have the reason for its existence within itself? In other words, that the “explanation lies not in an external ground but in the necessity of its own nature”?  Now, considering that we generally “trust our modal intuitions on [ … ] familiar matters” , if we were to do otherwise with respect to the universe’s contingency, then the “non-theist needs to provide some reason for his skepticism other than his desire to avoid theism” . That is in respect to the first line of evidence about the universe’s contingency:
- (1’) Modal Intuitions
However, though isn’t necessarily a very compelling argument, there is also another line of evidence responsible for our justification in believing the universe to be contingent:
- (2’) The possibility of the universe existing without any concrete objects.
Respectively to (2’), Craig writes that
[i]t’s easy to conceive of the non-existence of any and all of the objects we observe in the world; indeed, prior to a certain point in the past, when the universe was very dense and very hot, non of them did exist. 
Thus, for example, if the universe were to exist with a different collection of quarks (i.e., fundamental particles or “building blocks” of matter), then it should be the case that the universe does not exist by the necessity of its own nature.  Thus, would have we demonstrated?
- (A) The universe is contingent
- (B) The contingent universe requires an explanation of its existence
- (B’) The contingent universe requires a causally prior an extended grounding in a necessary being.
- (C) The explanation of this necessary being’s existence is contained within itself (O’Connor, 2009)
-  Gottfried Leibniz, On the Ultimate Origins of Things, in Leibniz: The Monadology and Other Philosophical Writings, trans. Robert Latta (London: 1898) p. 1
-   W. L. Craig, Reasonable Faith, 3rd edn. (Wheaton: 2006) see pp. 106-111
-  Ibid., p. 106
-  Craig, see 106-111
-  Timothy O’Connor, Theism and Ultimate Explanation (Malden, MA: Blackwell Publishing, 2009)
-  Sections to quoting O’Connor will be found in chapters 3, 4, and 5, pp. 65, 68-72, 111-113, 116-117.
-  O’Connor, ibid.
-  William Lane Craig, quoted from The Mystery of Existence, ed. by John Leslie and Robert Lawrence Kuhn (Malden, MA: Blackwell Publishing, 2013) p. 157
-  Ibid.
-  Ibid.
-  Ibid., p. 158
-  Craig writes, “[A] universe composed of a wholly different collection of quarks is not the same universe as ours” (Ibid., p. 158). If this is the case regarding a logically possibly different universe, then it means that the contained concrete objects of the universe are themselves a reason to think that universe is a contingent object since they are by no means interconnected or related to the universe’s existence.