This is the 1948 debate between Jesuit Catholic Priest Frederick Copleston and philosopher Bertrand Russell on the “Existence of God”. A proper transcript can be found in The Collected Papers of Bertrand Russell, volume 11, ed. John G. Slater (London: Routledge, 1997) pp. 524-530, 532, 540-541, as well as The Mystery of Existence, ed. John Leslie and Robert Lawrence Kuhn (Wiley-Blackwell: 2013) pp. 53-55.
This is simply a portion of the debate between Copleston and Russell, and captures Copleston’s brief presentation of the Leibnizian Cosmological Argument, drawing upon the principle of sufficient reason as his referent to affirm the existence of God.
Leslie and Kuhn write in their review of the Copleston-Russell debate:
The historic debate between Bertrand Russell and Father Frederick Copleston features intricate fighting over Hume’s idea that being infinitely old could make a universe unmysterious. Copleston believes in a divine person, God. God possesses necessary existence, he says, because God’s essence and existence are identical. God’s nature actually is “to exist.” However we don’t have “any clear intuition of God’s essence as yet” so we cannot, just by contemplating this extraordinary essence, have our proof that God exists. Instead we deduce God’s necessary existence from the fact that the universe would otherwise have to be “its own cause,” which Copleston views as an absurd idea. Even if successive stages of the universe formed an infinite chain, each link caused by an earlier one, this could not remove the need for God. Without God, there would be nothing to give existence to the chain as a whole. 
- Copleston: As we are going to discuss the existence of God, it might perhaps be as well to come to some provisional agreement as to what we understand by the term “God”. I presume that we mean a supreme personal being, distinct from the world, and creator of the world. Would you agree – provisionally at least – to accept this statement as the meaning of the term “God”?
- Russell: Yes, I accept this definition.
- Copleston: My position is the affirmative position that such a being actually exists, and that his existence can be proved philosophically. [ … ] For clarity’s sake, I will divide the argument into distinct stages. First of all, I should say, we know that there are at least some beings in the world who do not contain in themselves the reason for their existence. For example, I depend on my parents, and now on the air, and on food, and so on. Secondly, the world is simply the real or imagined totality or aggregate of individual objects, none of which contain in themselves alone the reason of their existence. There isn’t any world distinct from the objects which form it, any more than the human race is something apart from the members. Therefore, I should say, since objects or events exist, and since no object of experience contains within itself the reason of its existence, [ … ] the totality of objects must have a reason external to itself. That reason must be an existent being, and this being is either itself the reason for its own existence, or it is not. If it is, well and good. If it is not, then we must proceed further. But if we proceed to infinity in that sense, then there’s no explanation of existence at all. So, I should say, in order to explain existence, we must come to a being which contains within itself the reason for its own existence – that is to say, which cannot not-exist
- Russell: This raises a great many points and it’s not altogether easy to know where to begin, but I think that, perhaps, in answering your argument, the best point with which to begin is the question of a necessary being. The word “necessary” I should maintain, can only be applied significantly to propositions. And, in fact, only to such as are analytic, that is to say such as it is self-contradictory to deny. [ … ] I don’t admit the idea of a necessary being, and I don’t admit that there is any particular meaning in calling other beings “contingent.” These phrases don’t for me have a significance except within a logic that I reject. [ … ] A being that must exist and cannot-not exist, would surely, according to you, be a being whose essence involves existence.
- Copleston: Yes, a being the essence of which is to exist. But I should not be willing to argue the existence of God simply from the idea of His essence because I don’t think we have any clear intuition of God’s essence as yet. I think we have to argue from the world of experience to God. [ ..] [A]re you going to say that we can’t, or we shouldn’t, even raise the question of the existence of the whole of this sorry scheme of things, of the whole universe?
- Russell: Yes. I don’t think there is any meaning in it al [ … ]
- Copleston: My belief is that what we call the world is intrinsically unintelligible, apart from the existence of God. You see I can’t believe that the infinity of the series of events [ … ] 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.
- Russell: It is quite all right if you mean by explaining it simply finding a cause for it.
- Copleston: Why stop at one particular object? Why shouldn’t one raise the question of the cause of the existence of all particular objects?
- Russell: Because I see no reason to think there is any. The whole concept of cause is one we derive from our observation of particular things. I see no reason whatsoever to suppose that the total has any cause whatsoever.
- Copleston: To say that there isn’t any cause is not the same thing as saying that we shouldn’t look for a cause. The statement that there isn’t any cause should come, if it comes at all, at the end of the inquiry, not the beginning. In any case, if the total has no cause, then to my way of thinking it must be its own cause, which seems to me impossible. Moreover, the statement that the world is simply there if in answer to a question, presupposes that the question has meaning.
- Russell: No, it doesn’t need to be its own cause, what I’m saying is that the concept of cause is not applicable to the total.
- Copleston: Then you would agree with Sartre that the universe is what he calls “gratuitous”?
- Russell: The word “gratuitous” suggests that it might be something else. I should say that the universe is just there, and that’s all.
- Copleston: I can’t see how you can rule out the legitimacy of asking the question how the total, or anything at all comes to be there. Why something rather than nothing? That is the question. The fact that we gain our knowledge of causality empirically, from particular causes, does not rule out the possibility of asking what the cause of the series is [ … ]
- Russell: I can illustrate what seems to me your fallacy. Every man who exists has a mother, and it seems to me your argument is that therefore the human race must have a mother, but obviously the human race hasn’t a mother; that’s a different logical sphere.
- Copleston: Well, I can’t really see a parity. If I were saying “every object has a phenomenal cause, therefore, the whole series has a phenomenal cause,” there would be a parity; but I’m not saying that; I’m saying, every object has a phenomenal cause if you insist on the infinity of the series; but the series of phenomenal causes is an insufficient explanation of the series. Therefore, the series has not a phenomenal cause but a transcendent cause.
-  Leslie and Kuhn, p. 43