Leibniz's Principle of Sufficient Reason

Comparison of Aquinas' treatment of infinite regress with Leibniz’s Principle of Sufficient Reason

One can see that Leibniz’s cosmological argument, although not as fully developed as Aquinas’, relies on the assumption that there cannot be an infinite regress of causes.

In an essay he wrote in 1697 called On the Ultimate Origination of Things, Leibniz writes,
“However far you go back to earlier states, you will never find in those states a full reason why there should be any world rather than none, and why it should be as it is. Therefore, even if you suppose the world eternal, as you will still be supposing nothing but a succession of states and will not in any of them find a sufficient reason... it is evident that the reason must be sought elsewhere.”

Leibniz argues that there must be a sufficient reason to explain the universe. He illustrates his point with an analogy like the one above:

“Let us suppose the book of the elements of geometry to have been eternal, one copy always to have been written down from an earlier one; it is evident that, even though a reason can be given for the present book of a past one, nevertheless out of any number of books taken in order going backwards we shall never come upon a full reason... why there are books at all, and why they were written in this manner.”

When one has a question about the origin of being, multiplying more and more being does not answer the question. Even by multiplying being to infinity, we still lack an answer. We need instead a sufficient reason or, as Aquinas calls it, an Unmoved Mover.

Aquinas on Infinite Regress

Our tendency is to think of infinite regress in a purely temporal way: an endless series stretching back in time, without end.

In his First Way (the Argument from Motion), Aquinas argues that we cannot go on indefinitely looking for a cause for things that are moved by another.

Aquinas does not use the term “infinite regress”. Like the label ‘cosmological’ itself, these are terms added by later commentators to his argument. Aquinas says of the relation between things that move from potency to act: “this cannot proceed for infinity” (Hic autem non est procedere in infinitum). His meaning is that the state of affairs cannot be dragged out endlessly to avoid admitting an Unmoved Mover.

The argument against infinite regress is not simply a temporal infinite regress. This is more of a concern for form of the Kalam version of the cosmological argument (at least William Lane Craig’s version of it) but it is not the focus of the First Way.

Aquinas is more concerned about the relationship between things that are ‘moved’ from outside of themselves—things that move from potency to act, from ‘becoming’ to ‘being’. You cannot have an infinite class of things in a state of becoming without anything that brings them into being.

Consider for example a student who is learning a new language you have never heard before. You ask him, “How are you learning to speak this language?” or, in Aristotelian more terms, “What act is bringing about your actualisation as a speaker of this language?”

He replies, “I am being taught by a teacher.” There’s no surprise there; we would expect as much. But imagine his teacher then comes into the room, and we ask her the same question, and she gives the same answer. So far, we’re still not very surprised: just as the student is learning now, so the teacher also needed to learn from someone.

But imagine more and more people kept entering the room and kept giving the same answer. Eventually we would start to wonder, “What is the source of this language? I understand that people are being taught it all over the place, but where does the language come from?”
Even if a billion people all gave the same answer, the same question persists: where did this language come from? You can see that even if an infinite number of people gave the same answer, the question is still not answered.

The problem has nothing to do with time. The problem has to do with the ultimate source of the language: where did it originate? How have these people learnt this language? The question is the same for one person, a million, a billion or an infinite number. All we’re doing by adding more and more people to the explanation is simply postponing the problem.
Aquinas wants to know, what is the source of all being? We do not answer the question by simply adding more and more beings to the argument: the world, the solar system, the Big Band, some quantum fluctuation—whatever. None of them answer the question: what is the source of all actualisation?

Existence & Essence

“What a thing is” and “that a thing is” refer to a thing’s essence and existence. The “what” is its essence; the “that” is its existence.

Consider the case of the Sasquatch. For generations, people have claimed to have caught glimpses of this half-man, half-ape like creature lurking about in the forests of Canada. “What is it?” someone asks of the beast; “what does it look like? What does it eat?” This line of questioning is focussing on the creature’s essence, its traits. What makes a Sasquatch different from a big ape? When we establish what a thing is, we are establishing its essence.

But notice that in establishing a things essence we are not establishing its existence. You could become a world expert in the nature of the Sasquatch: where the legend originated; what height it is supposed to grow to; what it would likely eat; how many people have claimed to have seen it; that is is smelly; that it has big, dirty toenails; what parts of Canada it is likely to inhabit. But all this information about its essence doesn’t bring us any closer to the question: “Does the Sasquatch exist?” It may or may not exist, but knowing lots of stuff about its essence does not help us answer questions about its existence. It may be more likely that it does not exist. Or perhaps we will all be surprised and excited one day to find that such a creature has indeed been shot and bagged.

So we can say that essence and existence are two distinct things. “What a thing is” and “that a thing is” are not the same thing: at least in reference to the Sasquatch and—for that matter—all creatures, real or not.

But notice how this separation of essence (“whatness”) and existence (“thatness”) does not apply to everything. It does not, for starters, apply to the sum, 3 + 5 = 8. What the sum is and its existence cannot be separated. In essence, it is a sum. Specifically, its essence is the sum of 3 + 5. Does it make sense to say that this sum might not exist? The fact that we understand it’s essence implies that there is something we understand. There must be something that exists in order to be understood.

Of course, the sum does not exist in the same way that donkeys and cabbages exist. It has a purely conceptual existence: it exists in the mind. But to know its essence is the same thing as knowing its existence.

So there are things for which essence and existence are different as in the case of Sasquatch, lasagne, the Prime Minister and cornflakes. And there are also things for which essence and existence are the same as for sums and ideas.

Anything in which existence and essence are not the same are called contingent things. It is possible that they do not exist; and if they do exist, it is possible that they can go out of existence. On the other hand, things in which existence and essence are the same or occur together are necessary. They are necessary because the fact of their existence cannot be separated from the fact of their essences. You cannot say that 3 + 5 is a sum which equals 8, and then deny that there is such a sum.