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Quodlibet 35-How Can Anything Exist Apart From an Infinite Being?

Friday, November 04, 2011
The laws of identity and non-contradiction say that a being, at any given moment, is either X or Y, not X and Y (if X and Y are opposites). Now, it is of the very identity of infinity to be limitless; thus, how can anything exist apart from an infinite Being, who "fills" existence up totally by being infinite? The Divine Substance is infinite, so how can there be any other substance than the Divine Substance, consisting in and of those Three blessed Persons? Does the existence of beings other than the infinite Being not contradict the law of identity for the infinite Being? If one Being is of infinite immensity, there can be no other beings... infinite or finite!

Let me start by trying to summarise your position: First, you asked, “how can anything exist apart from an infinite Being?” Secondly, you argued that the laws of logic and the nature of existence suggest that it is not possible for anything else to exist if an infinite being exists. Thirdly, you concluded that such a position was both counter-intuitive and incompatible with the Catholic religion. Clearly, it’s the second point that’s crucial. It’s your application of the laws of logic and your reflection on the nature of existence that lead to the conclusion that if an infinite being exists nothing else can exist. Let’s look at your second point then.

In effect, there are two strands to your argument- one logical and the other metaphysical. I’ll take the logic first. Aristotle proposed three fundamental logical laws- the law of identity, the law of non-contradiction and the law of the excluded middle. What do these laws mean? Well the law of identity means anything is the same as itself. Therefore, if A is a thing, then A is the same as itself. What about the law of non-contradiction? Well, just as you put it, nothing can possess contradictory characteristics. Accordingly, the same thing cannot be both A and not A. A cat for example cannot be white and not white. What about the law of the excluded middle? It means either A is true or not A is true. For example, either ‘it is raining’ is true or ‘it is not raining’ is true. There is no middle ground between the two.
Now let’s assume that (i) there is an infinite being and that (ii) being infinite and being finite are contradictory. With these assumptions in mind, let’s apply these logical laws to your question “how can anything exist apart from an infinite Being?” Well firstly, by the law of identity, an infinite being will be identical to itself. Secondly, by the law of non-contradiction and our assumption that being infinite and being finite are contradictory, an infinite being cannot also be a finite being. Thirdly, by the law of the excluded middle, there are no beings that are neither infinite nor finite. None of this, however, excludes finite being existing alongside infinite being. I conclude then that there is nothing in the laws of logic to justify the claim that the existence of an infinite being excludes the existence of finite being.

What about your metaphysical point though? Here you argue that “an infinite Being… "fills" existence up totally by being infinite.” The implication is that there is no ‘room’ for anything else to exist! How could this be though? Existence isn’t a space or a place that can be filled and if it isn’t such a space, then there’s no issue with filling it.

To sum up; I cannot see any logical or metaphysical grounds for maintaining that the existence of an infinite being entails that no finite beings exist. We could go on to argue that given finite beings exist, there must be an infinite being. That’s actually St Thomas’ procedure but it’s a story for another day. In the meantime, I hope I have been of some help.

Fr. Dominic Ryan OP. -Guest contributor , St. Dominic's Priory, London


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