This is the weekly Q & A blog post by our Research Professor in Philosophy, Dr. William Lane Craig.


Dear Dr Craig,

In your work on abstract objects, you have mentioned that there could exist necessary beings which exist "ab alio", that is, dependent for their existence on other necessary beings.

My question is this: Let's suppose for the argument's sake that such ab alio necessary beings exist, is their existence an exception (or somehow relevant) to the premise of the teleological argument according to which everything which exists exist in virtue of a necessity of its own nature or in virtue of an external cause?

I ask this, because such a premise poses a mutually exclusive bifurcation between necessary beings, on a side, and contingent beings, on the other side.

But ab alio necessary beings are both necessary and dependent for their existence on a external cause, hence providing a third category of beings apparently not included in the premiss of the teleological argument.




Dr. William Lane Craig’s Response

Dr. William Lane Craig

You’re astute in seeing the connection between abstract objects which are necessary but dependent in their existence and a particular argument for the existence of God, Carlos—you just got the label wrong: it’s Leibniz’s argument from contingency, not the teleological argument.

It seems odd to say that something could exist dependently but nevertheless necessarily. But so-called absolute creationists, who maintain that God has created abstract objects like numbers, sets, and other mathematical objects, maintain that in every possible world God creates such things via His intellectual activity. Hence, even though these things necessarily exist, they depend for their existence on God. This claim may rest uneasily with a biblical doctrine of creation, which holds that nothing exists co-eternally with God, but still the idea of necessary but dependent being seems philosophically coherent.

So when we get to Leibniz’s argument from contingency, we need to make room for beings that exist necessarily but dependently. Usually this distinction gets glossed over in order to communicate an already difficult argument to a popular audience. But I use the language of “existing by a necessity of its own nature” precisely to indicate a being which exists not just necessarily but a se (independently) rather than ab alio (dependently). So in contrast to a being which exists by a necessity of its own nature there will be dependent beings, beings which exist by some external cause.

Usually these dependent beings are called contingent beings because they are contingent upon the existence of some cause. But the problem is that in modal logic “contingency” entails “non-necessity”—contingent beings exist only in some but not all possible worlds. But we’re dealing here with beings that are contingent in one sense of the word but not contingent in another sense of the word.

I try to avoid this terminological confusion by saying that a being either exists by a necessity of its own nature or else depends on an external cause. We can then explain, if pressed, that beings which do not exist by a necessity of their own natures exist either contingently (in only some possible worlds) or necessarily (in all possible worlds) but in either case ab alio (through an external cause).

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