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Every cosmological proof for God’s existence must assume some form of the principle of sufficient reason (PSR). For they must argue the existence of the universe cannot be simply a brute fact, without any cause or explanation.
Simplified, the PSR states that there is no contingent fact that is a brute fact; but that every contingent fact has an explanation. (A contingent fact is a fact about the world that could be otherwise, like me typing this right now; a necessary fact is one which exists in all possible worlds, like truths of mathematics.) A necessary fact can be said to be “self-explanatory” insofar as its denial would result in a logical contradiction, thus it must be. A contingent fact, however, needs its explanation from something else; its denial does not involve a contradiction.
For instance, the First Way of Aquinas (the argument from motion) assumes that nothing just moves for no reason or cause; it doesn’t just pop from potentiality to actuality, but it needs a sufficient reason, some other entity already in act moving it.
And the problem is that the PSR, stated this way, leads to a contradiction. Imagine a world with a set of contingent facts (which could in theory be an infinite set). Now, contrary to Hume, even an infinite set is not “explained” in the sense the term is meant by the PSR, because even though every member of the set has an explanation, a world without that set but with all other features the same would not involve a logical contradiction. For any set therefore, even an infinite set, an explanation must be sought outside the set. (There are also circular sets where A explains B and B explains A, of course.) But we’re always at the same problem, if all we have are contingent facts - the set is never explained. Thus it is argued, in every cosmological proof, that recourse must be had to something necessary. But what is logically entailed by a necessary fact is also itself necessary. Thus, the options are denial of the PSR (which would invalidate all cosmological proofs) or biting the bullet and denying contingency, saying that this world is the only possible one.
I’ve seen some Catholic metaphysicians with Ph.D.s attempt to grapple with this, not very successfully I might add. I’ve read things like “explanation does not mean entailment” pray tell then what does it mean? I’ve read an attempt to deny the above argument, claiming that a contingent set is “explained” when all its members are explained. It’s a serious issue for the Church has dogmatically declared BOTH that the existence of God can be known through created things AND that God created freely without any sort of compulsion or constraint.
Simplified, the PSR states that there is no contingent fact that is a brute fact; but that every contingent fact has an explanation. (A contingent fact is a fact about the world that could be otherwise, like me typing this right now; a necessary fact is one which exists in all possible worlds, like truths of mathematics.) A necessary fact can be said to be “self-explanatory” insofar as its denial would result in a logical contradiction, thus it must be. A contingent fact, however, needs its explanation from something else; its denial does not involve a contradiction.
For instance, the First Way of Aquinas (the argument from motion) assumes that nothing just moves for no reason or cause; it doesn’t just pop from potentiality to actuality, but it needs a sufficient reason, some other entity already in act moving it.
And the problem is that the PSR, stated this way, leads to a contradiction. Imagine a world with a set of contingent facts (which could in theory be an infinite set). Now, contrary to Hume, even an infinite set is not “explained” in the sense the term is meant by the PSR, because even though every member of the set has an explanation, a world without that set but with all other features the same would not involve a logical contradiction. For any set therefore, even an infinite set, an explanation must be sought outside the set. (There are also circular sets where A explains B and B explains A, of course.) But we’re always at the same problem, if all we have are contingent facts - the set is never explained. Thus it is argued, in every cosmological proof, that recourse must be had to something necessary. But what is logically entailed by a necessary fact is also itself necessary. Thus, the options are denial of the PSR (which would invalidate all cosmological proofs) or biting the bullet and denying contingency, saying that this world is the only possible one.
I’ve seen some Catholic metaphysicians with Ph.D.s attempt to grapple with this, not very successfully I might add. I’ve read things like “explanation does not mean entailment” pray tell then what does it mean? I’ve read an attempt to deny the above argument, claiming that a contingent set is “explained” when all its members are explained. It’s a serious issue for the Church has dogmatically declared BOTH that the existence of God can be known through created things AND that God created freely without any sort of compulsion or constraint.