See here for content about the status as a proof and value for religious faith of arguments for the existence of God. It is also needed for some philosophy dialogues questions about the relevance of reason and philosophical argument for religious faith.
Aquinas 3rd Way
Aquinas’ argument from contingency.
P1 – Everything is contingent
P2 – There cannot be an infinite regress of contingent things
C1 – The chain of contingent things must stop at some point and since everything is contingent, there cannot have been anything before then. So, at one point there was nothing.
P3 – If at one point there was nothing, there would be nothing now, since nothing comes from nothing.
C2 – There is something now, therefore there couldn’t have been nothing in the past, therefore it cannot be the case that everything is contingent, so there is a necessary being which began this chain of contingent things. That thing we call God.
The premise that everything is contingent leads to the absurd conclusion that something must have come from nothing. Since that is false, what led to it (that everything is contingent) must be false, so there must be a necessary being which started the whole process.
Hume and the fallacy of composition
It is a fallacy to assume that properties of the parts of something must be properties of the whole. In the case of the universe, Aquinas rightly points out that all the parts of the universe must have a cause or be contingent. However it is the fallacy of composition to assume that therefore the universe itself as a whole must have had a cause or be contingent. Bertrand Russell illustrated this by pointing out that just because every human has a mother, that doesn’t mean the human race has a mother. Note that Hume is not claiming to know that the universe had no cause. He is merely pointing out that it is invalid to argue from the parts of the universe having a cause to the universe itself having one. While the properties of the parts of something may indeed be the properties of the whole, that isn’t necessarily the case and it is the fallacy of composition to assume so.
Copleston: one cannot be sure that the analogy applies. Copleston’s point can be illustrated with the example of the brick wall. The bricks of a brick wall are made of brick, but so is the whole wall. In other words, in the case of a brick wall and its bricks, the parts are like the whole. Copleston is pointing out that the relation of the universe to its parts may be more like that brick wall to its bricks than the human race to its members.
Russel responds that Copleston is the one making the argument, he is the one who needs to be sure.
Russell and the brute fact argument
Why must there be a reason for something’s existence? The universe could just be a brute fact, meaning there might be no reason for its existence. there could be an infinite regress of objects or even universes.
Copleston’s response: is that the brute fact argument is like sitting down at a chess board and claiming it’s a draw because you refuse to make a move. How can one do Philosophy if some things have no explanation?
Criticism of Copleston: Reality is not here to make sense to us. By saying the brute fact argument is an invalid move, Copleston is not actually showing it to be false. Science and philosophy are about finding out what is true. If it could be true that something has no reason/cause/explanation, then philosophy should be open to that possibility.
The possibility of an infinite regress
The infinite regress is an important factor in the cosmological argument. If there is an infinite regress of objects going back in time forever, then the cosmological argument fails because there would have been no first cause or mover.
Hume on the possibility of an infinite series. If there is an infinite regress of objects going back in time forever, then the cosmological argument fails because there would have been no first cause or mover. Hume points out that in order for something to be impossible it must be self-contradictory. For example, a four sided triangle is impossible because a triangle having four sides is contradicts the definition of a triangle as a three sided shape. However, there doesn’t appear to be anything self-contradictory about the infinite regress. Therefore it is possible and so the cosmological argument rests on an assumption that the infinite regress is false when it could possibly be true.
William Lane Craig while defending the Kalam Cosmological argument argued that an infinite regress is impossible because Infinities cannot exist in reality. Craig points out that if a library had an infinite number of books, half red half green, and you were to take the red books out of the library then you would have taken an infinite number of books out but there would still be an infinite number left. This is because infinity divided by two is still infinity. His claim is that this is just not how physical objects in reality could possibly function so it’s absurd to think infinities could exist. Therefore the infinite regress cannot exist.
The infinite library is an example of an infinite number of physical objects, but the infinite regress could be a finite number of physical objects existing over an infinite amount of time. Craig has shown the absurdity of physical infinities but not temporal ones, which is what the infinite regress involves.
Aquinas claims an infinite regress is impossible because If there is an infinite regress, then time has existed forever. So there must be an infinite amount of time before the present moment. That means that to get to the present moment, an infinite amount of time must have passed. However, an infinite amount of time cannot pass. No matter how long you wait, even if you never stop waiting, you will never actually reach infinity. Every second you add is finite and can never total an infinite number of seconds. So there cannot be an infinite amount of time before the present moment and therefore there cannot be an infinite regress. Modern Physicists think that time could have begun at the big bang, which would fit with Aquinas’ argument.
However, Physicists also have theories that suggest that the time which began at the big bang might only have been the time of our universe, and there could be other times or other kinds of time. The “big crunch” theory suggests that universes could have been eternally expanding and contracting again. If a new timeline began upon each contraction, an infinite amount of time would never pass even though the process of expansion and contraction has been going on for an infinite amount of time. Or, perhaps time is not even the sort of thing that actually passes and the passing of time is some kind of illusion that 4th dimensional beings experience. Perhaps time cannot be measured in numbers. The point is we know very little about how time works and Aquinas’ philosophical argument makes assumptions that science may one day contradict.
Hume’s fork and the impossibility of a necessary being
“there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori” – Hume.
A necessary being must exist – it cannot be the case that it does not exist. This means we shouldn’t even be able to conceive (imagine) it not existing, without contradiction. However, Hume claims that whatever we conceive of as existing, we can conceive of as not existing. Hume concludes:
“The words, therefore, necessary existence, have no meaning.”
This argument references “Hume’s fork”:
A priori reasoning can only tell us about the relations between ideas, i.e. analytic knowledge (true by definition). E.g. “a bachelor is an unmarried man”.
A posteriori reasoning can only tell us about matters of fact, i.e. synthetic knowledge (true by the way the world is). E.g. “The sun will rise tomorrow”
Matters of fact, such as whether a being exists, cannot be established a priori, according to this argument. Hume’s basis for the fork is that if a particular truth is a matter of logic/definition, then it will be true or false no matter the factual state of the universe. E.g., one plus one will always equal two, regardless of what happens to be factually true of the universe. This suggests there is a disconnect between logical truth and factual truth. The term “necessary existence” seems to ignore this disconnect. It’s invalid to claim that a being’s existence is logically necessary, since a being’s existence cannot be established through logic. Since Hume’s fork has shown that logical truth is disconnected from factual truth, the idea that something could necessarily exist is incoherent.
The ontological argument therefore fails because it attempts to establish a matter of fact (God’s existence) through a priori reasoning. Also attacked is any argument which involves the incoherent idea of a necessary being (some cosmological arguments e.g. Aquinas’ 3rd way).
Hume conflates logical necessity and metaphysical necessity. Hume rejects the idea that ’God exists’ could be a necessarily true proposition, since we can conceive of God not existing, which shows that “God exists” cannot be necessarily true. However, what if the actual claim is that “If God exists, God exists necessarily”. This claim is not attributing logical necessity to the truth of a proposition; it is attributing metaphysical necessity to a being. This being, if it exists, exists necessarily because it does not depend on anything else for its existence. It’s not necessarily true that such a being exists, but if it does, its existence is necessarily.
Hume’s fork: even if we take arguments for God involving necessity to be attributing necessity to a being, not to a proposition, it’s existence still cannot be established by a priori reasoning. Matters of fact can only be inferred by a posteriori reasoning.
It could be inferred by a posteriori reasoning, however, such as is found in the cosmological argument.