diosangpastol
Dios - ang - Pastol
The Kalam Cosmological Argument for the Existence of God
I. The Kalam Cosmological Argument
1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.
In Defense of the Kalam
“Why does the universe exist?”
Have you ever asked yourselves this question? This is a question that has hounded the thoughts of man since time immemorial.
Well, the typical atheistic answer has always been 'we just do' and that the universe just 'exists' eternally and uncaused. But recent discoveries in mathematics and cosmology does much to cast doubt on this claim.
I.I. The universe began to exist
I.I.I. Philosophical Confirmation of Premise (2)
Actual Infinites and Reality
The very first of these problems are problems to do with actual infinites existing in physical reality. Most mathematicians recognize that actual infinites are mere ideas in your mind that have no place in reality. Why? Well, when dealing with actual infinites, mathematically, you get self-contradictory answers. For example, what is infinity minus infinity? And an infinite series of temporal events just is such an actual infinite.
In order to unpack this point, we must first distinguish between actual infinites and potential infinites. An actual infinite, indicated by the symbol aleph ℵ0, is an infinite that is complete. It is a number that is greater than the set of all natural numbers, {1,2,3,4,5,6,7,8,9...}. That is to say, all the elements of the infinite set is already there. A potential infinite is a number that always approaches the infinite but never actually gets there, represented by the symbol of a lying-down 8, the lemniscate, ∞. Say, 1,2,3,4,5,6,7,8,9... Such an infinite is really indefinite instead of infinite.
I.I.I.I. Impossibility of an Actual Infinite
1. An actually infinite number of things cannot exist.
2. A beginning-less series of events in time entails an actually infinite number of things.
3. Therefore, a beginning-less series of events in time cannot exist.
Premise 1:
Premise 1 draws it's strength from the logical contradictions that we would expect to see were actual infinites be possible in reality. Hilbert's Hotel, Craig's favorite illustration of the concept, will serve to illustrate this contradictions. And I quote:
Now, does anyone really think that such a Hotel could exist in reality? Obviously not. Our rationality then behooves to reject such a possibility but in doing so, we reject the possibility of an eternal universe.
Premise 2:
Premise 2 is obvious in it's implications. If the universe has existed for infinite time it would be an example of just such an actual infinite which we know to be absurd. Craig's choice of words here is interesting. By choosing to define time as events rather than as moments, he preempts a possible objection to the argument, that is that moments are relative.
Conlusion:
The conclusion we then draw from the argument is that the universe is not eternal and thus had a beginning to it's existence.
I.I.I.II. Impossibility of an Actual Infinite through Successive Addition
1. The series of events in time is a collection formed by successive addition.
2. A collection formed by successive addition cannot be actually infinite.
3. Therefore, the series of events in time cannot be actually infinite.
Premise (1) is fairly obvious. It states that a series of events in time, our temporal reality, is formed by successive addition of events. Say 1 second + 1 second + 1 second...
It is premise (2) that forms the core of the argument. It states that such a collection so formed is really a potential infinite, that is indefinite, and would never actually form an actual infinite. For think about it: 1,2,3,4,5,6,7,8,9,10... will always be approaching infinity but would never actually get there since an actual infinite is a number that is greater than the set of all natural numbers.
But since the series of events in time is a collection formed by successive addition, and a series so formed cannot be actually infinite, it follows logically that the series of events in time is not actually infinite.
I.I.II. Scientific Confirmation
I. The Kalam Cosmological Argument
1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.
In Defense of the Kalam
“Why does the universe exist?”
Have you ever asked yourselves this question? This is a question that has hounded the thoughts of man since time immemorial.
Well, the typical atheistic answer has always been 'we just do' and that the universe just 'exists' eternally and uncaused. But recent discoveries in mathematics and cosmology does much to cast doubt on this claim.
I.I. The universe began to exist
I.I.I. Philosophical Confirmation of Premise (2)
Actual Infinites and Reality
The very first of these problems are problems to do with actual infinites existing in physical reality. Most mathematicians recognize that actual infinites are mere ideas in your mind that have no place in reality. Why? Well, when dealing with actual infinites, mathematically, you get self-contradictory answers. For example, what is infinity minus infinity? And an infinite series of temporal events just is such an actual infinite.
In order to unpack this point, we must first distinguish between actual infinites and potential infinites. An actual infinite, indicated by the symbol aleph ℵ0, is an infinite that is complete. It is a number that is greater than the set of all natural numbers, {1,2,3,4,5,6,7,8,9...}. That is to say, all the elements of the infinite set is already there. A potential infinite is a number that always approaches the infinite but never actually gets there, represented by the symbol of a lying-down 8, the lemniscate, ∞. Say, 1,2,3,4,5,6,7,8,9... Such an infinite is really indefinite instead of infinite.
I.I.I.I. Impossibility of an Actual Infinite
1. An actually infinite number of things cannot exist.
2. A beginning-less series of events in time entails an actually infinite number of things.
3. Therefore, a beginning-less series of events in time cannot exist.
Premise 1:
Premise 1 draws it's strength from the logical contradictions that we would expect to see were actual infinites be possible in reality. Hilbert's Hotel, Craig's favorite illustration of the concept, will serve to illustrate this contradictions. And I quote:
“As a warm-up, let’s first imagine a hotel with a finite number of rooms. Suppose, furthermore, that all the rooms are occupied. When a new guest arrives asking for a room, the proprietor apologizes, “Sorry, all the rooms are full,” and that’s the end of the story. But now let us imagine a hotel with an infinite number of rooms and suppose once more that all the rooms are occupied. There is not a single vacant room throughout the entire infinite hotel. Now suppose a new guest shows up, asking for a room. “But of course!” says the proprietor, and he immediately shifts the person in room #1 into room #2, the person in room #2 into room #3, the person in room #3 into room #4, and so on, out to infinity. As a result of these room changes, room #1 now becomes vacant and the new guest gratefully checks in. But remember, before he arrived, all the rooms were already occupied!” [1]
Premise 2:
Premise 2 is obvious in it's implications. If the universe has existed for infinite time it would be an example of just such an actual infinite which we know to be absurd. Craig's choice of words here is interesting. By choosing to define time as events rather than as moments, he preempts a possible objection to the argument, that is that moments are relative.
Conlusion:
The conclusion we then draw from the argument is that the universe is not eternal and thus had a beginning to it's existence.
I.I.I.II. Impossibility of an Actual Infinite through Successive Addition
1. The series of events in time is a collection formed by successive addition.
2. A collection formed by successive addition cannot be actually infinite.
3. Therefore, the series of events in time cannot be actually infinite.
Premise (1) is fairly obvious. It states that a series of events in time, our temporal reality, is formed by successive addition of events. Say 1 second + 1 second + 1 second...
It is premise (2) that forms the core of the argument. It states that such a collection so formed is really a potential infinite, that is indefinite, and would never actually form an actual infinite. For think about it: 1,2,3,4,5,6,7,8,9,10... will always be approaching infinity but would never actually get there since an actual infinite is a number that is greater than the set of all natural numbers.
But since the series of events in time is a collection formed by successive addition, and a series so formed cannot be actually infinite, it follows logically that the series of events in time is not actually infinite.
I.I.II. Scientific Confirmation