Robin
Penultimate Amazing
- Joined
- Apr 29, 2004
- Messages
- 14,971
Here is the Kalam Cosmological Argument as stated by William Lane Craig:
1.0 Everything that begins to exist has a cause.
2.0. The universe began to exist.
So the conclusion of the two sub arguments for 2.0 would have to be the same as 2.0 in order for the argument to be valid, ie all the lines in red have to be the same. But clearly they are not.
If I submitted something like this to my old DM lecturer he would have fixed me with one of his famous withering stares and asked me if I was quite sure I understood the concept of a proof.
Here is how it might be fixed:
B(x) df x begins to exist
C(x) df x has a cause
A(x) df x is an actual infinite
R(x) df x is an infinite temporal regress of events
S(x) df S is a collection formed by successive addition
T(x) df x is a temporal series of events
1 (x) B(x) implies C(x)
2 B(u)
2.11 not poss exists x A(x)
2.12 (x) R(x) implies A(x)
2.13 not poss exists x R(x)
2.14 not B(u) implies R(u)
2.15 not B(u) implies not poss exists u
2.16 exists u
2.17 B(u)
2.21 not poss exists x S(x) and A(x)
2.22 (x) T(x) implies S(x)
2.23 not poss exists x T(x) and A(x)
2.24 not B(u) implies T(u) and A(u)
2.25 not B(u) implies not poss exists u
2.26 exists u
2.27 B(u)
3 C(u)
So there are two new premisses that would need to be defended:
2.14 not B(u) implies R(u)
If the Universe did not begin to exist then it would be an infinite temporal regress of events
2.24 If the Universe did not begin to exist then it would be an infinite temporal series of events
not B(u) implies T(u) and A(u)
I can see why he would be reluctant to defend these premisses.
Of course the argument, even if sound, would only prove that the Universe has a cause, not a God. He offers a rather preposterous kludge to explain why this cause has to be a God. I would love to see him even try to formalise that kludge.
1.0 Everything that begins to exist has a cause.
2.0. The universe began to exist.
(Sub argument 1)
2.11. An actual infinite cannot exist.
2.12. An infinite temporal regress of events is an actual infinite.
2.13. Therefore, an infinite temporal regress of events cannot exist
(Sub argument 2)
2.21 A collection formed by successive addition cannot be an actual infinite.
2.22 The temporal series of events is a collection formed by successive addition.
2.23 Therefore, the temporal series of events cannot be an actual infinite.
3.0. Therefore, the universe has a cause2.11. An actual infinite cannot exist.
2.12. An infinite temporal regress of events is an actual infinite.
2.13. Therefore, an infinite temporal regress of events cannot exist
(Sub argument 2)
2.21 A collection formed by successive addition cannot be an actual infinite.
2.22 The temporal series of events is a collection formed by successive addition.
2.23 Therefore, the temporal series of events cannot be an actual infinite.
So the conclusion of the two sub arguments for 2.0 would have to be the same as 2.0 in order for the argument to be valid, ie all the lines in red have to be the same. But clearly they are not.
If I submitted something like this to my old DM lecturer he would have fixed me with one of his famous withering stares and asked me if I was quite sure I understood the concept of a proof.
Here is how it might be fixed:
B(x) df x begins to exist
C(x) df x has a cause
A(x) df x is an actual infinite
R(x) df x is an infinite temporal regress of events
S(x) df S is a collection formed by successive addition
T(x) df x is a temporal series of events
1 (x) B(x) implies C(x)
2 B(u)
2.11 not poss exists x A(x)
2.12 (x) R(x) implies A(x)
2.13 not poss exists x R(x)
2.14 not B(u) implies R(u)
2.15 not B(u) implies not poss exists u
2.16 exists u
2.17 B(u)
2.21 not poss exists x S(x) and A(x)
2.22 (x) T(x) implies S(x)
2.23 not poss exists x T(x) and A(x)
2.24 not B(u) implies T(u) and A(u)
2.25 not B(u) implies not poss exists u
2.26 exists u
2.27 B(u)
So there are two new premisses that would need to be defended:
2.14 not B(u) implies R(u)
If the Universe did not begin to exist then it would be an infinite temporal regress of events
2.24 If the Universe did not begin to exist then it would be an infinite temporal series of events
not B(u) implies T(u) and A(u)
I can see why he would be reluctant to defend these premisses.
Of course the argument, even if sound, would only prove that the Universe has a cause, not a God. He offers a rather preposterous kludge to explain why this cause has to be a God. I would love to see him even try to formalise that kludge.
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