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Apr 27th, 2012 | syntax:
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Various formulations of the Kalam cosmological argument have been made. I found the one here on Theopedia. It is already presented in standard form as follows:
1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.
This argument is deductive, as there is no probability involved. The conclusion is stated with no uncertainty.
In order to put it on a truth table, I had to replace the variable "whatever" with "universe," then I treated it as implication: "the universe began to exist implies it had a cause." This takes the form of A ⊃ B / A // B, and is truth functional valid, as the only instance in the truth table where both premises are true, the conclusion is also true.
Anything can be asserted about the unknown and we would be unable to determine if such an assertion was true or false. As contradictory assertions of unknown truth value can easily be made about the unknown, we cannot treat them as true, so we must treat them as false. The premises contain such assertions. Therefore, the argument is not sound. In order to support this, I need only demonstrate that one premise must be treated as false. Which premise is is treated as false depends on the definition of "begins to exist" the arguer intended.
If the arguer intended that "begins to exist" refer to formation from previous material, then the first premise is known to be true based on the human understanding of physics. However, in this case, the second premise would be treated as false since the arguer provided no reason to think that the universe formed from previous material.
Alternatively, if the arguer meant "begins to exist" as formation from nothing, then the first premise is treated as false, because the arguer provided no reason to think that scientists have ever determined any rules regarding formation from nothing, including cause and effect. It is not necessary to show the second premise is treated as false; but it would also be, as the arguer provided no reason to think the universe came into existence from nothing either.