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There are a number of major flaws and logical fallacies in the argument:
  1. The biggest flaw in the argument is that it does prove anything, but instead replaces the supposed problem with a larger problem. If the universe was made by a god because nothing can exist without cause, then something must have "caused" God.This is often countered by saying that God is the exception to the rule, however if God is the exception to the rule why cannot the universe be the exception to the rule without God.
  2. The original argument is non-specific: It states there must be a First Cause but doesn't say that the First Cause had to be God or a divine being. There are an infinite number of causes other than a human-inspired god that could have caused the creation of the universe. The creator of the universe need not even be supernatural, or sentient or intelligent to satisfy the argument of "first cause".
  3. The argument makes the assumption that a causal chain of events cannot be infinite, that it must terminate at a point. While the nature of cause and effect is observed by experiment (within the limits of the uncertainty principle at least), whether this chain can be infinite or not is certainly not mandated by experiment and is only inductively prefered.
  4. It forgets the fact that matter and energy necessarily exist and are not contingent: The 1st Law of Thermodynamics and the Law of Conservation of Mass state that matter or energy cannot be created, nor destroyed. Therefore, there cannot be a state where matter or energy does not exist. Because of this, matter and energy necessarily exist. Therefore, this argument doesn't apply to matter or energy.
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Who rejected the cosmological argument?

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What does the cosmological argument teach us about God?

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What are the criticisms of cosmological argument?

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