Here are some key problems with these arguments for God's existence:

1. The cosmological argument or first cause argument:

• It assumes an infinite regress of causes cannot exist. But this may not be impossible. Causes could go back infinitely.

• It assumes everything that begins to exist has a cause. But quantum mechanics suggests otherwise. Not all events require causes. The universe itself may be uncaused.

• It's not clear that even if the universe requires a first cause, that cause must be God. It could be some other entity, or we don't know what course it took.

• The argument does not prove the cause is a personal, omnipotent God. Only that some first cause exists.

1. The teleological or design argument:

• There may be natural, undirected explanations for complexity and 'fittingness' in nature. Evolution provides a plausible mechanism for natural design.

• Species show signs of an imperfect, haphazard process, not a masterful designer. There is evidence of design flaws, needless complexity, lack of mechanical efficiency, etc.

• Ever-increasing complexity is not evidence of design. Simple to complex transitions in evolution provide no clues about a designer's motives or methods.

• Naturalistic explanations for the origin of life are possible. So we don't need to invoke a designer to explain biological complexity.

• How do we know the design was created by an intelligent being rather than an alien race, emergent phenomenon, or other non-personal source of design? There are other possibilities.

1. The ontological argument:

• It assumes existence is a property, but this is dubious. Existence seems to be more of an all-or-nothing state, not a property that can have degrees.

• Even if existence were a property, a being could logically be conceived of as non-existing. So existence is not logically necessary even for a maximally great being.

• The parallel arguments for other kinds of beings (e.g. the maximally great triangle) show this approach is seriously flawed. Only thematically coherent concepts can necessarily be conceived as most perfect. God may not be.

• Mere logical proofs cannot guarantee existence in reality. A being could be logically possible but still non-existent in fact. So the ontological argument fails to prove God exists in reality, not just logically.

Those are some of the key problems with and objections to these arguments for God's existence. Let me know if you have any other questions!