Legion
Here are a couple of versions of the fine tuning argument for atheism, courtesy of Iron Chariots. Given your claims of expertise in logic - pretty amazing you are completely unaware of this.
"To restate the argument, in the form of the Transcendental argument for the non-existence of God :
Let X be "the combination of physical constants which is necessarily capable of sustaining life" and Y be "the combination of physical constants which is necessarily incapable of sustaining life".
1. X is necessary, in whole or part Y is necessary, in whole or part. 2. If theism is true, then divine creation obtained the universe. 3. If divine creation is true, then all in the universe is contingent to God's act of creation, and nothing in the universe is necessary (God could have created any universe). 4. If theism is true, then no X or Y can be necessary or have a necessary part (from 2 and 3). 5. Theism is false (from 1 and 4).
If a theist denies premise 1, they would deny the fine-tuning argument, since the first premise of this argument is the same as the first premise of the fine-tuning argument.
In a similar form of the argument:
1. If theism is true, then divine causation obtained the universe. 2. If divine causation obtains, then all facts of the universe are contingent upon God's act of creation. 3. If theism is true, then life can arise under any possible physical condition. (from 1 and 2) 4. If theism is true, then fine-tuning is invalid. (from 3)
Maybe the transition from premise 2 to 3 requires further justification. Denote the physical constants by {X; Y; Z} and the obtainment of life by L and negation by ~.
A fact of the universe is that {X--> L; Y--> ~L; Z--> ~L}. That is, X can result in life, and Y and Z can not result in life.
Since the fact is contingent upon God's act of creation, then it is not necessary and so can be altered.
If it can be altered then the following can be true {X--> L; Y--> L; Z--> L}, such that God could make anything result in life, or life consist in any environment. Basically, X, Y, and Z are irrelevant to God if divine causation obtains."