I'd like to discuss and explore the Teleological Argument, so I offer the following version:
1. The universe is fine-tuned for life.
2. The fine-tuning of the universe is due to either physical necessity, chance, or design.
3. It is not due to physical necessity or chance.
4. Therefore, it is due to design.
Here are some of my thoughts:
You should be careful about using the term "fine-tuned" in the opening premise, since it already implies a goal-oriented activity (the tuning process). I think people know what you mean, but there is probably a better way to word it so that it does not appear to presuppose what you are trying to prove.
I do not understand what you mean here by "physical necessity". The concept of necessity implies the existence of an unfulfilled "need" of some kind. And any such unfulfilled need will, of course, remain unfilled unless something comes along to fulfill it. When it does, it is either by chance or design. So the term "physical necessity" does not appear to offer an option which in any way removes the requirement for one of the other options. In fact, it only appears to try to describe in what WAY the process of life happens.
Another thing to consider is the concept of "meaning". What if someone designed life, but with no apparent meaning or purpose. In that case it would be "designed" but very much arbitrary. With no apparent goal for this creator's actions, even those actions came upon us merely by ... chance. So in order to rule out chance, you need to show there is "meaning", that is, a real "goal" that is evident (or communicated).
As a logical argument, whatever other folks here may say, the outline you gave is valid. It may not be "sound". But it is valid. For those who are unfamiliar with the difference, here is a valid, but unsound argument:
1. All cows fly.
2. Jessie is a cow.
3. Therefore, Jessie flies.
That is valid because IF the premises are true, then the conclusion is true. But that is also unsound because, well, the first premise is wrong.
So your argument is valid, but yes, we would need to show that the first three premises are actually true. For anyone who is willing to accept those premises based on your evidence, they must rationally accept your conclusion. But until then, no.