If I may address your second point first, in examining the natural world, there is no logical reason that discounts non-natural explanations from being a valid conclusion.
This is true, but there is also no logical reason to accept non-natural explanations as being true without investigating a phenomenon as thoroughly as possible. More to the point, let's take a look at particular category of non-natural explanations, specifically "humans did it". For example, artificial selection in breeding, electrical lights, air conditioning, computers, and automobiles, just to name a handful of innovations on a very, very long list. In each of those things, we can legitimately say that "so-and-so invented it", and it will be true. But it won't explain that thing, or how to do it; saying that the Wright brothers invented the airplane doesn't explain how to make one, or how we can make a heavier-than-air plane fly in the first place.
Moreover, without the natural explanations underlying the non-natural ones, the non-natural ones aren't possible. Without the "equal but opposite" reaction caused by an airplane's wing pushing down on the air, thus causing the air to push up on the wing, an airplane couldn't stay aloft, let alone take off. Without exception, everything invented by humans is underlain by the natural explanations that make it possible. So that means that even a non-natural explanation for something will still be underlain by the natural principles which make it possible - therefore the purpose of science is to discover those natural principles.
As I have written, biological life is replete with examples of design that are far more advanced than our own designs. Given the fact of the extreme mathematical improbability of random mutations and natural selection to generate specified complexity and the fact that we experience the causal ability of intelligence to design analogous systems, the presence of a designing intelligence can only be discarded by willful ignorance or philosophical bias.
With all due respect, the only thing you're actually accomplishing by saying things like this is to demonstrate your own "willful ignorance" and "philosophical bias". It's plainly dishonest to pretend that your own position is the only valid one, and the other position must have only come about because of ignorance and bias. I don't deny that it's possible for life on Earth to have been designed, but the fact remains that even if it was, the designer either had to have been designed by something else, or else it came about naturally. There really aren't any other options available to explain the existence of such a designer in the first place. About the only one I can think of is that it literally sprung fully developed out of nothing - even though that's even more wildly improbable than random mutations and natural selection generating complexity.
Claiming "intelligence did it" doesn't help matters any, in other words, because you still have to explain that intelligence somehow, and point to the evidence it left of its own existence (and not by saying that the very things you're evaluating are that evidence, because that's a circular argument). Logic and philosophy can't do that either, because you still have to evaluate the conclusions you draw through them in the real world, lest you accept things like Aristotle's elements or Plato's forms.
Philosophical naturalism holds that the everything that exists does so within the spatiotemporal universe, that everything, in theory, is reducible to the language of natural science and explainable in scientific theories. In order to show naturalism false, all that is required is to demonstrate that it is plausible that at least one thing exist outside the spatiotemporal universe; in other words, if something that exists can not be reduced to mere physical properties, then naturalism is false.
Of course, the problem is demonstrating this without relying on naturalism, in such a way that other people can verify it without falling prey to something like Plato's forms.
I contend that the mind and mental states are different from the brain and brain states. In order to show that two things are different, I will use the law of the indiscernibility of identicals which states that for x and y, if x and y are identical, then for any property P, P will be true of x if and only if P is true of y. Essentially, everything is identical to itself. If there is a property that is true of x but not of y, x and y are not identical and thus, two different things. Though there are more, three examples should demonstrate that mental states have different properties than brain states, and thus are two different things and not reducible to natural descriptions.
Even if they do have different properties, it does not follow that they are not reducible to natural descriptions. The properties of the Macintosh operating system are different than that of Windows, which is itself different from Unix/Linux. But that in no way shows that those things are not reducible to natural descriptions.
First, intentionality is a property of mental states and not brain states. This refers to the 'of-ness' or 'about-ness' of our mental states. Our thoughts are always about something. We think about tomorrow, or about that new car, or about our next forum post. On the other hand, intentionality is not a property of physical objects. Neurons are not 'about' the next bill payment. Physical objects can be in spatial or causal relation, but they are not about any thing the way that mental states are.
All this shows is that the mind is different than the brain, which is true in the way that a computer program is different than the hardware that it runs on. Yet, were it not for the hardware, the program could not run. A single transistor can't run Windows; does that mean that Windows can't be reduced to physical properties?
Second, mental states are incorrigible, that is, we cannot be mistaken about our mental state. We are incapable of not knowing what we are thinking. Explaining our thoughts can be difficult or we may be wrong in our thinking but we do not have to explain our thoughts to ourselves. We know our mental states incorrigibly. Certainly, we can be and often are wrong when it comes to knowing physical objects, including brain states. We do not know physical objects incorrigibly.
This is demonstrably false. People are mistaken about their mental states all the time. On top of that, we rationalize our perceptions and memories all the time, often to the point where they barely even resemble reality. A person can fool themselves into thinking that they're happy when they're actually sad, for example. And that doesn't even touch on the subconscious, which we are incapable of perceiving. Therefore, mental states are not incorrigible, because we cannot even perceive anything in the subconscious to begin with, we can deceive ourselves about our mental states, and we can simply be wrong about them.
Third, personal identity is best explained through the existence of a mind. One does not have the same body as when one was younger and, yet, one is the still the same person. If our personal identity is explained in purely physical terms, we would have to admit we are a different person. Changing just one cell would create a new person. However, we know this is not the case. Introspectively, we are all aware that we have maintained our personal identity over time. A mind best explains this continuity of personal identity over time.
This is even worse than the last point. First off, identity is a factor of both body and mind. The mind changes alongside the body; the physical changes our bodies undergo influence and change the mind. Indeed, sudden or severe enough changes in the body can kill a person, thus ending their personal identity. Notably, this goes above and beyond injuries, diseases, and the like. Systemic shock, such as being taken into a sufficiently different environment, can and has killed people. What that means is that the body (and mind) are capable of adapting to changes within a certain degree, and anything beyond that is risky. Ordinary physical changes (such as cell replacement, puberty, and the aging process) are gradual, and our bodies are adapted to them. More significant physical changes can possibly kill us, thus ending our personal identity.
Second, our awareness of our personal identity is not total or even particularly reliable. We lose that awareness while we're sleeping, for example. And if you think back to your actions in the past, it can often seem like you were a totally different person back then (especially if you've dramatically changed since then). In fact, that's the truth; we were different people back then, because of mental and physical differences. It's not our sense of personal identity that causes us to associate those actions with ourselves, it's our memories of having done them. Therefore, personal identity is not all that it's cracked up to be.
Since I am sure it will come up, simply because changes to the brain can change one's mental state, it does not mean they are the same. The fact that mental states and brain states are causally connected in not sufficient to say they are identical. To be identical, tt is necessary so have the same properties. As I have shown, the mind and mental states have different properties than the brain and brain states. Therefore, they are not the same thing, the mind is not reducible to a physical description and thus, naturalism is found deficient.
Just because the mind and the brain are different does not show that the mind is not reducible to basic physical properties. It simply shows that they are different, albeit related. In fact, it would be foolish to argue that the brain and the mind were the same, because they clearly are not. So why are you now triumphantly trying to claim that because the mind and the brain are not the same thing, that the mind is not reducible to basic physical properties and therefore naturalism is found deficient? Do you really think that this question of the differences between the brain and the mind has never been addressed before? And as I showed, your points in no way address whether the mind can be reduced to its basic physical properties. You need to do more than simply say that it is not same thing as the brain to do that - and that doesn't even touch on the flaws in the points you raised.
If a mind exists in a non-spatiotemporal state, intelligent design is all the more likely. In fact, the existence of a mind is more explainable, perhaps even expected, if ID is true.
Irrelevant, as you have not shown that minds exist in a "non-spatiotemporal state".
Regarding the falsification of ID, as with all scientific theories, it is not logically possible to falsify. One can always posit logical possibilities to overcome obstacles. More appropriately, ID can be refuted easily by producing a clear, defined and demonstrable naturalistic pathway to generate specified complexity. If random mutation, natural selection, and lots of time were adequately capable or even marginally possible of such a task, I don't think intelligent guys like Stephen Jay Gould would be submitting theories such as punctuated equilibrium or Crick's directed panspermia?
I don't think you understand what falsification means when it comes to science, and frankly, I question your understanding of science in the first place. You see, science is built around demonstrating hypotheses through evidence and testing, and you tie all those hypotheses together to eventually form a theory (provided, of course, that the hypotheses hold up under testing). It is not predicated on pure logic the way you seem to assume it is. People do not just formulate logical possibilities to overcome problems in science, because science depends on testable evidence, which logic cannot provide.
Because a scientific theory is formulated by combining a number of tested hypotheses, what that means is that if someone finds new evidence that isn't explained by those hypotheses, or that seems to contradict some of them, you don't just throw out the whole theory. You reexamine the existing hypotheses in light of the new evidence, and discard/revise them as necessary. Once you've done that, you have a new hypothesis and a better theory, because any hypotheses that were falsified by the new evidence are discarded.
Finally, the reason intelligent design is not accepted as a theory is because it's based on the idea that its adherents have that certain things are impossible (notably, without actually having evidence of that impossibility, let alone having tested it). If intelligent design were based on testable evidence, the way that every single other scientific discipline is, then it could be evaluated. As it stands, one must either agree or disagree with it, because its basic premise is that life cannot have come about naturally, and it does not provide any way to test this. That isn't scientific, therefore intelligent design is not science.
In the end, philosophical naturalism is unlikely and natural explanations have been insufficient. Alternatively, the exist of a mind is plausible and intelligence is the only known cause of specified complexity. Why must every conceivable naturalistic possibility be examined before intelligent design gets a fair hearing? Why not assume apparent design is actual design?
Because humans have a very strong tendency to assume things based on what they think they know, known as an argument from ignorance. The only way we know of to counter this is to minimize assumptions, ala Occam's razor. To put it bluntly, intelligent design contains far too many assumptions to be taken seriously. Even if there were no known explanation, it would still not be reasonable to just assume "intelligence did it", because it's far more likely that our knowledge is just lacking.
That leaves aside the fact that your logic had a number of errors in it, most notably the fact that you didn't even touch on whether the mind could be broken down into basic physical principles. You simply assumed that since the mind wasn't the same as the brain, that the mind couldn't be broken down into basic physical principles; yet, a computer program is not the same as the hardware it runs on, yet we can break computer programs down into basic physical principles. Consider that an illustration of the danger of making assumptions.