Logic, as in rational thinking or reason, is already a part of science. But ways that people have used in order to explore or think about the universe beyond just science could be things like philosophy, introspection, meditation, and yes, religion.<quoted text>
So we do accept that science ITSELF has limits.
However, at the point where science becomes limited; is there nothing that we can use, no faculty or mechanism by which to investigate and observe what science itself is too limited to assist us with?
Yes. And that faculty is logic.
It is logic that allowed Einstein to perform a thought experiment WHICH WAS PROVEN ACCURATE years after he performed it.
This should have demonstrated that logic and reason are most effective in discovery IF USED ACCURATELY.
But then there was PolyMath.
Yes, science is limited. It explores and investigates the mechanistic, naturalistic aspects of the universe. That's it. If you want to explore beyond that (or explore if there IS something beyond that) you need to rely on something else. Different tools for different jobs.
The reasons we have these debates at all is because some people think that the mechanistic explorations science does somehow conflicts with the other explorations they are doing.
Let me give you an example. Presumably you believe God created rainbows. But at some point you probably learned about how rainbows are made by light going through rain droplets. Did learning that undermine your belief that God created rainbows? Of course not, that was just the mechanism by which rainbows are formed.
Same thing with Evolution or the Big Bang Theory or whatever other science. Evolution is the mechanistic explanation for the diversity of life on Earth. That's it.