From here I've arrived at the point where our working model is that we think with our minds and we have senses to sense the natural world.
But on closer examination, by our minds, these senses appear to be fallible, so we concoct methods for gaining confidence in particular sense experiences. On even further examination we discover that our reasoning and other cognitive faculties can also be fallible, so we take steps to account for that observation too. So all we can do is construct experience and look for multiple ways of confirming what we experience to gain confidence in it, to give credibility to it, to compensate for the fallibilities. When we do this rigorously we call this science. Science gives us the best and most reliable explanation of our cognitive and sensory experiences, accounting for and accommodating for our fallibilities the best it can.
Note that this is an entirely inductive experience, from the particular to the general. Induction lies on top of no firm and absolute foundation, it is true. An inductive argument indicates some degree of support for the conclusion but does not ensure its truth. So, just to make it clear, none of this is offered as a proof! Of anything.
For any of the detail along the way we might use deductive reasoning, which is often thought to be more thorough, more concrete. This does not mean that deduction is always the better choice. Deduction is fine if you construct a valid argument; and if you have true premises then you have yourself a 'sound' argument, the most sure argument there is. But it's an illusion to think you can have a sound deductive argument at the limits of philosophy, in metaphysics - you can never be sure your premises are true! Why? Because all we have are our thoughts and our senses - we have no prior premises and arguments upon which to build our starting premises. So, if someone tells you they have a proof that, say, God exists, it's baloney, because it always relies on presupposition, and the presupposition can't be guaranteed to be true. If someone wants to offer you 'evidence' for God, that's a different matter and should be treated seriously.
We are fallible human beings. The very best we can do is accumulate data, examples, lots of them, and compare them and subject them to any tests we can. We create hypotheses, of which Richard Feynman said they could just as well be guesses. Any old random guess won't usually do - we could be here forever checking every possible hypothesis - something some theists think atheist are claiming (and what Pirsig mistakenly thought was a problem, in ZAMM - more of that in another post). Of course we base hypotheses on prior experience that appears to work. This is induction and science in action.
Science concludes (this means best explanation so far, not we're absolutely certain) that according to our senses and reasoning there is a physical world out there. It gets a bit quirky sometimes - e.g. quantum physics - but so far nothing has been found to refute this tentative conclusion. I mean, really, nothing! You have to consider what it would mean to refute this. You would have to find something that isn't physical. This is a tall order. Before sub-atomic particles were figured out the world was still physical. Discovering the sub-atomic particles didn't introduce some magic into the universe - it was simply that we discovered something we didn't know was there before, but is still considered part of the physical universe.
This is what will happen with any 'paranormal' effect or 'energy' that might exist. If it exists, then when it is found, that is when there is evidence of it, then it too will become a part of our physical description of the universe. The reason the paranormal is ridiculed so much isn't because we know it to be false absolutely, it's that fantastic claims have been made, but no evidence has been found to support them. Astrology? No evidence.
Evidence is the route to discovery and the support and maintenance of ideas and theories and facts. No evidence? Then it might as well not exist. Not, you note, that it doesn't exist! Science is not saying anything in particular does not exist. It only says to what extent there is evidence to support an idea. If we can't see it, taste it, feel it, etc., then we might as well act as if it doesn't exist, even if it does, for how can we tell the difference. We can happily go about our daily lives as if the speed of light does not have a limit, because in our daily lives we never reach that limit.
We can also ignore God as an entity because whether he exists of not makes no apparent difference. This means that despite the fact that theists can't prove God exists and atheists can't disprove it, it's irrelevant, because there is no evidence, and that's sufficient.
Many theists realise this and no longer require the existence of God as an entity 'out there' - See Rob Bell (h/t Lesley's Blog). But that doesn't mean theists have dealt with the problem of human fallibility in relation to faith. I'll get to that in another post.