What you are missing is that the modern science method doesn't answer anything but a few " how" questions, if indeed those are accurate. Faith was needed and still is, to answer the " Why?" questions.
This is clearly false.
For example, science can answer the question of 'why' atoms bond to each other to form molecules. They do so because of energy minimization and the way that electrons are shared between atoms quantum mechanically.
Science can answer 'why' nuclear fusion happens inside of stars: the pressure and temperatures are high enough to strip the nuclei of their electrons and to overcome the potential barrier between nuclei.
Science can answer 'why' an epidemic spreads: people don't take sufficient precautions of the correct sort, which allows the virus to transfer from one person to another.
Science can answer 'why' planets orbit stars: the force of gravity has a certain form and that leads to precisely the types of motion we see in planets.
So, science can and does answer many 'why' questions.
And the *way* it answers 'why' questions is by finding more fundamental laws that can be used to deduce the behaviors we want explanations for. it does this all the time in all areas of science.
But, what cannot happen is the answer 'why' the fundamental laws are as they are. Why not? because any possible explanation would have to be based in a *more* fundamental law.
In fact, since science can only calculate from the material universe it makes it impossible to know if it's accurate.
The history of the subject shows that you are wrong. We can and do determine the level of accuracy (called error bars) on every observation. This is what helps us control the propagation of inaccuracies in our analyses.
Because our minds are part of that universe. If that's all they are, we have no reason to trust our intellects.
Well, we should NOT have absolute trust in them: we know of many situations where we can easily be lead astray. We are subject to confirmation bias, optical illusions, social pressures, etc. The whole reason for the scientific method is to help guard against those issues.
And this is precisely why *faith* is such a poor way to discover truth. it is the essence of confirmation bias, allowing social pressures to dictate viewpoints, and allowing for 'feelings' to lead us astray. The whole notion of faith is *precisely* what needs to be guarded against in order to find out truths about the world.
They would be completely controlled by an unbroken chain of blind causation. We, then, are just fizz in the bottle of the universe and our thoughts are no more under our control than the solar system is. Only if something exists outside of the material can we objectively view the workings of the universe. In fact, it seems that perhaps we can alter reality with only our minds. This is where religion has always informed us... outside the physical sphere there must be another, greater reality that answers the " Why"? questions.
Again, this is clearly false. We evolved to be able to distinguish threats in an environment. An inability to do so lead to dying off. So, while we cannot have absolute confidence in our senses, we can have at least some. And this is why testing, observation, and exploration is so important: we *know* that we miss a lot and need to find other ways to explore.
One of the ideas in the scientific method is that ideas need to be tested to see when they are *wrong*. By finding out the limitations to our ideas, we can more confidently apply them when they do work. but this also means there needs to be a continual pushing of limits: more accuracy in our observations, more possible types of observation to be made, more ways to explore and measure, etc.
We *know* there are things our senses cannot detect because we have detected them! We know infrared light is there because we figured out how to detect it even though we cannot directly see it ourselves. Same for ultrasound, or xrays, or subatomic particles, etc. We *can* detect these even though we cannot detect them directly with our senses.
This seems to be an aspect you are missing.