Hmm I agree with some points and disagree with others.
Let's start with maths again, where we seem to be in agreement:
Assuming (as we both seem to be for now) that mathematics is pure expression of logic and reason: if you can prove something mathematically, you "know it", and if you can't prove it mathematically, you "don't know it".
With apologies to real philosophers, let's call known mathematical facts "truth".
It is possible for things to be real without us being able to express their truth accurately. This is what science does: it/we make observations and adjust our understanding based on experiments that make use of those observations.
These experiments can be complex - like firing electrons through sheets of metal to determine their physical structure - or they can me simple - like attempting and (for now) failing to walk through a wall. Based on the results of those experiments, we make technological progress, and potentially in the future, we will discover some technology, or a "more correct" fact about humans, or walls, that will enable us to develop a technology that allows us to walk through them.
However, in our current moment, we can scientifically demonstrate that it is better to leave the house by the front door than to attempt to walk through the wall.
Again with apologies to real philosophers, let's call these kind of empirical facts "knowledge".
With these definitions, knowledge and truth are not the same thing. We could look at truth as "perennial knowledge" or perhaps knowledge as "temporary truth until proven otherwise". Knowledge is falsifiable. Truth is not. Mathematics itself has a whole branch of study dedicated to measuring how likely knowledge is to be true: probability.
As our scientific knowledge, and technology improves, we're able to better see, measure and interpret the world, and the probability that our knowledge is truth gets higher. There are of course local maxima, and there are also step-changes with technological innovations and so on.
My argument is that we can "know" both "truth" and "knowledge", but knowledge is subject to change over time with appropriate evidence. Importantly, you can draw logical/mathematical conclusions from knowledge and call that truth. E.g: that people cannot walk through walls is knowledge, and therefore that leaving the house via the front door is a BETTER option than through the wall is a logical truth.
---- Breather time ----
Now we come to the third part of the spectrum:
> If you believe in the scientific method
Belief/religion/dogma/etc. These rotate the direction of reasoning and say: "We KNOW the reason, and evidence to the contrary is not able to change this belief". (See also: "motivated reasoning").
In effect, "belief" is a way of creating "truth" just like mathematics. And it suffers the same "problem" that "once proven, it cannot be unproven". The distinguishing difference between belief-as-truth and mathematics-as-proof is that people can't walk through walls.
So my question for you is: Is the best way to leave your house by walking through the wall?
- If you answer "Yes", you are exercising belief
- If you answer "No", you are exercising science
- If you answer "I don't know", then your day-to-day actions will decide for you. (Unless, like me, you never leave the house and the point is moot.)
> It is possible for things to be real without us being able to express their truth accurately.
Of course you might not need to make up your mind for something to be real. It is very possible that there are real things that your mind is not even aware of, so if that is the case it would be impossible for things to become real only after you've made up your mind about them.
> So my question for you is: Is the best way to leave your house by walking through the wall?
I don't know and I don't care.
Even if it is theoretically possible to know what is the best way to leave my house, the evaluation required to get there is in competition with all the other things I could be doing. I can find no compelling reason for why I would want to do that. Having no clue seems like a perfectly fine state to be in, in this case.
I leave my house by way of door because someone once told me that was the way and I have blindly followed their gospel since. I've given it no further consideration and certainly haven't made up a mind about it or anything related to it. I don't know and that's fine. It could be that the door is the worst way to leave and that the wall is better, but it doesn't really matter, does it?
> make up your mind / ... mind is aware of
These are not at all the same as "express their truth accurately".
> I don't care
An interesting assertion, given the length of this thread. But I do agree it's possible to go through life only believing what others tell you. We all live in a world discovered and created by those who came before us.
> These are not at all the same as "express their truth accurately".
Nor do they need to be, but making up your mind is the topic of discussion that we are having, so that is what we are going to talk about.
> An interesting assertion, given the length of this thread.
How so? I don't care about how to best leave a house, and us not moving on to that topic supports that. Using that idea as a rough analogy or example to grease discussions around the actual topic at hand is not the same as it being the topic.