Error reduction is not uncertainty elimination. Improved experiments and refined hypotheses can reduce the error, but some uncertainty will always be present, no matter how small.
Well, my 'thinking' here (I use the term loosely) is not just error reduction, but elimination of possibilities. Sort of a Sherlock Holmes thing - when you have eliminated all possibilities but one, the remaining explanation, no matter how unlikely, is correct.
For example, I give you a data point: A man and woman are arguing, and the woman accuses the man of infidelity.
person 1: ah, they are married, and are having a fight.
person 2: ah, a woman's friend caught her friend's husband cheating, and is telling him to stop.
person 3: ah, they are shooting a movie
person 4: ah, they are practicing for a play they are in
Now, add a data point: A man in a chair marked "director" yells "cut" at the end of the argument
-or- they put down sheafs of paper after the argument, you walk up and read them, and they have the argument printed verbatim on them
-or- etc.
Throw in 20 or so data points, and we can explain what is going on with certainty. For example, suppose they were really shooting a movie. For each new data point, the person arguing for a real marriage spat would have to create more and more convoluted explanations, and each subsequent data point would easily invalidate the explanation. With enough data points, it becomes impossible to create a logically coherent 'marriage' theory. And this is in the mushy world of human behavior, where it is pretty hard to get solid data. For example, they
could be shooting a movie, but really suffered infidelity in their lives, and even adopted the the words of the script to have their own argument. Hard to disprove in itself, but pretty unlikely, and easy to falsify if in fact there was no infidelity, for example.
So, for something like the existance of gravity, I argue we know it exists, as a fact. 4+ billion people, that's trillions of observations
a day since the dawn of recorded history in a wide variety of situations. I suggest any alternative explanation for gravity (like I'm staying on my chair right now because I was glued to it) has been rendered impossible to be true. Not unlikely, impossible. We may or may not have yet done the mental manipulations to prove this to our satisfaction, but that doesn't mean it is not possible in principle.
For example, assume a Euclidian space. We could measure right triangles for a long time, and use inductive reasoning to come up with x*x + y*y = z*z. But eventually somebody, perhaps with the name Euclid, will derive that equation from the axioms (premises) and definitions of Euclid geometry. Henceforth, no other equation can be considered as a possibility for the equation of a hypotenuse. There's no chance for it to be correct, no matter how small.
I suggest the same is possible, in principle, in science, given the premises that there are a small handful of laws that nature obeys, that they can be codified in math like systems, and that the universe is material.
But I dunno.
