Well, besides, even with double-blind studies that are impeccably done, and things which fit well into the structure of science, you can never say anything at all can be said with no doubt because of the nature of science.
You can only say that according to this mathematical model, and these equations, and this theory, this is the best way or representing this thing until a better way of representing it comes along. People who believe in science do the same thing. They think something is proven or explained just because there happens to be a convenient representational model. Everything remains mysterious even after it has been given a working reprentational model, which is what science is.
Math, itself, is mysterous and since all science is modeled using math, then what science shows to us also has to remain mysterious. The more you closely inspect any mathematical model, the wierder it gets. Calculus shows, for example, that apparently no whole number can ever really be reached. You can only get closer and closer and closer to that whole number. In reality, even after you've gone to the millionth decimal place, there are still an infinite number of decimal places between that number and the real whole number and you still have to eventually just say, "it's 3, not 2.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999..."
Lets show the strangeness of numbers a second. It is quite easy to show how confusing the concept of math is by taking something as horribly simple as 2 plus 2 could ever equal four. If there are an infinite number of numbers between 1 and 2, which the number line seems to imply, and for an infinitely long period of time you could pick yet another number which would fit between 1 and 2, thus making the number 2 sort of like a mountain that nobody can ever climb, and then isn't there an infinite gap between 1 and 2? And, if the same thing can be said about the gap between 0 and 1. So, if there is an infinite leap between the number 0 and the number 1 and and infinite gap between the number 1 and the number 2, then why isn't every number plus any other number infinity? In the case of the distance between the number 0 and the number 2, Wouldn't that mean that there's such a thing as an infinity that is two times bigger than another infinity? So, with those facts in mind, how does 2 plus 2 equal four? And, after you've added 2 to 2, why did it work but by definition that someone arbitrarily made up that 2 plus 2 equals four. How can there be an infinite jump between every number and every other number, yet have two numbers seem to be equally spaced upon the number line.
There are far more mysteries to math than just that, though. All of math is a mystery. Like irrational numbers like Pi or e. How many irrational numbers are there? Nobody can say. But, irrational numbers prove that decimal numbers do not fill up the number line completely. That even if you took every possible number and divided them by every other number on to infinity, there would still be an infinite number of gaps in the number line that could potentially be filled with an irrational number. And, there's no way to prove that even if you could figure out every irrational number in the world, if the decimals plus the irrational numbers would ever fill the number line completely. In fact, there's probably a way to prove that they wouldn't.
So, math is a very strange thing. It almost seems to be a thing which shouldn't work, but it does. The only way you can make it make any sense at all is by saying, "the distance between zero and 1 equals the distance between 1 and 2 because that's how we originally defined it. By definition, the distance from zero to 2 is twice the distance between zero and 1 because we defined it that way at the beginning.
Science is the same thing. A truth, in science, is generally accepted as truth if from many different methods the same conclusion is reached. But, some things in life, there's only one way of reaching a certain conclusion (let's say that string theory is a good one where many don't really believe that there are long strings out in outer space that we just can't see, and there's no other model which implies there are actual strings out there somewhere) yet people are starting to "believe" in string theory, even though they don't really think there are strings out there (but some do think the strings can be thought of as being real things).
Much of science is like that. In the old way of thinking, the model of the atom where the proton was a ball and electrons circled around it - they thought that was how an atom actually looked like. Then, probabilithy theory hit the fan and that model was exploded, no longer did the unseeable atom look like that, but looked like different-shaped probability clouds.
I think most people would have said there was "no doubt" that an atom looked like a planet with moons circling around it and now that an atom is thought of as a probability cloud, is that what an atom "really looks like"? does it mean that is what an atom really looks like? So, with a mathematical model one has to always understand it is a model, not necessarily reality as we'd determine reality and certainly the words "no doubt" have nothing to do with science.
Math equations which model an aspect of nature tend to also prophysize or imply some other thing (sometimes completely unrelated to the original problem, which is strange).
But, there's really no such thing as "no doubt" in science.
Because of the nature of science, and the nature of math, it's impossible to say anything has no doubt. You can only say that it shows us a certain aspect of something, or a certain way of looking at it until a new model is found. Then, you still can't say there's no doubt that that model is reality either.
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