Isn't the meaning of the scientific method basically distilled into "I believe this to be true, now I am going to spend the next several years trying to disprove this belief."?
Ish. Popper said that's how it
should work, but you'll notice we'd been doing science for a while before Popper came along. I suspect for most scientists, what they're actually doing is "I believe this to be true, now to find some experiment that supports my hypothesis over the competition"*. Which is not a bad way to go about it, really. The ideal falsificationist that will abandon the most cherished belief at the first experimental result that goes the other way exists only in the minds of some philosophers of science.
Postulates, axioms, primitive notions. Things that can't be broken down further. If those things are somehow "false" then a lot of things need revising. It would quite disconcerting if "A does not equal to A".
I don't know that there's any meaningful sense in which "A=A" can be false. A belief about the physical world can be said to be false if it doesn't match against reality. What can I contrast "A=A" with, to show it to be false?
A logical statement can only be said to be "false" if it does not follow from the axioms of a certain logical system. If someone says that 1+1=3, I can use the Peano axioms to prove that 1+1=2 and derive a contradiction. I cannot do the same for "A=A", because that's one of the Peano axioms itself. If I derive "~(A=A)" then Peano arithmetic is inconsistent, so "A=A" and "~(A=A)" are equally meaningless results.
I'll comment more after watching the video.
*The cynic in me would alternatively suggest "This is true, but I won't get published without some sort of experimental result", which I don't think covers most scientists but certainly
some.
EDIT
After watching the video:
Mostly, I think Yaezakura covered it. They meant one thing, the people arguing with them thought they meant another.
While I do think they spelled out what they meant pretty well, I can understand the reaction. "Science takes faith too!" is one of those stock phrases that is used to imply "...and therefore any piece of bullshit I come up with is equally or more valid".
Other than that, expanding on my point about axioms above:
The video brings up Euclid's fifth postulate as an example of an axiom that was later rejected, which is a valid point with some subtleties. Euclidean geometry doesn't fully correspond to the geometry of space-time, but that is not the same as saying that Euclidean geometry is false. It does mean that the theory that space-time can be described as an Euclidean space is false.
The math is the math. To shamelessly steal an example, if you try to use addition to count apples, it will work out great, because if you have one apple in a basket and put another apple in the basket, the basket will now contain two apples. If you try to use for clouds, though, you may run into trouble, because if one cloud collides with another cloud, the result is one bigger cloud. This doesn't mean 1+1=1, it means that cloud-counting isn't modelled properly by addition. Similarly, space-time isn't modelled properly by Euclidean geometry (thought it works well enough for many purposes), but all that implies is that the mathematical object Euclid's postulates talk about is a model of other things.
