So technically, in math we refer to the core “ideas” from which all mathematics is derived as axioms, which we hold to be true until found to be false/self-contradictory/redundant. We arrive at these by describing the world, so it’s more like - “if you agree to the following statements, then you must also agree to the entirety of mathematics”.
Continuing with the occupational pedantry, I think there is some confusion lies in conflating “fact (repeatable observation)” with “fact (tested causal mechanism)”
So, kinda not really, but kinda? This is more philosophy but i think the idea is that as long as we can ensure that “there exists a statement for which there is a piece of evidence that can prove a statement false, but no evidence exists after significant testing and experiments” IRL we can use this interchangeably with “I have found a causal mechanism that causes this phenomena and can replicate the effect while controlling for confounding variables”. Statements under both are true and correct to the best of our understanding.
Right, so that, er is not what we are talking about. You seem do be under the impression that “facts” are undisputable. They are not. We believe them, because we can put them to every test we can think of, to build a body of evidence that lends credence to a ‘theory’, hence the requirement for statements to be falsifiable.
This theory of knowledge is a hard requirement for any field associated with research and is well defined. In this case, we must default to the NULL hypothesis ( X does not exist) because we cannot formulate a falsifiable statement for ( X does exist). We can falsify our NULL by providing evidence for X ( X is this, X is here, X can do this). However, for most tests we default to alpha = 0.05 for statistical significance because of convention, and because data must be gathered in batches, sometimes inaccurate. Likewise, proving life on Mars is hard, because we must first falsify every other possible theory before we can claim “the presence of this compound cannot be explained by any other theory aside from the presence of life” as we cannot observe anything directly.
I am not going to teach a lower level stats class in a comment section, but our physicist is correct in stating that this is a belief , because that is what it is - a extremely well tested belief, that we can consider to be “fact” in common parlance. You could of course chose not to believe it, if you can disregard all of human achievement.