Practically every argument you’ve ever had is the same. Not because no one ever changes their mind, yelling or any other cliche about confrontational discussions but because all arguments about evidence ultimately focus on just three numbers.
Admittedly this sounds simplistic but it turns out all empirical arguments are about the prior probability of a theory, which is how typically is the hypothesis being proposed true and the two consequent probabilities of a theory, which, respectively are how likely we are to see the evidence we see if the theory is true and how likely we are to see the evidence if the theory is false. Once there is agreement on these we could simply plug those numbers into Bayes’ theorem and out would come the answer to how confident you should be in the proposed hypothesis.
Strangely even arguments over deduction could be said to be a mere abstraction from these three numbers which deal with what would be the case if we could know with certainty that something is definitely true or false.* Indeed all arguments over whether or not a theory is falsifiable, and all arguments with people who don’t value evidence, are ultimately arguments over the two consequents. Likewise all arguments about the empirical utility of faith are arguments about systemically skewing these three numbers such that someone overestimates the prior probability of their theory (sometimes going so far as to assign a probability of 1**), overestimates how well their theory predicts the evidence and underestimates how well alternative theories account for that evidence.
The usefulness of acknowledging this simple fact is in clarity. It’s much harder to talk past each other in a debate if you make it clear which of these three numbers some piece of evidence is supposed to effect. As far as I know, while some people belittle the utility of science, very few will consciously attack the usefulness of math. Oh wait.
*For example take the classic syllogism “All men are mortal. Socrates is a man. Therefore Socrates is mortal.” This could be said to demonstrate if we new with 100% that all men are mortal and that Socrates is indeed a man we would know with 100% certainty that Socrates is mortal. Given we can’t actually know this, or anything else about the outside world, with 100% certainty all of deduction could be said to be a big “what if.”
**It turns out if you insert a prior probability of 1 no matter what you put in for your other two variables (other than zero) the posterior probability you get out is 1. In other words, it is a mathematical certainty that if you go in thinking “no evidence can change my mind,” that in fact no evidence will change your mind even if your theory predicts the opposite of the evidence we observe. This, needless to say, guarantees unshakable faith is not a path to truth.