Hello I'm trying to figure out the probability that the law of non-contradiction is correct from an unbias point of view. I know that as a law of thought people will be compelled to say 100% but I'm talking from an unbias point of view like whether meanings exist outside of our conscious experiences and reality not needing to conform with what makes sense to us.

So A does not equal not-A is one possibility then another is A does equal not-A as another possibility. Given 2 possibilities that would have me thinking that the probability is 1/2. But when I thought about it more, it gets tricky when you consider the consequences of if the law of non-contradiction being not true. In that scenario meaning breaks down and math becomes unreliable. So 1=2, circle-squares, 1+1=3, 1+1=2 all are equally valid with nothing in make them invalid statements in a reality where true is false and true is not false all at the same time.

So given the possibility that math is unreliable I was trying to work that into the probability to get a more accurate probability. Kinda like if you found the probability of something but then are told that the computing device you just used has a likihood of producing errors, how do you factor in for that? So maybe it's (1/2)*(1/2) when you have to factor in for the likelihood that probability theory doesn't work. Or maybe it's still 1/2 if the "math stops working" is not independent of law of contradiction being true so you can't multiple them like that as if they're independent events. But if math doesn't work then maybe that rule doesn't apply either.

I was thinking maybe instead of the probability being 1 / (1+1) it's more like whatever E(Xy) is as y approaches infinity of E(Xn+1) = (E(Xn)*1 ) / (E(Xn) + 1 ) where E(X0) = 1 because when you factor in for the likelihood of math not working you'd probably get some new value less than 50% to represent the likelihood of math not being reliable. But then that new value could face scrutiny since it was derived with mathematics. So I suspect that there'd be an infinite recursive calculation involved here to factor in for the likelihood of math being unreliable regardless of whatever I compute here.

If you do that math you should see this pattern:
E(X0) = 1
E(X1) = 1/2
E(X2) = 1/3
E(X3) = 1/4
etc...
then I guess the likelihood of the law of non-contradiction being true is whatever this series approaches, 0% then.