I have read online and personally believe that every statement has some degree of ambiguity to it. With this in mind, I was wondering how any propositions can be true. For example, I have heard some people say that math is absolute truth (because math is based on a system of rules/axioms) -- e.g. 2+2=4 is absolutely truth (assuming you are using proper axioms, like the Peano axioms). How can this be the case, though, if all statements are ambiguous? Wouldn't this mean that are multiple ways to interpret the axioms, and only one of those ways can be correct? Are the axioms completely unambiguous? How could you prove that they are unambiguous?
On a related note, why, after reading the Peano axioms (for example), can all humans seem to agree on the same properties? Why can all humans agree that 2+2=4? Even if there is a level of ambiguity to the axioms, how are humans able to converge on the same meaning? Thank you!
Clarification: I think the real point I was going at was ambiguity. Yes, I understand that 2+2=4 is true, and I understand that this can be shown with pebbles. However, thinking about the English language, for example, I could tell you that something is red. The red we have in our minds, though, may be different (I might be thinking of a crimson and you may be thinking of a scarlet). However, with math, I can ask you what 2 plus 2 is and you will say 4. There is no ambiguity, at least for humans. Why is this? You may say that we have defined a set of rules for the word plus: if I have 2 of something and I plus 2 to that something, I have 4. But how have these rules been formulated in such an unambiguous manner that no one will dispute them? Why can't the English language work the same way? I am looking for why/how, fundamentally, something can be totally unambiguous.