You implicitly used an axiom to ignore the differences between the apples. Someone else could use different axioms to talk about the sizes of the apples (1 larg

You implicitly used an axiom to ignore the differences between the apples. Someone else could use different axioms to talk about the sizes of the apples (1 large + 1 small = ?), or the color of the apples (1 red + 1 green = ?), or the taste of the apples (1 sweet + 1 sour = ?). People "axiom" their way out of 1+1=2 in this way: by changing the axioms, they change the topic, so they change the conclusion. I observe this pattern in disagreements very often.