[amavect]

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.

[LudwigNagasena]

I have used appropriate axioms, not arbitrary axioms. If you want to talk about size or color or taste, you would use “axioms” appropriate for you case.