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You can’t axiom your way out of 1 apple and 1 apple being 2 apples together. So axioms are not really that arbitrary.
by LudwigNagasena 1y ago
You can’t axiom your way out of 1 apple and 1 apple being 2 apples together. So axioms are not really that arbitrary.
- scoofy 1y agoThey are, by definition. The reason why we choose them is exactly to map a deductive framework onto an inductive reality.
- LudwigNagasena 1y agoThat doesn’t seem to match the definition of “arbitrary”.
- scoofy 1y agoWe can choose whichever axioms we want. There is still arguments over the axiom of choice, but nobody cares because it’s entirely helpful.
- amavect 1y agoYou 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 1y agoI 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.