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> It isn't as if it was possible to doubt that 2+2=4 before the invention of the Peano axioms.

It certainly was; primitive cultures frequently lack words for medium-high numbers like 10, and have been known to lack 4. Unsurprisingly, those people are generally uncomfortable when asked to manipulate quantities that high. (They may use other methods, like having a collection of stones which is known to match the number of sheep in a flock, and "counting" sheep as they arrive by moving a stone from one pile to the other. If you failed to move a stone, you're missing a sheep.)




Not having a word for 4 and doubting that 2+2=4 aren't the same thing. The former means that you cannot understand what the proposition means, while the latter means that you do understand what it means, but aren't convinced that it's true.




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