I’m suspicious of claims that supposedly do not require justification
Mathematical claims do require justification. They even require stronger justification than empirical claims: mathematical proof. As Doug S explained, the proof that 2+2=4 is
2+2 = 2+(1+1) = (2+1)+1 = 3+1 = 4 QED.
(Using the definition of 2, the associativity of +, the definition of 3 and the definition of 4 in that order).
Empirical claims, such as “2+2=4 is related to earplugs or apples” do not require proofs, but they do require evidence.
Mathematical claims do require justification. They even require stronger justification than empirical claims: mathematical proof. As Doug S explained, the proof that 2+2=4 is
2+2 = 2+(1+1) = (2+1)+1 = 3+1 = 4 QED.
(Using the definition of 2, the associativity of +, the definition of 3 and the definition of 4 in that order).
Empirical claims, such as “2+2=4 is related to earplugs or apples” do not require proofs, but they do require evidence.