2+2=4 is not an instance of Kantian a priori knowledge

contra what most philosophers believe.

Even if you define 2 as (1+1) and 4 as (1+1+1+1), it does not follow from these definitions that 2+2=4 because (1+1)+(1+1) is not the same thing as (1+1+1+1). This is because nothing allows you here to open the brackets.*

If even this is not an instance of a Kantian a priori, then probably Kantian a priori does not exist. But neither does it mean that the knowledge that 2+2=4 is empirical in the narrow sense of being testable by experiment. It is empirical in the broader, Aristotelian sense.

*This beautiful short explanation I owe to Roger Penrose’s great book “The Emperor’s New Mind”.

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