This is false modesty. This is assuming the virtue of doubt when none ought exist. Mathematics is one of the few (if not the only) worthwhile thing(s) we have in life that is entirely a priori. We can genuinely achieve 100% certainty. Anything less is to suggest the impossible, or to redefine the world in a way that has no meaning or usefulness.
I could say that I’m not really sure 2+2=4, but it would not make me more intelligent for the doubt, but more foolish. I could say that I’m not sure that 5 is really prime, but it would hinge on redefining ‘5’ or ‘prime’. I could posit that if 2+3 reproducibly equaled 4, I would have to change my view of the universe and mathematics, but were I to suggest that argument held any weight, I might as well start believing in God. Define any paradox you like and there will never be a correct answer. The solution is not to accept doubt, but rather to ignore truly unsolvable paradoxes as foolish and useless.
The problem in creating the parallel probability statements is not in the surety, for they would all almost certainly be mathematical as well, but in the daunting task of finding and stating them. This is not reason, this is a threat! “If you assign X probability, are you willing to spend X hours finding parallels?” We react in the negative not due to the reasonability of the rebuttal but rather the daunting task saying yes would hypothetically place upon us. Our chance to perform the task correctly is likely significantly less than that of the probability we have assigned.
This is false modesty. This is assuming the virtue of doubt when none ought exist. Mathematics is one of the few (if not the only) worthwhile thing(s) we have in life that is entirely a priori. We can genuinely achieve 100% certainty. Anything less is to suggest the impossible, or to redefine the world in a way that has no meaning or usefulness.
I could say that I’m not really sure 2+2=4, but it would not make me more intelligent for the doubt, but more foolish. I could say that I’m not sure that 5 is really prime, but it would hinge on redefining ‘5’ or ‘prime’. I could posit that if 2+3 reproducibly equaled 4, I would have to change my view of the universe and mathematics, but were I to suggest that argument held any weight, I might as well start believing in God. Define any paradox you like and there will never be a correct answer. The solution is not to accept doubt, but rather to ignore truly unsolvable paradoxes as foolish and useless.
The problem in creating the parallel probability statements is not in the surety, for they would all almost certainly be mathematical as well, but in the daunting task of finding and stating them. This is not reason, this is a threat! “If you assign X probability, are you willing to spend X hours finding parallels?” We react in the negative not due to the reasonability of the rebuttal but rather the daunting task saying yes would hypothetically place upon us. Our chance to perform the task correctly is likely significantly less than that of the probability we have assigned.