Re: [ot][spam][personal] nothing is impossible

a=1 b=2 prove that a+b=3 disprove that a+b=4 # in a proof situation, we are temporarily writing as if the axioms are always true. # there are additionally hidden axioms which are the rules used for the proof. # hence, our conclusion is true only under the conditions that all of the axioms # and all of the rules are also true. # this difference can come into play in formal logic where “if” has a nonintuitive meaning # hard # could use formalization of meaning of + and = with variables and literals a+b=1+2 1+2=3 a+b=3 3!=4 a+b!=4 # could use formalization of meaning of = and != and relation to prove and disprove # how did the contradiction arise from constraints on the parts? # maybe within the meanings of e.g. = .