In my essay on the definition of the Cartesian product, I point out that knowing what the Cartesian product is, specifically, the elements that make up the set, does not tell you what the Cartesian product ought to be, i.e., the universal properties definition of the Cartesian product that specifies how the product is actually used and what the product actually means in relation to other sets.
There is also the logical question of who precedes the other of normativity and alethicity, e.g. consider the Berry Paradox.
"The smallest positive integer not definable in under sixty letters" (a phrase with fifty-seven letters).
The space of all propositions as one reaches second order logic is hazardous. It has to be constrained before evaluation can take place, in this case by restricting the scope of "definable" with some chosen format, a matter of norm, not truth. That feels to me a bit like an is that demands an ought, in math.
There is also the logical question of who precedes the other of normativity and alethicity, e.g. consider the Berry Paradox.
"The smallest positive integer not definable in under sixty letters" (a phrase with fifty-seven letters).
The space of all propositions as one reaches second order logic is hazardous. It has to be constrained before evaluation can take place, in this case by restricting the scope of "definable" with some chosen format, a matter of norm, not truth. That feels to me a bit like an is that demands an ought, in math.