Is-ought in math
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.
Surprisingly, any set can be used as the Cartesian product, but only some sets are optimal, and only if they’re used a certain way. Whether a set is the Cartesian product, therefore, depends on whether it is the peak of an order—whether it is an ought.
Sets are distinguished from each other only by how they are used, i.e., by mappings between them. The elements that “define” sets are interchangeable squiggles, so sets are kind of like indistinct lumps that acquire properties by how they are used or perceived by other mathematical objects, such as maximum and minimum. This means that the properties are relational and not due to the set itself, and emerge without a privileged cause. It’s all perception and use, no is without ought.
Also, I can’t tell the difference between how a mathematical object is used and how it is perceived, indicating that the unity of perception and action applies to math as well as to the behavior of organisms.
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.