It's all about the deep questions.
A familiar problem for the philosophy of mathematics is the ontology of mathematics. One view, platonism, maintains that the things that mathematicians talk about, ultimately sets, actually exist as mind-independent abstract objects. Here’s one problem for the view that I’ve come up with, although being no expert in the field, it could have some conceptual mistake.
1. If platonism is true, there is a fact of the matter as to what cardinalities sets can be.
2. If there is a fact of the matter as to what cardinalities sets can be, we can take the union of one set for every cardinality that there is.
3. The resulting set A must have the same cardinality as one of its subsets A’, since by hypothesis there exists subsets of A with every cardinality.
4. The resulting set A must have at least the same cardinality as the powerset of A’, since the powerset of A’ is a distinct cardinality and there must be a subset of A with the cardinality of the powerset of A’.
5. Therefore, the resulting set A must have a cardinality both equal to and not equal to (greater than) A’.
6. Therefore, platonism is false.
Morality As a Community of Ideally Rational Desires
Although I stand by my error-theory position about folk morality, that doesn’t exhaust the possible questions about morality. Finding a substitute for the term that has sound philosophical grounds but throws away the unsatisfiable intuitions behind the word is desirable. I take this paper to make two claims. The first, philosophical, claim is to give a framework of what an ideally rational person should desire, and how an ideally rational person ought to live and act by consequence, in the context of a community. The second, more speculative empirical claim, is that the fleshing out of this framework with regard to human communities coheres enough with our rough, commonsense understanding of morality as to deserve to be called the name. If not, we should simply discard morality as a group of outdated notions and abide by the framework set out in the first claim, because that is what we have the most reason to follow. Read more of this post