Hamming Questions for Philosophy

I was just taking a break by rereading this heartwarming little essay , which you should definitely check out. This made me think about what some "Hamming Questions" for philosophy are (i.e. big questions, which we nonetheless seem to be in a position to reasonably attack now)

1. Is there a meaningful distinction between statements that are "true by convention" and those that "state substantive claims about the world"? If not (I would guess there is not) what genuine distinction are people getting at when they say:
-it's a matter of convention that mountains have to be 100 feet
-the fact that I am a US citizen is a social/conventional truth (?)
-deliciousness and disgustingness are not something independently in the world but something that we project onto the world (???)
I suspect different things are at stake in each of these cases.

2. Why, despite our ability to quickly learn new words like `table', `policeman' and `gouche' has it proved to be so hard (impossible?) for philosophers to produce elegant necessary and sufficient conditions for the application of these terms using more primitive ones. Is it...
-that in learning new words we learn paradigm cases not definitions? (but cf. the known problems with e.g. trying to account for understanding "green apple" in terms of composing paradigm cases of "green" and "apple")
-that there is an adequate definition for being a policeman etc. to be found but they are ugly enough to be considered by linguists not philosophers (e.g. maybe they typically have many special clauses)?
-that external facts about natural kinds help determine the extension of terms like policeman, in a way that either gives these terms a very messy relationship to the extensions of other terms that we understand and/or makes it epistemically difficult for us to figure out what these relationships are?
-that there are clean necessary and sufficient conditions to be given, but `atoms' of these definitions turn out to be metaphysically wild and wooly notions like `purpose' `agent' `blameworthy' so that providing necessary and sufficient conditions for claims about policemen, tables, etc. in terms of primitives like these doesn't feel like (and maybe isn't) making philosophical progress.

2' Why has it proved so hard for philosophers to paraphrase away ceterus paribus clauses, despite their apparently unproblematic use in the sciences.

3. Do facts about forcing independence and large cardinals have any consequences for the trilemma about how to think about the height of the hierarchy of sets. If mathematical facts can't decide this issue, what can?

4. What are the truth or assertability conditions for claims about literary "function" e.g. x foreshadows y, x alludes to y, x raises questions about whether y? Provide a metaphysical story about what makes statements of the above kind true, plus corresponding "logic" of literary criticism e.g. a formal algorithm that captures many if not all truth/assertability preserving inferences about literary function? Does this
-bonus: add axioms and inference rules to your logic of literary function until you get something that captures all intuitively valid forms of argument, or prove that no recursively axiomatizable logic can do this.
-bonus: determine what if any relationship there is between claims about literary function and biological function (I guess Kant thought there was a connection but he clearly likes cute solutions too much to be trustworthy on a matter like this!)

5. In virtue of what does a piece of music count as expressive of sadness, excitement etc.? If these facts are relevant to some parameter like species or prior musical tradition state the relevant parameter. This is an old and daunting question but...
Currently fashionable psychological research into how pieces of music produce similar *judgements* about expressing sadness excitement etc. in different people may suggest promising new proposals with regard to the philosophical question of what features of music make it *count* as expressing sadness, excitement etc. What kinds of lower level features do people seem to be causally responding to when they say that a piece of music is sad, and what if any general-purpose causal reasoning is involved in these judgements?