I don’t see anything here that is not a mixture of physical facts and logical facts (that is, truths about causal events and truths about premise-conclusion links).
Eliezer, a couple of comments ago I switched my focus from whether there is more than just physical and logical facts to whether “morality” refers to something independent of humanity, like (as I claimed) “rationality”, “integer” and “P!=NP” do. Sorry if I didn’t make that clear, and I hope I’m not being logically rude here, but the topic is confusing to me and I’m trying different lines of thought. (BTW, what kind of fact is it that there are only two kinds of facts?)
Quoting some background from Wikipedia:
When the Peano axioms were first proposed, Bertrand Russell and others agreed that these axioms implicitly defined what we mean by a “natural number”. Henri Poincaré was more cautious, saying they only defined natural numbers if they were consistent; if there is a proof that starts from just these axioms and derives a contradiction such as 0 = 1, then the axioms are inconsistent, and don’t define anything.
My question is, how can these questions even arise in our minds, unless we already had a notion of “natural number” that is independent of Peano axioms? There is something about integers that compels us to think about them, and the compelling force is not a set of axioms that is stored in our minds or spread virally from one mathematician to another.
Maybe the compelling force is that in the world that we live in, there are objects (like pebbles) whose behaviors can be approximated by the behavior of integers. I (in apparent disagreement with you) think this isn’t the only compelling force (i.e., aliens who live in a world with no discrete objects would still invent integers), but it’s enough to establish that when we talk about integers we’re talking about something at least partly outside of ourselves.
To restate my position, I think it’s unlikely that “morality” refers to anything outside of us, but many people do believe that, and I can’t rule it out conclusively myself (especially given Toby Ord’s recent comments).
Eliezer, a couple of comments ago I switched my focus from whether there is more than just physical and logical facts to whether “morality” refers to something independent of humanity, like (as I claimed) “rationality”, “integer” and “P!=NP” do. Sorry if I didn’t make that clear, and I hope I’m not being logically rude here, but the topic is confusing to me and I’m trying different lines of thought. (BTW, what kind of fact is it that there are only two kinds of facts?)
Quoting some background from Wikipedia:
My question is, how can these questions even arise in our minds, unless we already had a notion of “natural number” that is independent of Peano axioms? There is something about integers that compels us to think about them, and the compelling force is not a set of axioms that is stored in our minds or spread virally from one mathematician to another.
Maybe the compelling force is that in the world that we live in, there are objects (like pebbles) whose behaviors can be approximated by the behavior of integers. I (in apparent disagreement with you) think this isn’t the only compelling force (i.e., aliens who live in a world with no discrete objects would still invent integers), but it’s enough to establish that when we talk about integers we’re talking about something at least partly outside of ourselves.
To restate my position, I think it’s unlikely that “morality” refers to anything outside of us, but many people do believe that, and I can’t rule it out conclusively myself (especially given Toby Ord’s recent comments).