Yet again: I never said morality was arbitrary.
So morality is like chess, but there's some sort of grounding for why we should play it? I am confused as to what your position is.
What use is a new improved rationalised system of mathematics which can't support 2+2=4?
I'm not sure what you mean by that. If I'm following your analogy correctly then this is somewhat wrong. Any reasonable general philosophy of metamathematics would tell you that 2+2=4 is only true in certain axiomatic systems. For example, if I used as an axiomatic system all the axioms of ZFC but left out the axiom of infinity and the axiom of replacement, I cannot then show that + is a well-defined operation. But this is an interesting system which has been studied. Moreover, nothing in my metamathematics tells me that that I should be more interested in ZFC or Peano Arithmetic. I am more interested in those systems, but that's due to cultural and environmental norms. And one could probably have a whole career studying weak systems where one cannot derive 2+2=4 for the most natural interpretations of "2", "+","=" and "4" in that system.
To return to the original notion, just because a metaethical theory has to support that someone within their more and ethical framework has "murder is wrong" doesn't mean that the metaethical system must consider that to be a non-arbitrary claim. This is similar to just because our metamathetical theory can handle 2+2=4 doesn't mean it needs to assert that 2+2=4 in some abstract sense.
For example, if I used as an axiomatic system all the axioms of ZFC but left out the axiom of infinity and the axiom of replacement, I cannot then show that + is a well-defined operation.
I know this is a sidetrack, but I don't think that's right, unless we're omitting the axiom of pairing as well. Can't we use pairing to prove the finite version of replacement? (This needs an induction, but that doesn't require the axioms of replacement or infinity.) Hence, can't we show that addition of finite ordinals is well-defined, at least in the sense that we ha...
People who grow up believing certain things,
even if they later stop believing them,
may not quite realize how the beliefs sound to outsiders...
(SCENE: A small cottage in Nazareth.)
Joseph: Mary, my dearest fiancée, there's something I've been meaning to talk to you about.
(Mary's shoulders slump. Slowly, as if under a heavy burden, she turns around to face Joseph.)
Joseph: You seem to be getting fat around the waistline, and throwing up in the morning, and, er, not getting any periods. Which is odd, because it's sort of like -
Mary: Yes! I'm pregnant! All right? I'm PREGNANT!
Joseph: How is that possible?
(Mary's shoulders slump further.) Mary: How do you think?
Joseph: I don't know, that's why I'm asking you. I mean, you're still a virgin, right?
(Mary looks up cautiously, and sees Joseph's face looking blankly puzzled.)
Joseph: Well?
Mary: God did it.
Joseph: You had sex with -
Mary: No! Haha. Of course not. I mean, God just snapped his fingers and did one of those miracle things and made me pregnant.
Joseph: God made you pregnant.
Mary: (Starts to sweat.) Yes.
Joseph: Mary, that is just so... completely...
(Mary's eyes squeeze shut.)
Joseph: ...COOL!
(Mary opens her eyes again, cautiously.)
Mary: You think so?
Joseph: Of course! Who wouldn't think so? Come on, we've got to tell everyone the news!
Mary: Maybe we should keep this between just the two of us -
Joseph: No, no, silly girl, this is way too important! Come on!
(Joseph grabs Mary's wrist and drags her out of the house. SCENE: The gathering square of Nazareth. A dozen well-dressed men, and the town's head rabbi, look on Joseph and Mary impatiently.)
Rabbi: What's this all about, Joseph? I trust there's a good reason for the fuss?
Joseph: Go ahead, Mary! Tell them what you told me.
Mary: Um... (She swallows.) God made me pregnant.
Rabbi, looking stern, yet understanding: Now, Joseph, you know you're not supposed to do that before -
Joseph: No, no, you don't get it! She's still a virgin! God made her pregnant directly!
(There's a long pause.)
Man #1: So, what you're saying here, basically, is that Mary tells you she's a virgin.
Joseph: Uh huh!
Man #2: And you haven't had sex with her.
Joseph: Uh huh!
Man #3: And now she's pregnant.
Joseph: Precisely!
Man #4: So you think that God did it.
Joseph: What other explanation could there be?
Rabbi: Joseph, that is just so... unbelievably...
(Mary holds her breath.)
Rabbi: NEAT!
(Mary exhales.)
Man #5: A miracle! A miracle right here in Nazareth!
Man #6: Wow! I thought that miracles only happened in Jerusalem!
Man #7: Come on! Let's spread the good news!
(They depart. SCENE: Mary is alone with her friend, Betty, in Betty's house.)
Betty: "God did it."
Mary: I panicked! It was all I could think of!
Betty: So who's the real -
(Mary lifts an eyebrow significantly. There's a brief pause.)
Betty: Ah. So that's why the rabbi went along with it.
Mary: Well, he thinks he's the father, anyway. Why, does it matter?
Betty: It puts some things in a different light.
Mary: Like what?
Betty: The rabbi has been telling all the pretty young girls that you, Mary, are the ultimate embodiment of feminine virtue, and when they grow up, they should be just like you -
Mary: I just feel so awful about the whole mess. What kind of thing is this to have hanging over my child's life?
Betty: You've got to put things in perspective, dearie. You told one little white lie. It's not as if you caused the fall of the Roman Empire.
Mary: But what if the Romans hear about it? I don't want my baby to end up being crucified!
Betty: No one's going to obsess about it that long. In a couple of months this whole thing will blow over.
Mary: I hope you're right...
(Exeunt Omnes.)