After all, my original goal was to show that the thought experiment “let’s imagine the Earth before there was life on it, and see, we have a strong intuition that these questions still have the same answers even then” is ill-defined: without maps, the questions can’t be asked.
In this context, my point is that having a map in the future, or in a hypothetical future, or only in our world where we construct the question is enough to pose the question, and after that you can ask it about worlds that don’t have maps and would never have them. So the thought experiment won’t be ill-defined if you use (refer to) a human mind to pose it (and you do), even though that mind is not a part of the thought experiment.
A: “Some say that judging the situation as funny or not funny is inextricably tied to humans and their particular values, but I think that’s not true. Imagine the Earth millions of years ago, before any humans were around, and imagine [insert a funny scene with some awkward behavior of dinosaurs and/or their offspring]. Even though no humans were around to laugh at these, I can’t help but think that the scene was funny. You don’t need humans to define what’s funny.”
B: “Some say that judging the arithmetical truth is inextricably tied to humans and their particular values, but I think that’s not true. [Repeat the scene with rocks on the beach billions of years ago]. I can’t help but think that 3 rocks + 2 rocks = 5 rocks in that scene. You don’t need humans to recognize 2+3=5 as valid”.
Now, your point works equally well on A’s and B’s stories. In A’s story, your point says that it’s possible to define the situation as funny (even though presumably we agree that funniness is very much anthropomorphic to a large degree) by reference to a map which is yet to come, or which exists outside of the imagined world. And I agree with that. But that’s not enough for A. What A wants to “sell” to you is the notion that funniness exists on its own terms within that imagined world, completely independent of the existence of humans and of their values. A really wants to see the situation as funny “on its own”, not because you, a human, is there/was there/will be there/could be there to judge it so.
Now, I happen to think that A’s position is indefensible, bordering on silly. Moreover, I imagine that B also feels that way about A’s statement. B thinks their statement is much more objective and “inherent” to the imagined world than A’s statement. B really wants to see 2+3=5 “objectively” embedded within the scene they’ve described without reference to hypothetical humans and their map to parse it, construct mental entities out of it, and count them. It won’t satisfy B if you say “Sure, there are 2+3=5 rocks on that beach, and that’s an objective statement about the situation, but only in the same sense as if you said the rocks were funny-shaped; in both cases you can say the questions are well-defined in Vladimir_Nesov’s sense, relying on the eventual/hypothetical humans coming along and providing a map to make sense of the questions”.
I think that B would disagree with that claim and consider their story much superior in “objectivity” to A’s. And my point is that B is wrong and A and B’s stories have the same status in that respect. I can present that status by saying the questions about funniness/number of rocks are ill-defined because no humans are around to parse them; or I can follow you and say they’re well-defined but only by virtue of humans eventually appearing to parse them. But I feel that there’s little to no difference between these two presentations; the important point is that B’s story has the same status as A’s.
And, since I’m apparently not satisfied with the length of this comment so far, I’ll reiterate that I don’t think this turns the laws of arithmetics into humanity-tied, “subjective” rules. I do think B’s final sentence is correct and you do not need humans to define 2+3=5 as valid. I just don’t see B’s story at all as evidence towards that conclusion. It doesn’t work as evidence for that. And that, I guess, is my original point 2.
In this context, my point is that having a map in the future, or in a hypothetical future, or only in our world where we construct the question is enough to pose the question, and after that you can ask it about worlds that don’t have maps and would never have them. So the thought experiment won’t be ill-defined if you use (refer to) a human mind to pose it (and you do), even though that mind is not a part of the thought experiment.
Let me draw an analogy.
A: “Some say that judging the situation as funny or not funny is inextricably tied to humans and their particular values, but I think that’s not true. Imagine the Earth millions of years ago, before any humans were around, and imagine [insert a funny scene with some awkward behavior of dinosaurs and/or their offspring]. Even though no humans were around to laugh at these, I can’t help but think that the scene was funny. You don’t need humans to define what’s funny.”
B: “Some say that judging the arithmetical truth is inextricably tied to humans and their particular values, but I think that’s not true. [Repeat the scene with rocks on the beach billions of years ago]. I can’t help but think that 3 rocks + 2 rocks = 5 rocks in that scene. You don’t need humans to recognize 2+3=5 as valid”.
Now, your point works equally well on A’s and B’s stories. In A’s story, your point says that it’s possible to define the situation as funny (even though presumably we agree that funniness is very much anthropomorphic to a large degree) by reference to a map which is yet to come, or which exists outside of the imagined world. And I agree with that. But that’s not enough for A. What A wants to “sell” to you is the notion that funniness exists on its own terms within that imagined world, completely independent of the existence of humans and of their values. A really wants to see the situation as funny “on its own”, not because you, a human, is there/was there/will be there/could be there to judge it so.
Now, I happen to think that A’s position is indefensible, bordering on silly. Moreover, I imagine that B also feels that way about A’s statement. B thinks their statement is much more objective and “inherent” to the imagined world than A’s statement. B really wants to see 2+3=5 “objectively” embedded within the scene they’ve described without reference to hypothetical humans and their map to parse it, construct mental entities out of it, and count them. It won’t satisfy B if you say “Sure, there are 2+3=5 rocks on that beach, and that’s an objective statement about the situation, but only in the same sense as if you said the rocks were funny-shaped; in both cases you can say the questions are well-defined in Vladimir_Nesov’s sense, relying on the eventual/hypothetical humans coming along and providing a map to make sense of the questions”.
I think that B would disagree with that claim and consider their story much superior in “objectivity” to A’s. And my point is that B is wrong and A and B’s stories have the same status in that respect. I can present that status by saying the questions about funniness/number of rocks are ill-defined because no humans are around to parse them; or I can follow you and say they’re well-defined but only by virtue of humans eventually appearing to parse them. But I feel that there’s little to no difference between these two presentations; the important point is that B’s story has the same status as A’s.
And, since I’m apparently not satisfied with the length of this comment so far, I’ll reiterate that I don’t think this turns the laws of arithmetics into humanity-tied, “subjective” rules. I do think B’s final sentence is correct and you do not need humans to define 2+3=5 as valid. I just don’t see B’s story at all as evidence towards that conclusion. It doesn’t work as evidence for that. And that, I guess, is my original point 2.