Thanks for sticking with this, I am trying to hone my arguments on this topic and you are helping.
There exists a relationship between how many nuts squirrel B eats, and how many times squirrel A deposited a nut in the tree.
That relationship does not depend on my observations.
Yes it does.
You are implying that there is some sense of reality that is independent of how we think about it. I agree with that. But your statement adopts a "human mind" centric interpretation which makes it false.
For example, from the perspective of the universe at the level of quarks, the reality within the story's space-time is unchanged by our later observations of the written story. It is independent of our observations.
However, the relationship that you identified has no meaning from the quark perspective. We wouldn't know if a squirrel ate a nut or if a nut ate a squirrel. At that level, there are no concepts for squirrels and nuts -- or counting; those are higher level abstractions.
For convenience, let's call them X, instead. You aren't denying the existence of X, merely asserting that X isn't arithmetic.
The relationship you identified is real and it has meaning; but that meaning is found within the context of your mind and does not describe some intrinsic property of the universe, it describes an interpretation of your observations.
But I will say that if that's true, then arithmetic isn't very interesting, except perhaps linguistically. Sure, maybe arithmetic only occurs in minds, or in human minds, or in English-speaking minds. I can't see why I ought to care much about that.
The interesting thing is X.
Here is why you should care:
Here at LW we are working toward rationality. We want to improve the correspondence between our map and the territory. We want to know what the truth is and how to carve reality and its joints. We want to make ourselves immune to obvious fallacies such as the mind projection fallacy.
My claim is that the context principle -- that all meaning is context dependent -- is essential to understanding existence, truth and knowledge; it provides traction for solving problems and toward achieving our goals.
Consider a particular system, S1, of a squirrel eating a nut.
S1 can be described in a lot of different ways. The way I just described it is, I agree with you, a human-mind-centric description.
But I could also, equally accurately, describe it as a particular configuration, C1, of cells. Or a particular configuration, A1, of atoms. Or a particular configuration, Q1, of quarks.
Those aren't particularly human-mind-centric descriptions, but they nevertheless describe the same system. Q1 is, in fact, a description of a squirrel eating a nut, even though there'...
Certain kinds of philosophy and speculative fiction, including kinds that get discussed here all the time, tend to cause a ridiculous thing to happen: I start doubting the difference between existence and non-existence. This bothers me, because it's clearly a useless dead end. Can anyone help with this?
The two concepts that tend to do it for me are
* Substrate independence/strong AI: The idea that a simulation of my mind is still me. That I could survive the process of uploading myself into a computer running Windows, a cellular automaton run by this guy, or even something that didn't look like a computer, mind, or universe at all to anyone in the outside world. That we could potentially create or discover a simulated universe that we could have ethical obligations towards. This is all pretty intuitive to me and largely accepted by the sort of people who think about these things.
* Multiverses: The idea that the world is bigger than the universe.
My typical line of thought goes something like this: suppose I run a Turing Machine that encodes a universe containing conscious beings. That universe now exists as a simulation within my own. It's just as real as mine, just more precarious because events in my reality can mess with its substrate. If I died and nobody knew how it worked, it would still be real (so I should make provisions for that scenario). Okay, but Turing Machines are simple. A Turing Machine simulating a coherent universe containing conscious beings can probably arise naturally, by chance. In that case, those beings are still real even if nobody on the outside, looking at the substrate, realizes what they're looking at. Okay, but now consider Turing Machines like John Conway's Fractran, which are encoded into an ordered set of rational numbers and run by multiplication. I think it's fair to say that rational numbers and multiplication occur naturally, everywhere. Arithmetic lives everywhere. But furthermore, arithmetic lives *nowhere*. It's not just substrate-independent; it's independent of whether or not there is a substrate. 2+2=4 no matter whether two bottlecaps are being combined with two other bottlecaps to make four bottlecaps. So every Turing-computable reality already exists to the extent that math itself does.
I think this is stupid. Embarrassingly stupid. But I can't stop thinking it.