I think it’s a question of basic epistemology. The mathematics of humans are a generalized system of symbols used to communicate and solve problems, many of which pertain to phenomena in the world at large. The symbols are invented, while the principles are discovered.
Part of the rabbit’s hole of human perceptual crisis is that people often rabidly refuse to acknowledge the differences between map and territory - because manipulating the map - the symbol - can fool one into feeling omnipotent.
Yes, symbols “exist”, but they exist as artificial abstraction about concrete reality. I couldn’t count the number of times when I remind people that “X” is a symbolic human concept, and I get dogpiled upon that “LOL Hey everybody, Popo says that “X” doesn’t actually exist!”
I keep trying, without success, to re-find stuff Quine may or may not have said about the empirical evidence for number, using his standard rabbits. I.e. that you couldn’t really refer to the meaningfulness of ‘ten rabbits’ without inferring a counting boundary inside which they may be counted. All you could ever say was ‘some rabbits’. But the concept of addition/augmentation itself doesn’t seem to have to bother itself with confinement or boundaries and thus need not concern itself with a ‘noticing mind’.
This seems like self-promotion but there are a bunch of relevant links concerning informationality and computability in the thread: I recommend the whole thing.
But! Most importantly, concerning the informationality and computability hypotheses would be the main point of the thread: The Simulation Hypothesis.
Now, it’s not much of a spoiler, but the question about simulation turns out to be the least interesting aspect of the thought-experiment presented in the lecture.
If anybody wants to get a little bit of a handle on why I would think that all possible configuration states of the human mind can be said to somehow exist in potentia, then this is a fun way to start:
[quote=“LemoUtan, post:27, topic:96733”]
I keep trying, without success, to re-find stuff Quine may or may not have said about the empirical evidence for number, using his standard rabbits.[/quote]
You should do a search on “gavagai” instead of “rabbit”.
It’s a human language with universal consequences, imo, much like thought, but that’s another rabbit hole…
P.S. However, I believe all creatures, great and small, think, so that’s another complication. The universe is truly complex, moreso than I can ever understand, maybe.
I think I understand that you are wanting to stress the constructed nature of mathematics here. But when mathematics can be used to do things like find elementary particles, plot planetary motion and build space probes… well there must be a very deep resonance between these human models and the structure of reality itself. The operating principles of the universe might not be “mathematics” but their tractability to mathematical modelling surely points to something like it.
Descartes thought and existed.
A rock did not think but still existed.
Harry Potter thought but did not exist (outside fiction).
The Philosopher’s stone did not think, and did not exist.
That’s all four possible combinations of two binary conditions.
