Is mathematics invented or discovered?

Isn’t it more likely to have been a swim?

I wish someone had told be that before I made the trip out there today. Was so looking forward to their raspberry-brie-endive salad.

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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’.

I think.

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You really think so? I’m glad they didn’t. He sounds like he’s way out in left field.

The interviewer looks familiar, though.

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I like to think that mathematicians invented ways of discovering it.

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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:

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[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”.

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Discovered.

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.

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I feel like the order topology only really gets starts to get interesting at ω+1.

Or - even better - ω1. However, if you take an ultrapower of ℤ (which some people call ℤ again) the ordering can get very interesting indeed.

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You doods are dropping maths in the last fourteen minutes plus one.

Jargon, in-crowd, and all that. It’s good, just selective.

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I know. It didn’t help.

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.

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http://www.smbc-comics.com/comic/arbitrarily

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Z ↦ Z2 + C

Discovery.

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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.

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Cantor preferred the term transfinite set.

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If I understand you correctly, then I think we agree.

Like the cogito ergo sum argument, ascribing axioms to the nature they describe conflates the subjective with the objective. For example, if I write a computer program that runs a simulation which calls for an abstract object or property - for example: one electron, or one topology, or one polygon of a given dimension within the defined scale of the program - every time it renders a thing or moves a thing, and that abstraction exists as a single entry in a single instance of a library in memory, then it’s more accurate to say that part of that thing is the same part as all other instances of the same part in all other things. Now, I’m not saying this is necessarily true. It could quite well not be. But the mere fact that it can’t be disproved casts doubt on the uniqueness of things. It could well be that the very axioms of mathematics which we’ve happened as a species to analyze the universe with are in no way special to the universe, and that there are other axiomatic systems which yield equally valid descriptions.

The question I would then have is whether there is a more fundamental logic that can show different mathematical systems to be logically related. If not, we’d have to face the possibility that different axiomatic mathematical systems describing what we think of as the same natural universe might be fundamentally incompatible, which then casts doubt on our concept of a unified reality. This is in fact what I was getting at months ago in the Simulation Argument thread, that our very understanding of what a simulation is and isn’t might be hopelessly naive…that, on one hand the things we call simulations which we make simple versions of in computers and on paper, and on the other hand the thing we call base reality or physical reality or even just not an artifact, might only be two simple categories in a much larger phase space of heretofore imagined alternatives.

We might eventually have to face the possibility that being finite and limited to subjective knowledge, we can never truly know the whole elephant. But in realizing that the part we’re grasping isn’t the whole elephant, we might at least expand our tool-set(s) for understanding more of the elephant.

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I’m not seeing “taught to us by aliens” among the options.

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We were waiting for Goedot.

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