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395b78 comments on Mathematics as a lossy compression algorithm gone wild - Less Wrong
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What is a universe without humans?
We are limited to subjective observations, and can not confirm what objective observations of the universe would be.
I'd like to argue in this comment that mathematics is an implied property of the universe. We might "mistake" to think that mathematics are governing the universe, but rather the way the universe works can be described from our subjective perspective with the seemingly abstract entity of mathematics. The universe contains mathematics in the way it exists.
Claiming that mathematics exist in some other dimension, is just about as reasonable as claiming that apples exist in another dimension.
If there's someone who can proove that they've broken the laws of physics while performing mathematics, then they have a valid basis for mathematical realism.
Would a different universe have different maths?
What d'ya mean by “different” and by “maths”? Sure they would use different notation but it'd denote mathematical structures isomorphic to our own.
I was trying to follow through 395's premise. If maths is implied by the universe, then other universes would imply other maths, n'est ce pas.
What does "objective observations of the universe" mean?
Having knowledge that would not be limited by being an observer, a small part of the universe.
What is time if you're not a creature existing in time?
That is not the usual objective/subjective distinction.
Who/what is the subject of "having knowledge"?
In my opinion that is irrelevant as long as the information is not limited by the nature of the observer. However I don't intend to say that "having knowledge" could have a meaning outside some sort of a subjective thing having it. So I'd like to separate the idea of some kind of truth from a subjective experience of having it. If there is any truth like that. If there was, how could we know, if we don't currently? Does it make sense to contemplate on the possibility of there being knowledge we can't have? We are limited and we can't really think outside the box. Knowing that we can't think outside the box, does not provide the capacity to suggest everything that could be outside the box.
Depends on the value of can't. We can't have the knowledge in the library of Alexandria..but counterfactually we could have had.
That's a pretty well-trodden philosophy topic :-)