Sure, I agree that's the case, but "numbers" is not a thing. — Metaphysician Undercover

Actually I believe that numbers ARE things - that our physical reality is based on mathematics, and numbers are at the heart of everything. But we'll put that aside for the moment because you and others may not agree with it. 'I can infer that there are infinite numbers, therefore I can infer that there is an infinite thing' is NOT the argument I was making in my last post, I was arguing that just because we can't empirically observe an infinite thing doesn't mean that it's always unreasonable to assume the existence of an infinite thing. Numbers was just an example. Here's another example: something caused the big bang. In the absence of any evidence indicating that this event could only happen once, the hypothesis that are physical laws which cause big bangs to spontaneously happen at random point in time and space is more simple and relies on fewer assumptions than the hypothesis that something caused only one big bang to happen and then something else stopped that process from reoccurring. Because of this I can infer that a multitude of big bangs have always been and will always be happening, and therefore there is an infinite multiverse.

I went through this already. It is unreasonable to assume that any thing is infinite because such an assumption impedes our capacity to know that thing, and it is also impossible to know that a thing is infinite. So it's not the case that it is impossible that an infinite thing exists, in reality, but it is impossible to know that any given thing is infinite, and detrimental to the understanding of that thing, to assume that any given thing is infinite. Therefore it is unreasonable to assume that there is an infinite thing in reality. — Metaphysician Undercover

You may not be able to observe through empirical evidence that an infinite thing exists, but that doesn't mean it's unreasonable to infer that it exists. Take numbers, for example. I cannot count all the way to infinity, but I can infer that there are infinite numbers from the fact that if there were a finite biggest number then asking 'what is that number plus one' would break that limit.

I asked for the list, not a description of it. — Metaphysician Undercover

I think that is a reasonable way to define an infinite set of numbers, it is used all the time in mathematics. Just because he didn't list all those numbers separately doesn't mean they don't all exist. You were complaining earlier that infinite sets are inherently undefined. '2n, with n being any integer' is an example of how to define an infinite set.

Your claims seem a little arbitrary. Especially your claim that the multiverse being seen on the one hand as a multitude and on the other as a single object makes it self-contradictory. A bunch of bananas is both a single object and a multitude of bananas.

I don't think it's a good idea to rely on human intuition when it comes to physics. The human brain has evolved to cope with our everyday experiences, not with the laws of physics. Think about relativity and quantum mechanics - very unintuitive!

Do you have any logical reasoning (not involving human intuition, but based on the laws of physics or mathematics) for why an infinite thing could not exist in reality?

I don't think the concept of a set having to be 'collected' quite applies to what can and cannot exist in reality. I may not be able to create an infinite collection, or even imagine all the members of an infinite set, but reality doesn't have to 'collect' anything - infinite things can exist simultaneously without having to be created one by one.

I think you're taking the English language a little too far, using its structure to decide what can and cannot exist in reality. Think about your reasoning: I chose to say 'the' multiverse, which leads you to think that the multiverse is an object, and therefore bounded, and therefore an infinite multiverse is a self-contradictory concept. So you're deciding that an infinite multiverse doesn't exist simply because I used the word 'the'?

Okay, I agree with you that an object should be bounded. But I don't consider the multiverse to be an object. In fact, I think that the multiverse is a mathematical construct and that all the objects that we perceive around us are just emergent behaviours of the mathematical laws governing our reality.

I suppose it is possible that our concept of numbers is wrong, but saying that humans are not omnipotent and therefore don't understand everything doesn't make it likely that we are wrong about numbers, in my opinion. Just possible. It's important to keep the mind open to all possibilities. But we have no evidence that our understanding of numbers is wrong, so by the law of occam's razor I think it's fair to assume that numbers are real until some evidence shows us otherwise. I also think that if we were to reject the existence of numbers we would need some alternative hypothesis for why putting an orange next to another orange results in a group of oranges.

I'm not sure I agree that an infinite thing is ill-defined, or that the multiverse is an object, or that objects have to be bounded. It might be difficult to imagine an infinite thing but I don't think it breaks the laws of physics. Not that I'm saying you are wrong, just that I personally am unconvinced.

Yeah, it probably is. Mathematics represents reality so well that I think sometimes people get carried away.

I suppose this is really more a discussion of the definition of the word set rather than whether the universe could be infinite, so I'll agree with you that with the definition that humans have given the word set, the term 'infinite set' is illogical :P

I find it interesting to wonder about at what level of complexity consciousness arises. If you look at things from the subpersonal view, the separate parts of the brain don't seem to be conscious, there doesn't seem to be one particular brain activity that causes consciousness, and yet when you combine all the parts and look at a person as a whole they are conscious.

Why do sets have to be bounded? What about the set of all integers - is that not a proper set?

Hi SophistiCat, the physicist who said it was Max Tegmark. The first half of his book Our Mathematical Universe is very good, but in the second half he starts extrapolating a bit too much from the measure problem, and seems to think that any set that has the measure problem can't actually exist.

Your definition of the measure problem makes much more sense!