Philosophy Discussion Forums | A Humans-Only Club for Open-Minded Discussion & Debate

[Steve3007]

As a kid I read someplace that infinity is proved by the fact that for any boundary that we can imagine, we can also imagine the outside of that boundary.

In what sense do you use the word "proved" here?

In mathematics and logic, a proof is a demonstration of a logical necessity. It doesn't, in itself, tell us anything about the physical world; it tells us something about the system of logic we're using. In a logical system, it elucidates the necessary consequences of propositions. It says "if X were true then, if we're being logically consistent, Y would also necessarily be true". An example in mathematics would be the proof that the square-root of two is an irrational number.

But the word "proof" is also sometimes used as an approximate synonym for the word "test". In that usage, it is an experimental or observational test of an empirical proposition. As in the expression "the proof of the pudding is in the eating". A completely different usage from the first one.

Sometimes those two usages are conflated or it is not made clear which is being used, or whether some other sense is being used.

[Marvin_Edwards]

As a kid I read someplace that infinity is proved by the fact that for any boundary that we can imagine, we can also imagine the outside of that boundary.

In what sense do you use the word "proved" here?

In mathematics and logic, a proof is a demonstration of a logical necessity. It doesn't, in itself, tell us anything about the physical world; it tells us something about the system of logic we're using. In a logical system, it elucidates the necessary consequences of propositions. It says "if X were true then, if we're being logically consistent, Y would also necessarily be true". An example in mathematics would be the proof that the square-root of two is an irrational number.

But the word "proof" is also sometimes used as an approximate synonym for the word "test". In that usage, it is an experimental or observational test of an empirical proposition. As in the expression "the proof of the pudding is in the eating". A completely different usage from the first one.

Sometimes those two usages are conflated or it is not made clear which is being used, or whether some other sense is being used.

I probably should have used another word then. The notion of infinity is "unavoidable", because we can always imagine space outside of any boundary that we can imagine. It is very comfortable to imagine a universe as a cozy space to live in, something that encompasses everything. And yet our universe was once a single lump of highly condensed matter that exploded in a Big Bang and continues to expand (or maybe it's actually contracting again and only appears to be expanding because the stuff near the center is accelerating toward the middle again).

But why wouldn't it be possible that beyond the boundaries of our own universe there would be another universe going through its own cycle of Big Bangs and Big Crunches. Perhaps there are an infinite number of them exploding like popcorn all over the place.

It would of course be impossible to confirm this scenario. But we're seen one, so...

[Marvin_Edwards]

Endless is about eternity, or infinite time. In theory, we are always precisely in the middle of eternity, with one eternity behind us and one eternity ahead of us (1/2 of eternity is also an eternity).

[Steve3007]

I probably should have used another word then. The notion of infinity is "unavoidable", because we can always imagine space outside of any boundary that we can imagine.

If you did continue to use the word "proved" then it seems to me that you'd be using it in roughly the first sense that I mentioned. I think what you're saying is essentially the same as pointing out that there are an infinite number of natural numbers because for any number we can think of it's always possible to think of a larger one. So this appears to me to be a statement about the logical structure of the abstract concepts that we create in our attempts to describe the empirically observed world, not a statement about that world itself.

It is very comfortable to imagine a universe as a cozy space to live in, something that encompasses everything.

I don't know about it being "cozy". But the question of whether it encompasses everything depends entirely on how you're using the word "universe". I tend to use it as a collective term for everything has ever existed or ever will exist. But I'm sure other definitions are available.

But why wouldn't it be possible that beyond the boundaries of our own universe there would be another universe going through its own cycle of Big Bangs and Big Crunches. Perhaps there are an infinite number of them exploding like popcorn all over the place.

It would be possible, so long as you don't use the definition of the word "universe" that I use. For any conversation to work, you'd have to tell me what definition you're using.

[Terrapin Station]

As a kid I read someplace that infinity is proved by the fact that for any boundary that we can imagine, we can also imagine the outside of that boundary.

Being able to imagine something doesn't imply that it's the case. That's the error of St. Anselm's ontological argument (for the existence of God), for example.

Not that we're really imagining infinity anyway. We're just imagining boundaries being exceeded, for however long, however many iterations we imagine that. Those imaginings are going to be very finite.

[Marvin_Edwards]

It would be possible, so long as you don't use the definition of the word "universe" that I use. For any conversation to work, you'd have to tell me what definition you're using.

A "universe" is a ontological real object consisting of matter in one of four states: (1) a highly condensed ball approaching the point of exploding or (2) a highly expanded distributed mass to the point where collapse begins or (3) collapsing or (4) expanding.

[Steve3007]

A "universe" is a ontological real object consisting of matter in one of four states: (1) a highly condensed ball approaching the point of exploding or (2) a highly expanded distributed mass to the point where collapse begins or (3) collapsing or (4) expanding.

Ok, understood. Given that that is how you're using the word "universe", I agree that it would be possible for another universe, or many other universes, to exist beyond our own. To you, a universe is an object in the same sense that the planet Earth is an object. To me, as I've said, it isn't. To me it's essentially a synonym for "everything".

[Marvin_Edwards]

A "universe" is a ontological real object consisting of matter in one of four states: (1) a highly condensed ball approaching the point of exploding or (2) a highly expanded distributed mass to the point where collapse begins or (3) collapsing or (4) expanding.

Ok, understood. Given that that is how you're using the word "universe", I agree that it would be possible for another universe, or many other universes, to exist beyond our own. To you, a universe is an object in the same sense that the planet Earth is an object. To me, as I've said, it isn't. To me it's essentially a synonym for "everything".

Right. I would call the 'everything' "infinity".

[Terrapin Station]

Ok, understood. Given that that is how you're using the word "universe", I agree that it would be possible for another universe, or many other universes, to exist beyond our own. To you, a universe is an object in the same sense that the planet Earth is an object. To me, as I've said, it isn't. To me it's essentially a synonym for "everything".

Right. I would call the 'everything' "infinity".

"Everything" may not be infinite.

[Steve3007]

"Everything" may not be infinite.

I agree.

[Marvin_Edwards]

"Everything" may not be infinite.

I agree.

Okay. Then what contains it?

[Steve3007]

Okay. Then what contains it?

Why does it have to be contained?
If it was contained it wouldn't be everything.

[Terrapin Station]

I agree.

Okay. Then what contains it?

Yeah, the question doesn't make sense to me, either. For some reason you're thinking that it necessarily would need to have a "container," but I don't know why you'd be thinking that.

(This is yet another thing, in conjunction with his absence and your sudden appearance on the board, that makes me think that you're a slightly alternate persona for creation, by the way)

[Steve3007]

This recent direction in the conversation seems to me more reminiscent of RJG/gater.

[Steve3007]

But I wouldn't want to tar Marvin with that brush. It's all too easy to see superficial similarities between people and jump to the conclusion that the similarities go deeper.