# Is the universe infinite

• B

## Main Question or Discussion Point

First we have to agree on the definition of infinite:

https://en.m.wikipedia.org/wiki/Actual_infinity

So:

- Potentially infinite is the process of continued and potentially endless iteration (IE a limit).
- Actually Infinite is the result of an unbounded number of iterations; IE NOT DEFINED (IE an infinite set)

So at best the universe can be potentially infinite, but it is not Actually Infinite.

jbriggs444
Homework Helper
2019 Award
I disagree with the definitions you are using for potentially and actually infinite. But it does not matter. There being no empirical way to distinguish which (if either) standard our universe meets, there is no scientific relevance. This is pure philosophy and out of bounds for discussion here.

This is maths not philosophy

The universe is part of the material world. How exactly are do you square the material world with actual infinity? You don’t. Actual Infinity does not exist in the material world hence the universe is finite.

Staff Emeritus
2019 Award
This is maths not philosophy
The first five words in the link you posted are "In the philosophy of mathematics".

Actual Infinity does not exist in the material world
Why do you think so?

PeroK
Homework Helper
Gold Member
PeroK
Homework Helper
Gold Member
The universe is part of the material world. How exactly are do you square the material world with actual infinity? You don’t. Actual Infinity does not exist in the material world hence the universe is finite.
Gee, that was easy!

Why do you think so?
Give me one example of the Actually Infinite from nature.

Give me one example of the Actually Infinite from nature.
No, it's not how it works. If you propose a theorem, *you* need to prove it. Not me.

I’m proposing that the complete absence of actual infinity in nature is empirical evidence for the non existence of actual infinity.

phinds
Gold Member
2019 Award
Give me one example of the Actually Infinite from nature.
Danny, you are hung up on a personal theory that you can't justify. Best quit while you're behind. Follow the old adage of "when you find yourself in a hole, stop digging".

jbriggs444
Homework Helper
2019 Award
I’m proposing that the complete absence of actual infinity in nature is empirical evidence for the non existence of actual infinity.
That is backwards. You need empirical evidence for the absence of actual infinity from nature before you can claim it.

phinds
Gold Member
2019 Award
I’m proposing that the complete absence of actual infinity in nature is empirical evidence for the non existence of actual infinity.
Oh, you REALLY should have quite while you were behind.

PeroK
Homework Helper
Gold Member
Give me one example of the Actually Infinite from nature.
Nature is understood in physics through mathematical models. The only viable model of spacetime (currently at least) is as a continuum. This is an "uncountable" infinity of points. There's no way to model spacetime as, say, a lattice of finitely points in a grid.

That's one sort of physical infinity.

One of the main models from General Relativity (and the one that best fits the data) is of a universe of infinite extent. That's a second sort of infinity.

Whether you can ever demonstrate that the universe really does have infinite extent is another matter. But, you cannot thereby assume the opposite, which is that the universe must have a finite physical extent.

Actual Infinity does not exist exist mathematically.

There is no number X such than X > all other numbers.

I know set theory defines actual infinity but it does it as an axiom; it just states it exists without proving anything (https://en.m.wikipedia.org/wiki/Axiom_of_infinity)

phinds
Gold Member
2019 Award
Actual Infinity does not exist exist mathematically.
now that's just silly. We even have a symbol for it.

There is no number X such than X > all other numbers.
So, what? Infinity is not a number. You're still digging.

The only viable model of spacetime (currently at least) is as a continuum
The only possible reality is that the material world is discrete. At the same time, the only viable why to model it is continuous. Catch 22.

PeroK
Homework Helper
Gold Member
Actual Infinity does not exist exist mathematically.

There is no number X such than X > all other numbers.

I know set theory defines actual infinity but it does it as an axiom; it just states it exists without proving anything (https://en.m.wikipedia.org/wiki/Axiom_of_infinity)
If you take the natural numbers: $1, 2, 3 \dots$.

Either there is a largest natural number or there is not. If there is, then the set is finite and ends at some, presumably very large, number. Or, there is no largest number, in which case the set is "infinite", by definition.

Mainstream mathematics assumes the latter: there is never a number to which you cannot add 1.

But, to be honest, that's only the start of things. Assuming, for example, that $\sqrt{2}$ exists. And, developing the Real numbers involve concepts of mathematical infinity at various stages.

"Finite" mathematics is only a small branch of the whole subject.

PeroK
Homework Helper
Gold Member
The only possible reality is that the material world is discrete.
It's not the only possible reality. It's only in your mind that the other possibilities are excluded.

Continuous leads to Zeno’s paradoxes. A paradox is indicative of an underlying false assumption, in this case that reality is continuous.

phinds
Gold Member
2019 Award
Zeno's paradox is a MISUSE of "continuous", not any kind of reflection of anything real. You're still digging.

PeroK
Homework Helper
Gold Member
Continuous leads to Zeno’s paradoxes. A paradox is indicative of an underlying false assumption, in this case that reality is continuous.
Zeno's paradoxes are really pretty poor in my view. They are of perhaps some historical interest, but mathematical thinking has moved on a long way since the Greeks.

jbriggs444
Homework Helper
2019 Award
The measure problem

https://en.m.wikipedia.org/wiki/Measure_problem_(cosmology)

Goes away with a finite universe.
The argument you propose seems to be:

"We do not know how to do probabilities correctly in an infinite multiverse"
"The universe has to be such that we can model it"
"Therefore the universe is finite"

There are at least two problems with that argument.