Actual and potential infinities

[shunyadragon]

I would like to dialogue with those interested concerning the nature of infinities in math, philosophy, and cosmology.

For example many traditional theologians argue for the impossibility of actual infinities as justification that the universe is finite and must have a source. The old Kalam argument, which I may comment on later. Comment on these arguments if you like. Are actual infinities possible?

I believe that time and space are best described as possible potential infinities. Could infinite time and space be described as vectors from arbitrary points?

 

[Hurkyl]

This isn't a theology forum, so you are unlikely to get any useful dialog on that topic.


As for dealing with the infinite, AFAIK the general consensus is that mathematics treats the general notion superbly. And the general trend is that if you can make precise statements, then you are likely to get a clear, straightforward, and unambiguous answer.

None of your statements are very precise.

 

[CRGreathouse]

Actual vs. potential has nothing to do with the infinite in mathematics. I recommend the philosophy forum: your question seems to be one of metaphysics.

 

[shunyadragon]

Actual vs. potential has nothing to do with the infinite in mathematics. I recommend the philosophy forum: your question seems to be one of metaphysics.

I was looking for a mathematical basis for understanding actual and potential infinities as they would apply to physics and cosmology. The application to the philosophy and theology question would only be to understand how the math applies to the questions and issues.

 

[shunyadragon]

This isn't a theology forum, so you are unlikely to get any useful dialog on that topic.


As for dealing with the infinite, AFAIK the general consensus is that mathematics treats the general notion superbly. And the general trend is that if you can make precise statements, then you are likely to get a clear, straightforward, and unambiguous answer.

None of your statements are very precise.

That is what I am looking for, straight unambiguous answers from the math perspective. I believe actual and potential infinities are defined from the math perspective, How would that apply to physics and cosmology.

 

[SW VandeCarr]

That is what I am looking for, straight unambiguous answers from the math perspective. I believe actual and potential infinities are defined from the math perspective, How would that apply to physics and cosmology.

Like Hurkyl implied; math handles the concept of infinity in a precise and unambiguous way. In physics and cosmology it is a philosophical issue as it must deal with the extent, composition and history of the universe in an imprecise way because of limited knowledge. By definition "potential" infinities only exist in terms of a particular hypothesis or theory.

 

[Hurkyl]

That is what I am looking for, straight unambiguous answers from the math perspective. I believe actual and potential infinities are defined from the math perspective, How would that apply to physics and cosmology.

If you made a precise definition, you could get an answer.

For example, if you asked the specific question "What is the cardinality of the set of events in space-time, as defined by General Relativity?" -- or more loosely speaking, "According to General Relativity, how many points are there in the universe?" -- you would get the answer "c", which is an infinite cardinal number.

(This has nothing to do with the speed of light -- c is the traditional name for this cardinal number, which I believe comes from the word "continuum". It is equal to 2^{\aleph_0})


However, if you ask "Are actual infinities possible?" you won't get a good answer, because nobody knows what precisely you mean. (including yourself, I expect)