Weblog of a Christian philosophy student

Weblog of a Christian philosophy student. Please feel free to comment. All of my posts are public domain. Subscribe to posts [Atom]. Email me at countaltair [at] yahoo.com.au. I also run a Chinese to English translation business at www.willfanyi.com.

Location: Melbourne, Victoria, Australia

Friday, July 30, 2010

Two kinds of infinite

Is there something infinite?
Do you need an infinite to 'start everything off'? Does there need to be an infinite at the foundation of reality?

If the answer to these questions is 'yes', then is there anything that we can conclude about the nature of this infinite? Can we conclude, for example, that it must be a God? Or can it be something like the universe?

Thinking about the infinite, I want to make the case that there are actually two kinds of infinite, that are very different, that could have started everything off. God would be one kind of infinite and an infinitely old multiverse would be an example of the other kind.

The two kinds can be illustrated by a thought experiment. Imagine a chair. Now imagine an infinite number of chairs.

You can't, of course, really imagine an infinite number of chairs. But the idea makes sense on some level.

Anyway, if you could really imagine it, then have you imagined an infinite? Of course, yes, you've imagined an infinite; an infinite number of chairs.

Now, have you imagined something completely infinite?

No. Because although there are an infinite number of chairs, chairs are finite objects.

So there you have a concept that is partly finite and partly infinite. That is, an infinite quantity of a finite thing; chairs.

Can you imagine something completely infinite in every way? Without any finite aspects, unlike with the infinite number of chairs?

Well, just like really imagining an infinite number of chairs, no, you can't. But the idea of a completely infinite thing makes sense.

A completely infinite object would have to contain everything that an infinite should contain, which is, well, 'everything'. But, the thing is, it can't contain everything in a way that splits the infinite into pieces. Then there wouldn't be one completely infinite thing, but two, or three, or an infinite number of infinites, and how can there be more than one of something that contains everything there is? So you can only have one 'completely infinite' infinite and that cannot have divisions and differences within itself. So it has to be an indivisible unity, or continuum. Paradoxically, this means it has to contain everything, somehow, in a way that doesn't allow for differences or divisions. Try to imagine that!

So a completely infinite object has to contain everything in a singular, indivisible continuum, one that doesn't have any distinctions and yet somehow contains everything anyway (so it isn't some content-less 'grey blob').

(Note: presumably, we ourselves don't need to BE the infinite as long as you make an exception: if something within the continuum is caused to manifest real, actual distinctions/differences, then it will stand 'apart' from the infinite while also existing inside it.)

So those, apparently, are the two kinds of infinite you can have.

Now, what, if anything, can we conclude from this?

If the universe, or multiverse, is infinitely old, then the world comes from the first kind of infinite discussed.

If God exists, then the world comes from the second kind of infinite discussed (and somehow the indivisible continuum is a person!)

Okay. Now, do we have any reason to prefer one of these infinites as an explanation of the world to the other?

There isn't any knockdown argument favouring one, as far as I know. But I do think it's a bit neater if the world comes from something completely infinite, i.e. the second kind, rather than something where the infinite and the finite are combined. Because if the universe/multiverse has finite aspects, like a finite number of dimensions, or a finite number of superstring membranes, or suchlike, which it must have, it isn't a 'completely infinite' infinite, and that isn't as, sort of, 'simple' as an idea.

Labels: , ,


Post a Comment

<< Home