Mathematical thinkers and the infinity of God

[Neoplatonist]

I have two goals in this post:

1.To collect a list of the many clever thinkers on the forums who use mathematical models, examples, and concepts to help reason through theological and philosophical issues. (This will be a resource and a guide leading me back to particular threads I might enjoy.)

2.I am also curious to hear if anyone has seen or constructed a proof other than a variant of Anselm’s Ontological that would show why God has to have an infinite amount of each property x.

Look forward to meeting you and to hearing your thoughts!

 

[adawgj]

Hi, unfortunately I’m not trained in the fields of philosophy or mathematics.

However, since I’m a student of history I can think up some people who might have mathematical models.

Blaise Pascal or Rene Descartes might have. I need to read there work though.

 

[Bob_Crowley]

I have two goals in this post:

1.To collect a list of the many clever thinkers on the forums who use mathematical models, examples, and concepts to help reason through theological and philosophical issues. (This will be a resource and a guide leading me back to particular threads I might enjoy.)

2.I am also curious to hear if anyone has seen or constructed a proof other than a variant of Anselm’s Ontological that would show why God has to have an infinite amount of each property x.

Look forward to meeting you and to hearing your thoughts!

I’m not a mathematician, or versed in formal logic, but I’ll have a go at it.

If each property x has a boundary, that is, it’s not infinite in itself, then for God to be infinite He would then need to have an infinite number of properties. But is that possible?

You’ve only then got two choices -

1. He has an infinite amount of each property x, or …
2. He has an infinite number of finite properties.

But since we can’t prove either case, then it remains conjecture.

 

[Neoplatonist]

I’m not a mathematician, or versed in formal logic, but I’ll have a go at it.

If each property x has a boundary, that is, it’s not infinite in itself, then for God to be infinite He would then need to have an infinite number of properties. But is that possible?

You’ve only then got two choices -

1. He has an infinite amount of each property x, or …
2. He has an infinite number of finite properties.

But since we can’t prove either case, then it remains conjecture.

Nice approach, Bob. What if we step back one step, though, and ask: Why does God need to be infinite (the set up in your main if/then statement)? Why not just, say, 1,000 times more x or y (or “being”) than the universe (or the next thing in the hierarchy of being.)

 

[Bob_Crowley]

Nice approach, Bob. What if we step back one step, though, and ask: Why does God need to be infinite (the set up in your main if/then statement)? Why not just, say, 1,000 times more x or y (or “being”) than the universe (or the next thing in the hierarchy of being.)

Let’s take the zero point ie. absolute nothingness.

Then it explodes so to speak. Or in religious terminology, out of the void the Logos speaks.

There is nothing to stop it, so it must move to infinity. I suppose that’s one way of describing it.

Maybe when God chose the “Big Bang” to create the universe, where everything came from nothing, maybe He was saying something about Himself in the process. Then He went a step further and made us in His triune image - mother, father, child / mind, body, soul etc.

Mind you, this is all over the top conjecture. The only one who could answer your question is God Himself.

However we often say God is Love, or as Christ said, “Only God is Good”. Why is it that intrinsic being has to be good? Or love?

I can only think that the two are bound up together ie. God’s being is contingent upon His also being Good and Love (with a capital G and L respectively).

 

[Bahman]

I have two goals in this post:

1.To collect a list of the many clever thinkers on the forums who use mathematical models, examples, and concepts to help reason through theological and philosophical issues. (This will be a resource and a guide leading me back to particular threads I might enjoy.)

2.I am also curious to hear if anyone has seen or constructed a proof other than a variant of Anselm’s Ontological that would show why God has to have an infinite amount of each property x.

Look forward to meeting you and to hearing your thoughts!

I have a argument for that which is based on the fact that a finite change doesn’t change an infinite being:

1. God does not change
2. Creation was a part of God’s thought
3. Creation has a beginning hence this require a change in God
4. (1) and (3) contradict each other unless God is infinite and creation is finite

 

[Neoplatonist]

I have a argument for that which is based on the fact that a finite change doesn’t change an infinite being:

1. God does not change
2. Creation was a part of God’s thought
3. Creation has a beginning hence this require a change in God
4. (1) and (3) contradict each other unless God is infinite and creation is finite

Why 1? That sort of begs the question.

Why 3? That is, why would having the thought from all eternity mean creation had to begin in the instant of his thinking? Could he not have had a thought in n dimensions which could only graph onto space-time as an unfolding?

Why is infinite God the only way around? I’m not sure I see the steps implied.

 

[lp22]

sorry to post here. bob Crowley I’ve been anxious to find you having read you have here a story about your father appearing. you mentioned you posted the whole story but I can’t find it. would you kindly point me to it? and did you start this site? thank you.

 

[Bob_Crowley]

sorry to post here. bob Crowley I’ve been anxious to find you having read you have here a story about your father appearing. you mentioned you posted the whole story but I can’t find it. would you kindly point me to it? and did you start this site? thank you.

If you look at the profile section of any Forums contributor, you’ll find there’s a facility where you can email a correspondent directly.

I suggest you send me an email that way, and then I’ll send you the narrative via a few emails. I can’t send it in one piece as it takes up more room than the system allows.

No I certainly didn’t start this site. Someone else did all the hard work setting up Catholic Answers Forums.

And I didn’t start this particular topic either.

 

[lp22]

I did of course. sorry, must run.

 

[rossum]

mathematical thinkers and the infinity of God

Your first problem is that there is more than one infinity in mathematics. The infinity of the natural numbers is different from the infinity of the real numbers. Cantor described an infinite(!) number of infinities: Aleph-0, Aleph-1, Aleph-2 etc. One of the unsolved problems of mathematics, the Continuum Hypothesis, is whether the infinity of the real numbers is the same as Aleph-1 or different.

Unless both you and your interlocutor are working at the same level of mathematical knowledge, then you are likely to be talking at cross-purposes. Depending on the axioms you are working from, mathematics can get very very strange.

rossum

 

[Neoplatonist]

Your first problem is that there is more than one infinity in mathematics. The infinity of the natural numbers is different from the infinity of the real numbers. Cantor described an infinite(!) number of infinities: Aleph-0, Aleph-1, Aleph-2 etc. One of the unsolved problems of mathematics, the Continuum Hypothesis, is whether the infinity of the real numbers is the same as Aleph-1 or different.

Unless both you and your interlocutor are working at the same level of mathematical knowledge, then you are likely to be talking at cross-purposes. Depending on the axioms you are working from, mathematics can get very very strange.

rossum

Yes! Great point, Rossum—one of the many reasons to love mathematics.

I’m curious to hear which kind of infinity you think makes the most sense for talking about God’s attributes and whether we can establish a proof for why he would have to have this or that attribute in infinite degree/amount. A reductio approach is fine.

 

[Gorgias]

Unless both you and your interlocutor are working at the same level of mathematical knowledge, then you are likely to be talking at cross-purposes.

This.

That is the reason why, although I love mathematics, I tend to try to not use it in theological or philosophical discussions (unless someone has opened with a mathematical example or premise). There are much more accessible ways to describe theological concepts.

Neoplatonist:

I am also curious to hear if anyone has seen or constructed a proof other than a variant of Anselm’s Ontological that would show why God has to have an infinite amount of each property x.

Just off the top of my head, I think I’d point to Aquinas’ discussion in the Summa Theologiae of God’s perfection (I.4) and the names of God (I.13). If God is not perfect – that is, if He is not the apex of each good quality – then He is not God. This isn’t precisely equivalent to “possessing an infinite amount of x”, but rather, speaks to God as being the perfection of each x.

 

[Neoplatonist]

This.

That is the reason why, although I love mathematics, I tend to try to not use it in theological or philosophical discussions (unless someone has opened with a mathematical example or premise). There are much more accessible ways to describe theological concepts.

Just off the top of my head, I think I’d point to Aquinas’ discussion in the Summa Theologiae of God’s perfection (I.4) and the names of God (I.13). If God is not perfect – that is, if He is not the apex of each good quality – then He is not God. This isn’t precisely equivalent to “possessing an infinite amount of x”, but rather, speaks to God as being the perfection of each x.

Well, at the risk of this turning into a thread about Aquinas, doesn’t this just open the question of how we can relate to “perfection” in more analytic terms?

Aquinas presents us with a separate but related concern by building so much on his claim that the less perfect must be caused by the more perfect (in terms of efficient, not material). How could we establish that except by (faulty) induction as Aquinas did?

 

[rossum]

I’m curious to hear which kind of infinity you think makes the most sense for talking about God’s attributes

If you look at the top right of my posts you will see that I am Buddhist. My underlying axioms are very different from those of the Abrahamic religions. To take just two: “everything changes” and “nothing has a soul”. That gives me a very different perspective on the gods.

rossum

 

[Neoplatonist]

If you look at the top right of my posts you will see that I am Buddhist. My underlying axioms are very different from those of the Abrahamic religions. To take just two: “everything changes” and “nothing has a soul”. That gives me a very different perspective on the gods.

rossum

Yet, you’re on here, so you must have some good familiarity with the working principles of the Abrahamic religions. ?] There are lots of constructs and spaces in math that we’re able to reason about and prove propositions regarding without having to believe they are, then, real.

I certainly understand if it’s just a matter of it not appealing to you. Nice to have you on here keeping the discourse honest, nonetheless.

 

[OurLadysServant]

Plato’s theory about Creation and God.

There was nothing. Someone created all creation. We’re creatures. There’s a Creator .

QUOTE=Neoplatonist;12498491]I have two goals in this post:

1.To collect a list of the many clever thinkers on the forums who use mathematical models, examples, and concepts to help reason through theological and philosophical issues. (This will be a resource and a guide leading me back to particular threads I might enjoy.)

2.I am also curious to hear if anyone has seen or constructed a proof other than a variant of Anselm’s Ontological that would show why God has to have an infinite amount of each property x.

Look forward to meeting you and to hearing your thoughts!

 

[Neoplatonist]

Plato’s theory about Creation and God.

There was nothing. Someone created all creation. We’re creatures. There’s a Creator .

QUOTE=Neoplatonist;12498491]I have two goals in this post:

1.To collect a list of the many clever thinkers on the forums who use mathematical models, examples, and concepts to help reason through theological and philosophical issues. (This will be a resource and a guide leading me back to particular threads I might enjoy.)

2.I am also curious to hear if anyone has seen or constructed a proof other than a variant of Anselm’s Ontological that would show why God has to have an infinite amount of each property x.

Look forward to meeting you and to hearing your thoughts!

That part about creation from nothing is another whole problem.

That being said, why does creating something mean the creator has to be infinite in some way?

 

[Neoplatonist]

Consider, for instance, if we pick some attribute, like intelligence. As far as I know, archangels are not said to have infinite intelligence, so we can render it as somehow commensurate with human intelligence. For the sake of argument, let us posit that the archangels have an IQ of 1,000 (whatever that would mean). Many times more than the most intelligent human that ever lived.

What would result, then, if God had an IQ of only, say, 100,000? A hundred times more intelligent than the most brilliant of the next order of beings. Would some absurd consequence or contradiction follow?

Similarly with other positive attributes, like goodness or beauty. What bad conclusion could we derive if God were only 100 fold (or 1,000 fold, or 10,000 fold) more good (or beautiful) than the archangels?