Did God create numbers?

[Radagast]

intrinsic

What kind of intrinsic property?

The usual logicist approach, for good reason, is to define 5 to be a specific set. Benacerraf has criticised that.

But it seems like you want to define 5 to be the property that 5-element sets have in common, which sounds a little circular.

 

[Radagast]

... you can encode the natural numbers with a type definition:

type nat = Zero | Successor nat

One advantage of this is that you don't need a complex predicate which is true just of the natural numbers -- the natural numbers are captured by the type.

So to reiterate, I would say that the natural numbers are on much more solid footing.

I agree.

 

[JonF]

What kind of intrinsic property?

I'm not sure what you are asking for here?

The usual logicist approach, for good reason, is to define 5 to be a specific set. Benacerraf has criticised that.

But it seems like you want to define 5 to be the property that 5-element sets have in common, which sounds a little circular.

It's not circular at all, since i mathematicly define this property as all sets bijective to a 5 element set i constructed.

 

[Radagast]

I'm not sure what you are asking for here?

A definition. Or at least a codomain.

It's not circular at all, since i mathematicly define this property as all sets bijective to a 5 element set i constructed.

I presume you mean that "5" is the equivalence class of sets that can be placed in one-to-one correspondence with {, , , , }

However, this definition doesn't give you the natural numbers, since it includes infinite cardinals as well. And there are a few other problems, which is why numbers aren't usually defined that way.

 

[JonF]

A definition. Or at least a codomain.



I presume you mean that "5" is the equivalence class of sets that can be placed in one-to-one correspondence with {, , , , }

However, this definition doesn't give you the natural numbers, since it includes infinite cardinals as well. And there are a few other problems, which is why numbers aren't usually defined that way.

I make no claim of it being an equivalence class. Since then I would have to claim it on some specific set. I am pretty sure this removes your objections.

 

[Radagast]

I make no claim of it being an equivalence class. Since then I would have to claim it on some specific set.

In that case, I have no idea what you're claiming. Perhaps if you expressed your idea in formal mathematical notation it could be properly evaluated.

But going back to the OP, I think problems arise in any scheme that has numbers "emerging" out of sets of objects, whether objects in the created universe or otherwise.

 

[cjordan08]

God created everything known to man. You can either accept the fact or believe on how you personally feel. It's even the 4th book in the Bible.

 

[Wiccan_Child]

God created everything known to man. You can either accept the fact or believe on how you personally feel. It's even the 4th book in the Bible.

Not exactly. According to the Bible, God created everything made. He didn't create anything that was never made (i.e., anything that has always existed). If numbers were never made,

And it should go without saying that the Bible isn't automatically right about everything.

 

[Radagast]

Not exactly. According to the Bible, God created everything made. He didn't create anything that was never made (i.e., anything that has always existed).

I have to agree with Wiccan_Child here. I think numbers were not created, but always existed within God.

 

[Nooj]

I have to agree with Wiccan_Child here. I think numbers were not created, but always existed within God.

Could you explain what you mean by that?

 

[Radagast]

Could you explain what you mean by that?

I think I said this before... numbers, I believe, have existed eternally within the mind of God, or more specifically, within the Logos or rational aspect of God. Since Christians believe that the Logos created the universe (John 1:3), this explains what Eugene Wigner once referred to as the “unreasonable effectiveness of mathematics in the natural sciences.”

 

[faithful99]

It seems to me that it's self evident that God created numbers, else we would have one of everything, for 1 is the next after nothing (zero). When you look at life it involves many mathematical principles. But mathematics can only explain the known, once a profound unknown is revealled mathematics as we know it may change.

 

[Radagast]

It seems to me that it's self evident that God created numbers...

As Trinitarian Christians, we need to believe that the number 3 existed before creation. And if 3, then logically all the others too.