Numbers

[bolinstephen]

I argue that the concept for a number, say 23 is unchanging and therefore eternal and therefore uncreated. I just came across this quote, in relation to this discussion: “To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.” —Hilda Phoebe Hudson.

23 always equals 23. Time has no impact on the 23-ness of 23. 23 always and will always equal 23. The question that is up for debate is did 23 always equal 23? Did the number 23 have a beginning? I say no. There never was a time when 23 did not equal 23. Therefore, 23 has no beginning, no end and no change and is therefore eternal.

If what I am arguing is correct, the number 23 and all numbers where x=x, are eternal with God. Yet to say numbers are “part” of God(I understand God has no ‘parts’) I am not comfortable with.

Biblically, there may be some justification. The word was in the beginning with God and it was God. Wisdom was in the beginning with God. Perhaps numbers, too, are in the beginning with God and have the same relationship with God as the word?

 

[tonyrey]

I argue that the concept for a number, say 23 is unchanging and therefore eternal and therefore uncreated. I just came across this quote, in relation to this discussion:

“To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.” —Hilda Phoebe Hudson.

There is very good reason to believe that spiritual beings, facts and numbers are eternal but not co-eternal with God! Only the Creator** exists** for all eternity; otherwise the definition “He Who Is” would not be true - unless numbers are an aspect of divinity (which seems unlikely). It seems more likely they are a product of Creation - although endless and indestructible like the spiritual world:

1In the beginning was the Word, and the Word was with God, and the Word was God. 2He was in the beginning with God. 3All things came into being through Him, and apart from Him nothing came into being that has come into being.…

John 1:1-2

Surely numbers are an attribute of creatures not the Creator. To argue that 1 and 3 co-exist with God leads to the strange conclusion that they are the only numbers that exist for all eternity!

 

[rossum]

I argue that the concept for a number, say 23 is unchanging and therefore eternal and therefore uncreated.

23 (base 4) = 11 (base 10)
23 (base 5) = 13 (base 10)

The meaning of symbols is neither unchanging nor eternal, and different scripts use different symbols.

Mathematics is probably a bad example to use, since all Mathematics is based on unproven axioms, the Peano Axioms in the case of the non-negative integers. Using a different set of axioms would result in a different set of numbers.

The classic example is geometry. Depending on which version of the Parallel Axiom you use, you can get Euclidian, Spherical or Hyperbolic geometry, each of which has different properties.

$0.02

rossum

 

[Rhubarb]

Philosophy of math is a huuuuuge, complex, and ancient branch of philosophy. It seems that you lean towards Realism regarding mathematical objects. But that depends what you mean by “concept of a number.” MY personal concept of 23 was created when I learned it. Concepts of 23 predate me. Some people would say that 23 exists independently of human thought altogether. Some people would say that “23” is just an idea-tool we use to express a relationship between objects. Some say 23 is a property a set can have, or a property of an element of a set, or the properties within a set.

I think in terms of mathematical objects as they relate to God (if for the sake of argument we take God as granted) there are interesting questions. Did mathematical objects exist before creation - before a time when there was anything to count? Or is it creation that gives mathematical objects their substance? I think these questions aren’t so clear.

 

[tonyrey]

Philosophy of math is a huuuuuge, complex, and ancient branch of philosophy. It seems that you lean towards Realism regarding mathematical objects. But that depends what you mean by “concept of a number.” MY personal concept of 23 was created when I learned it. Concepts of 23 predate me. Some people would say that 23 exists independently of human thought altogether. Some people would say that “23” is just an idea-tool we use to express a relationship between objects. Some say 23 is a property a set can have, or a property of an element of a set, or the properties within a set.

I think in terms of mathematical objects as they relate to God (if for the sake of argument we take God as granted) there are interesting questions. Did mathematical objects exist before creation - before a time when there was anything to count? Or is it creation that gives mathematical objects their substance? I think these questions aren’t so clear.

As far as I can see, numbers are only concepts but also facts. Even if no one can count how many atoms exist there is a definite answer - which is another nail in the coffin of materialism! Numbers are real even though they are intangible and further evidence that there is a framework of order and purpose in the universe.

 

[sirach2v4]

23 did not always “exist” independent of God, to a believing person. “23” is a concept of a mind, divine in the first instance or human in a derived sense, by creation.

I don’t have more education in math than the wimpy first two years of college math, which in my case weren’t so spectacular or theoretical.

Math, and science in general, are based on observations, hypotheses, theorems, etc. and these are based on assumptions. The results that confirm hypotheses tend to support the assumptions that precede them – until something comes along to upset that.

I had a brief encounter with imaginary numbers – to talk of a subject that I have otherwise completely forgotten about. I wish I could say something relevant, but I cannot.

Perhaps 23 may be thought of as an illusion, very dependent on one’s point of view, like the Big Dipper in the sky. From a different point of view, it may be a Ham Sandwich.

23 apples is not a property of the apples, but merely a hypothetical construct of an observer.

 

[tonyrey]

As far as I can see, numbers are only concepts but also facts. Even if no one can count how many atoms exist there is a definite answer - which is another nail in the coffin of materialism! Numbers are real even though they are intangible and further evidence that there is a framework of order and purpose in the universe.

I forgot to add that as numbers presuppose the existence of different beings they must exist in the spiritual as well as the physical universe - “beyond” time and space but not prior to Creation.

 

[Rhubarb]

What do you think it means to say that “numbers are real”?

 

[Gorgias]

“23” is a concept of a mind, divine in the first instance or human in a derived sense, by creation.

Math, and science in general, are based on observations, hypotheses, theorems, etc. and these are based on assumptions. The results that confirm hypotheses tend to support the assumptions that precede them – until something comes along to upset that.

Hmm… except that the things observed precede the observation of them. It’s not that the ‘concept of 23’ came into existence when it was first observed – it pre-existed the observation (otherwise, it could not have been observed in the first place)!

However, to suggest that the ‘concept of 23’ (as opposed to the various representations of that concept, such as octal or binary or decimal, as rossum discusses) pre-dates creation seems odd. Before there was any ‘thing’ (or, therefore, any change in things, and therefore, any temporal dimension), what would it mean for there to be a ‘23’? At best, if numbers are abstractions for things (and things can be counted using these abstractions), then all we have in eternity is ‘simplicity’ and ‘unity’ (of God). Even positing a number ‘2’ or ‘3’ is problematic.

23 apples is not a property of the apples, but merely a hypothetical construct of an observer.

23 apples is certainly a property of a collection of apples, independent of any observer!

 

[tonyrey]

What do you think it means to say that “numbers are real”?

Numbers are not a human invention. Even before man existed water consisted of** two** hydrogen atoms and **one **oxygen atom. Reality consists of far more than physical objects.

 

[Rhubarb]

Numbers are not a human invention. Even before man existed water consisted of** two** hydrogen atoms and **one **oxygen atom. Reality consists of far more than physical objects.

No, I totally agree with you. At least about the water. But the last part isn’t a conceptual analysis of number, or of reality, or objects. That’s the rub when it comes to trying to give a complete account of numbers. To say that numbers are ‘real’ requires one to explain what it means to be real. That generally raises a host of other problems. The great philosophers and mathematicians have been struggling with these problems since Plato at least, and they’re still up for debate now.