Creationists: How do you test for "truth"?

[Subduction Zone]

The existence of God is not one of his premises.

How is that a flaw in logic? You are now placing the burden of proof of not only the existence of a god, but the existence of your version of God upon yourself. Are you up to it?

One does not make unwarranted assumptions in a premise.

 

[blü 2]

There is a difference between knowing about something and knowing something. It's very simple. To the person who is incapable of percieving the spectral color yellow that color is unknowable. They will never percieve it as someone who does. Yet it exists.

It may be unavailable to some people as a direct perception but as an element in the set of EM phenomena even wholly blind people can understand the concept, know what they're talking about, since they can perceive too cold, cold, cool, warm, hot, too hot and so on.

The inability to directly perceive certain things and processes is an ordinary feature of being human, whether individual atoms, very distant stars, your own organs, the center of the earth, and so on. It doesn't equate to unknowability.

 

[Polymath257]

The existence of God is not one of his premises.

Why would it be if it isn't necessary?

 

[sandy whitelinger]

The color *you* see is also unknowable to me. Whether we see 'the same' color or not is unknowable. And that is true whether or not either of us is blind or sighted. That doesn't make the color unknowable.

I'm not quite sure I understand what point you are making. There is a HUGE difference between something that is detectable (colors, radio waves) and something that is truly unknowable. The latter might as well not exist because it cannot ever be detected.

It is a simple point. There are things that are known to exist yet are unknowable. Most exist in mathematics. For example what is the first fractal value greater than 0.

I was first just trying to establish that the unknowable can be known of. I didn't know the Color Blind James experience was going to be such a difficult concept to put forth.

 

[Polymath257]

It is a simple point. There are things that are known to exist yet are unknowable. Most exist in mathematics. For example what is the first fractal value greater than 0.

Sorry, but this is factually wrong about the mathematics. We *know* there is no 'first fractal after 0' (I assume you mean 'fraction' and not 'fractal' here--fractals are very different things). So your claim that we know such to exist is wrong.

In this case, the value isn't unknowable. It simply doesn't exist and provably does not exist (take any value more than 0; half of it is less than the original and still larger than 0).

I might suggest not debating math you don't understand with a professional mathematician.

I was first just trying to establish that the unknowable can be known of. I didn't know the Color Blind James experience was going to be such a difficult concept to put forth.

We can know that we do not know certain things. That I fully agree with. But I disagree that we know that there is anything that is inherently unknowable.

 

[sandy whitelinger]

There is a HUGE difference between something that is detectable (colors, radio waves) and something that is truly unknowable. The latter might as well not exist because it cannot ever be detected.

Evidently there is a number called Graham's number, used in a mathmatics equation that is so large that the known universe couldn't represent it. It can't be known but is known to exist.

 

[sandy whitelinger]

Sorry, but this is factually wrong about the mathematics. We *know* there is no 'first fractal after 0' (I assume you mean 'fraction' and not 'fractal' here--fractals are very different things). So your claim that we know such to exist is wrong.

In this case, the value isn't unknowable. It simply doesn't exist and provably does not exist (take any value more than 0; half of it is less than the original and still larger than 0).

I might suggest not debating math you don't understand with a professional mathematician.




We can know that we do not know certain things. That I fully agree with. But I disagree that we know that there is anything that is inherently unknowable.

So one over infinity doesn't exist?

 

[Polymath257]

So one over infinity doesn't exist?

Depends on context.

If you are doing limits and the numerator goes to 1 and the denominator to infinity, the quotient goes to 0.

Infinity isn't a real number, so 1/infinity is simply not defined in the real numbers.

When working on the one point compactification of the complex plane, the added point is often called infinity the function z->1/z is extended to an analytic function on the sphere having value 0 at infinity.

I can go through a few other contexts. But it certainly does not exist in the sense you seem to think it does.

 

[Subduction Zone]

So one over infinity doesn't exist?

I don't have Polymath's education, but since infinity is not a number it does not technically exist. But it can be expressed as a limit. The limit of y =1/x is zero as x approaches infinity.

Proof of 1/x as x approaches infinity equals 0

ETA: I was a bit too slow.

 

[sandy whitelinger]

Depends on context.

If you are doing limits and the numerator goes to 1 and the denominator to infinity, the quotient goes to 0.

Infinity isn't a real number, so 1/infinity is simply not defined in the real numbers.

When working on the one point compactification of the complex plane, the added point is often called infinity the function z->1/z is extended to an analytic function on the sphere having value 0 at infinity.

I can go through a few other contexts. But it certainly does not exist in the sense you seem to think it does.

I get it now.

 

[Polymath257]

I get it now.

One other comment: mathematics is full of what could be designated as 'useful fictions'.

For example, ALL of mathematics ultimately is based on set theory. But as it is developed, we have very different definitions of, say, the natural numbers (0,1,2,3,..), the integers (..,-3,-2,-1,0,1,2,3,...), the rational numbers (fractions), the real numbers (intuitively, all possible decimals), and the complex numbers (including the square root of -1).

The actual definitions given do NOT have the natural numbers as a subset of the integers. But, there is a 'useful fiction' that allows us to *think* about the natural numbers that way. Since all we are interested in is the relationship, such useful fictions can be quite helpful as long as they preserve all important structures (and what is important depends on the context).

So, there are several very different notions of 'infinity' in mathematics. There are limits, where no 'actual' infinity is ever required. There are cardinals, which essentially look at the 'size' of a set, where there are infinitely many different sizes of infinity. There are 'added points' where some structure is supplemented by an additional point (or several points) called a point 'at infinity'. There are ordinals (representing the order structure as opposed to just the size).

If wanted, I could come up with quite a few other examples, but these are the primary contexts for the use of the symbol of 'infinity'. Some are 'useful fictions', others are actual mathematical objects. And, there are contexts where those not aware of how math is done *think* it might be done and are just wrong.

 

[sandy whitelinger]

One other comment: mathematics is full of what could be designated as 'useful fictions'.

For example, ALL of mathematics ultimately is based on set theory. But as it is developed, we have very different definitions of, say, the natural numbers (0,1,2,3,..), the integers (..,-3,-2,-1,0,1,2,3,...), the rational numbers (fractions), the real numbers (intuitively, all possible decimals), and the complex numbers (including the square root of -1).

The actual definitions given do NOT have the natural numbers as a subset of the integers. But, there is a 'useful fiction' that allows us to *think* about the natural numbers that way. Since all we are interested in is the relationship, such useful fictions can be quite helpful as long as they preserve all important structures (and what is important depends on the context).

So, there are several very different notions of 'infinity' in mathematics. There are limits, where no 'actual' infinity is ever required. There are cardinals, which essentially look at the 'size' of a set, where there are infinitely many different sizes of infinity. There are 'added points' where some structure is supplemented by an additional point (or several points) called a point 'at infinity'. There are ordinals (representing the order structure as opposed to just the size).

If wanted, I could come up with quite a few other examples, but these are the primary contexts for the use of the symbol of 'infinity'. Some are 'useful fictions', others are actual mathematical objects. And, there are contexts where those not aware of how math is done *think* it might be done and are just wrong.

A mathematical reality?

 

[sandy whitelinger]

Depends on context.

If you are doing limits and the numerator goes to 1 and the denominator to infinity, the quotient goes to 0.

Infinity isn't a real number, so 1/infinity is simply not defined in the real numbers.

When working on the one point compactification of the complex plane, the added point is often called infinity the function z->1/z is extended to an analytic function on the sphere having value 0 at infinity.

I can go through a few other contexts. But it certainly does not exist in the sense you seem to think it does.

Let me ask you this, is infinity a concept that doesn't "exist." Is it only a boundary?

 

[Polymath257]

Let me ask you this, is infinity a concept that doesn't "exist."

Well, one of the axioms of set theory, as typically done, is known as the 'axiom of infinity'. In essence, the axiom states the existence of an infinite set.

So, in mathematics as it is done today, infinite sets exist.

 

[sandy whitelinger]

Well, one of the axioms of set theory, as typically done, is known as the 'axiom of infinity'. In essence, the axiom states the existence of an infinite set.

So, in mathematics as it is done today, infinite sets exist.

Is infinity, as a concept, a boundary?

 

[sandy whitelinger]

Well, one of the axioms of set theory, as typically done, is known as the 'axiom of infinity'. In essence, the axiom states the existence of an infinite set.

So, in mathematics as it is done today, infinite sets exist.

Is a "set" of infinity that has an unknowable value?

 

[blü 2]

It is a simple point. There are things that are known to exist yet are unknowable. Most exist in mathematics. For example what is the first fractal value greater than 0.

Mathematics is a system of concepts, not of things. Irrational real numbers like pi, objects of zero (point), one (line) or two (plane) spatial dimensions have no counterpart in reality. In the absence of a brain holding the concept of them they don't exist.

When you say 'fractal value', are you referring to the topological dimension of a fractal?

And whatever your answer, unknowability is a wholly different thing to 'not presently known'.

 

[sandy whitelinger]

Mathematics is a system of concepts, not of things. Irrational real numbers like pi, objects of zero (point), one (line) or two (plane) spatial dimensions have no counterpart in reality. In the absence of a brain holding the concept of them they don't exist.

Useful concepts though?

 

[sandy whitelinger]

When you say 'fractal value', are you referring to the topological dimension of a fractal?

I never knew auto correct would cause such a stir. It should have been fraction. Math guy showed me the error of that one.

 

[blü 2]

I never knew auto correct would cause such a stir. It should have been fraction. Math guy showed me the error of that one.

Then we have 'fraction value greater than 0'. And the mathematical answer would appear to be, 0+(1 infinitesimal).