God Must Exist: Infinite Regression is Impossible

[We_Are_VENOM]

[We_Are_VENOM]

Yeah, since the fact that I can obviously succeed in taking my first step only concludes that there is a finite distance between my starting point and my first step.

I think the point being missed is that even a finite distance can be subdivided into an infinite number of segments. That's just simple math and easy to show. Starting from the start point, make a segment half the distance to the end point. That's segment 1. For each subsequent segment, repeat the process. From the end of segment N, create a new segment that is half the distance to the end point. N is infinite unless you have found a distance that can't be cut in half.

Have you found a distance that can't be cut in half? Only then would the NUMBER of segments be finite.

Clearly the size of each subsequent segment approaches 0, but it's always possible to cut any segment in half. If you only ever walk half way from your current position to the final position you will never reach the end.

Obviously if you don't walk half the distance, but the full distance, you will reach the end. That doesn't negate the fact that there are an infinite number of segments that can be created.

Im sorry but with all due respect, I just fail to see how my point is being addressed.

Shout out to bluegreenearth for at least acknowledging the conundrum.

[JoeyKnothead]

From Post 170:

Sure, you can explain it until the cows come home...but notice how you are saying EVERYTHING but replying directly to my point.

Instead of trying to make sense of what is absurd, you need to understand why it is absurd in the first place.

I don't think it's absurd at all.
Take a measurement, divide by two. Divide that by two...
Soon enough, the pretty thing hollers out "suppertime", so ya stop to eat, then ya set back to dividing again, up til all the stars get turned off.

Because on one hand, the idea is that there are an infinite amount of points between step 1 and step 2.
So when I take one step, Ive successfully traversed all of the points between 1 and 2 (an infinite amount).

Yep. We can divide that distance an infinite amount of times.
We're not reinventing rockets here.

However, if I was tasked to count every single point (in numerical order) between 1 and 2, for some "reason", I will never arrive at the second point.
Yet, I had no problem arriving at 2 when I took the step, despite traversing the same amount of points that is preventing me from arriving at the second point if I was to begin counting.
You've yet to address this conundrum.

I'm not responsible for this conundrum, I'm just pointing out a simple statement of fact - we can divide any measurement an infinite amount of times.
I can't help if such a condition causes discomfort or confusion.

To your point, anything measured can be divided an infinite number of times...this is theoretically true....but when you apply that concept to the real world, you get contradictory results...because if what you say is true, motion would be impossible...as one would never be able to reach any single point, if that were the case.

Notice, we're doing our division after the initial measurement, or step, has been taken.

Not only that, but even if I were to successfully traverse infinity with a single step, I would traverse infinity in a finite proper time, which is equally absurd, but for a completely different reason.

You might wanna sit down for thisn, but we can divide that time an infinite amount of times.

So either way, the entire concept is fundamentally flawed.

Yeah, the fundamental flaw can't possibly be your inability to understand

[DrNoGods]

[Replying to We_Are_VENOM in post #171]

You've yet to address this conundrum.

There is no conundrum. This whole thing boils down to countable vs. uncountable infinite sets. When you take the first step, that is part of a countable infinite set (integers) and you could keep stepping and counting each step one by one to (theoretically infinity if you were, say, a god who never died). You can assign each step a number and therefore count them. But the number of intervals or segments within one step is part of an uncountable infinite set (real numbers) as there is no limit to the number of divisions each unit step can be divided into whether the intervals are evenly spaced, or not.

So you can count individual steps using integers, but you cannot count the number of intervals that comprise one step if those are described using real numbers. If you place some limit on the "smallest" interval, then of course you've created another countable infinite set because you've defined the length of an interval.

The example of dividing one step by half so that interval #1 is 1/2 of a step long, then dividing that interval by half so that interval #2 is 1/4 of a step long, etc. is a simple geometric series that converges to exactly 1 (ie. sum(n=1,infinity) of (1/2)^n = 1). But it takes an infinite number of sums to get to 1 (step).

[We_Are_VENOM]

[Replying to JoeyKnothead in post #173]

As I presumed, my points arent being addressed. You gave entire quotes of what I said without even touching the points.

You can have the last word...and as far as im concerned, my points still stand.

[JoeyKnothead]

[Replying to JoeyKnothead in post #173]
As I presumed, my points arent being addressed. You gave entire quotes of what I said without even touching the points.
You can have the last word...and as far as im concerned, my points still stand.

I've addressed your points, only to have you offer dismissals such as "makes no sense", and "absurd".
That you refuse to accept as fact that which is fact is a problem you gotta figure out.

And that fact is that any measurement can be divided an infinite amount of times.

This fact does NOT rely on the refusal of folks to accept it. It does NOT rely on one's admitted inability to make sense of it. It does NOT rely on one's declaring it "absurd".

So go on, live your life in refusal of reality.

[We_Are_VENOM]

There is no conundrum. This whole thing boils down to countable vs. uncountable infinite sets.

When you take the first step, that is part of a countable infinite set (integers) and you could keep stepping and counting each step one by one to (theoretically infinity if you were, say, a god who never died). You can assign each step a number and therefore count them. But the number of intervals or segments within one step is part of an uncountable infinite set (real numbers) as there is no limit to the number of divisions each unit step can be divided into whether the intervals are evenly spaced, or not.

First off, please tell me what you mean by "uncountable infinite sets".

I dont know what that means.

So you can count individual steps using integers, but you cannot count the number of intervals that comprise one step if those are described using real numbers.

Excuse me, but what would stop me from counting the number of intervals that comprise of one step?

If you place some limit on the "smallest" interval, then of course you've created another countable infinite set because you've defined the length of an interval.

The example of dividing one step by half so that interval #1 is 1/2 of a step long, then dividing that interval by half so that interval #2 is 1/4 of a step long, etc. is a simple geometric series that converges to exactly 1 (ie. sum(n=1,infinity) of (1/2)^n = 1). But it takes an infinite number of sums to get to 1.0, so you still can't count every interval within that one step even though it converges to 1 (step).

So I cant count every single interval within that one step, but with one step, I can traverse every single interval within that step.

I cant traverse it by counting, but I can count it by stepping??

Makes no sense.

[benchwarmer]

Yeah, since the fact that I can obviously succeed in taking my first step only concludes that there is a finite distance between my starting point and my first step.

I think the point being missed is that even a finite distance can be subdivided into an infinite number of segments. That's just simple math and easy to show. Starting from the start point, make a segment half the distance to the end point. That's segment 1. For each subsequent segment, repeat the process. From the end of segment N, create a new segment that is half the distance to the end point. N is infinite unless you have found a distance that can't be cut in half.

Have you found a distance that can't be cut in half? Only then would the NUMBER of segments be finite.

Clearly the size of each subsequent segment approaches 0, but it's always possible to cut any segment in half. If you only ever walk half way from your current position to the final position you will never reach the end.

Obviously if you don't walk half the distance, but the full distance, you will reach the end. That doesn't negate the fact that there are an infinite number of segments that can be created.

Im sorry but with all due respect, I just fail to see how my point is being addressed.

You said:

I dont know the precise amount...but the answer must lie in the "finitude".

I clearly showed the amount is infinity and not finite or "finitude" which I can only assume is your made up way of saying finite.

Your point seemed to be that there is a conundrum where none actually exists.

Let's try a different way:

If you want to reach point B from point A, you must travel the distance between them. Let's call that B - A. If the length of your stride is S, then you can traverse the distance by taking (B - A) / S steps. I think you get that since you talk about taking 1 step to get from A to B. This assumes a stride length of B - A.

Now, what many have tried to explain is that if you decide to cut your stride in half EVERY time you take a step (including the first 1), you are never going to reach B from A.

You seem to be confusing stride lengths.

If you are feeling silly and decide to take a step that is always 1/2 the distance remaining to your end goal, you will obviously never reach it.

Example:

Distance to from A to B = 1 meter

1st step: .5000 m Total: .5000 m
2nd step: .2500 m Total: .7500 m
3rd step: .1250 m Total: .8750 m
4th step: .0625 m Total: .9375
...

You can take no amount of steps using this method and reach your goal.

If you get tired of the exercise and decide to go back to a stride length that covers the remaining distance, only then can you reach your goal.

If your point is that there in NOT actually an infinite number of possible segments between any given 2 points (unless they are the same point of course) then you wrong. If your point is that you are confused how this is possible, just do the math. If your point is simply you find the idea of an infinite set within a finite distance 'odd', then OK, but that's the fun of math.

[DrNoGods]

[Replying to We_Are_VENOM in post #177]

First off, please tell me what you mean by "uncountable infinite sets".

This is a standard math term for describing a set such as real numbers where the set is infinite (ie. has an infinite number of elements), but because there are also an infinite number of numbers between any two numbers, it is impossible to actually count them. Contrast this to the integers which is also an infinite set, but there is nothing between 1 and 2, or between 2 and 3, etc. This set is called a countably infinite set, because it is possible to count the individual elements even though the set runs to infinity in each direction (positive or negative).

Excuse me, but what would stop me from counting the number of intervals that comprise of one step?

Because there is an infinite number of them. You could start counting using the series mentioned earlier (1/2 + 1/4 + 1/8 + 1/16 ... where the fractions represent the fraction of a full step that each interval represents), but the closer you get to a full step (1) the smaller the intervals get and it never stops. The intervals keep getting smaller and smaller, just like the interval between any two real numbers. So you can start counting, but you'll never get to 1 untill you count an infinite number of ever decreasing intervals.

So I cant count every single interval within that one step, but with one step, I can traverse every single interval within that step.

I cant traverse it by counting, but I can count it by stepping??

Makes no sense.

Integer (1 step) vs. real number (infinitely divisible). That is the difference. Using real numbers, the number of intervals making up a full step is an infinite number. Only if you define the length of an interval (however small you want to make it ... eg. the diameter of an H atom) can you define how many there are that make up 1 step.

Here are some links for the series 1/2 + 1/4 + 1/8 ..., and the "Dichotomy Paradox":

https://en.wikipedia.org/wiki/1/2_%2B_1 ... _%E2%8B%AF

https://en.wikipedia.org/wiki/Zeno%27s_ ... my_paradox

[Bust Nak]

what would stop me from counting the number of intervals that comprise of one step?

Because there is an infinite number of them...

Careful, there is an infinite number of integers, yet we can count them all. We cannot count the number of intervals here because there isn't a one to one match to natural numbers.

[DrNoGods]

[Replying to Bust Nak in post #180]

Careful, there is an infinite number of integers, yet we can count them all. We cannot count the number of intervals here because there isn't a one to one match to natural numbers.

Right ... that was my original point about countably infinite (eg. integers) vs. uncountably infinite (eg. real numbers). The 1/2 + 1/4 + 1/8 ... interval size example seemed relevant because you can count each interval just like with integers, and that series does converge to 1 (Venom's "step"). So it is a countably infinite set, but unlike the integers the spacing between each element is not constant and gets progressively smaller as you count, and continues to get smaller ad infinitum so that the "smallest" interval is undefined and simply approaches zero as you count forever.

Maybe a better question for Venom is whether he can complete the count of intervals within one step. Being countable does not mean the count can be completed ... that is only true if there are a finite number of intervals (however many, but less than infinity) within a step.