The Kalam Cosmological Argument

[For_The_Kingdom]

Now, moving right along..to my second analogy..

The Sandman: imagine there is a particular man, with an infinite amount of sand at his disposal. The man can never run out of sand, because he has an INFINITE amount. Imagine the man is standing above a bottomless hole (or pit)..and what is meant by bottomless? Well, if something was to fall in the hole, it would fall forever and ever, because the hole is bottomless..no foundation.

Got it?

Now, suppose the man is shoveling sand into the bottomless pit..and imagine the man was shoveling sand into the pit for eternity...he never began, and he never stopped..he has been shoveling for eternity.

The man's goal is to keep shoveling until he has successfully filled the entire hole with sand, until the sand reaches the top of the hole, and is thus, FILLED.

The million dollar question is; how long will it take the man to fill the hole with sand?

Answer: the man will NEVER fill the hole with sand. Why? Because the hole is bottomless, that's why. If you can't reach the bottom, from the top...then how can you reach top, from the bottom??

Hmm.

This example is analogous to the reality of our world...if you can't go back in time (a past boundary), then how can you possibly reach any present point?

The man shoveling: Represents the PRESENT moment in time, as the man is presently shoveling.

Bottomless hole: Represents past eternity, of which there is no beginning to time.

Sand: Represents events in time, and as the sand is traveling in the hole, this is analogous to going back in time.

The ONLY possible way to fill the hole entirely with sand, is if there is a BOTTOM FOUNDATION to the whole. If there is a foundation at the bottom, the sand can successfully reach the man at the top, where he is PRESENTLY shoveling.

Likewise, the only POSSIBLE way for us to reach the present moment if there is a past boundary/foundation/beginning of time. If there is a past boundary, the events which led up to today can successfully...led up to today.

One final problem with the concept of an actual infinity..is the quantities itself. Think about it, if the past is eternal, that would mean..

That the total amount of seconds amounts to infinity..
The total amount of minutes amounts to infinity..
The total amount of hours amounts to infinity..
The total amount of days amounts to infinity..
The total amount of weeks amounts to infinity..
The total amount of months amounts to infinity..
The total amount of years amounts to infinity..
The total amount of decades amounts to infinity..
The total amount of centuries amounts to infinity..

and finally..

The total amount of millenniums amounts to infinity..

There is an obvious problem here, because each of those intervals/measurements of times, each one has different values!!! Yet, all would have the same value if they are infinite!!

This is an obviously clear absurdity..which can not reflect reality.

In closing, there are many different ways one can demonstrate the absurdities which comes come an actual infinity...the point of this thread is to prove, that an absolute beginning is necessary..and by "beginning", I mean a "beginning of all beginnings".

There had to be ONE, SINGLE, INITIAL action, which all other actions resulted from. There is just no way out of it. Neither science, nor any scientist can help you here. Neither philosophy, nor any philosopher can help you here. Neither math, nor any mathematician can help you here.

And finally, God himself, he can't even help you here. God can't neither fill the hole with sand, or reach equal distance of infinity.

So, in conclusion; the universe began to exist, because it is logically impossible for any thing within "time", to exist eternally within time. So, if nothing "within" time can be eternal, it follows that the universe itself cannot be eternal, for the same reasons that everything WITHIN the universe cannot be eternal.

You cannot have an eternal universe with only finite parts (events) within the universe. If the parts are finite, then so is the universe.

Oh, and btw, save all of the "But, what about God, God also would have to have a beginning"...save all of that talk, because the universe is the subject of interest right now.

So, as I've just proven, on logical grounds...that it is absolutely, positively necessary for the universe to begin to exist.

[FarWanderer]

Well of course I can't negate what you are saying, because you are begging the question. Again.

Your arguments are all based on the assumption that there is any "reaching" to do. Reaching from when? Some point in time infinitely long ago? There is no such thing.

Ok, so carry this acknowledgement over to naturalism...because on such a worldview, the past is eternal on an infinitely long timeline.

So with this latest acknowledgement, what does this imply?

Nothing.

Infinite past = coherent
A point in time infinitely long ago = incoherent

You've just contradicted yourself. If an infinite past is coherent, how is it that "a point in time infinitely long ago" is incoherent?

Because there is no "point" that can represent an infinite value.

An infinite past is made up of "points in time, infinitely long ago".

No. An infinite past is made up of points, each a finite amount of time ago, but extending infinitely.

Zero. And it would be in integers. Not natural numbers.

Natural numbers are integers...so to make a distinction of the two is to show that you don't understand what is going on here.

Natural number: the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.

This was a failed "gotcha" moment at its finest.

And to put even more icing on the cake..

In mathematics, the natural numbers are those used for counting


https://en.wikipedia.org/wiki/Natural_number

Do you see that? Natural numbers are using for COUNTING...and what did I use "natural number" in the context of??? COUNTING.

See what I mean? All of this ignorance and failed/illogical objections, just because they know that at the end of the argument, there is a God.

SMH.

I was not correcting you on the meaning of "natural number". I was rejecting your premise that today has some natural number assignable to it countable from some absolute beginning. The fact that I said "zero" should have tipped you off on that. When I say today is day zero, it's because I am rejecting the paradigm of an absolute beginning all together.

Which brings me to...

Do you know what it means to beg the question? Because you do it pretty much every post.

Begging the question as far as what?

You just say that "the universe has a beginning because the universe has a beginning", over and over again, just rewording it in various ways.

When you argue that today must have some natural number value assignable to it after counting from "the earliest day", you may as well be saying "the universe has a beginning because it has an earliest day".

I hope the circularity is clear. Now, if only you could prove the universe actually has an earliest day, then you can win the argument.

[Bust Nak]

If infinity-infinity=infinity leads to absurdities then, infinity under certain conditions, can lead to absurdities.

You affirm the first premise.

In that sense, equality under certain conditions can lead to absurdities; subtraction under certain conditions can lead to absurdities; everything under certain conditions (i.e. when misused) can lead to absurdities.

And Ive established that indeed there are conditions where infinity-infinitycan be equal to infinity.

Where the conditions are "if you appeal to intuition instead of mathematics."

*sigh* You just keep saying the same thing over and over as though the statement infinity-infinity is undefined properly addresses the math.

It does, end of story. Infinity-infinity is undefined, nothing you can bring to the table can challenge that, no amount of explain why infinity-infinity is undefined would allow you to say Infinity-infinity = infinity.

Ive linked you to an article where it was mathematically shown that infinity-infinity can equal infinity.

But it doesn't though; it merely showed why infinity-infinity is undefined.

Ive linked you to a video where it was shown mathematically how infinity " infinity can equal infinity (as well as negative infinity and zero).

It stopped being mathematical when she wrote infinity-infinity = infinity. You/she can't do that.

Heres a couple more links showing how infinity-infinity can equal infinity when evaluating limits...

None of them shows how infinity-infinity can equal infinity. Instead it show various ways to avoid running into infinity-infinity. These sites, being academic, have been very careful with their wording; they spoke of limits, of manipulations and tricks, of circumvent infinity-infinity to get an answer. Note how deliberately they are to avoid stating infinity-infinity=infinity.

If you want to continue to hold this position that infinity-infinity cannot ever equal infinity then go ahead and show me where the math in the video and other links was incorrect.

The first one is easy, the author did that for me already: "This is not correct of course..."
The video, when she wrote infinity-infinity = infinity.
The last two links are fine, they are correct.

And thats because she showed mathematically how infinity-infinity can equal infinity, -infinity, and zero. Do you understand what it means when they say indeterminate?

It means there is no answer, i.e. does NOT equal infinity, -infinity, nor zero.

Well whos intuition about infinity is correct then?

Georg Cantor's?

It seems intuition is all we have if infinity isnt real.

We still have mathematics.

Go ahead and show me where infinity has been shown to exist in the real material world.

The size of the universe is as close as I can get.

Hilberts Hotel only works with the countably infinite.

Hotel rooms are countable, so what's the problem?

Which presumes an infinite universe. What evidence is there that the observable universe has infinite space?

Bait and switch, infinite universe as opposed to observable universe. The observable universe is finite in size.

It was done with mathematics, Bust Nak.

It stopped being mathematic when people say infinity-infinity = infinity.

No it means its a mathematical argument.

The article literally tells you it's incorrect.

If infinity isnt a number and we therefore cant use mathematical arguments how do you propose to demonstrate infinity actually exists?

But you can use mathematical arguments on infinity, you just have to follow mathematical rules, e.g. no claiming "infinity-infinity = infinity"

It does no such thing. It simply tells us that infinity is not a number but that they will think of infinity as a very large number, so large there isnt another number larger than it.

Tell me what the very next sentence says after what you quoted here.

How else should we think of infinity in the context of numbers?

As not a number but as a limit.

[otseng]

No, there is no language barrier..you must be slow on the mental draw or something.

You are being disingenuous...and it is a crying shame that someone is going through so much trouble as to not admit that they were simply wrong.

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[Bust Nak]

I agree, subtracting infinity from infinity is an incoherent concept. Now, does this mean that it is impossible for me to have EVER have/had an infinite amount of things??

No, it is not impossible.

Is it possible to have an infinite amount of anything (actual infinite amount). Yes or no.

Yes, it is possible; assuming you mean metaphysically possible instead of physically possible.

So, if I see with my own two eyes that you are beating your wife...does it make any sense to say to you "Hey, Bust Nak, if you are beating your wife, you need to stop".

Kinda, it would make more sense to just say "you need to stop beating your wife.

See where I am going here?

No, because it wasn't as clear as "seeing with my own two eyes" whether you would answer yes or no to my question. Which is still left unanswered by the way.

Do you, or do you NOT have an infinite amount of red balls after subtracting an infinite amount of black balls...yes or no?

Yes.

The answer is obviously yes (as you admitted)...so why are you still maintaining that the answer is false, after previously admitting that you will have an infinite amount.

I have not been "maintaining that the answer is false" though. I have consistently told you that there is an infinite amount of red balls left. Instead, I have been pointing out that your claim that "infinity-infinity=infinity" is false.

The fact that no red balls were removed is just a "fun fact" (an irrelevant, fun fact, at that), and has no barren on the truth value of you subtracting an infinite amount of black balls and still having an infinite amount of red balls.

How is it irrelevant when it is the explanation of why I would still have an infinite amount of red balls? It might be trivial, but it is not irrelevant.

The most clear, blatant, and text book example of a red herring that I've ever seen on this great forum.

It's not a red herring, I am trying to explain the math to you.

But since the question is not how many black balls are in the pile after you've subtracted them, that point is completely irrelevant.

It was not supposed to answer that question, the relevance comes in where it explains where you are going wrong, in thinking infinity-infinity = infinity.

Disingenuous. Ahh yes, I can safely move on from you after the blatant disingenuousness coming directly from your fingertips.

Pointing things out about you scenario you'd rather I don't point out, isn't disingenuity on my part.

Now, I am satisfied/content. Bust Nak, you can have the last word as this conversation (at least on my end) shall continue without you.

Never mind answering the questions above, either. Your choice..just know that I won't be responding.

Sure, you are under no obligation to answer my posts. I am used to my challenges being left unanswered. Not that your answers of "red herring" and "disingenuous" are that much better than no answers at all.

[For_The_Kingdom]

Because there is no "point" that can represent an infinite value.

So if the past is eternal, wouldn't the totality of every single event in time amount to infinity? Yes or no.

An infinite past is made up of "points in time, infinitely long ago".

No. An infinite past is made up of points, each a finite amount of time ago, but extending infinitely.

Dude, you just said "an infinite past"...and I said "infinitely long ago".

They mean the same thing..yet, for some strange reason, you disagreed with what I said.

*shrugs*.

I was not correcting you on the meaning of "natural number". I was rejecting your premise that today has some natural number assignable to it countable from some absolute beginning.

If that is all you were rejecting, then the mere mention of "they are integers, not natural numbers" was completely irrelevant to the discussion.

Second, if the past is eternal (as it would have to be on naturalism), nothing is stopping a person (me) from assigning a natural number to every day which led to 9-26-18, and putting the days in numerical order.

Nothing is prohibiting me from doing so, OTHER than the fact that it is impossible to do..it can't be done, which is why you nor anyone else can do it.

The fact that I said "zero" should have tipped you off on that. When I say today is day zero, it's because I am rejecting the paradigm of an absolute beginning all together.

Sure, you can systematically reject anything you like..but there are certain implications that comes with what you are rejecting...which is why my challenge for you to assign a natural number to all of the days which led to today, and put them in numerical order from earliest to latest (present day)...my challenge still stands.

Now which number will you assign to today? Each member of this infinite set is discrete, and you are free to assign numbers to each member. Go ahead.

You just say that "the universe has a beginning because the universe has a beginning", over and over again, just rewording it in various ways.

1. Our universe cannot exist without time
2. Time had a beginning
3. Therefore, our universe had a beginning

Wow, I like this syllogism even better than that of the KCA.

When you argue that today must have some natural number value assignable to it after counting from "the earliest day", you may as well be saying "the universe has a beginning because it has an earliest day".

I'm not sure how that follows. Looks like a non sequitur to me.

I hope the circularity is clear. Now, if only you could prove the universe actually has an earliest day, then you can win the argument.

No, it isn't clear.

[FarWanderer]

Because there is no "point" that can represent an infinite value.

So if the past is eternal, wouldn't the totality of every single event in time amount to infinity? Yes or no.

If you define the past by events, then yes there would be an infinite number of events. However, I do not see how this might make sense of a "point" representing an infinite number of events past.

An infinite past is made up of "points in time, infinitely long ago".

No. An infinite past is made up of points, each a finite amount of time ago, but extending infinitely.

Dude, you just said "an infinite past"...and I said "infinitely long ago".

They mean the same thing..yet, for some strange reason, you disagreed with what I said.

They do not mean the same thing. On a graph, an infinite past is an unbounded region of (time)<(now), whereas at best "infinitely long ago" just gets an arrow pointing towards the past.

I was not correcting you on the meaning of "natural number". I was rejecting your premise that today has some natural number assignable to it countable from some absolute beginning.

If that is all you were rejecting, then the mere mention of "they are integers, not natural numbers" was completely irrelevant to the discussion.

I said "in integers". Not "they are integers".

If I had simply said "zero" then you would have likely thought I failed in my reading comprehension to notice that you said "natural numbers" and proceeded to give me a meaningless lecture under false pretenses. I specified that I was speaking in terms of integers precisely to avoid that. And it happened anyway. Go figure.

Second, if the past is eternal (as it would have to be on naturalism), nothing is stopping a person (me) from assigning a natural number to every day which led to 9-26-18, and putting the days in numerical order.

Nothing is prohibiting me from doing so, OTHER than the fact that it is impossible to do..it can't be done, which is why you nor anyone else can do it.

Well, by golly, that would be the point. It is merely your assumption that the universe is obligated to make countable its number of days past.

The fact that I said "zero" should have tipped you off on that. When I say today is day zero, it's because I am rejecting the paradigm of an absolute beginning all together.

Sure, you can systematically reject anything you like..but there are certain implications that comes with what you are rejecting...which is why my challenge for you to assign a natural number to all of the days which led to today, and put them in numerical order from earliest to latest (present day)...my challenge still stands.

Now which number will you assign to today? Each member of this infinite set is discrete, and you are free to assign numbers to each member. Go ahead.

Of course I understand the implications. When I say your argument is circular then I am saying your premises and conclusions imply each other.

If the number of days past are countable, then the universe has a beginning.
If the universe has a beginning, then the number of days past are countable.
If the number of days past are countable, then the universe has a beginning.
If the universe has a beginning, then the number of days past are countable.
If the number of days past are countable, then the universe has a beginning.
If the universe has a beginning, then the number of days past are countable.
If the number of days past are countable, then the universe has a beginning.
If the universe has a beginning, then the number of days past are countable.
If the number of days past are countable, then the universe has a beginning.
If the universe has a beginning, then the number of days past are countable.

Is the circularity apparent yet?

Or perhaps your argument could be formulated as follows:

P1) The number of days past are countable
P2) The number of days past are not countable if the universe is past time-infinite
C) Therefore the universe is not past time-infinite

You keep yelling P2, but I (and presumably benchwarmer and Bust Nak) don't have a problem with P2. The disagreement is with P1, for which you have offered nothing in terms of supporting argument.

You just say that "the universe has a beginning because the universe has a beginning", over and over again, just rewording it in various ways.

1. Our universe cannot exist without time
2. Time had a beginning
3. Therefore, our universe had a beginning

Wow, I like this syllogism even better than that of the KCA.

It's not a replacement, but a supplement. The conclusion of the above argument is P2 of the KCA, not the conclusion of the KCA.

[Bust Nak]

So if the past is eternal, wouldn't the totality of every single event in time amount to infinity? Yes or no.

Yes. The thing that you kept missing is that none of these event happened "infinitely long ago."

Dude, you just said "an infinite past"...and I said "infinitely long ago".

They mean the same thing..

Incorrect. Nothing in the infinite past happened infinitely long ago, as such they do not mean the same thing.

This should have been fairly trivial: think of the number line - there are infinitely many integers, yet every single one of the integer is finite. As such I can assign an integer, in sequence to every day of an infinite past without any difficulty.

Second, if the past is eternal (as it would have to be on naturalism), nothing is stopping a person (me) from assigning a natural number to every day which led to 9-26-18, and putting the days in numerical order.

Right, that much is simple: today is day 0; yesterday is day 1; the day before that is day 3 and so on. It's easy. It's just a variation of my "zero step" answer from your earlier attempts at issuing a challenge.

Nothing is prohibiting me from doing so, OTHER than the fact that it is impossible to do..it can't be done, which is why you nor anyone else can do it.

Incorrect. It can be done and benchwarmer has done it here.

Sure, you can systematically reject anything you like..but there are certain implications that comes with what you are rejecting...which is why my challenge for you to assign a natural number to all of the days which led to today, and put them in numerical order from earliest to latest (present day)...my challenge still stands.

That wasn't the challenge though, when you issued the original challenge there was no mention of an "earliest day." Now you might well have "earliest day" in mind back then, but that wasn't what you wrote. Assuming there was only ever one challenge in your head and you have merely forgotten to say "earliest day" in all your excitement, then the following objection applies:

The challenge is malformed. There is no such thing as an "earliest day" in an infinite past.

As it was worded originally: "give me the discrete number to the numbered day of today" (i.e. without the mention of an "earliest day,") the challenge was fine, as such have been answered.

I'm not sure how that follows. Looks like a non sequitur to me.

Well, it certainly renders your challenge meaningless.

No, it isn't clear.

Let me have another go at explaining then: There is no such thing as an "earliest day" in an infinite past, thus it makes no sense to ask us to number days from an "earliest day." The problem does not lie with an infinite past, it lies solely within the request.

There is no such thing as an "earliest day" according to the thesis of an infinite past, as such our inability to answer questions about an "earliest day" does no harm to our position.

As an analogy: There is no such thing as "God's creator" according to the Christianity, as such your inability to name "God's creator" does no harm to Christianity.

Without the mention of an "earliest day," i.e. merely challenging us to assign a natural number to today like you did originally is trivially simple - we can literally pick whatever number we like. Is that clear enough?

[Bust Nak]

P1) The number of days past are countable
P2) The number of days past are not countable if the universe is past time-infinite
C) Therefore the universe is not past time-infinite

You keep yelling P2, but I (and presumably benchwarmer and Bust Nak) don't have a problem with P2. The disagreement is with P1, for which you have offered nothing in terms of supporting argument.

I guess it's worth pointing out that I do have a problem with P2, if by countable we go with Cantor's idea of countable in set theory: the number of days past are countable even if the universe is past time-infinite, as there is a one to one correspondence of days to integers.

Granted it looks like by "countable" F_T_K is insisting on counting from the "earliest day." Only in this particular sense, would the days in an infinite past be not countable.

[FarWanderer]

[Replying to post 158 by Bust Nak]

Yes, I know I was being loose with the definitions. I just wanted to minimize possible distractions from the main point.

[Goose]

In that sense, equality under certain conditions can lead to absurdities; subtraction under certain conditions can lead to absurdities; everything under certain conditions (i.e. when misused) can lead to absurdities.

And by misuse you mean something like not following the rules (i.e. infinity-infinity is indeterminate) which have been put in place to avoid running into absurdities (i.e. infinity-infinity=infinity)? You dont think those rules actually eliminate the existence of the absurdities themselves though, do you? Because they dont.

But as long as you agree infinity-infinity=infinity leads to absurdities thats all I need. Youve virtually conceded the point that infinity can entail absurdities. In fact, every time you declared infinity-infinity is undefined you reaffirm the existence of these absurdities.

Where the conditions are "if you appeal to intuition instead of mathematics."

Patently false. I appealed to mathematics to show that infinity-infinity can equal infinity. You have to show how the math in those links is incorrect.

It does, end of story. Infinity-infinity is undefined, nothing you can bring to the table can challenge that, no amount of explain why infinity-infinity is undefined would allow you to say Infinity-infinity = infinity.

All you are doing here is repeating yourself. You just keep telling me "Infinity-infinity is undefined." As though that settles the matter. But that doesnt make the absurdities non-existent.

Ill tell you what though. The next time you take a calculus test and are asked to evaluate the limit of X -> 0+ (3/X " 1/X) (example L3 in section 2). Just put down as the answer Infinity-infinity is undefined or You cant do that! or There is no answer! or something along those lines. See if you get your answer marked as correct.

You wont. But go ahead and do it anyway.

But it doesn't though; it merely showed why infinity-infinity is undefined.

What article are you reading? The article in question doesnt even use the term undefined.

It stopped being mathematical when she wrote infinity-infinity = infinity.

Patently false assertion. It was mathematical the whole time. Its not like she switched from math to conjugating a verb in French half way through. If you mean her math was incorrect then go ahead and show me where it was.

You/she can't do that.

Of course we can. And when we do, we find contradictions and absurdities.

None of them shows how infinity-infinity can equal infinity.

Another false statement.

The example of the trivial limit L3 in section 2. Its an infinity-infinity form and the answer is infinity. But go ahead and show where he went wrong in the math.

What about the examples of the trivial limit L1 and L2 in section 2 which also both take the indeterminate form infinity-infinity and are shown to be equal to 0 and 3 respectively? Are those wrong too? Because the math that got 0 and 3 as answers for L1 and L2 is the same math that showed the limit of L3 is equal to infinity.

Heres another one. Go to example 11.

Go ahead though. Break the math down for me.

Instead it show various ways to avoid running into infinity-infinity.

Right. Because by avoiding it, they avoid the absurdities. They cant eliminate the existence of the absurdity. They can only use tricks to try to get a meaningful answer.

These sites, being academic, have been very careful with their wording; they spoke of limits, of manipulations and tricks, of circumvent infinity-infinity to get an answer.

Im not sure what you mean by circumvent infinity-infinity to get an answer. But they do use tricks to ascertain some kind of meaningful answer from the indeterminate form infinity-infinity. Sometimes the answer is infinity.

Note how deliberately they are to avoid stating infinity-infinity=infinity.

Noted. Now how do you know that it was deliberate? And what does what they dont say prove? As though there is some special meaning behind not explicitly stating infinity-infinity=infinity. Not to mention you are knocking down a strawman anyway. No where have I argued that infinity-infinity=infinity in some kind of determined sense. Ive maintained from the start that infinity-infinity can equal infinity; that it depends; that it is one of numerous possible answers. Hence, the absurdity.

And why would those cites state infinity-infinity=infinity (as though it were determined) anyway when the whole point of discussing the indeterminate form infinity-infinity in the links is to point out the form can have numerous answers, one of which can be infinity? Mathematicians, when they encounter the indeterminate form infinity-infinity, while evaluating limits, dont just walk away and say, Its undefined. Next question. Each indeterminate case needs to be worked through using the tricks to find the limit. Sometimes the answer is infinity. It just depends.

The first one is easy, the author did that for me already: "This is not correct of course..."

The author didnt say This is not correct of course..." in relation to the math. Nice try.

Oh and by the way, I guess this means everything that was in that article is incorrect then since as youve argued in post 138, It literally tells you the argument is starting with an incorrect premise. Therefore, the article must be incorrect when the article goes on to show how infinity + infinity = infinity.

The video, when she wrote infinity-infinity = infinity.

Argued by pure assertion. Tell me where the math was incorrect in the example she used: limit of (3n " n) = infinity-infinity = infinity.

The last two links are fine, they are correct.

But they illustrated the same point, just using different examples, as the girl in the video. That when evaluating limits the indeterminate form infinity " infinity can yield different answers. In the three examples from section 2 in this link, where the indeterminate form infinity-infinity is found, the answers are equal to 1, 3, and infinity respectively.

[Indeterminate] means there is no answer, i.e. does NOT equal infinity, -infinity, nor zero.

Thats just simply wrong. But you stick with there is no answer the next time you are asked to evaluate limits in a calculus test and come across an indeterminate form like infinity-infinity.

Georg Cantor's?

You mean the guy who apparently attributed his theory to a revelation from God? You mean his intuition is correct?

• My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined it from all sides for many years; because I have examined all objections that have ever been made against the infinite numbers, and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.*

*Cantor to Heman, June 21, 1988, from a draft version in Cantor's letter-book for 1884-1888, pp. 179, in the archives of the Niedersachsische Staats- und Universitatsbibliothek, Gottingen. See also Dauben 1979/1990, p. 298.

http://heavysideindustries.com/wp-conte ... Cantor.pdf

But okay. Cantor is the man then.

We still have mathematics.

What does that mean? Are you suggesting that the conceptual realm of mathematics can show infinity actually exists in the real world?

The size of the universe is as close as I can get.

Setting aside the circularity here I didnt ask for close. I asked you to show me where infinity has been shown to exist in the real material world. Look, we both know it doesnt. I just want to see you say it.

Hotel rooms are countable, so what's the problem?

Sure the rooms are countable (they are countably infinite). The problem is what happens when an uncountably infinite amount of guests show up looking for rooms? There will no longer be the same cardinality between the infinite sets of hotel rooms and guests. Which means there wont be enough rooms available for the new guests even though its a hotel with an infinite amount of rooms.

Setting that aside, the initial paradox is that the hotel is full, every room is occupied with a guest. Yet it can accommodate an infinite amount of new guests, even though its supposed to be full with no rooms available. That is the paradox.

Ten new guests can check in yet there are no more guests in the hotel than there were before the new ones arrived, theres just infinite guests. An infinity of new gests could arrive and yet there are no more guests in the hotel than before the new ones arrived, theres just infinite guests. This could be repeated an infinite number of times and there wouldnt be even one more guest in the hotel than there was before. Making matters worse, guests in rooms {1,3,5...} can all check out and yet there would be no less guests in the hotel than before they checked out, still infinite. Even though rooms {1,3,5,...} are all empty now. Thats the absurdities that infinity affords.

You dont think such a hotel really exists do you?

Bait and switch, infinite universe as opposed to observable universe. The observable universe is finite in size.

What do you mean by bait and switch? In post 130 I originally asked you, But I would ask, how can you actualize in the real material world an infinite amount of money without running into absurdities like the possibility of filling the observable universe with dollar bills?

You answered in post 138, Not if there is infinite space in the universe.

To which I asked in post 149, What evidence is there that the observable universe has infinite space?

The question was originally given in context to the observable universe. You switched and answered in the context of the universe.

So now that youve acknowledged the observable universe is finite in size. I will ask you the same question again.

How can you actualize in the real material world an infinite amount of money without running into absurdities like the possibility of filling the observable universe with dollar bills?

It stopped being mathematic when people say infinity-infinity = infinity.

Of course it's mathematic. Its just math you dont like because it leads to absurdities. So you say stuff like, Hey, thats not allowed! But its not allowed because it leads to absurdities. And yet you maintain theres nothing absurd about infinity.

The article literally tells you it's incorrect.

It doesnt say the math is incorrect.

But you can use mathematical arguments on infinity, you just have to follow mathematical rules, e.g. no claiming "infinity-infinity = infinity"

But thats just a rule put in place to avoid the absurdities. The absurdities themselves dont become non-existent simply because a rule to avoid them has been issued.

Tell me what the very next sentence says after what you quoted here.

Ill quote the whole paragraph.

• Most students have run across infinity at some point in time prior to a calculus class. However, when they have dealt with it, it was just a symbol used to represent a really, really large positive or really, really large negative number and that was the extent of it. Once they get into a calculus class students are asked to do some basic algebra with infinity and this is where they get into trouble. Infinity is NOT a number and for the most part doesnt behave like a number. However, despite that well think of infinity in this section as a really, really, really large number that is so large there isnt another number larger than it. This is not correct of course but may help with the discussion in this section. Note as well that everything that well be discussing in this section applies only to real numbers. If you move into complex numbers for instance things can and do change.

When they say, this is not correct of course... they are referring to treating infinity like a number (which it isnt, its just an idea) where there isnt any number larger than it. They arent saying the math and everything to follow is wrong. I mean what would be the point of the article then? The way the article has outlined how infinity will be thought of is consistent with mathematical uses of infinity. The article is also consistent with Cantors set theory where sets of infinites can be thought of as being different sizes.

As not a number but as a limit.

What do you mean here? By definition infinity is without limit or boundary. How can we then think of infinity as a limit? Or do you mean we can say the limit is infinity if we mean there is no limit?