What if science/mathematics is necessarily the same thing as spirituality/religion?

Photolysis I don't mean that one should believe in everything, although if people never believed in stuff that wasn't proven yet, well then it would never be any breakthroughs.

But you don't need to put up a fight I am very scientific, in fact sometimes I only believe in it because of the science behind it (Sometimes because of own experience, carefully analyzed but that is subjective) most of it is of course not FULLY proven yet, but there are science that makes it seem rational.

So there are proof out there, and many other people get the same result, examples: Thomas Campbell and Robert Monroe
But since you can't publish a report and say "They obtained information without knowing it before!" and proving that they didn't knew before.
It is's unfortunately only a proof for those who take part of the experiment.

http://www.youtube.com/watch?v=uwu8qwXjdjs

http://noetic.org/

It happens to be so that science is making some spiritual things look possible and logical at the same time, but since all paranormal things that even though it is starting to get scientifically proven it still have the supersticious mark in it's name so well people wont accept it until it's accepted by the general scientific community and then generally by the public. Infinity is a good example, not proven with an photograph (I know how stupid that sounds xD But you get my point) but it is shown by matemathics and rational thinking and an accepted view by the majority of the people.

I mean why do you believe the earth is round? (Don't get me wrong I do too :P) But if your never up in space and actually see it, how then can you actually KNOW? Yeah through (possibly faked) videos and math and calculations well it's still technically remains a theory then.
Although an accepted one.
(Yeah I know you can look at the horizont blabla but there are still people who say that they with math have shown that it's flat o. O)
So ultimately it comes down to seeing it.

And I am trying to say that paranormal events have explanations, it's just that we don't understand how yet. We don't exactly know what the consciousness is, does that mean that it doesn't exist either then?

I was like you before and so was my friend. We said that people exaggerated things and it was all bullshit, but then my friend had an OBE himself and obtained information that was unknown to him before, and after that he was far from skeptical it's obvious of course since he had experienced it himself.
Is it then so stupid of me to believe my friend? For now I choose to believe but when I experience it myself I will know.

So if you Photolysis would experience an OBE, let's say a neardeath experience and got information that you knew you hadn't heard before like a family secret nobody ever talked about and you heard it from a dead relative in a "dream". He told you a secret and later on you confirm it with your alive mother.

Would you then say that one is giving direct experiences "too much" significant weight? (I added too much because it seemed like that was what you ment).

And is that claim then a paranormal claim that is EXACTLY as you said it - a crock of shit?

if NO - We are on the same page when it comes to what's personal proof for astral projection.

And the paranormal claim for the day - my friend had that situation in one of these experiences:

http://www.dreamviews.com/f19/interv...rt-2-a-136828/

Of course one can say that it is a false claim, well then I say remain open for the possibility because what if it isn't?

I am not trying to make you say "I totally believe you!! WOW COOL!" but I don't want you to say "Nah I don't believe you, what have you smoked bro?" but to make you say "Hmm I can't believe in it myself, but I am open for the possibility and it might be possible" then if you are interested you can do your own research and see if you can prove it to yourself. Because it is a very subjective experience, but because of that it doesn't mean that all of it is false.

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Originally Posted by mcwillis

http://1.bp.blogspot.com/_FHTRx0P2N4...0/untitled.jpg

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Originally Posted by Xei

lol... where on Earth did this come from?

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From a random blog in the nether regions of the Internet. I thought it would be a lighthearted addition to the thread. It may have been on perhaps page 78 of the google search that I did; God knows where it is...

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Originally Posted by nietstein

Photolysis: how do you prove that infinity does not equal 0?

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By proving that you can't construct an injective function from ℕ to ∅, which is extremely easy.

There is no plan. I don't see how you can possibly believe that, seeing the things you claim to see. Care to enlighten me? because this conversation is going nowhere.

Xei: Truly, I don't know. How would that work? I can't claim that zero definitely equals infinity, nor could anyone else at this point in time. Like Mastermind said, what is logical today, might not be tomorrow. It just seems that in some way, this must be true, though there is no proof for it at this time.

Planeswalker: How can you be so sure there is not a 'plan'? What if everything has already happened? Time cannot be linear in the sense that we perceive it, if it even really exists. What would you say to this: “Experience teaches us no less clearly than reason, that men believe themselves free, simply because they are conscious of their actions, and unconscious of the causes whereby those actions are determined.” -Baruch de Spinoza.

Have you not ever had the feeling that something that happened was a 'miracle'? Or that it was meant to be? We could easily reason away such a belief of these instances as irrational given the logical nature of our minds. It's much easier to leave it to a combination of randomness and individual action, this idea is comfortable for our egos. Tell me this, are you so sure you exist? Could you be a figment of your own imagination? What is the 'you' that you think you are? Is it your body? Is it your mind? Is it your spirit?

Think carefully about this. You can reject it as silly if you like, many would, and your unwillingness to consider it would mean simply that you cling to the confines of the 'reality' that you know. And that is just fine, I wouldn't wish it any other way, because it would be all that could have happened. :)

I cannot "enlighten" you. I can only do what it is that I am doing. Ultimately, you will either consider it or you won't. You must make the 'choice' of whether it is to be or not to be.

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Originally Posted by nietstein

Xei: Truly, I don't know. How would that work? I can't claim that zero definitely equals infinity, nor could anyone else at this point in time.

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Correct, because it can proven false extremely easily. It's about as easy as proving that no bachelors are married.

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Like Mastermind said, what is logical today, might not be tomorrow. It just seems that in some way, this must be true, though there is no proof for it at this time.

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Except that's obviously bullshit and my response to him pointed out exactly why. And that was for matters of science and observation. What you're talking about now it's matters of mathematics and logic, which consists of indubitable statements which can never and have never been proven wrong.

Well, you would have to know with absolute certainty what the future holds for it to be "bullshit" as you so have so eloquently labeled it. The concepts of zero and infinity are not so logically clearly cut and rational as you would like to believe they are. It sounds to me as though you would have happily claimed the earth was flat because other people said so. If there were not people willing to open their minds beyond the conventional logic of their time, where would we be today? Perhaps with an earth that is 'indubitably' flat and the center of the universe because others were fearful of the notion that it could be any other way.

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Originally Posted by nietstein

I cannot "enlighten" you. I can only do what it is that I am doing. Ultimately, you will either consider it or you won't. You must make the 'choice' of whether it is to be or not to be.

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If you cannot "enlighten" me then you aren't an agent of enlightenment. Watch yourself bro

But to back you up,

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Originally Posted by nietstein

how do you prove that infinity does not equal 0?

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Originally Posted by Xei

By proving that you can't construct an injective function from ℕ to ∅, which is extremely easy.

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Originally Posted by nietstein

I can't claim that zero definitely equals infinity, nor could anyone else at this point in time. Like Mastermind said, what is logical today, might not be tomorrow. It just seems that in some way, this must be true, though there is no proof for it at this time.

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Originally Posted by Xei

Except that's obviously bullshit

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Xei, if you retrace logical steps you've previously utilized it is obvious there is only one way for nietstein's claim to be true and that is if it is an axiom. You've mentioned before how

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Originally Posted by Xei

In the end all you're left with is a set of axiomatic conjunctions, supported by observation. If you subject a positively charged particle to an electric field, it will accelerate. Why? The question is meaningless. It just always has done. There's no cause, and no logical implication. It could fail to happen and we would not be able to raise any objections.

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and even how the faculties by which we obtain truth (aka knowledge of axioms) are not a priori and completely wrong. So it seems instead that the bullshit is how you're actually in agreement with nietstein, in agreement over how infinity and 0 have potential to be one and the same thing.

But before I continue what do ℕ and ∅ represent? I only ever went up to Algebra III in an academic environment. Hng

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Originally Posted by mcwillis

http://3.bp.blogspot.com/_FHTRx0P2N4...s400/chart.jpg

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Now I don't understand this math but it seems his perfection was at zero at the time of his birth. Does that mean abortion is okay?

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Originally Posted by nietstein

Well, you would have to know with absolute certainty what the future holds for it to be "bullshit" as you so have so eloquently labeled it. The concepts of zero and infinity are not so logically clearly cut and rational as you would like to believe they are. It sounds to me as though you would have happily claimed the earth was flat because other people said so. If there were not people willing to open their minds beyond the conventional logic of their time, where would we be today? Perhaps with an earth that is 'indubitably' flat and the center of the universe because others were fearful of the notion that it could be any other way.

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Do you even read other people's posts before you write this rubbish? That was rhetorical; obviously you don't.

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Originally Posted by tempusername

Xei, if you retrace logical steps you've previously utilized it is obvious there is only one way for nietstein's claim to be true and that is if it is an axiom. You've mentioned before how

and even how the faculties by which we obtain truth (aka knowledge of axioms) are not a priori and completely wrong. So it seems instead that the bullshit is how you're actually in agreement with nietstein, in agreement over how infinity and 0 have potential to be one and the same thing.

But before I continue what do ℕ and ∅ represent? I only ever went up to Algebra III in an academic environment. Hng

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Wow, I'm flattered you've being paying so much attention. But I don't really espouse the view that there is no such thing as truth. Truth comes in degrees of certainty, or ubiquity. Some truths come in degrees so high that it's insane not to believe them, and certainly insane to firmly believe otherwise. These truths are demonstrated via observations and inferences so pervasively ubiquitous that it makes no sense to dispute them.

At any rate, one thing I cannot permit is people using nonstandard language to make nonsense statements and pass them off as wisdom.

By definition, two sets have the same number of elements if you can construct a 'one-to-one' relationship from the elements of one to the elements of the other. For instance, if you have a set of five sheep, you can label the sheep one to five, and this defines a one-to-one mapping between the set of sheep and the set {1, 2, 3, 4, 5}. Or the set {2, 4, 6, 8, 10}; you can construct a map from this to {1, 2, 3, 4, 5} which sends each number to half of itself (and sending stuff in the other direction doubles it). The number 5 is literally defined as those sets which can be put into a one-to-one mapping with {1, 2, 3, 4, 5}. The number 0 is defined as those sets which can be put into a one-to-one mapping with {}, or '∅', the set of no elements, and the number 'infinity' is taken to mean those sets which can be put into a one-to-one mapping with {1, 2, 3, 4, ... }, or 'ℕ', the set of all positive whole numbers. The number of even numbers is thus infinity, for example, because again we can send 2 to its half, 1, 4 to 2, 6 to 3, and so on; this is a one-to-one map.

If you think about this for a bit, it's obvious that this formalism corresponds exactly to our common concepts of counting, 0, and infinity.

Is infinity equal to 0? Well, simply by the definition of the terms, this is equivalent to asking if we can send a one-to-one map from ℕ to ∅. Can we? No, obviously not. Because for a start we would need to map 1 (which is in ℕ) to something in ∅, yet there is nothing to map it to, because by definition ∅ is has no elements to be mapped to. Therefore infinity cannot be equal to 0.

It is anticipated that the OP will retort that this is not somehow what he meant. As the only thing that I have done is defined exactly what we commonly mean by the words he used, this will be an admission of the fact that his post was at best a failure of communication, at worst meaningless in the first place; in common parlance, 'bullshit'.

I've had one too many Tuborgs and this post may be overly long and rambling, sorry if that's the case.

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Originally Posted by nietstein

Photolysis: how do you prove that infinity does not equal 0?

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A) by the very definition of zero and infinity.
B) reductio ad absurdum. If they are equal you have to throw out huge swathes of mathematics and areas of science because you get absolutely nonsensical values and the terms become meaningless.

Running statements through such basic sanity checks is a very good way to avoid coming out with complete bullshit.

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Originally Posted by MasterMind

Photolysis I don't mean that one should believe in everything, although if people never believed in stuff that wasn't proven yet, well then it would never be any breakthroughs.

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Nonsense. You don't have to believe in something before it is 'proven'. For rational people it's the very act of gathering sufficient evidence to prove it that leads to acceptance of it as fact. Follow where the evidence takes you, and if it's strong enough the belief comes naturally.

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but then my friend had an OBE himself and obtained information that was unknown to him before, and after that he was far from skeptical it's obvious of course since he had experienced it himself.
Is it then so stupid of me to believe my friend? For now I choose to believe but when I experience it myself I will know.

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And how can anyone possibly confirm or disprove such anecdotes? How can anyone possibly determine if your friend had or did not have any exposure to the information, even if he wasn't consciously aware of the fact. How can I determine it's not confirmation bias.

And is it stupid to believe something like this simply based on an anecdotal account? Yes it is. You're considering something a fact based entirely on the word of someone else with no reliable data or control.

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So if you Photolysis would experience an OBE

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The first thing I'd do is test if it was a dream or not. I'm confident that would be a spectacular success.

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got information that you knew you hadn't heard before like a family secret nobody ever talked about and you heard it from a dead relative in a "dream"

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And how could I determine truly that I'd never heard it? That I hadn't gathered fragments of evidence to piece something together? That it wasn't a lucky guess?

So no, I wouldn't give it any weight. The most I could do is say "I cannot fully explain this".

The only way to prove anything is a controlled experiment. If these claims have any truth to them, they should easily pass these tests. Remote viewing, OBEs, astral project etc. have failed every single controlled test I can find. If they have passed one and I am unaware of it, please link the paper so I can read it for myself.

Has anyone read the article? http: //ww w.bpramana.or g/scientific-spirituality/math .htm Because no one has said anything about it... I never stated it as fact, the title starts with "what if", so if your just going to assume its wrong because of the base 10 math system, then there's no point in frustrating yourself like you seem to be. If you don't ever think outside the box, you'll stay trapped in it...

Here is both experiments done in labs and people's stories: http://reconnection.lima-city.de/OBE...ion/index.html

Photolysis based on what you just wrote I juste have to say that Robert Monroe reason in the same way. But as I said the problem is that the only one you can prove it to is yourself and the one you are doing the experiment with, so it is impossible to prove to someone outside the experiment that they didn't had the information before and even to yourself, but these controled experiments have been done in labs, and also by people generally. Of course their got to be people who lie so I don't take it as facts.

It seems like they haven't published a scientific article, since they saw that it was no use.

It sort of like the experiment where they tried to teach a monkey to use sign language, they actively used it to "communicate" with it outside the lab, but as soon as it was in a control lab he got nervous and couldn't do it. But they still had videos of the monkey using the sign language on video, although when it comes to OBE it just can't be videotaped :( Here is a trailer of that monkey buisness xD http://www.youtube.com/watch?v=IHoviCO7lpE

Robert Monroe considered his OBEs as dreams for about a year, until he got experiences of seeing his friends, he knew his friend was ill so he went to visit him and expected him to be in bed so he went to his bedroom and looked for him (creepy much xD?), then he saw that he wasn't there so he went out in the yard and saw that he was out walking and had a robe on him, a red one.
Then he saw the mans wife with a coat getting there and he couldn't hear what they said, but she looked worried.

The next morning he talked with them and he had noted time and the experience, and it matched exactly what had happened at that time.

This can of course be viewed as a coincidence, but there are more experiences like this that he experienced through out his life.

And he is a very pragmatic man, when he first experienced a lucid dream or OBE the first thing he did was to get to a frined who is a doctor to get checked out because he thought he was getting crazy. Robert Monroe explains his first OOBE. - YouTube - here is an interview.

But as I said there is no way of us to know that this happened than to experience it ourselves. We can't know that a person have had a lucid dream just based on their story because they can lie, but since it's accepted we can do it even though we actually can't know for sure. Sure we can look at the brainwaves but you can do that on an OBE as well.

So if I am out of body and see an angel saying that I am going to save the world I am of course not going to believe it, because by then I would view it as mindcreated, but if I see and even hear my friend talking about something and then can confirm it with my friend the next morning AND tell the exact time of when it was said and explain it in detail, well then I would say it's rational to believe that something more than "just a dream" was going on. Not to mention that you can actually pick up a book and read it in an OBE in contrast to a dream. It is said anyway. It can still not be regarded as truth until you see it for yourself.

But you are right it might be stupid to believe in this, since I haven't even experienced it myself, I jsut trust my friend that was a skeptic but after an experience suddenly believed it, although he was a big skeptic and so was I. So for me this is like a religion, based on a story. But I choose to believe it, because if it is true it has very valuable consequences and is very useful. But I never said I knew, I only said that I believed.

The difference between this and a religion is that you can experience and prove it to yourself while you are alive, I mean in contrast to knowing that heaven and hell exist or something.

But don't worry Photolysis, I am actively doing attempts myself. So if or when I succeed, I can try to get to your place, tell something about your house that I just not couldn't had known before and I hope that you would agree with that I didn't knew it by then X . X

In other words I want to prove this "crock of shit" to skeptics :) Because by then I hope it's rational to believe it even though it's not scientifically accepted?

Monroe have exact steps of how to attain this state and based on those, I have a lot to work on... If you watch this video I am on Condition B now, but it takes time to relax yourself to the point where you feel the vibraton, I have managed to do it a few minutes after I went to bed, but I need to have a clear mind and relaxed body so for now I practice meditation to handle that.

Robert Monroe OBE Technique - YouTube

And even if I manage to get out of body, I need to practice moving around and get familiar, this is a lucid dreaming forum so I guess you understand how strange it feels in a different environment, when you first lucid dream for example.

My friends didn't believed in lucid dreams, then they had one themselves, I might no be able to make you have an OBE, but I can try to do what I can to prove it to you, proving a skeptic would probably make it a less crazy belief.

So peace and love Photolysis :sunflower: Let's say that I am a crock of shit for now ^-^. But I hope to prove you wrong ;)

Sweet dreams. You won!.. For now :( MasterMind out :poof:

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Originally Posted by nietstein

Has anyone read the article? http: //ww w.bpramana.or g/scientific-spirituality/math .htm Because no one has said anything about it... I never stated it as fact, the title starts with "what if", so if your just going to assume its wrong because of the base 10 math system, then there's no point in frustrating yourself like you seem to be. If you don't ever think outside the box, you'll stay trapped in it...

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Yet again you haven't actually read anybody else's posts other than your own. How wise.

What if butter/mayonnaise is necessarily the same thing as hippos/elephants?

Respectively?

That's ridiculous, I read everything that everyone wrote. What exactly is it that you think I missed? Is your claim that I didn't read everything an excuse for you to have not read the article? Because that would make you... "bullshit". You can say anything you want, if you didn't read the article, and therefore don't have anything to say about it, then you sir, are simply being a douchebag.

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Originally Posted by nietstein

Because no one has said anything about it... I never stated it as fact, the title starts with "what if", so if your just going to assume its wrong because of the base 10 math system, then there's no point in frustrating yourself like you seem to be. If you don't ever think outside the box, you'll stay trapped in it...

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This post clearly demonstrated that you are not reading what anybody else is saying, because people have addressed this misconception several times, and yet instead of rebutting, or modifying your views, you simply repeat the claims over and over.

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Originally Posted by Xei

But I don't really espouse the view that there is no such thing as truth. Truth comes in degrees of certainty, or ubiquity. Some truths come in degrees so high that it's insane not to believe them, and certainly insane to firmly believe otherwise. These truths are demonstrated via observations and inferences so pervasively ubiquitous that it makes no sense to dispute them.

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I find it inconceivable that truths come in degrees of certainty. The relativity of so many things within the universe surely constitutes the ubiquity of particular truths, especially when it comes to Earthly or human things. Though I can't correlate relativity to degrees of certainty. Certainty is more so a property of human understanding than truth, no? People can have different levels of clarity/certainty/understanding about a truth but that doesn't effect the tangibility of the truth.

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this post may be overly long and rambling, sorry if that's the case.

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It isn't. And now that I've relearned this bit about functions thanks to you I might actually be able to back up nietstein's claim. Though I am sort of hesitant to defend it after seeing you retort basically as Xei expected, nietstein ;\

But hey

All I can think about is Russel's Paradox. In defining ∅ as a set with no elements do we not instantaneously ascribe that the set cannot be an element--that it cannot be a member of itself? By distinguishing ∅ at all, do we not create a Russel set? ∅ cannot be a member of itself because it has no elements, yet in satisfying that definition of itself, it inevitably and contradictorily becomes a member of itself, an element, a 1.

So

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Is infinity equal to 0? Well, simply by the definition of the terms, this is equivalent to asking if we can send a one-to-one map from ℕ to ∅. Can we? No, obviously not. Because for a start we would need to map 1 (which is in ℕ) to something in ∅, yet there is nothing to map it to, because by definition ∅ is has no elements to be mapped to. Therefore infinity cannot be equal to 0.

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??

can't create an injective function
definitions of zero and infinity (both are sketchy, the concept of infinity has changed before, and may change again)
reductio ad absurdum: it produces an absurdity in context of our current number system

I've been keeping count, it would be absolutely absurd for me to post this and not read what people have said about it. You assume that I haven't read because I'm not ultimately convinced that our system of math and reasoning is perfect.

So pretty much: several times is 3 reasons in 2 posts? Briliant... And I can guess that you've all but refused to read the article since you're clearly not going to say anything about it? Why do you refuse to read it? Because it must fundamentally disagree with the only number system you know? It's much easier to assume I'm crazy and irrational, because that's what the Greeks would have done, right?

Do you find it reasonable to assume that 1=.9~, which our number system must assume? Are they truly perfectly equal? Because they would have to be for our number system to have perfect, infallible reasoning. It depends on a linear definition of time, saying that each 'now' has at least some quintessentially small duration.

The length of each 'now' is 0, it defies measurement. So if I live to be 87 years old, how many 'nows' have I experienced? Is the result any different if I live to be 92? Oh, but, wait, THATS right, you can't divide by zero... is that rational? What about the ball that leaves my hand and is thrown into the air, arching and landing on the ground? What is the total number of positions it occupied? Sure, it would be nice to place a number on them, but ultimately you cant. Our number system can't represent the perfection that is reality. It clings to a steady, linear model of time and space, something that science is increasingly showing us is not the case.

No doubt you will present more reasons why our number system disproves these ideas, or somehow erringly compensates for them; and get upset because you have convinced yourself that I am stupid. Additionally, you won't have anything to say about the article because you'll probably refuse to read it and tell yourself it's automatically wrong. So much for open minded discussion...

Seems like you're convinced you know the answers. It has to be wrong because it doesn't fit with what you know. You must know more than this guy...

"I am the wisest man alive, for I know one thing, and that is that I know nothing." -Socrates

Riddle me this:

.9~=1
1/3=.3~
2/3=.6~
3/3= ... .9~ or 1? Which is it? Can there be .9~ spoons? There must be one spoon according to our system, how could there be .9~ spoons?. Does the spoon exist or not?

There is no spoon...

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Originally Posted by tempusername

I find it inconceivable that truths come in degrees of certainty. The relativity of so many things within the universe surely constitutes the ubiquity of particular truths, especially when it comes to Earthly or human things. Though I can't correlate relativity to degrees of certainty. Certainty is more so a property of human understanding than truth, no? People can have different levels of clarity/certainty/understanding about a truth but that doesn't effect the tangibility of the truth.

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This really comes down to semantics; I didn't really define what I meant by truth properly. I was pretty drunk so I wasn't bothered. Basically what I'm saying is that any assertions with meaning are basically of the form, 'this is a pattern in experience'. For instance, stuff falls down to Earth with nothing supporting it. This truth is extremely ubiquitous, which in my terminology is equivalent to saying that it is virtually always observed. We don't really 'know' it as some kind of general principle, universal and detached from reality, though. It could fail to work between 12.00am and 12.05pm tonight; we can raise no logical objection. And there are many instances in the past where something was assumed to be universal but just turned out to be extremely common in the limited domain that was previously observed; there were rare or hidden counter examples.

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It isn't. And now that I've relearned this bit about functions thanks to you I might actually be able to back up nietstein's claim. Though I am sort of hesitant to defend it after seeing you retort basically as Xei expected, nietstein ;\

But hey

All I can think about is Russel's Paradox. In defining ∅ as a set with no elements do we not instantaneously ascribe that the set cannot be an element--that it cannot be a member of itself? By distinguishing ∅ at all, do we not create a Russel set? ∅ cannot be a member of itself because it has no elements, yet in satisfying that definition of itself, it inevitably and contradictorily becomes a member of itself, an element, a 1.

So

??

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No, for Russel's paradox to work, you need to be considering the SET OF SETS which are not elements of themselves. There's nothing wrong with just a set on its own that is not an element of itself. In fact the definition of number I provided comes directly from Russell himself (c.f. An Introduction to Mathematical Philosophy). And Russell banished such paradoxes from his foundation by ruling out putting sets inside sets (this basically banishes self-reference), so in fact all sets are trivially not members of themselves ({}, N, whatever), precisely because they are sets, and thus by definition can't be found inside themselves, as 'themselves' are not allowed to contain any sets.

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Originally Posted by nietstein

can't create an injective function
definitions of zero and infinity (both are sketchy, the concept of infinity has changed before, and may change again)

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Yet again you've failed to pick up on the basic message people have been giving you from the start. WORDS AREN'T REAL, SINGULAR THINGS. This should be extremely easy to understand. You're talking about infinity: this means you PICK a definition for infinity, you PROVIDE it, and you STICK TO IT. The statement, 'the concept of infinity could change', is absolutely absurd and fatuous. Words are tools by which we communicate concepts. You are the one who chooses the concept you want to discuss, and denote it by some word. If somebody comes along tomorrow and decides that they're going to use the word 'infinity' to refer to 'dog', it has zero bearing on this conversation whatsoever. Why on Earth do you think it does? They will be having a conversation about dogs. Your conversation will still be about whatever it was that you defined. Do you think words are some kind of divinely ordained incorporeal objects, floating around the universe and capriciously changing their singular and ultimately authoritative meaning? That's incredibly sloppy thinking.

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Originally Posted by nietstein

Riddle me this:

.9~=1
1/3=.3~
2/3=.6~
3/3= ... .9~ or 1? Which is it? Can there be .9~ spoons? There must be one spoon according to our system, how could there be .9~ spoons?. Does the spoon exist or not?

There is no spoon...

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They're just different expressions for the same number. Just like you can simultaneously have 0.5 + 0.5 spoons and 1 spoon.

Yet again you show your extreme confusion about how definitions, words, and meaning works.

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Originally Posted by Xei

No, for Russel's paradox to work, you need to be considering the SET OF SETS which are not elements of themselves. There's nothing wrong with just a set on its own that is not an element of itself. In fact the definition of number I provided comes directly from Russell himself (c.f. An Introduction to Mathematical Philosophy). And Russell banished such paradoxes from his foundation by ruling out putting sets inside sets (this basically banishes self-reference), so in fact all sets are trivially not members of themselves ({}, N, whatever), precisely because they are sets, and thus by definition can't be found inside themselves, as 'themselves' are not allowed to contain any sets.

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Okay well that clears a lot of shit up then. So if

• the "law of sets" or whatever banishes sets from basically being meta
• sets contain elements
• sets are defined by the unique properties of their elements

why the fuck is 0 even considered a set? Is it not a rule that all sets should be mappable? Isn't it inevitable the rule exists considering the essence of an element as well as how the concepts "set" and "element" are inseparable?

Quote:

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Originally Posted by Xei

The number 0 is defined as those sets which can be put into a one-to-one mapping with {}, or '∅', the set of no elements

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This definition seems pretty meaningless and if anything is a contradiction.

As a disclaimer, I'm only asking you why because I assume my question is probably elementary and that you are way more fluent in math than I

So how is it that we can refer to them as the same thing? You reason that 0 cannot equal infinity because we cannot create an injective function from ∅ to ℕ. We could say 1=1, 2=2, 3=3 etc. or 0.5=1, 1=2, 1.5=3 etc. or .00001=1, .00002=2, .00003=3, etc. and we could keep going further and further down, but we could only ever come increasingly close to ∅ as we make new functions, because it is assumed that there can never be nothing. By the same token of reasoning, .9~ can infinitely approach 1, but it cannot be defined as the same thing. For it to work, we would have to put a limit on infinity. 0.0~1=1 (consider it the smallest 'conceivable' value without equaling ∅) to .9~=infinity, it could never equal 1, so 0.9~ =/= 1, because if there cannot ever be nothing, then there cannot ever be infinity.