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  1. #191
    Blah Orangey's Avatar
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    Quote Originally Posted by BlueWing View Post
    So a finite set is one that is connected with any natural number. For instance, 4,5, or 6. What is the difference between this an the one to one correspondence?
    Wait...okay I think I said something incorrectly. A finite set is always countable, and this means that its members have one to one correspondence with some subset of the natural numbers.

    The only type of set that can possibly be uncountable is the type that has greater cardinality than the set of natural numbers. Every other set, finite and infinite (if it has cardinality equal to the set of natural numbers) is countable.

    So yes, if countability requires one to one correspondence to the set of natural numbers, and all finite sets are countable, then they do indeed have one to one correspondence with the set of natural numbers.

    I am aware that some people define countability as only applying to infinite sets. In other words, by this definition, the only countable sets are infinite. The use of these competing definitions might be where some of the confusion in this thread is coming from.
    Artes, Scientia, Veritasiness

  2. #192
    Occasional Member Evan's Avatar
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    ^BW is saying that an infinite set cannot be countable.

    He is wrong.

    That's the source of confusion.

  3. #193
    Senior Member reason's Avatar
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    dissonance,

    I edited the my original post. But the original definition was fine, since the set of natural numbers is a subset of the set of natural numbers.
    A criticism that can be brought against everything ought not to be brought against anything.

  4. #194
    Occasional Member Evan's Avatar
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    ^True.

  5. #195
    desert pelican Owl's Avatar
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    Is BW even using "countable" in the way mathematicians use it? I've the impression that he's more concerned with the paradoxes involved with the existence of an actual infinite, (similar to those used in the Kalam cosmological argument--but directed against the existence of God instead).

  6. #196
    Occasional Member Evan's Avatar
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    Quote Originally Posted by Owl View Post
    Is BW even using "countable" in the way mathematicians use it?
    Not at all.

    I've the impression that he's more concerned with the paradoxes involved with the existence of an actual infinite, (similar to those used in the Kalam cosmological argument--but directed against the existence of God instead).
    No, I don't think he's talking about paradoxes. He's claiming that the universe is infinite as a premise.

    Not even necessary for his argument, he could make the same claims if he defined the universe as containing all things. His use of the word infinite just confuses the issue because he's not familiar with the mathematical concepts.


    Essentially, if the universe contains all things (and times), then God could not have created it. Totally reasonable argument, and I agree.

  7. #197
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by dissonance View Post
    Not at all.



    No, I don't think he's talking about paradoxes. He's claiming that the universe is infinite as a premise.

    Not even necessary for his argument, he could make the same claims if he defined the universe as containing all things. His use of the word infinite just confuses the issue because he's not familiar with the mathematical concepts.


    Essentially, if the universe contains all things (and times), then God could not have created it. Totally reasonable argument, and I agree.

    Dissonance, you're confused on two things.

    BW is only saying that the 'highest infinites' that Rodgers was talking about are non-countable. This I argue is the absolute infinite, which is indeed non-countable. However, I do maintain that many sets that mathematicians refer to as infinite are countable. I have described this in detail in my exegesis of Rodgers. I think it is a mistake to call those sets infinite, but I do not deny that they are countable.

    Owl, however, did put it adequately that I am concerned with the paradoxes of the infinite. As much of the OP was devoted to depicting the relationship between the infinity of the universe and the possibility of the existence of the Judeo-Christian God. As well as how slippery the concept of infinity is, and how much confusion this idea has caused many of those who endeavored to clearly define it. This is what the exegesis of Rodgers and Cantor was almost exclusively about.

    Secondly, the number I cited may indeed be possibly expressed in a ratio format. (I did not bother doing the calculations for that number)That was not the point. There is a certain class of numbers which could not be classified in a fraction or a ratio, they are called the irrationals. Look it up in a mathematical dictionary. The reason why they could not be expressed in a fraction is because their last decimal never ends, this part of such a figure is infinite.

    Now, as a matter of whether space is subjective or not, or how you say everything is filtered through human perceptions, so it all is subjective. Yes, that is true, even that unconscious representation of the concrete, physical world is subjective to a degree. (This is the part of Kantian metaphysics that I introduced in this thread). Come on though, lets not be silly here. What is more subjective, our sensation of a computer screen in front of us, or our perception of time? Obviously if there is anything that is as close to being completely objective as possible, it is the concrete external world, as that is filtered through our subjective scope of cognition as little as something could possibly be.

    A third matter to address to you is, say we have a set of natural numbers for example. We know it is infinite. Nothing stopping us from counting all these numbers. Yet, if we literally attempted to count them, we would run out of paper to perform the whole task. As the numbers never end. Even if every person in the world was doing this for thousands of years, day in and day out, we still would not be able to count them, as there is never an end to this procedure. In such a case, it is indeed possible to count them, but not possible to finish counting them. Seems to be that the non-countable is a more adequate rendition of the state of this case then countable.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

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  8. #198
    Occasional Member Evan's Avatar
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    ^K. I'm over the nitpicking now.

    So is this essentially your argument?
    Premise: the universe contains all things in all dimensions, including time.
    Therefore:
    a) The universe cannot have been created, as created implies a finite time.
    b) God could not exist except as a subset of the universe.

  9. #199
    no clinkz 'til brooklyn Nocapszy's Avatar
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    Quote Originally Posted by BlueWing View Post
    The fact that there is one end, it is not completely infinite. It is, as I argued before is finite, unless an entity is completely boundless. For the sake of simplicity, only the completely boundless entities ought to be regarded as infinite. As boundlessness is the quintissence of infinity, and the defining quality of finitude is having limits.

    What term has been misapplied and how?
    Figure it out yourself. You're good at that right?


    You're a tough kiddo nocap, I already know! No need to attempt to prove this to me. Very entertaining Ne bounces, unfortunately this isnt philosophy, but with some careful revision may pass for some good philosophical poetry. Hint: try bringing some structure to your thinking, its back to being all over the place, alas, you seem to have been improving in your previous short post.
    Jesus...
    You put structure where it doesn't belong.
    I'm plenty structured. You're just not trying to understand.
    This is laziness.
    You're just as bad as any of those religious morons who believe God has to exist because of the birds and the bees. You're not analyzing, you're believing what's easier to believe, just like you're ignoring me because it's easier than paying attention.
    But I've figured it out. You're ignoring important parts of my argument because you don't know how to refute what stance I pose. It's too hard.

    Come on -- for a Thinking dominant, you certainly do avoid a lot of challenges!

    An entity that has any restrictions is not completely infinite, as aforementioned in this post. You know all this, and I need not explain it to you again.
    Yes that's true. My point is that you don't know the universe is infinite. You don't. You don't because you can't. You can't because there's no proof, only an assumption. The universe doesn't have to be infinite for it to include all that there is.



    I don't see the relevance?
    You wouldn't. I'd say why, but I'll get an infraction.

    However if you did look up the damned thing, you'd see the relevance instantly. Though I'm not so sure anymore... I used to think you're N, but now I'm not convinced.
    we fukin won boys

  10. #200
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by dissonance View Post
    ^K. I'm over the nitpicking now.

    So is this essentially your argument?
    Premise: the universe contains all things in all dimensions, including time.
    Therefore:
    a) The universe cannot have been created, as created implies a finite time.
    b) God could not exist except as a subset of the universe.

    Yes, mostly so, however, time, and other dimensions of this finite world are an entailment of the infinite absolute realm. But, indeed, they cannot exist separably from the infinite realm because all things derived from there. I could argue here why this is so, but that is not directly relevant to your last post. We could engage in such an inquiry next, if you wish.

    But yes, the bottom line is, God could not exist completely separately from the universe and that is anathema to creationism.



    Quote Originally Posted by Nocapszy View Post
    Figure it out yourself. You're good at that right?


    Jesus...
    You put structure where it doesn't belong.
    I'm plenty structured. You're just not trying to understand.
    This is laziness.
    You're just as bad as any of those religious morons who believe God has to exist because of the birds and the bees. You're not analyzing, you're believing what's easier to believe, just like you're ignoring me because it's easier than paying attention.
    But I've figured it out. You're ignoring important parts of my argument because you don't know how to refute what stance I pose. It's too hard.

    Come on -- for a Thinking dominant, you certainly do avoid a lot of challenges!

    Yes that's true. My point is that you don't know the universe is infinite. You don't. You don't because you can't. You can't because there's no proof, only an assumption. The universe doesn't have to be infinite for it to include all that there is.



    You wouldn't. I'd say why, but I'll get an infraction.

    However if you did look up the damned thing, you'd see the relevance instantly. Though I'm not so sure anymore... I used to think you're N, but now I'm not convinced.
    1) I know the universe is infinite for the following reasons.

    Axiom 1:Nothing comes from nothing.
    Axiom 2: We know that the universe exists.
    Inference: Because it could not have come from nothing, it must have always existed. Therefore it is infinite. Okay, perhaps it is an outcome of another created thing? But what made the original or the first cause? It must have made itself? (Like Christians say God made himself), no that cannot be the case, as this is saying the same thing as 'something came from nothing'. Therefore, the only alternative that we see is that it always existed, or is infinite.



    I am sincerely trying to understand what you're saying, I could speculate to what your intended meaning is, unfortunately, to get a clear and exacting picture of your views, what you have presented does not suffice. It is the case because your ideas seem to be much too scattered. They are not presented in any order that I could discern (despite my sincerest efforts to look for such an order) and you seem to be saying far too much at the same time.

    I am interested in your ideas and therefore ask that you present them one piece at a time and make a conscious effort to structure what you present as rigorously as possible.

    As a friendly recommendation, you ought to avoid making personal referrences in your posts. (E.G, you're wrong, you're a cheater..etc..I know I am right and no further theory can disprove that. It is irrelevant to the idea you have in mind and for this reason makes your thoughts even more difficult to understand)
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

    “No man but a blockhead ever wrote, except for money.”---Samuel Johnson

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