03-10-2012, 10:58 PM | #326 |
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It doesn't have a static shape and yet it does. It is dynamic and yet it is not. Such is the nature of infinite objects: they may have a conceptual "form" (e.g. the infinite square) but they are ever expanding one step beyond where last you fixed them ... and yet to even use the word "expansion" is not correct because they were already there.
Can you imagine a stack of coins that is infinitely tall? Yes. Would you say to me, "Ah, but how do you know it's a line?" No. That would be pedantic. We establish that "it is a pile which approximates a line that is infinitely tall." The same thing goes for the infinite square. "Can you imagine a 'square' which has infinitely wide diameter?" Why, yes I can. Bounded and yet boundless, the "bounded" aspect is what lends you to want to call it a square yet the boundless aspect is lent to it by its infinite diameter. If I could show it to you in my mind, it'd be easier. Unfortunately, I cannot.
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03-10-2012, 10:59 PM | #327 |
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I said to tell me what it looks like, not its definition.
And Deoxys, you just showed a picture of a delimited, although conceptually infinite square, since each side of the square is infinitely divisible into an infinitude. Seriously guys. Describe to me what an infinite square looks like in your head. All I can do is picture a really big square, or picture a blank slate where the edges of the square have left my mental image. I can't picture an infinite square as it truly is. Tdos: According to the Christians, God's existence is a necessary precondition for all things. The universe's existence is dependent on his. The Christians will argue that God logically has to exist. I might have messed up the whole thing v. being distinction - a being is really just a specific type of thing. I'm not good enough at Thomistic philosophy to really discuss the distinction between will and being and why God has to be prior and stuff like that. Last edited by Amras.MG; 03-10-2012 at 11:04 PM. |
03-10-2012, 11:03 PM | #329 | |
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03-10-2012, 11:04 PM | #330 | |
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(1) I can't show you it in the physical world and (2) you're not able to conceive of it yourself? I mean, the best any of us can do is to try and put it into words. And most people will pick words, unfortuantely, that you'll then utterly tear apart. (e.g. what you just did with Deoxys, "LOL DELIMITED BUT CONCEPTUALLY INFINITE I CAUGHT YOU") The thing is, he's doing the best he can to explain it to you in words. And maybe you're right that he's thinking of something which isn't truly "an infinite square." But it doesn't mean ... ... you know what, this is pointless. You'll refuse to believe anyone's attempts to explain what an infinite square is anyway, so comforted are you by the analogy as it cross-applies to God: Because after all -- if Man can conceptualize Infinity, then it means he can conceptualize God. And this must not be so, by your world view. So you're going to reject Rangeet's or my claims tooth and nail anyway. Making this not a debate about humanity's ability to conceptualize paradoxical geometry (e.g. the infinite sphere) but instead an argument about whether Man can really understand God's scope or not.
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03-10-2012, 11:05 PM | #331 |
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No, this is absolutely wrong. The blank slate is a blank slate. You aren't conceptualizing a square anymore.
And Talon that's certainly an almost-poetic thought but we're dealing with logic. It can't be bounded and yet boundless at the same time. The foundation of logic is that a thing cannot be both x and not x at the same time in the same way. And Talon I'm not really that set in my ways - I'm just observing that we can't conceptualize an infinite square. I did this more to show Rangeet what he was doing wrong than to try to apply it to God... that's just you assuming things right there. Also it's really annoying having three people jump down my throat at the same time. |
03-10-2012, 11:09 PM | #332 |
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Well then, Amras. Why don't you tell me how you can think of a benevolent God who seemingly made men his toys so some of then could be sent to heaven or to hell according to their choice which may or may not follow his will.
No, really. I can think of an infinite square but I can't explain it to you. If you can explain that to me then you win this round. Feel free to take your time.
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03-10-2012, 11:13 PM | #333 | |
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I wish I could say I believe you, but you just haven't given me any proof at all. I'm not going to take it on faith that you can do something that has escaped philosophers for thousands of years... even if Talon claims he can do it. |
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03-10-2012, 11:25 PM | #335 | |
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Like I said, debating infinity is an exercise in condescension -- it always is -- so really, it's one best avoided for now. Not in the mood to debate it. Was only defending Rangeet from your accusation that he must be "doing it wrong" (not your exact words, of course) if he's claiming to be able to conceive of infinity.
But as for something you wrote about logic ... Quote:
"And yet the photon is both a wave and not a wave." "And yet red is both the beginning and the end of the color spectrum as it applies to RGB color overlays from the visible spectrum. (a.k.a. the purple end of this is a paradox the result of which is our biology)" "And yet a 2-dimensional planar object can have only one face. (e.g. the Möbius strip)" Paradoxes are all around us. Obviously you will argue that some of them can only be had in reality by cheating the system (e.g. physical Möbius strips), that others are phenomena that are purely the results of our imperfect minds playing tricks on us (e.g. how red can both be what we see fading into orange as well as fading out of purple on a color wheel despite the fact that our knowledge of the UV-Vis spectrum tells us that we ought not to see a "color wheel" at all), and that others still are merely classified as paradoxes due to our imperfect and incomplete knowledge of the system being discussed (e.g. wave-particle duality for photons). I'm not interested in arguing any of these platforms with you tonight. I'm only mentioning them to illustrate that while we do operate as logical beings, (1) paradoxes are seemingly all around us and (2) if not all of us then at least some of us are able to conceive of them. If we were not, we would not have quantum mechanics, for example.
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03-10-2012, 11:26 PM | #336 | |
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"seemingly made men his toys so some of then could be sent to heaven or to hell according to their choice which may or may not follow his will" To Christians, men are not toys to be controlled by God. They are not randomly assigned heaven or hell or anything like that. Any good Christian will say that we don't actually know if anyone is in Hell, and many Protestants will also say that we don't know if anyone is in Heaven. We don't know how the Judgment works, or anything like that. But you seem to be skipping a step. Why jump to God's relation with man if you aren't even willing to grant that God exists? Talon, if you're going to deny ~(x & ~x), then this debate is over. I am not going to argue with someone who denies the laws of logic. It's not worth it. |
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03-10-2012, 11:28 PM | #337 |
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The area of an infinite rectangle can be described as the improper integral from 0 to infinity of the function f(x)= C, where C is an arbitrary constant.
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03-10-2012, 11:29 PM | #338 |
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This still doesn't answer my challenge! I'm not asking for a definition, I'm asking for a mental description, a visual one.
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03-10-2012, 11:30 PM | #339 |
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But that is a visual description. In fact, it is an exact definition.
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03-10-2012, 11:32 PM | #341 | |
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Is it really that hard? Or are you just trying to misunderstand me? I agree Tdos, I either get a plane, or a really large rectangle right at the boundaries of my mind. |
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03-10-2012, 11:33 PM | #342 | |
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Rangeet is doing something similar with God. You argue that before he's even allowed to explore God's relationship with Man that he must first answer whether God exists or not. Not only is this arbitrary restriction unfair ... it's not even applicable: because he's doing exactly what you're asking of him! He's directly tackling the question of God's existence by way of attacking God's relationship with Man. He's saying, "If the Christian God is true, then ..." and reaching a logical conclusion about what sort of relationship you would expect the Christian god to have with mankind. And then, a posteriori, he concludes that since God clearly does not have any such relationship with Man, it calls into question whether God is even real in the first place or not. I'm not going to say that he's making the deepest, fullest case against God here, but to say that he can't poke holes in God's relationship with Man until he satisfies you that God isn't real to begin with is silly. It is those very holes, amongst others, which he is using to prove his case.
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03-10-2012, 11:34 PM | #343 |
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Picture a rectangle. It has the dimensions x and y. Those dimensions continuously get larger and larger at any given rate.
Infinity will never reach a finite value, thus, the conceptualization of it will never remain in a fixed state, and will be constantly increasing. We can never be AT infinity, we can only approach it.
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03-10-2012, 11:39 PM | #344 | |
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Also, answer my question. Do you agree that ~(x & ~x)? And Chaotic, that's significantly different from actual infinity. |
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03-10-2012, 11:43 PM | #346 |
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Infinity simply means something without bound.
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03-10-2012, 11:45 PM | #347 | |
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Also as far as all-knowing: just because God knows what I'm about to do doesn't mean he caused me to do it. I know Chaotic. That's why I'm saying you can't visualize it. Ugh. Seriously guys. |
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03-10-2012, 11:48 PM | #349 | |
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Christians believe a lot of things, as do you. Some Christians even believe different things, just like you believe different things compared to other 14 year olds, or even other humans. I know, shocking. |
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03-10-2012, 11:48 PM | #350 |
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I don't know. I visualize it. But everyone is different.
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