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A good ole paradox

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A good ole paradox

smerdyakov
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Posted 11/27/08 - 07:31 PM:	#11
jorndoe wrote: Kind of hard to prove/disprove anything without some definitions.. Probably prudent to ask exactly how you define "God", and/or what qualities/etc you ascribe to such an entity. I defined it later, or at least what I thought was the only suitable definition. God has either: (1) nothing-being; (2) finite-being; (3) infinite-being. These are the only three categories I think can be logically drawn as a basis for the "bare-bones" definition of God, and all else would follow from it (omniscience, omnipotence, omnipresenence, etc). (1) If God is nothing, then no sense arguing about his existence; (2) If God is finite, then I'm God, and there's no sense in arguing about my existence (I assure you, I exist ); (3) If God is infinite, then that implies that God possibly exists, and if so, in a way distinct from me--something finite. If we are to discuss God, I think God has to fall into (3) if we are arguing for his existence, or category (1) if we are arguing against the existence of God. As for the qualities that would be attributed to an infinite Being, I think it is reasonable to include the 'omni-s' simply because they follow from something infinite. But as for a definition of God: Infinite Being. I know that's a terse definition, but I think it's the only definition that can be given with certainty (given that God exists). From this definition, I think that it is impossible to irrefutably prove the existence of something purely infinte, which I have argued above.

dreamweaver
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Posted 11/28/08 - 04:43 AM:	#12
Your argument against an infinity fails because of the simple fact that you make a big jump in presuming that finite minds cannot 'comprehend' (a better/clearer way to say this is "can meaningfully talk about") infinite things. A simple example is jorndoe's signature -- we always talk about infinite series and sequences in Mathematics, and we get very meaningful results. Your argument against a finite being equally fails because of a leap of logic. If you consider the gods from Greek mythology, they are surely finite in the sense that they appear to operate within Nature only (without some external existence), and yet they are significantly more powerful than you. A "higher being" does not have to be infinite, and yet many people would be happy to call such things gods. Simply because you are a finite being, it is not to say that all finite beings are you, that's just clearly a non sequitur.
Dos moi pou sto kai kino taen gaen. ~ Archimedes

Tisthammerw
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Posted 11/29/08 - 10:29 AM:	#13
smerdyakov wrote: I was thinking something like this: To prove the existence of God is impossible. I understand God to be infinte. To prove that God exists is to prove that God is not infinite. That is to say, to make such a proof implies that human reason, which is finite, is capable of proving something that is infinite. This seems to me an impossibility(maybe i am making a leap here)--the same way trying to have a thought about 'nothing' is impossible. It is actually possible for finite beings (humans) to prove something that is infinite. In mathematics we finite humans have been able to prove that some infinities are larger than others. See for instance Cantor's diagonalization argument. It is true that if there is a God, we will not be able to fully comprehend him any more than we can fully comprehend infinity. None of this means we can't have rational justification for the existence of God any more than Cantor can't have rational justification for thinking the infinity of real numbers is bigger than the infinity of natural numbers.
Knowing is half the battle; the other half is a really big gun.

jimRH7
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Posted 11/29/08 - 12:17 PM:	#14
dreamweaver wrote: Your argument against an infinity fails because of the simple fact that you make a big jump in presuming that finite minds cannot 'comprehend' (a better/clearer way to say this is "can meaningfully talk about") infinite things. A simple example is jorndoe's signature -- we always talk about infinite series and sequences in Mathematics, and we get very meaningful results. I agree. furthermore, just because we don't understand something doesn't mean we cannot prove it exists. I don't understand the electronics in my mobile phone - it doesn't stop it from existing.

crunchy
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Posted 11/29/08 - 09:47 PM:	#15
It seems the problem has been as identified as the inability to conceive of God, not whether he exists or not. Perhaps one could make the argument that because of our ability to conceive of him occurs despite this problem he must exist!

jorndoe
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Posted 11/30/08 - 08:34 AM:	#16
Tisthammerw #13 wrote: It is actually possible for finite beings (humans) to prove something that is infinite. In mathematics we finite humans have been able to prove that some infinities are larger than others. See for instance Cantor's diagonalization argument. It is true that if there is a God, we will not be able to fully comprehend him any more than we can fully comprehend infinity. None of this means we can't have rational justification for the existence of God any more than Cantor can't have rational justification for thinking the infinity of real numbers is bigger than the infinity of natural numbers. Math and "God" is a world apart, however. Cardinality in set theory is on quite firm ground; it has even been shown that the continuum hypothesis cannot be proven within certain specific axiomatic theories. And, thus far I have yet to come across a sensible and coherent definition of God. But, hey, feel free to come up with such a precise definition, and subsequently prove existence â€” I dare you. smerdyakov #11 wrote: (1) nothing-being (2) finite-being (3) infinite-being The 1^st seems a bit of a selfcontradiction in terms, but I guess you mean nonexistent? As for the 3^rd, you have previously referred to spacially infinite (infinite volume?), but it's not clear if that's all you mean. Some people prefer temporally infinite as well, and infinite in more animated qualities such as wisdom or whatever (omni*). I'm not sure, but I'm guessing some people even believe that there is an entity which is infinite in all respects/qualities/properties. Anyway, so, a mix of the 2^nd and 3^rd may also be what you meant? Mathematical infinites often fall back on WeierstraÃŸ' definitions (e.g. proving an infinite sum..). crunchy #15 wrote: It seems the problem has been as identified as the inability to conceive of God, not whether he exists or not. Perhaps one could make the argument that because of our ability to conceive of him occurs despite this problem he must exist! Yet such an argument only proves that God exists in someone's head, that is, not independently of the conceivers.
People are to themselves what they think; people are to others what they do. ∞ ∑ 1/i² = π²/6 i=1

Tisthammerw
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Posted 12/01/08 - 07:25 AM:	#17
jorndoe wrote: Math and "God" is a world apart, however. Even if true, none of this affects the point I was making here. The claim that "human reason, which is finite, is capable of proving something that is infinite...[is] an impossibility" is false. Math provides a counterexample. Agreed? jorndoe wrote: And, thus far I have yet to come across a sensible and coherent definition of God. OK, I'll bite. What was so incoherent/insensible about my definition in the "Explaining Theism etc. to a Child" thread? jorndoe wrote: But, hey, feel free to come up with such a precise definition, and subsequently prove existence â€” I dare you. Ditto. I dare you to prove atheism.
Knowing is half the battle; the other half is a really big gun.

Farmer Joe
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Posted 12/04/08 - 01:49 AM:	#18
I see it like this, we could make an infinitely long attempt at a definition of God, and fail miserably with much frustration. We cannot do things beyond what we are capable. In a sense, we can't put God in a box. But, we can put Him on the other side of the window of our conception. The size of the wndow is the knowledge we have about Him, the clarity of what we see through the window is obviously the understanding of what we know. The only safe way to positively define God is this, God is God. He's the complexity of simplicity, an infinite singularity.

norman
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Posted 12/06/08 - 05:05 AM:	#19
Farmer Joe wrote: I see it like this, we could make an infinitely long attempt at a definition of God, and fail miserably with much frustration. We cannot do things beyond what we are capable. In a sense, we can't put God in a box. But, we can put Him on the other side of the window of our conception. The size of the wndow is the knowledge we have about Him, the clarity of what we see through the window is obviously the understanding of what we know. The only safe way to positively define God is this, God is God. He's the complexity of simplicity, an infinite singularity. Though, that in itself is just another conception. That's like trying think of what a mirror looks like without looking in it. All you will ever see is an image of yourself, i.e. your own projection.

YuceL
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Posted 12/08/08 - 11:39 AM:	#20
norman wrote: Though, that in itself is just another conception. That's like trying think of what a mirror looks like without looking in it. All you will ever see is an image of yourself, i.e. your own projection. Besides, our conceptual window to "god" is also infinitely small, as we lack any and all logically verifiable information on him.

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