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Would it be correct to state that no single element, no matter how large, would be able to prove itself without the aid of another separate infinitesimal element? Does the absence of an logically correct infinitesimal element A to prove another element B(assumed at first to be existing), make element B logically non-existent?

[Added Information]: In simple words, is the idea that something can be proven from itself logically sound? Does "something" without an external logically consistent proof outside its own system, (no matter how small) make it logically inconsistent?

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    Does a thing need to be proven to exit? – Cort Ammon Dec 12 '15 at 3:38
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    I'm struggling to understand what you are asking here. I think you need to add some context to your question. – Nick R Dec 12 '15 at 3:41
  • Yes...In short, "element A can be proven by another entirely separate, logically-consistent element B, therefore A exists. Otherwise, A is not logically consistent, and hence non-existent" – XL Bros Dec 12 '15 at 3:47
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    What do you mean by the word "element" here? It's an odd word choice, and the question is worded in an obtuse and abstract enough way that it's hard to grasp what you're asking. Can you reword it? – virmaior Dec 12 '15 at 4:12
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    A person is a person, no matter how small... Which is to say I'm confused by your wording as well. By infinitesimal do you mean extremely small, or extremely large? Or something else? [and, please edit the statements in your actual question by clicking "edit" at the bottom of your question, rather than suggesting how to read it in the comments ] – LightCC Dec 12 '15 at 9:38
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You presume that existence is based on a mathematical proof, which is not a well agreed upon assumption. For instance, virtually every religion disagrees with your assumption. Thus it will be difficult to convey any results of that assumption without stating it. Most people believe there are things that exist for which they have no proof, suggesting you may be redefining existence is a way dissimilar to how others use it.

That being said, you may want to check out Dan Willard's self verifying theories. They are mathematical theories which prove their own consistency. They would be where I would look first. They escape Godel's incompleteness theorem, which would be a strong first step.

ponders: how does the universe exist by this definition?

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    Thank You. I Would Check Willard's Theories And Get Back To This Thread With My Conclusions – XL Bros Dec 12 '15 at 16:55
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Can something be proven from itself

Traditionally, this would be seen as wrong-headed as it leads to circular reasoning; but a more subtle analysis which takes separates the 'something' into natural parts, and then constructs a coherent rationale for the relations between the parts, and of the parts to the whole; and perhaps, between the relations themselves shows that we can have a rationale that hangs together, and makes sense - this position is called coherentism.

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