Mathematical Proofs are just that! Proofs!

#1
Whether a proof of God or a proof of global warming, mathematics has an inherent truth to it.
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#2
What formal proofs demonstrate are some of the logical implications of an initial set of premises.

The conclusion of a formal proof needn't be true, unless the original premises were.
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#3
Is which reality? (Just kidding).

Reminded me of a Lawrence Krauss quote in which he stated, I'm paraphrasing, that in time the distances between galaxies will be so great that any new civilization that develops will find no evidence     of the rest of the universe yet they will develop a believable theory of their origins and the math will agree. Not sure what that says about math.
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#4
(Nov 16, 2017 02:46 PM)Zinjanthropos Wrote: Is which reality? (Just kidding).

Reminded me of a Lawrence Krauss quote in which he stated, I'm paraphrasing, that in time the distances between galaxies will be so great that any new civilization that develops will find no evidence     of the rest of the universe yet they will develop a believable theory of their origins and the math will agree. Not sure what that says about math.

like the statistical probability of life in the universe.
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#5
(Nov 16, 2017 03:17 PM)RainbowUnicorn Wrote:
(Nov 16, 2017 02:46 PM)Zinjanthropos Wrote: Is which reality? (Just kidding).

Reminded me of a Lawrence Krauss quote in which he stated, I'm paraphrasing, that in time the distances between galaxies will be so great that any new civilization that develops will find no evidence     of the rest of the universe yet they will develop a believable theory of their origins and the math will agree. Not sure what that says about math.

like the statistical probability of life in the universe.

I do believe math is used to calculate odds. So when I roll a pair of dice there's proof that the chance of obtaining a 7 is greater than any other combination. Doesn't mean it happens that way and the same goes for Ostro's math proofs. Are the odds of proving God less than astronomical, or are they undefinable when the zero multiplier is tossed in? 

Can math prove something that has no chance of being proven? Is there a limit to things that can be proven? I mean can math prove a lump of coal will turn into a mouse? I don't know but there are certainly more impossible things you can try proving than what's actually possible, IMHO of course.
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#6
(Nov 15, 2017 09:33 PM)Yazata Wrote: What formal proofs demonstrate are some of the logical implications of an initial set of premises.

The conclusion of a formal proof needn't be true, unless the original premises were.

Thank you for that insightful and eye opening response.
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#7
(Nov 16, 2017 09:34 PM)Zinjanthropos Wrote: Can math prove something that has no chance of being proven?

Yes, there are plenty of mathematical proofs that don't correspond to any physical process. Math, like logic, need only be internally consistent to its own axioms.
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#8
(Nov 16, 2017 11:13 PM)Syne Wrote:
(Nov 16, 2017 09:34 PM)Zinjanthropos Wrote: Can math prove something that has no chance of being proven?

Yes, there are plenty of mathematical proofs that don't correspond to any physical process. Math, like logic, need only be internally consistent to its own axioms.

I might need to add a cosmological constant to prove that Smile.  Pretty easy to prove something mathematically by adding something no one even knows exists, just to make the equation work.
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#9
(Nov 16, 2017 11:28 PM)Zinjanthropos Wrote:
(Nov 16, 2017 11:13 PM)Syne Wrote:
(Nov 16, 2017 09:34 PM)Zinjanthropos Wrote: Can math prove something that has no chance of being proven?

Yes, there are plenty of mathematical proofs that don't correspond to any physical process. Math, like logic, need only be internally consistent to its own axioms.

I might need to add a cosmological constant to prove that Smile.  Pretty easy to prove something mathematically by adding something no one even knows exists, just to make the equation work.

If the initial premises are valid the conclusion will always be valid, by the preceding logic. There are no exceptions. This is the internal consistency of mathematics. Hypothetical entities or not.
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#10
(Nov 16, 2017 10:41 PM)Ostronomos Wrote:
(Nov 15, 2017 09:33 PM)Yazata Wrote: What formal proofs demonstrate are some of the logical implications of an initial set of premises.

The conclusion of a formal proof needn't be true, unless the original premises were.

Thank you for that insightful and eye opening response.

Anything to help, Ostro.  Big Grin

Here's an example:

1. (Premise) If Emmanuel Macron is President of France, then Madrid is the capital of France.

2. (Premise) Emmanuel Macron is President of France

Therefore

3. (Conclusion) Madrid is the capital of France

The proof is entirely valid (an example of modus ponens) but the conclusion is obviously false.

That's because premise #1 is false (even if #2 is true).

The moral of the story is that just because somebody produces what they insist is a logical or mathematical "proof" of something, doesn't necessarily make the conclusion true. The proof might be invalid (it might contain a logical error somewhere) or the initial premises of the argument might not all be true.
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