(December 10, 2013 at 6:02 am)Rayaan Wrote: Even in mathematical systems, a logician named Kurt Godel (in his Incompleteness Theorem) proved that there are certain axiomatic statements which we know are true, but still they cannot be proved to be true.
"Godel showed that provability is a weaker notion than truth, no matter what axiom system is involved " - Douglas Hofstadter
http://www.miskatonic.org/godel.html
Isn't that where scientific thinking comes in? There are problems in Mathematics that have not been solved, however all the evidence points to them being true.
For example say we couldn't prove Pythagoras' Theorem. We could cut out thousands of triangles and measure them and they would all fit the rule. We can never say with 100% certainty it holds, as we might find a triangle that doesn't fit the pattern.
It begs the question how did Gobel know something was true in the first place? In mathematics it's definitely not some deep held feeling that it is true, and probably a process like with the triangles.
I don't think* you can prove that a circle has diameter 2*pi*r, I think it's something you have to assume by measurement alone.
* Please let me know if this isn't true, I'm not a Pure Mathematician
(December 10, 2013 at 6:27 am)max-greece Wrote: Not sure I agree with this:
Theist - someone who believes there is a God.
Atheist - someone who does not believe there is a God.
Agnostic - holds neither opinion - usually on the basis of insufficient evidence either way.
Whilst either the theist or the atheist may be 100% certain of their belief it isn't actually required:
I believe there is a God, but I may be wrong - still theist.
I do not believe there is a God but I may be wrong - still atheist.
IMHO and all that.
The burden of proof lies on the person making the claim "A God Exists". No evidence is required to disbelieve the claim.
An Atheist is not making a positive claim, they just do not accept the claim.
As with the rolling dice example, you can disbelieve "the dice will be a 6" without having to believe "the dice won't be a 6". In this example I would disbelieve both claims.
"The dice will be a 6" is the equivalent of the Theist claim, so disbelieving this statement makes me a dice Atheist. I still have no opinion on what score the dice will give, and it could well be a 6.
Having said all that, most people I know would disagree with all this and just call themselves Agnostics!