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One thing I've learned is that it's actually very difficult to make a really comprehensive case for a belief.  On some level, it's even actually impossible, and so I don't think that requiring a level of proof of 'indisputable' is even really fair.  I think it can be argued that no arguments are indisputable.  One conclusion of Godel's incompleteness theorems is  that math, and therefore logic itself, cannot prove itself capable of self-consistency, and thus cannot prove itself as a correct system.  

And I simply do not recognize completely non-mathematical frameworks as capable of proof in any meaningful way.  Observations are key in science, and observation is not inherently mathematical in nature, but observation by itself tells you nothing.  I observe an object falling towards the ground.  Does that mean the object is alive and moving of its own volition (and thus a falling rock must be alive)? Does it mean objects can only move towards the ground, never towards the sky (and thus planes and rockets are impossible)?  If I feel happy about an event, does that mean that event happening again will bring me the same happiness, regardless of other context (If I enjoyed a movie once, will I enjoy it by that same amount no matter how many times I watch it, and thus I can spend all my free time simply watching that one movie)? To assign meaning to an event, we must use a process of reasoning about that event, which is separate from the observation of the event itself. 

Even if we move outside science and into the realm of larger philosophical thought, this is the case.  In our lives, most of us assign certain events as good or evil.  I maintain that such assertions are inherently non-scientific in nature.  Oh, we can talk scientifically about how many people believe that this or that is good or evil, and what they might do as a result, but science can say nothing about whether something is good or evil.  Nevertheless, a large number of people seem to be of the opinion that it is meaningful to talk about acts in terms of good and evil (myself included).  I assert that even nihilism, the assertion that good and evil don't exist, is non-scientific in nature, since science inherently   cannot prove the nonexistence of something (it can only firmly establish existence and provide increasing evidence for nonexistence).

But we can use logic to talk about good and evil, about what is good and evil and whether or not these things exist.  Such is the question of countless philosophies which have arisen throughout time. 

But those philosophies come to greatly disparate conclusions, and if one thinks about any one philosophy long enough, one starts to see holes.  Some people find this distressing and so prefer not to think about it.  Or prefer to deny the existence of this limitation, as it enforces an undesirable limitation on themselves.  For if it is the case that not only are humans fallible at applying logic, but that *logic itself is fallible*, true certainty is forever out of our reach.

But I tend to think that a flawed understanding is better than no understanding at all.  We can make a solid case for our beliefs without expecting that we can make an airtight one.  We can strive towards comprehension without ever expecting to fully reach it.

This  is also why I find utter confidence in the correctness and airtightness in one's arguments for a belief tends to undermine my confidence in the person espousing that belief.  A person can have as much confidence in themselves and their beliefs as they think is merited, but they should also understand that there are and always will be not only internal limits, but inherent external limits to their ability to prove those beliefs to others.

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