Unproven Belief

I read the article on page 174-175 by Leo M. Chalupa. This article is about three of the authors beliefs: that the human brain is the most complex entity in the
known universe, that we will eventually succeed in discovering all there is to discover about the world if we live long enough, and that science provides the best means of understanding the world. I will address each of these claims separately. The first statement would be fairly easy to disprove, but is very hard to prove. To prove this false, all that is necessary is finding an object in the universe more complicated than our brain. To prove it true, it would be necessary to observe every object in the universe. The second statement is provably false. Given the uncertainties inherent in logic itself, it is impossible to have a complete understanding of the world. The third part of this statement is the only one that is truly unprovable. I agree that, of the methods we have found, there appears that science is the best for finding the truth, but there very well may be a better one out there.

xkcd comic by Randal Monroe

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Idealogical Immunity

All systems of belief have axioms. These are statements that are hopefully both obvious and fundamental. If chosen well, a simple set of axioms allows one to build up a consistent and powerful system of logic. The problem comes when these axioms are wrong. In formally defining geometry, Euclid based the field off of the following axioms:

1.  A straight line segment can be drawn joining any two points.
2.  Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

These mostly worked, but as Gauss showed, the fifth is not always true (specifically in spherical or hyperbolic geometries). Euclid's problem wasn't being wrong, but rather creating unnecessary restrictions that narrowed his world view.

Since the beginning of history, humans have tried to create systems of axioms that do not lead to contradictions, and that allow all knowledge to be either proven or disproven. Thanks to Kurt Gödel, one of the best mathematicians of all time, we now know that this is impossible. Any system of logic will, by necessity, either be incomplete, or be completely wrong. I think that the ideas I am ideologically immune to are those that are my axioms for understanding the world. For me, these tenets are:

• For a theory to be true, it must be the one to best explain what is observed.
• If  two theories produce the same results under all circumstances, they are equally valid (and whichever is simpler should be used).
• If something is not measurable (measurable here meaning having definite state), it is not real.

These beliefs are fundamental to the way I approach the world, and I can not think of any evidence that would cause me to change them, because without them I would have no way to interpret other evidence.