Thursday, September 3, 2015

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.
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4 comments:

  1. AnonymousSeptember 8, 2015 at 6:53 AM

    I have a question about your second axiom! They are all good and very thoughtful, but here is my question: Why is simplicity the decisive feature between theories of equal empirical adequacy? Are there other features that you can imagine factoring in?

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    1. Oscar SmithSeptember 8, 2015 at 5:34 PM

      The simpler theory is chosen for 2 reasons. First of all, simpler theories are less likely to be over-fit, increasing the reliability when the usage of the theory is extended past the data it was created with. The second reason is simpler: if two theories will give you the same data, why do more work?

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  2. AnonymousSeptember 9, 2015 at 5:20 AM

    I am curious about the second and third axioms of your belief systems.
    First, the second axiom states that for two theories to be equally valid, they must both produce the same results under all circumstances. To my mind, the testing of anything under all circumstances is a practical impossibility.

    As well, in regard to the third axiom of your belief system, I can't be sure I am reading this correctly without assurance of your intention to include both "not"s. Do you really mean to say that that which is measurable, meaning having definite state, is not real? Or, do you mean to refute the reality of anything which cannot be measured?

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    1. Oscar SmithSeptember 9, 2015 at 9:23 AM

      The second axiom does not state that for two theories to be equally valid, they must produce the same result in all situations. But, rather, that if they Do, one can not be more or less valid. In hindsight, I should have said instead that two theories are equally valid for domains which they produce the same answers. For example, relativity is more correct than Newtonian mechanics at high speeds, but at low speeds. Newtons laws are used because they are far easier to work with and give (basically) correct results

      Also, typo that is now fixed

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