Gödel's Incompleteness Theorem & How to Think About Mathematics

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In this video, I discuss Gödel's Incompleteness Theorem and its relationship to mathematical philosophy.

  1. Garrett Mayer
  2. math
  3. mathematics
  4. epistemology
  5. thought
  6. mind
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I agree that the best proof of something might be in its ‘reality’ (can it be seen/recreated in the real world), but… mathematics are actually mental constructs of ‘real’ relationships, and for a long time human beings have been able to use math to ‘stretch’ into aspects of reality that we just are not able to measure directly (maybe because we don’t have the right measurement tools, or senses; consider, for example, our ability to discuss ‘lesser’ (2-dimensional), or even ‘greater’ (4-dimensional) dimensions, even though we live in a 3d world (by the way, your explanation of a ‘line’ as ‘having a width’, even though it shouldn’t, is a perfect example of this: a real line cannot be perceived or created in our universe, but we can ‘represent’ it with a drawn line in pencil because we can ignore its very thin width or that it curves slightly on the surface of the paper on the surface of the Earth; same thing with real points which are only 1-dimensional).

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