(Provably) Unprovable and Undisprovable... How??

Comments · 313

• TO

  @tom.prince · 2 years ago · pinned

  It doesn't detract from the video, but for the pedants, I'll point out that there are various points in the video where the logic depends on the hidden assumption that system of axions is consistent. In particular, the claim that a statement implying a contradiction means that the statement is unprovable depends on the system being consistent.

  737

• AL

  @altofdish · 1 year ago

  <a href="https://www.youtube.com/watch?v=1RRpC7FDfEQ&amp;t=311">5:11</a><br>normal person: this can be distributed on the right<br>utterly deranged individual (pure mathematician): we must commute and then distribute

  92

• SE

  @Segmentimental · 1 year ago

  This is the first video where I think I understood everything.

  191

• MO

  @ModusTollendoTollens · 2 years ago

  when 0 deploys his integral domain expansion, every stranger loses it&apos;s cero-divisor qualities, even forcing them to have inverse in the finite domain

  282

• MR

  @MrSamwise25 · 2 years ago

  A+ video. It took a while for me to understand the difference between &quot;ZFC as foundations&quot; and &quot;ZFC as an object of mathematical study&quot;.

  173

• FO

  @fofodooddi · 4 months ago

  did you just forget to say YOU JUST ASSUMED THE LAW OF THE EXCLUDED MIDDLE?

  18

• SP

  @spyresoblazka · 1 year ago (edited)

  Ohhh that makes so much sense. To make sure I&apos;ve got it: taking one model (set of axioms we&apos;re setting to true and don&apos;t contradict each other),<br>- If we add one more (consistent) axiom and prove the theorem is true, then the original model cannot possibly prove the theorem is false<br>- If we add one more (consistent) axiom and prove the theorem is false, then the original model cannot possibly prove the theorem is true<br><br><br>So if we can find two different axioms that accomplish both of these, then the original model and theorem are independent.

  68

• GO

  @Gordy-io8sb · 2 years ago

  <a href="https://www.youtube.com/watch?v=1RRpC7FDfEQ&amp;t=454">7:34</a> Rings with characteristic 2: Allow us to introduce ourselves.

  74

• AM

  @amari343 · 2 years ago

  Wow! I&apos;ve been interested in Godel&apos;s silly theorems for a while, and this was a great explanation of unprovability! Thank you!

  158

• TH

  @thesecondderivative8967 · 2 years ago (edited)

  Oh this makes sense. What you&apos;re saying is that it is similar to the parallel postulate or ZFC? Where something is unprovable and not unprovable from a given set of axioms because it is possible to construct a system where it can work and where it doesn&apos;t from said axioms?

  107

• NI

  @nickfaire · 9 months ago

  <a href="https://www.youtube.com/watch?v=1RRpC7FDfEQ&amp;t=95">1:35</a> DID YOU JUST ASSUME THE LAW OF THE EXCLUDED MIDDLE???? 🦅🦅🦅🦅

  24

• AW

  @awesomethegreatamazing2651 · 2 years ago

  I’m very happy see content like this. Please continue to make content.

  71