Comments by "xybersurfer" (@xybersurfer) on "Propositions as Types - Computerphile" video.

  1. it's an interesting topic. but i honestly think the explanation can use some work. some more examples showing the correspondence between proofs and programs would be nice (where all the steps are shown). i also don't think everyone is familiar with functional programming types and proof trees (so a lot of inbetween steps or transformations seem to be missing)
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  2. John Hightower it depends on the meaning you give to "This statement". let's call "This statement" "f(x)". then "This statement is false" is the proposition: f(x) = ¬f(x) then you can give it 2 interpretations 1. if "f(x)" is just a meaningless symbol to you, then you get a simple contradiction as a proposition: P = ¬P which simply has the value false 2. but, if you you interpret "¬f(x)" as the definition of "f(x)", then you get an infinite recursion. which computers have problems with of course: f(x) = ¬f(x) = ¬(¬f(x)) = ¬(¬(¬f(x))) ... etc in this way, the sentence "This statement is true" has the same infinite recursion problem because of self reference. recursion is supposed to have a decision about whether to continue or end (or it's just an infinite loop). computers have problem with it. because it does not make sense. the program is trying to do something with no hope of an answer. you can see it as computers having difficulty but you could also see it as us having difficulty telling them what to do (it's a blurry line)
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  3. ​ @Rockyzach88  this video seems to skip past a lot of the introductions, compared to other videos on this channel. making it harder to take an interest
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