Logic

   TODO: intro

   TODO: relationship of logic and math, which comes first etc.

   Power of logic is limited (for more please read this excellent resource:
   http://humanknowledge.net/Thoughts.html) -- though logic is the strongest,
   most stable platform our knowledge can ever stand on, it is still not
   infinitely powerful and has its limits, despite what any reddit [1]atheist
   tells you or even what he believes. This sadly [2]dooms us to certain
   eternal inability to uncover all there is, we just have to accept from a
   certain point we are blind and not even logic will help us. [3]Kurt Godel
   (along with others, e.g. Tarski) mathematically proved with his
   [4]incompleteness theorems that we simply won't be able to prove
   everything, not even the validity of formal tools we use to prove things.
   See also [5]knowability. Even in just intuitive terms: on the lowest level
   we start using logic to talk about itself, i.e. if we e.g. try to prove
   that "logic works" using logical arguments, we cannot ever succeed,
   because if we succeed, the proven fact that "logic works" relies on the
   fact that logic indeed works; if it perhaps doesn't work and we used it to
   prove its own validity, we might have simply gotten a wrong result (it's
   just as if we trust someone saying "I am not a liar", he may as well be
   lying about not being a liar). By this logic even the previous sentence
   may or may not actually be true, we simply don't know, sometimes the best
   we can do is simply hold on to stronger or weaker beliefs. Imagine we have
   a function isTrue(x) that automatically checks if statement x is true
   (returns true or false), now image we have statement y that says isTrue(y)
   = false; our isTrue function will fail to correctly evaluate statement y
   (it can't return neither true nor false, both will lead to contradiction)
   -- this is a proof that there can never be a computable function that
   decides whether something is true or not. Logic furthermore cannot talk
   about many things; it can tell us how the world works but e.g. not WHY it
   works like it does. Checkmate [6]atheists.

See Also

     * [7]knowability
     * [8]science

Links:
1. atheism.md
2. doom.md
3. godel.md
4. incompleteness.md
5. knowability.md
6. atheist.md
7. knowability.md
8. science.md