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Logic
Logic (from Greek logos -- reason) is the study of how to make rational reasoning.
TODO: moar stuff here, 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 atheist tells you or even what he believes. This sadly 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. Kurt Godel (along with others, e.g. Tarski) mathematically proved with his 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 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 atheists.