January 11, 2009
Employing the evolution-given brain, humanity has succeeded so far in accumulating extraordinary amount of knowledge, including that of the natural universe. But that abundant pile is always haunted by epistemological anxiety regarding the truth, the consistency, and the completeness of the knowledge.
Along with its assertion that the Platonic mathematical universe can never be reduced into a finite set of symbols and a bounded group of axioms, Gödel Theorem shows that a consistent knowledge is incomplete and a complete knowledge is inconsistent. For any consistent formal, recursively enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both simultaneously consistent and complete.
How can humanity be rested assured of the accumulative knowledge on universe’s birth, when the incredibly vast distance of space and time makes it impossible for humanity to directly witness the birth of the universe?
“Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.” — Possible Worlds and Other Papers (1927), p. 286, J. B. S. Haldane.
How can human race complete the knowledge of the universe and all within, being aware of the impossibility of gaining complete knowledge of an object for one who is entrapped inside of it, while realizing the improbability of going outside of the universe he lives in?