Why prove something?
In our never-ending pursuit of truth, we want to find, dissect, understand everything. Through the scientific method we undoubtedly land at the crossroads of rigour and validity resulting in an inherent need to prove stuff. We humans are capable of visualising only three Dimensions and cannot even comprehend the complexity and abstractions of reality. We have defined the notion of dimensions and we prove a variety of stuff in these dimensions. But if we have integers and real numbers and fractions, why can’t we have fractional dimensions or in fact imaginary dimensions. We are in fact bounded by our senses and furthermore our ability to think. If we further take this to dimensions of nonsense that are non quantifiable by science. Will proofs work here? Definitely not, because such stuff is just nonsense. PS: Fractional dimensions do exist, but you must have gotten the point.
I believe that the proofs we pursue so blindly cannot prove why proofs work. Why should proofs prove just because they logically convince us? We are basically chalking out blueprints to convince that our initial axioms of logic and reasoning were right all along, but the sad truth is that the probability of this being right in the first place is 0%.(Yes 0% not a typo because in mathematics we see the probability of a single event occurring in a world of infinite possibilities is 0)
Some additional Notes:
Although this may all seem to be a rephrased version of the famous Godel's Incompleteness theorem, this simple meta argument still holds water.
One of the first proof's for a simple 1+1=2 in shown in Principia Mathematica which starts from the bare minimum and works it's way up. The proof is pretty large and well developed.
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