The father of math (Euclid) wrote a book named Elements. The book is full of axioms and here are some of them I am interested in:
- Things equal to the same thing are also equal to one another.
- And if equal things are added to equal things then the wholes are equal.
- And if equal things are subtracted from equal things then the remainders are equal.
- And things coinciding with one another are equal to one another.
- And the whole [is] greater than the part.
Few years ago I came to the idea that Euclid could be (is..) wrong about the No.5.
Why I think he is wrong ? He is wrong because making decision on bigger/smaller (as a consequence: more/less, faster/slower etc.) is the (main) reason of all negative we have happening. Try to think about any conflict on the Earth and You will find at least two sides fighting for the same thing there. For example: fighting for bigger territory, fighting for more money, fighting for less problems, etc. I think that the concept of thinking (thinking that some bigger or smaller even exists) is false. However, it seams I cannot logically prove it being false or true, because the whole logic itself is made on top of such axioms...
So, let`s say (or just assume..) that some of axioms are wrong. The question is - what base should be used to prove axiom being wrong for the rest of the world? My own assumption is that I have to use the "what is valuable for society" base or even the "how it feels for society" base.
And, one more thing to mention. If I am not able to prove axiom being false or true (because false/true is part of the logic which is made on top of the axiom itself) then I would like to call "true" as "real" and "false" as "illusion", but would this be correct?