Originally Posted by

**prasit**
I rather think it is the opposite. In my view most, if not all, should be proven objectively.

Well, I'm sorry, but it really doesn't matter what you think. You can't prove any of these things objectively.

Anything you can think of that has anything at all to do with numbers cannot be proven objectively. Because, numbers do not exist.

Ever stubbed your toe on a seven?

No, I thought not. Numbers are simply a construct invented by humans to help us make sense of the world around us. The numbers themselves do not exist. You cannot walk into a wood and pluck a six off a tree, or mine a nine, or fish for a five. Numbers do not exist in anything other than our minds.

The whole of mathematics is built on a set of basic truths, they call them axioms and some folks call them postulates. They are simply a set of defining principles that you have to accept for everything else to work. The first of these axioms is: 1 is a natural number.

This is how maths gets around the fact that numbers do not exist; they just invent their numbers and proceed from there. There is nothing false about this, it is not a ploy to deceive anyone, it is just a way of making sense of the world in which we live. And, crucial point, it depends on you believing that 1 is a natural number.

So, you cannot objectively prove that 1 + 1 = 2 because 1 is just an idea, a symbol to which we attach some meaning. It does not exist and therefore cannot objectively be proven to do anything.

So, anything that requires counting or measuring cannot be proven objectively. There is, objectively, no such thing as an inch, or a mile, or a kilometre, or a dozen, or a gross, or a tonne. These are just ideas.

So you can't prove that a bear has four legs, but can you objectively prove that a bear exists?

Suppose you and I are stood in a zoo, looking over an enclosure in which you see a white furry creature with a black nose, and you point to this thing and say, "Look numbers, it's a polar bear." And I say to you, "Where?"

Now, how might you prove the bear exists?

Originally Posted by

**prasit**
Also would like to see examples of thing proven non-objectively

Almost everything you currently think of as having been proved has been proved within some system of rules similar to mathematics. This means that the "proofs" are only correct as long as we agree with their basic axioms, their fundamental principles. This is non-objective proof.