You can change symbols all you want, but when life appears in your simulation they won't care. If they put 2 items and then another 2 items, and 4 items are there - for all they care 2+2=4.

And if sometimes its 5 - they will do what we did with relativity when it turned out velocities doesn't add up like they "should". We haven't changed addition - we changed the equations used in physics.

I guess you could hand-made an intelligent life that is designed never to discover the true math.

If you put 2 male mice in a box with 2 female mice and wait a while, you may find 5 or more mice in the box. Or if you put 2 clouds in a box and later put 2 clouds in the box, you probably won't find 4 or 5 clouds in the box.

The act of putting things in boxes (after first perceiving and classifying them as discrete entities) and the abstract notion of addition are only as related as you need them to be for a given purpose.

> The act of putting things in boxes (after first perceiving and classifying them as discrete entities) and the abstract notion of addition are only as related as you need them to be for a given purpose.

Yes. That was my point. How would you change the abstract notion invented by creatures in your simulation if not by changing reality to shape their abstractions? And how do you change enough instances that their math develops in such way that 2+2=5?

I think our basic math (logic, set theory, integer math) with some exceptions (choice theorem) is the only useful consistent basic math there is.

The point I was trying to raise, though, is what if the concept of "adding two things" has no basis in the "real reality". I know its hard to grasp...but imagine a reality where there is no "+" or "-" operation.

But "+" and "-" operations are inherently time bound.

why? and what is "time?"

"time" is the basis, isn't it ?