@freedomain On the topic of 2+2=4, in math there are such things as complex numbers. To put it simply, it extends the number line from a 1 dimensional line to a 2 dimensional plane. The "i" component is the Y axis, while the "real" component is the X axis. The number 4 is written as "4+i×0", or just "4". If you move up 2 steps on the Y axis you get the complex number "4+i×2".

While this is a purely mathematical concept and may appear to have nothing to do with philosophy or real life, complex numbers have practical utility in various situations such as in fluid dynamics, AC circuit analysis, signal processing etc. So they do seem to point to real world phenomena and behavior of matter and energy.

Now imagine a 1 dimensional being who only deals with "real" numbers and is blissfully unaware of "i" AKA the Y axis. "2+2=(4+i×2)", which is false, would appear to him as "2+2=4". However to his knowledge and point of view these equations are equal and interchangeable. It's like an ant who can move north, south, west and east on the ground, but can't comprehend moving "down" or "up" in 3D. He cannot see or understand something which is "above" him, like a cloud. In a similar way, this 1 dimensional being can't comprehend "i" or the Y axis in 2D. While I admit this cannot be proved philosophically with our current tools of reason and evidence, this could illustrate a situation where "2+2=4" is false, if our perceptions are limited like the ant.

It could be that complex numbers are valid in some important way, perhaps they point to something divine (just look at how they produce the Mandelbrot fractal), and we as "1 dimensional beings" only deal with "real" numbers on the X axis when it comes to identifying objects in our world. For instance, we can hold 4 objects in our hand, we cannot hold 4+i×2 objects.

My attempt at making a philosophical proof that 2+2 may not be 4 is thus:

1. Complex numbers are true and valid in reality (see fluid dynamics, AC circuit analysis, signal processing)
2. Thus, the complex number "4+i×2" is valid
3. In our rational experience of the world, complex numbers would be reduced to only their "real" component (i.e. we cannot hold 4+i×2 objects in our hand, only 4)
4. "2+2 is not equal to 4+i×2" is valid
5. Given point 3, then the statement would become "2+2 is not equal to 4", and still equally valid

Point 3 is the biggest assumption, which has no straightforward practical way to be confirmed, since we may be like 2D ants with our senses and reasoning skills. Thoughts?