I used this example, because it is literally exactly what the guy said to my face. If I'd been making one up, I would have gone one better.
No, i looked at it. Tell me which numeral base you can use to make 2+2=4.3. I tried, it cannot be done. Not even by allowing fractional bases.
It's only possible if you change what "2" means, what "4" means and what the point sign "." mean. But that's clearly not what the guy was saying.
You can actually do it with a simple zero-point redefinition (similar to that used in programming for zero-based numbering systems). If we redefine the zero point of our numerical system to a value of -.3 (meaning the new value of "0" is equivalent to the normal system's value of .3) then the math works out wonderfully, with 2 + 2 = 4 in the new system being the equivalent of 2.3 + 2.3 = 4.6 in the "normal" one. Such a system would probably be called a ".7-based numbering system", since .7 would be the first "integer" of said system, and would indeed be mathematically valid.
That said there's no practical reason to use such a system, regardless of it's mathematical validity. One of the few reasons we use zero-based systems is due to some improvements in computing certain algorithms, but a .7-based system would have no such advantages and therefore would have no valid reasons for it's use over that of our normal 1-based numbering system or some computing process's zero-based numbering system.
And yeah, the idea that things like logic can be influenced by political and cultural ideas is really stupid. To reference a
xkcd comic:
Logic. It works, bitches.