Platonists think you can define them wrong if you're careless. Imagine having a spreadsheet with the population of each country. I can go and enter 1 billion f

Platonists think you can define them wrong if you're careless. Imagine having a spreadsheet with the population of each country. I can go and enter 1 billion for the US, and the spreadsheet will happily recalculate all the cells about, say, GDP per capita etc. based on my incorrectly modified input. Clearly just because I've set the US population value in my spreadsheet to 1 billion the actual population did not change. There is a real population count and if we don't use the correct one then all our output will be garbage too: garbage in, garbage out. Mathematics is like this spreadsheet, its input are the axioms and the outputs are various interesting theorems. Feed in wrong axioms and you get wrong theorems. Platonists believe in a realm of ideas, that math talks about something real, just like the spreadsheet talks about real human populations. Even though within the spreadsheet everything remains fine and consistent if I tweak the US population. It just doesn't correspond any more to reality. I myself am not a mathematical Platonist, I more of an engineer/practical person and see math as a survival tool of a bunch of primates on a rock floating in space, not something that taps into anything mystical. But the Platonist worldview also seems coherent.