Something I have had long discussions about, with several close friends who tend to be on the other side of the argument. Seems the topic is warm again! are new mathematical truths discovered or invented? http://www.sciencenews.org/view/generic/id/31392/title/Still_debating_with_Plato
If anyone cares I’m squarely on the invented side of the argument. I don’t buy the concept of absolute ideas that are somehow in a different sphere – and I don’t buy the challenge which says that it is proven wrong by the fact that so many different people and cultures come up with the same concepts. We live within similar bodies in the same universe!
I really don’t see a problem, here’s my point of view, simplistically:
- we think and imagine with our brains and bodies
- our body and brain works within the universe and within whatever laws and rules govern said universe
- our body and brain will therefore produce ideas and concept which mesh with the way the universe works, because that is the way our brain and body works
- it is therefore not surprising that people thinking about certain things will often come up with similar ideas and concepts
- entities whose functioning is totally different from us, say beings made of gas, or microscopically small, or very large, would come up with maths via a different route (a gas being for example would start with continuous concepts, perhaps), but as long as we are in the same universe once their maths becomes sufficiently advanced there would congruence between their mathematics and ours.
Of course it is made easier to think this being a physicist where so many models which were mathematically different on the surface turn out to be equivalent or related…
Update: just been told my paragraph on the gas entities was too short, it could be construed as a platonician idea. I was trying to say that any beings which we would be able to find a way to communicate with, well, if we can map our languages then they are probably “wired” enough like us that their mathematics would be translatable too, and there might be things to learn from each other. Not because the concepts exist as absolute, but because both us and those beings live within a specific universe and think using intelligence which runs on matter within that universe.
Inventing the mathematics of gas beings is still fun several years on