Plato’s Realm Of Forms Tells Us Nothing About Mathematics
We’ve all heard of Plato’s Realm of Forms. Unfortunately it tells us nothing about mathematics (or anything else).
What is the Realm of Forms?
The realm of forms is something Socrates exposits in Plato’s writings. For those who don’t know, Plato didn’t directly write his thoughts, instead he wrote discussions in which other people debated and reasoned.
The forms, he argues, are like when a prisoner in a cave sees the reflection of an object from the outside. You learn something of it, but it never compares to seeing the object itself.
If you want to hear from the horse’s mouth, see this section from The Republic.
This sort of thing is a big deal, because it remains a mystery what abstract concepts like numbers are. If there were no humans, would numbers exist? In what sense do they exist? (The phrase ‘in what sense’ is quite illuminating, as we shall see that Plato merely packages up our existing ambiguity and tries to link it to our senses)
P.S. it is contested whether Plato himself believed the Realm of Forms existed.
P.P.S I think Plato’s dialogues are a very fun read. I think my favourites were Phaedrus and The Symposium, both of which are quite raunchy (surprisingly for a…
