A mathematical definition is what the answer to a philosophical problem looks like. … An example I particularly like is the definition of a topological space. I don’t know for a fact that this is what people “really meant” when they pondered the nature of “space” … it doesn’t matter, because the power of this definition shows that it is what they should have meant.
I fear that this particular example might be a bit, um, pointless these days. But perhaps this simply reflects different intuitions as to what “a powerful definition” should ultimately look like.
I fear that this particular example might be a bit, um, pointless these days. But perhaps this simply reflects different intuitions as to what “a powerful definition” should ultimately look like.