What is a Hole? Ask a Mathematician.
A while ago I was talking to a friend of mine who studied philosophy. He said that he was annoyed in lectures when they spent ages discussing questions like “what is a hole?”, which seem to just send you in circles of semantics promising pointless conclusions. I’m also not a big fan of debates which boil down to semantics, but I dislike the question “what is a hole” for a whole other reason.
Back before humanity learnt about meteorology, we attributed weather patterns to Gods. It was perhaps once a philosophical question to ask “what brings the thunder?”, whereas now the question and answer are scientific in nature. This pattern has emerged in a huge number of areas and continues onwards as scientific and mathematical understanding progresses.
This is the issue with the hole question. Perhaps once it was solely philosophical, but maths, specifically topology, is more than adequate to ask and answer such questions. It also answers them with an astounding rigour and consistency, as is characteristic of mathematics. Once our other intellectual disciplines are mature enough to tackle these problems, it seems a waste to spend philosophical effort on them.
Of course there are still plenty of questions that the other disciplines can’t answer. What is right and wrong? How should we act? What axioms should our mathematical system take? These questions still remain primarily philosophical in nature. They are also fairly impossible to definitively answer, at least for now. The only certainties lie in mathematics, and even then you’re left with an “if this then that”, rather than a universal truth. Sciences and humanities provide increasingly less definite answers, but often these are good enough.
What of Philosophy then? I see it as the study of (currently) unanswerable questions. Does that make it useless? Of course not. Firstly, you can develop points of views and make decisions without needing to fully answer many questions. The exploration in itself has significant value. Secondly, you need an answer to the question “how we should we act” to even begin to function as a rational agent, it just doesn’t have to be perfect. These points aside, I do think there’s something beautiful about picking out some fundamental questions and saying “We cannot hope to answer these, but fuck it lets try anyway”.
Of course dividing questions up into “this is answered by field x” and “this is answered by field y” is very reductive. The boundaries of these fields far more blurry than a school or university curriculum lead you to believe, and in reality the best solutions are found by a combination of maths, science, humanities, and philosophy.
There are however several elephants lurking in this room. Who decides what is useful? Why should we care about usefulness? Why should we care about caring? Like the inquisitive child we could go down an infinite hole of these questions, and not make much progress. David Hume’s guillotine shows us that there is no way to derive statements of value purely from statements of fact. Furthermore, statements of facts themselves require assumptions about the nature of world and logical inference in order to be built upon. Clearly we require some fundamental fabric to begin our construction. Some axioms. A philosophical foundation.