The more I study mathematics, the less compelling philosophy becomes for me.
The reason is that certain intuitions you develop regarding a mathematical concept (say closed sets) can be overturned when you study them in a more general setting. (Properties one associates with closed sets of a familiar space, like the real line, fail to hold in more general topological spaces.)
I have specifically in mind the interactions between topology and real analysis - a topic that I may return to later - but to appreciate the point a bit, the reader need not know a whole lot of mathematics.
Quick intuition check: How many people do you need in a room so that with reasonable probability (say >%50) two people have the same birthday?
If your intuitions are as naive as mine, before analyzing you might think it's some high number like 180. But with the correct analysis, one can show that it's actually 23.
In mathematics, there are systemic ways to defeat faulty intuitions. Not so much in philosophy. Actually, a philosopher will base their entire case on intuitions regarding a certain case - a thought experiment. Especially in analytical philosophy - but if you want to do philosophy, analytical philosophy is the only game in town.
Here's one of the most famous thought experiments in the entire free will debate.
So the more I see my intuitions proven incorrect in mathematics, the more frustrated I become with philosophers' attempts to build cases based on speculative, intuitive thought experiments.
Aaron Swartz, may he rest in piece, essentially argued along similar lines here.
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