Tuesday, September 20, 2016

How to Get Very Confused About Mathematics

I linked to this screed in my previous post (I am aware of it because a reader sent it to me). The focus of it is whether or not infinite sets "really exist." The author claims they do not.

What he is asking here is an ontological question, about what entities really occupy our world and what ones are only imaginary. And that question may or may not interest someone. But it is completely irrelevant to mathematics!

For mathematicians, the only relevant question about infinite sets is, "If we posit they exist, does that enable us to do better / more interesting / more fruitful mathematics?" And if positing them advances mathematics, why in the world should the mathematician have any concern over whether or not infinite sets "really" exist, whatever it would mean for them to do so?

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"If your approach to mathematics is mechanical not mystical, you're not going to go anywhere." -- Nassim Nicholas Taleb