I would like to understand the "upsetting"-to-mathematicians nature of this question Freyd poses to demonstrate that "any language sufficiently rich that to be defined necessarily allows you to askquestions which don't have any conceivable answer but sound as if they should" (18:28). I get that we aren't supposed to actually solve the question, but is there an "undergrad" or "serious highschooler" breakdown of the math and why its unanswerable? I understand I'm taking a risk by asking as maybe the reason is something so obvious yet I'm missing it...
Edit since downvotes:Peter is a mathemathecian, this question is not supposed to be answered, yet is askable/makes sense. I'm asking for help understanding the math behind this unanswerable yet posable question.
Here he is on these type of questions:
any language sufficiently rich that to be defined necessarily allows you to askquestions which don't have any conceivable answer but sound as if theyshould we're used to that in a number of special cases we're used for instance inmathematics except this is a very Applied Mathematics to know that to ask what what frequencies are present in asignal at a given instance it just doesn't make sense you can't I mean the definition of frequency or how you wouldmeasure it is such that you can't ask that question without specifying a nonzerointerval
And here here is his brief explanation of why this question about zeta zeroes is so frustrating to mathematicians:
here's one which I like to throw atmathematicians as an example but I warn you people can get very upset at this one uh if somebodytakes set theory as a serious foundational language for mathematics I can pose to him because ofits untyped nature the question are there any simple groups that appear as zeros of the zeta function I've seenpeople get very angry at this I've seen people forget why I mentioned it say I didn't really ask it I only mentionedit I I've had I've had people come back to me two weeks later swearing at me forbringing up such an absurd question okay that's transparently absurd notice bythe way you have no way of answering it at all even if you took it for the moment seriously until you specify whatdefinition of group you have in mind and what definition of complex number and then after somebody specifiesthem I've challenged people now prove to me that there aren't any simple groups
However, I only have a small introduction to groups, and no serious academic knowledge of the zeta function, so I'm missing out. Peter's explanation in the second half of the last quote block isn't sufficient for my understanding. Is it possible to get a breakdown of the math and moral?
This is from “An Antiphilosophy of Mathematics,” Peter J. Freyd ~18:28 time stamp
