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If you want to understand the epistemic status of any formal object related to "infinity" in Mathematics, the best three starting points are Religion, Sociology

If you want to understand the epistemic status of any formal object related to "infinity" in Mathematics, the best three starting points are Religion, Sociology, and the History of Mathematics. I think a good History of World Religions course plus some focused reading on notions of infinity is likely more useful than an Analysis course for really understanding questions like "Are Real Numbers Real?" I do not think it is possible to divorce even modern notions of infinity from the deep impact that superstitious thinking has had on the direction of Mathematical thinking -- and thinking in general about anything remotely metaphysical, really -- for the last few thousand years (with only very recent counter-examples).

yamrzou 4y ago
Any specific readings you'd recommend?
- thwayunion 4y ago
  Yes, but unfortunately they require some digestion. This thesis isn't, for example, fleshed out in a single pop sci book or even dissertation or academic book afaict. It's more like: reading a lot about the history of philosophy, mathematics, and religion. (That said, I think most people in those three fields -- philosophy, history of mathematics, and religious studies at least as an academic field -- will agree in one way or another with the general sense that mathematical notions of infinity have definitely influenced and been influenced by religion and spirituality.) The closest single source that comes to mind, at least for one region of the world, might be Russell's history of western philosophy, which commits more time to both theology and mathematical history that is typical for that type of text. But, it's a big tome and only here and there provides nuggets of insight on this topic. Thinking about other sources, if you are interested in this thesis, I think you'd get a lot out of reading the works of people like Descarte, Leibniz, or even Godel. Also biographies about the same, because the writings by the men themselves are more like primary sources than summative/synthetic expositions. By which I mean, you have to study the text, its cultural context, and its impact on the history of mathematics (rather than just read and comprehend the words on the page). So reading the texts plus the biographies plus knowing enough about mathematics to understand how their ideas do and do not permeate the field will, I think, give you a decent sense for the thing I'm saying above. Sorry I don't have a single easily digestible podcast/book/audio book :(

yamrzou 4y ago

Any specific readings you'd recommend?

thwayunion 4y ago
Yes, but unfortunately they require some digestion. This thesis isn't, for example, fleshed out in a single pop sci book or even dissertation or academic book afaict. It's more like: reading a lot about the history of philosophy, mathematics, and religion. (That said, I think most people in those three fields -- philosophy, history of mathematics, and religious studies at least as an academic field -- will agree in one way or another with the general sense that mathematical notions of infinity have definitely influenced and been influenced by religion and spirituality.) The closest single source that comes to mind, at least for one region of the world, might be Russell's history of western philosophy, which commits more time to both theology and mathematical history that is typical for that type of text. But, it's a big tome and only here and there provides nuggets of insight on this topic. Thinking about other sources, if you are interested in this thesis, I think you'd get a lot out of reading the works of people like Descarte, Leibniz, or even Godel. Also biographies about the same, because the writings by the men themselves are more like primary sources than summative/synthetic expositions. By which I mean, you have to study the text, its cultural context, and its impact on the history of mathematics (rather than just read and comprehend the words on the page). So reading the texts plus the biographies plus knowing enough about mathematics to understand how their ideas do and do not permeate the field will, I think, give you a decent sense for the thing I'm saying above. Sorry I don't have a single easily digestible podcast/book/audio book :(