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See https://en.wikipedia.org/wiki/New_Foundations https://en.wikipedia.org/wiki/New_Foundations for another alternative foundation of mathematics.
by sanxiyn 6y ago
See https://en.wikipedia.org/wiki/New_Foundations https://en.wikipedia.org/wiki/New_Foundations for another alternative foundation of mathematics.
- dr_dshiv 6y agoThe original philosophical foundation of mathematics would be Pythagoreanism [1]. For instance, that there is a special, transcendent meaning to "oneness" or "twoness" — or more generally, that there is a basic harmony within mathematics that manifests in the harmonies of the cosmos. Here is a nice article on the sources of his mathematical contributions. https://www.sciencedirect.com/science/article/pii/0315086089900207/pdf?md5=f82cfebc9d937472cb2b6a4af44ae195&pid=1-s2.0-0315086089900207-main.pdf https://www.sciencedirect.com/science/article/pii/0315086089... [1] https://en.m.wikipedia.org/wiki/Pythagoras https://en.m.wikipedia.org/wiki/Pythagoras
- bawolff 6y agoTrying to find an axiomization of mathamatics and trying to find the metaphysics of mathamatics seem like two very different projects to me.
- dr_dshiv 6y agoHmm, getting to the bottom of axioms feels a lot like metaphysics, but open to why they'd be a different ballpark.
- bawolff 6y agoIn my mind, metaphysics is asking "why", axioms are asking "how"/"what"
- dr_dshiv 6y agoThat's fine. It's just that when you get to the very bottom of axioms, it can get a little weird. Like, is the underlying basis the one, the nothing or the all? Is it being or not being? That is metaphysical -- and has implications for the foundation of any axiom, no?
- bawolff 6y agoI'm not sure what it even means for the underlying basis to be one or nothing or everything (basis of what specificly?). That doesn't sound like an axiom thing to me.