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As a theorist, theories in physics describe experiments and mathematics is the study of formal axiom systems. So if you want to reject the axiom of infinity, th
by yk 10y ago
As a theorist, theories in physics describe experiments and mathematics is the study of formal axiom systems. So if you want to reject the axiom of infinity, that is fine. If you want to have stronger axioms, like large cardinal axioms, equally fine.^1 However from experience, babbling on about truth in mathematics does almost never lead anywhere interesting.
^1 Basically large cardinal axioms give you additional types of infinity.
- mattmanser 10y agoI'm guessing mindcrime's talking about Cantor and Godel and the continuum hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis I remember learning about them in the philosophy of maths, but have no idea if they have any consequences in Physics. And like /u/lasfter I'll stop there before I embarrass myself.
- yk 10y agoProbably, but in my view Godel's theorem basically states that there are limits to axiom systems. (In much the same way that you can not write a web server without touching sockets.) My point is, if it would be necessary to switch to a stronger axiom system than ZFC in physics, then one would do that, without claiming that that stronger system is real.
- mattmanser 10y agoI honestly can't tell if this is utter gibberish or a real comment...
- yk 10y agoYeah, I should stop commenting publicly on an ongoing thought process, before I figured out how to communicate that thought :/ Basically I am drifting towards hard mathematical anti-realism and towards a rather minimal scientific realism. (And when I saw the discussion I jumped the gun...)