From my “watched a YouTube video” understanding of Gödel’s Incompleteness Theorem, a consistent mathematical system cannot prove its own consistency, and any seemingly consistent system could always have a fatal contradiction that invalidates the whole system, and the only way to know would be to find the contradiction.

So if at some point our current system of math gets proven inconsistent, what happens next? Can we tweak just the inconsistent part and have everything else still be valid or would we be forced to rebuild all of math from basic logic?

  • gandalf_der_12te@discuss.tchncs.de
    11·
    1 day ago

    Realistically, that doesn’t happen. At least not if we consider mathematics to be the useful kind of mathematics. The stuff that helps you do statistics/finances/engineering. Because that type of mathematics is based on reality and for the mathematics to be inconsistent would mean that reality is inconsistent, and then we have much much bigger problems.

    As for the higher abstract maths (which is closer to philosophy anyways) yeah such things have happened many times and led to revolutionary insights each time. An example is when we started basing everything on set theory (which in medieval times did not really exist). But that’s a philosophical question, not one that concerns daily life.