Why isn't there a replication crisis in math?
The paper here seems to make absolutely zero distinction between deductive and inductive reasoning, which should be the entire point.<p>Math is an arbitrary framework, built from arbitrary axioms. It is deductive. Thus, all proofs are simply deduction. The knowledge here is <i>positive</i> knowledge, we can show things are true, false, or undecidable. There may be errors, but those are errors in execution.<p>Psychology is <i>not built on a framework</i>. It is inductive, we are trying to find axioms that map to the data we collect. Thus, all papers are trying to add/build it's arbitrary framework. The only knowledge here is <i>negative</i> knowledge, falsification, we know only what is a failed hypothesis. There <i>will</i> be errors, both in execution, and there will also be statistical errors in experimental results.<p>The entire point of the replication crisis is that we don't publish or pay attention to results that are boring, so the framework we build is built on skewed data. We don't reject previously popular papers that are now unfalsifiable (the idea that the <i>now unfalsifiable</i> Milgram experiment is still taught in every university psychology dept should be outrageous). The boring results need to be weight statistically against the interesting results, but aren't, etc. Nobody out there is arguing whether or not the axiom of choice is a <i>true</i> axiom? It sort of doesn't matter, it can't matter, because it's arbitrary by definition.<p>You can't have a replication crisis inside of a deductive framework <i>without changing the framework</i>. This doesn't happen too often, but we did see this during the shift from neutonian to einsteinian physics. The study of philosophy of science is fairly obscure, but is the center of this discussion.