Mathematical and Moral DisagreementShe finds some minor disagreements, but only support the idea that they agree on the fundamentals.
The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism.
She finds that mathematicians broadly agree on ZFC and first order logic as a suitable axiomitization of set theory and mathematics. The disagreements are about how much constructive proofs are to be preferred to nonconstructive ones, and the value of adding axioms to ZFC. Some regard the continuum hypothesis as a settled issue, while others look for new axioms to settle it.
This is like saying Democrats don't agree on whether to spend $3.5T or $3.6T.
These disagreements do not even affect what is publishable and what is not.
Wrong proofs do get published sometimes. Scott Aaronson
Continuing what’s become a Shtetl-Optimized tradition—see here from 2014, here from 2016, here from 2017 — I’m going to fess up to two serious mistakes in research papers on which I was a coauthor.I am surprised that so many serious errors made it past the editors and referees, but that is just sloppiness, and not any disagreement over fundamentals.
Here is a YouTube panel discussion on Does Math Reveal Reality? Unfortunately, physicists do most of the talking. At 1:22:00, cosmologist Max Tegmark says;
That's right, they call that the Level 4 Multiverse.No, that is not what I mean by pink elephants not existing. Tegmark denies that you can ever talk about hypothetical or counterfactual objects. He says that if you can talk about it, then it exists in some parallel or distant universe.
So when we talk about something existing if we say pink elephants don't exist, what we secretly tend to mean by that is while don't exist here on Earth or anywhere where we've looked, but maybe there is another planet really really far away where you actually have pink elephants.