Thursday, October 3, 2019

How there is mathematical pluralism

Mathematics is the study of absolute truth.

It is common for non-mathematicians to try to deny this. Sometimes they give arguments like saying that Goedel proved that mathematical truth is not possible. Goedel would never have agreed to that.

Mathematician Timothy Chow writes:
I would say that virtually all professional mathematicians agree that questions of the form “Does Theorem T provably follow from Axioms A1, A2, and A3?” have objectively true answers. ...

On the other hand, when it comes to the question of whether Axioms A1, A2, and A3 are true, then I think we have (what I called) “pluralism” in mathematics.
That is correct.

There are some axioms for the existence of very large cardinals, and some disagreement among mathematicians about whether those axioms should be regarded as true. But there is not really any serious disagreement about the truth of published theorems.

Other fields, like Physics, are filled with disputes about what is true.

1 comment:

  1. Roger,
    What the hell are you talking about? Seriously, are you drunk? It's true physics is filled with disputes, but at least they are supposedly/tenuously dealing with something connected to reality. Math has no such claim as practitioners of the art are mostly self professed dabblers in platonic metaphysics, so comparing it to an actual hard science in relation to 'absolute truth' is meaningless. An absolute truth in an entirely made up abstract system has no more significance than saying with certainty you know how many angels can dance on the head of a pin. You have absolute certainty... of something not actual.

    Math is the abstract study of systems of self consistent logic with numbers applied to it. You can create a potentially infinite number of logical internally consistent numerical fantasies that have NO MEANING or connection to any reality whatsoever (over 10^500 and counting), as has been handily demonstrated for the last forty years by the landscape problem which dogs Super String theory like a bad case of herpes. Math papers so convoluted and long-winded that even other mathematicians can't really understand them is now becoming vogue as well.

    Glorifying math as the pursuit of 'absolute truth' is just plain stupid and leads to endless elitist intellectual idolatry and circular onanism. It's not what Math is for.

    Any fantasy or fiction written in any language can be internally consistent. That doesn't make it 'true' outside of its own made up premise, even if its written in large hard to calculate numbers by self absorbed hierophants.