> > I don't know him; does he argue that 2+2=4 can be false? If so, I like
> > to see the argument; it would be fascinating.
>
> Well, in base 3, the argument wouldn't be false, it would be
> nonsensical.
But it isn't _in_ base three, any more than your above sentence is in German.
> The idea that "mathematics" is the language of
> nature was born in the sixteenth century and has now become part of
> "common sense." But this does not make it true.
"reborn" perhaps, but Pythagoras said it a long time before then. Being part of common sense doesn't make something wrong, either!
[...]
> > I don't know any phenomenologists who have this relativistic view of
> > mathematics you are trying to uphold; Husserl certainly didn't, as far
> > as I can tell.
>
> Think about the following:
[examples snipped]
A couple of points: mathematics isn't arithmetic, and your examples don't constitute some sort of alternatives to our mathematics, but are things that sit snugly within it.
> This is not relativism. It is the observation that mathematics is not a
> single thing....it is one or many collections of rules and precepts
> having to do with the classification and manipulation of numbers,
> shapes, collections, and spaces... which produce the most diverse
> results and realities. Some mathematical entities vary with culture,
> some vary with historical development, and I am arguing that there is no
> vantage point from which you could say this mathematical model is wrong,
> this one is right.
An internally inconsistent mathematical model is certainly wrong! And Gödel showed that much folk (meta-)mathematics was wrong, as you quote below. My main objection here is crypto-practical: I trust mathematics to carry my weight much more than I do metaphysics.
> See Godel on the "truth" of mathematics.
It's wildly unfair to claim that Gödel's result puts scare quotes round the truth of mathematical propositions.
John