Re: An uncountable countable set

Tony Orlow wrote:

Virgil wrote:

Mathematicians know better.

Define "better". Those that work in various areas of science share a notion which defines science. Theories which have no means of verification are not science, but philosophy. In mathematics, verification really consists of corroboration by other means, agreement between different approaches. In science, where you find a contradiction with your theory, it needs revision. So, the scientific approach to mathematics requires some criterion for universal consistency, as measured by the predictions of the various theories that comprise it. Where two theories collide, one or both is in error. I think that's better.

Precisely ! In mathematics, there are contradictory approaches, such as
constructivism (Brouwer) against axiomatism (Hilbert). Its practicioners
are asked to be "nice" to each other and to "reconciliate" the different
points of view, which turns out to be a hopeless task. Such a situation
would be unthinkable if mathematics aimed to be a science.

Han de Bruijn

.

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