Hi Alan,

***"But it provides an interesting and new perspective that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles. (28kb)"***

I agree with this quote from Kieu about a new perspective. As with all perspectives, each is one among many, depending on your point of view.

If you look at it from the viewpoint that there is such a thing as "Physical Principles" out there somewhere, then if Dick is right and these principles are tauological with the possibliities for certain features of sets of numbers, then you could conclude that these "Physical Principles" seem to impose limits on the mathematics of numbers.

If you look at it from the viewpoint that numbers somehow exist "out there", as maybe Alex or Plato might contend, then, as Dick has shown, the mathematics of these numbers seem to impose limits on Physical Principles.

If you look at it from Bishop Berkeley's point of view that there is only the mind of God and there is nothing else "out there", then if the thoughts of God are to be consistent, the conceptions of numbers or of a physical universe are one and the same thing, the limits on both being imposed by the requirement of consistency. Of course, that is not really a requirement, because God may also have inconsistent thoughts. If so, however, they would not lead to either the mathematics of numbers, or physical reality as we know it.

It all depends on how you look at it, I think.

Warm regards,

Paul