At 2:12 PM -0500 2/28/08, John F. Sowa wrote:
>
>PH> The term 'foundations' is well chosen. When building a house...
>
>The analogy with houses is misleading because gravity creates
>a preferred direction of building (although there are many cases
>where builders jack up a house to construct a new foundation
>under it). For mathematics, there is no inherent directionality. (01)
What has that got to do with my point? I didn't speak of directions.
If foundations were built in the air and houses hung from them (which
does happen in rare cases) the point, and the analogy, would apply. (02)
>PH> Similarly with mathematics and formal logic.
>
>Not really. .... no single system is the "foundation'.
>Instead, you have an open-ended collection of systems, and
>you can show relative consistency of one system in terms
>of another. That is very different from the idea of a
>single, privileged, universal foundation for everything. (03)
I agree. If you knew more about concrete foundation work, you would
know that this applies to real buildings also :-) (04)
But more seriously: in fact, in actual practice, there is a
privileged universal foundation for virtually all of mathematics, to
wit, ZFC. (05)
Pat (06)
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