Re: Yet another inane amateur Godel question

On Jun 17, 4:31 pm, Arturo Magidin <magi...@xxxxxxxxxxxxxx> wrote:
[ context snipped to save bandwidth ]
"Essentially undecidable"
sounds more like philosophy, in which case I might be tempted to
direct you to the great, late and lamented, Torkel Franzen's book on
not abusing Goedel.



"Essentially undecidable" is also a technical term. In mathematical
logic a (consistent first-order) theory T is essentially undecidable
if any consistent extension S is also undecidable. So a consistent
set of sentences T is essentially undecidable because we cannot add
any set of new sentences (in the same language I believe) to make a
set S containing T such that S is both consistent and decidable.
Do a Web search to find examples of theories T which are and
which are not essentially undecidable.

In the context of the original post, perhaps "problem" is being
confused with "theory" ?

Gerhard "Ask Me About System Design" Paseman, 2009.06.17
.

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