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It is an open question whether what I have called Hilbert's ultrafinitist program is possible, that is whether a natural base theory can prove the consistency of natural stronger theories. Please see

Is an ultrafinitist Hilbert's program doomed?Is an ultrafinitist Hilbert's program doomed?

So in this sense the Second Incompleteness Theorem is not redundant: there could be natural theories which prove natural stronger theories consistent.

In any case I'm of the opinion that proving self-consistency is a good test for a theory; that is, if a theory can't even prove its own consistency, that is a good reason not to accept the theory.

It is an open question whether what I have called Hilbert's ultrafinitist program is possible, that is whether a natural base theory can prove the consistency of natural stronger theories. Please see

Is an ultrafinitist Hilbert's program doomed?

So in this sense the Second Incompleteness Theorem is not redundant: there could be natural theories which prove natural stronger theories consistent.

In any case I'm of the opinion that proving self-consistency is a good test for a theory; that is, if a theory can't even prove its own consistency, that is a good reason not to accept the theory.

It is an open question whether what I have called Hilbert's ultrafinitist program is possible, that is whether a natural base theory can prove the consistency of natural stronger theories. Please see

Is an ultrafinitist Hilbert's program doomed?

So in this sense the Second Incompleteness Theorem is not redundant: there could be natural theories which prove natural stronger theories consistent.

In any case I'm of the opinion that proving self-consistency is a good test for a theory; that is, if a theory can't even prove its own consistency, that is a good reason not to accept the theory.

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It is an open question whether what I have called Hilbert's ultrafinitist program is possible, that is whether a natural base theory can prove the consistency of natural stronger theories. Please see

Is an ultrafinitist Hilbert's program doomed?

So in this sense the Second Incompleteness Theorem is not redundant: there could be natural theories which prove natural stronger theories consistent.

In any case I'm of the opinion that proving self-consistency is a good test for a theory; that is, if a theory can't even prove its own consistency, that is a good reason not to accept the theory.