> Logicians from different fields use terms in different ways. In
> provability logic and in recursion theory, soundness means often
> "arithmetical soundness".
Part of the reason for my particular viewpoint: there's a group of
professors at the college I work at who are working on bottom-up provability
of computer programs under specific constraints. "Soundness" for them means
the proof systems they use never prove a program is correct (meaning, it
meets formal, mathematically-written specifications) when it's actually
incorrect, provided the constraints are applied correctly. When the
constraints are not applied correctly, it's acceptable for the system to
prove things that aren't correct, and they still consider this sound for
> We agree then.
Yes, it's my fault for creating a semantics argument. I'm usually too busy
to even read the list...every once in a while something pops up and I feel
obliged to comment even when it's the middle of a conversation.
I actually have some questions for the list members that are relevant to the
list content, and this coming week is break. I may have a chance to post
them. They're much more on the philosophical side than the mathematical,
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