more from this thinker | more from this text
Full Idea
Soundness seems to be a notion essentially involving truth. At least I do not know how to fully express the soundness of Peano arithmetic without invoking a truth predicate.
Gist of Idea
Soundness must involve truth; the soundness of PA certainly needs it
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 22.1)
Book Ref
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.323
A Reaction
I suppose you could use some alternative locution such as 'assertible' or 'cuddly'. Intuitionists seem a bit vague about the truth end of things.
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |