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Full Idea
A proof of soundess or completeness is a test, not so much of the logical theory to which it applies, but of the theory of meaning which underlies the semantics.
Gist of Idea
Soundness and completeness proofs test the theory of meaning, rather than the logic theory
Source
Michael Dummett (The Justification of Deduction [1973], p.310)
Book Ref
Dummett,Michael: 'Truth and Other Enigmas' [Duckworth 1978], p.310
A Reaction
These two types of proof concern how the syntax and the semantics match up, so this claim sounds plausible, though I tend to think of them as more like roadworthiness tests for logic, checking how well they function.
| 11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
| 19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
| 19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
| 19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
| 19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
| 19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
| 19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
| 19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
| 19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
| 19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
| 19067 | A successful proof requires recognition of truth at every step [Dummett] |