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Full Idea
A plausible account is that the syntactic notion of consequence is for positive results, that some form of argument is valid; the semantic notion is required for negative results, that some argument is invalid, because a counterexample can be found.
Gist of Idea
Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples
Source
Michael Dummett (The Justification of Deduction [1973], p.292)
Book Ref
Dummett,Michael: 'Truth and Other Enigmas' [Duckworth 1978], p.292
A Reaction
This rings true for the two strategies of demonstration, the first by following the rules in steps, the second by using your imagination (or a tableau) to think up problems.
| 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] |