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Full Idea
For Dummett the semantics of the metalanguage is the external and objective source of the justification of deduction.
Gist of Idea
Deduction is justified by the semantics of its metalanguage
Source
report of Michael Dummett (The Justification of Deduction [1973]) by Robert Hanna - Rationality and Logic 3.4
Book Ref
Hanna,Robert: 'Rationality and Logic' [MIT 2006], p.67
A Reaction
This is offered as an answer to the Lewis Carroll problem that justifying deduction seems to need deduction, thus leading to a regress. [There is a reply to Dummett by Susan Haack]
| 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] |