Full Idea
Dummett argues that antirealism implies that classical logic must be given up in favour of some form of intuitionistic logic that does not have the law of excluded middle as a theorem.
Gist of Idea
Anti-realism needs an intuitionist logic with no law of excluded middle
Source
report of Michael Dummett (works [1970]) by Alexander Miller - Philosophy of Language 9.4
Book Reference
Miller,Alexander: 'Philosophy of Language' [UCL Press 1998], p.294
A Reaction
Only realists can think every proposition is either true or false, even if it is beyond the bounds of our possible knowledge (e.g. tiny details from remote history). Personally I think "Plato had brown eyes" is either true or false.