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Ideas for 'Semantics, Conceptual Role', 'works' and 'The Boundary Stones of Thought'

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2 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18799 Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt]
     Full Idea: Double Negation Elimination is a rule of inference which the classicist accepts without restriction, but which the intuitionist accepts only for decidable propositions.
     From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)
     A reaction: This cures me of my simplistic understanding that intuitionists just reject the rules about double negation.
18798 It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt]
     Full Idea: Although intuitionistic propositional and first-order logics are sub-systems of the corresponding classical systems, intuitionistic second-order logic affirms the negations of some classical theorems.
     From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)