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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic

[logic which uses 'provable' in place of 'true']

15 ideas
Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett]
Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock]
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
Is classical logic a part of intuitionist logic, or vice versa? [Burgess]
It is still unsettled whether standard intuitionist logic is complete [Burgess]
You can employ intuitionist logic without intuitionism about mathematics [Sider]
Intuitionist logic looks best as natural deduction [Mares]
Intuitionism as natural deduction has no rule for negation [Mares]
(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall]
Double negation elimination is not valid in intuitionist logic [Friend]
Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
Rejecting double negation elimination undermines reductio proofs [Colyvan]
It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt]
Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt]