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Full Idea
In intuitionist logic each connective has one introduction and one elimination rule attached to it, but in the classical system we have to add an extra rule for negation.
Gist of Idea
Intuitionism as natural deduction has no rule for negation
Source
Edwin D. Mares (Negation [2014], 5.5)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.202
A Reaction
How very intriguing. Mares says there are other ways to achieve classical logic, but they all seem rather cumbersome.
Related Idea
Idea 18789 Intuitionist logic looks best as natural deduction [Mares]
| 18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
| 18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
| 18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |