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Single Idea 18799
[filed under theme 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
]
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.
Gist of Idea
Intuitionists can accept Double Negation Elimination for decidable propositions
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.3
A Reaction
This cures me of my simplistic understanding that intuitionists just reject the rules about double negation.
The
15 ideas
with the same theme
[logic which uses 'provable' in place of 'true']:
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]
|