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Single Idea 8708
[filed under theme 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
]
Full Idea
In intuitionist logic, if we do not know that we do not know A, it does not follow that we know A, so the inference (and, in general, double negation elimination) is not intuitionistically valid.
Gist of Idea
Double negation elimination is not valid in intuitionist logic
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2)
Book Ref
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.107
A Reaction
That inference had better not be valid in any logic! I am unaware of not knowing the birthday of someone I have never heard of. Propositional attitudes such as 'know' are notoriously difficult to explain in formal logic.
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]
|