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Single Idea 18798
[filed under theme 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
]
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.
Gist of Idea
It is the second-order part of intuitionistic logic which actually negates some classical theorems
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.2
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]
|