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Single Idea 18832
[filed under theme 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
]
Full Idea
On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result.
Gist of Idea
Mathematical statements and entities that result from an infinite process must lack a truth-value
Source
Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.199
A Reaction
This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent.
The
15 ideas
with the same theme
[logic which uses 'provable' in place of 'true']:
18832
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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]
|