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Single Idea 13715
[filed under theme 4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
]
Full Idea
Not everyone who employs intuitionistic logic is an intuitionist about mathematics.
Gist of Idea
You can employ intuitionist logic without intuitionism about mathematics
Source
Theodore Sider (Logic for Philosophy [2010], 7.4.1)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.193
A Reaction
This seems worthy of note, since it may be tempting to reject the logic because of the implausibility of the philosophy of mathematics. I must take intuitionist logic more seriously.
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]
|