FOM: Intuitionism

[Robert Black]

>The principle
>
>    If a proposition cannot be known to be true,
>    then it can be known to be false
>
>is defended from an intuitionistic point of view in Martin-Löf
>"Verificationism then and now" in W. DePauli-Schimanovich, E. Köhler, and
>F. Stadler eds., The Foundational Debate: Complexity and Constructivity in
>Mathematics and Physics, pp. 187-196. Kluwer Academic Publishers,
>Dordrecht/Boston/London.

Isn't this trivial? Intuitionistically a proof that p is not provable 
is (by the definition of negation) precisely a proof of not-p. So 
translated into the symbolism of intuitionistic logic this is just 
'if not-p then not-p'! (Per Martin-Löf surely had something more 
interesting to say than that!)

By the same token it's trivial that 'neither p nor not-p is provable' 
is an intuitionistic contradiction, amounting to 'not-p and 
not-not-p'.

Robert

-- 
Robert Black
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD

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