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Intuitionistic Logic
No.13821068 ViewReplyOriginalReport
Quoted By: >>13821075 >>13821152 >>13821156 >>13821220
>In the semantics of classical logic, propositional formulae are assigned truth values from the two-element set ("true" and "false" respectively), regardless of whether we have direct evidence for either case. This is referred to as the 'law of excluded middle', because it excludes the possibility of any truth value besides 'true' or 'false'. In contrast, propositional formulae in intuitionistic logic are not assigned a definite truth value and are only considered "true" when we have direct evidence, hence proof. (We can also say, instead of the propositional formula being "true" due to direct evidence, that it is inhabited by a proof in the Curry–Howard sense.) Operations in intuitionistic logic therefore preserve justification, with respect to evidence and provability, rather than truth-valuation.
Why is the Law of excluded middle controversial?
I don't get it.
It seems to work fine.
Why is the Law of excluded middle controversial?
I don't get it.
It seems to work fine.
