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Ed3 wrote:The Excluded Middle is: (Not (Not A)) → A. If this is not the case then is it true that the following proposition is also true: (A ʌ -A)?
I am working on a post which has Brouwer /Constructivism as major subjects.
Thanks Ed
Ed3 wrote:Hi Carleas,
I'm sorry!!! I did screw up the representation of my question.
I should have written – (NOT (NOT A) → A) imply (A Ʌ -A)
It appears that you have written the correct form.
Apologies - Ed
Carleas wrote:As I understand your question, it's \( \neg ( \, \neg (\neg A)) \rightarrow A) \overset{?}{\rightarrow} (A \land \neg A) \)
i.e., if it's not the case that [not not A implies A], then [A and not A].
Ed3 wrote:The final “)” belongs after the arrow and not after the first “)”.
Ed3 wrote:Hi James,
I meant to ask the following:
Does the negation of the Law of the Excluded imply (A and Not A)?
If it does then it would be a giant disaster for Constructivism. (You can go to Wiki and search for the Principle of Explosion to see a proof that for all propositions, Q, (A and not A) imply Q). But I think you already knew that.
Thanks Ed
Meno_ wrote:But the law of the excluded middle has very important philosophical implication, therefore, so does the law of identity.
Existentialism has direct connections to the law of the excluded middle. The philosophy in that sense can derive the logic which underlies the existential argument. Historical inevitability reduces to that logic.
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