- #1
jk22
- 729
- 24
I search for a vector space based proof of the following :
The logic on values implies ~~v(A)=v(A)
If the value of A is v(A)##\in\{0,1\}## then it is simply ##1-(1-v(A))=v(A)##
But if we suppose A="the sky is red"
Then as on operator acting on A, ~A is not defined since for example ~A="the sky is not red" is a set in which by using the axiom of choice we could choose ~A="the sky is green" and then ~~A="the sky is not green" which does not imply that the sky is red as in the starting point.
So we have A##\subset##~~A.
Where could the proof of this based on orthogonal spaces be found ? Does it work only for dimension 4 and higher ?
The logic on values implies ~~v(A)=v(A)
If the value of A is v(A)##\in\{0,1\}## then it is simply ##1-(1-v(A))=v(A)##
But if we suppose A="the sky is red"
Then as on operator acting on A, ~A is not defined since for example ~A="the sky is not red" is a set in which by using the axiom of choice we could choose ~A="the sky is green" and then ~~A="the sky is not green" which does not imply that the sky is red as in the starting point.
So we have A##\subset##~~A.
Where could the proof of this based on orthogonal spaces be found ? Does it work only for dimension 4 and higher ?