Both are not~ vs. Not both are~

[forinfo]

Hello,

I want to thank all of you who have replied to the various questions I've posted so far.
The replies I've received have been wonderful, and they really helped me improve my English.

As usual, I'd appreciate your help on the following questions which are pretty confusing to me.

1) Both are not correct.
Does this sentence mean "Not both are correct" or
"Neither is correct"?

2) Every bird in the cage is not blue.
Does this mean "No bird in the cage is blue" or
"Not all birds in the cage are blue"?

[5jj]

These are questions discussed by students of logic rather than by students of language as such.

Neither sentence is natural in everyday English. For #1 we would say, "Both are incorrect' or 'Neither is correct'. For #2, depending on the meaning we wished to convey, we'd say either 'Not all of the birds in the cage are blue / Some of the birds in the cage are not blue' or 'None of the birds in the cage is/are blue'.

[forinfo]

Thank you for your reply. Sometimes I find myself spending much time dealing with sentences that don't sound natural in English. (Sentences that are offered as examples in grammar books.) I could immediately understand the meanings of the revised sentences you've offered.