Question about Negating Conditional Statements

orangetree_23

If you have a statement that says, "Not all A's are C's," then why can't negating that statement be "No A's are C's" in addition to "Some A's are not C's?"

equallyyoked

This is a good question. I thought the negation test did not always work for conditional statements.

Clemens_

'Not all A's are C's' and 'Some A's are not C's' mean the same thing, they aren't negations of another. For example, if I say 'Not all apples are green,' this means the same thing as 'Some apples are not green.'

Now, how do we negate a statement like this? If I say, 'Some apples are not green,' I maintain that there are in fact apples in colors other than green. So negating this would be, 'It is not the case that there are apples in colors other than green,' or simply, 'All apples are green.'

There also is a Wikipedia article on this subject, though it is a little on the technical side of things: https://en.wikipedia.org/wiki/Square_of_opposition