Curiouser and Curiouser!

Not

I'm currently reading Being Logical by D.Q.McInery. It's a book about being rational primarily in the form of constructing rational arguments.

I struck a problem on Page 53 where he talks about negative statements being tricky. He gives the example:

All dogs are not mongrels

and says:

We note the "all," a sign of universality, and the negative indicator "not," and we might be tempted too quickly to suppose that what we have here is a universal negative statement. In fact it is a particular negative statement.

Hrmm... I did jump to that conclusion. I follow his argument later where has says:

The key to the negative message of the statements can be expressed in the phrase "not all," which does not mean the same as "none"; it translates as "some." ... What the statement is saying, then, is:

Some dogs are not mongrels

Hrmmmm....

But the original statement was not "not all," but "all .. not" and I am puzzled then about how one can ever write a univeral negative statement. What is the universal negative form for this example? No dogs are mongrels expresses the idea but isn't a negative statement. The opposite seems to be to be the All ... not form which we are told isn't universal.

I'm confused.