# Logic question for grammarians...or grammar question for logicians

Tricky!
However, when you switch to percents you are not stating the same thing anymore. As, in fact, you noted yourself but apparently didn’t see. That is, the topic switches off of German and onto quantity. Though the structure remains the same, the sentence you propose would, to me, be more like
The percentage of my German friends is not 100%, or as the rephrased OP’s question goes, Not all of my friends are german.

However, logically speaking, “all” doesn’t mean 100%, it means (using ^ for OR operator)
case1 ^ case2 ^ case3 ^ case4 ^… ^ casen != 1. In other words, not one of the cases is true. What you seem to propose is that “all” means “AND” operation, where only one case needs to be false for the whole thing to be false. This is, IMO, the rephrased sentence.

What we are restating here, grammatically, is one of DeMorgan’s logic theorems. Depends on where we semantically put the “NOT” operator. To wit:

!(A ^ B) = !A x !B
2)
!(A x B) = !A ^ !B

As we can see, where we put the not depends on how many individual cases need to be excluded before we come to a definitive truth valuation.

“All” means each and every, and so we would use the OR operator.

After rereading my post, I would like to scratch it from the record and simply state the following in its place.

All of my friends are not German.
(quantity) of my friends are (quality).
All of my friends are (quality).

Whether this quality be a negative or an affirmative is irrelevant (as irrelevant, in fact, as DeMorgan to the case). The quality of “not being German” applies to each and every friend. For this statement to be treue, not one of “friends” may have the quality “not German.”

This is opposed to
Not all of my friends are German.
(quantity) of my friends are (quality).
Not all of my friends are (quality). For this to be true, at least one must be German.

I am restating the AND/OR argument here, BTW. Forget DeMorgan, which would apply to Not All of My Friends Are Not German, an interesting case indeed.

After rereading my post, I would like to scratch it from the record and simply state the following in its place.

All of my friends are not German.
(quantity) of my friends are (quality).
All of my friends are (quality).

Whether this quality be a negative or an affirmative is irrelevant (as irrelevant, in fact, as DeMorgan to the case). The quality of “not being German” applies to each and every friend. For this statement to be true, all of “friends” must have the quality “not German.”

This is opposed to
Not all of my friends are German.
(quantity) of my friends are (quality).
Not all of my friends are (quality). For this to be true, at least one must be German.

I am restating the AND/OR argument here, BTW. Forget DeMorgan, which would apply to Not All of My Friends Are Not German, an interesting case indeed.

Man, if this double posts I’m gonna bow out of this thread entirely…