Translating “Not all S is P”

Mr. Nance,

In Quiz 12 #1, students are to translate the statement into standard categorical form. Is this equivalent?
Original: Not everybody likes ice cream.
Teacher guide answer: Some people are not ice-cream likers.
My student’s answer: Some people are ice-cream likers.


Unfortunately, your student’s answer is not correct. Here is why.

To say “Not everybody likes ice cream” is to give the contradiction of “Everybody likes ice cream.” These two statements must have opposite truth values: one true, one false. Do you see it? Think of it this way:

Bill:  Everybody likes ice cream
Stu: Not everybody likes ice cream

In this disagreement between Bill and Stu, one of them is right, and one of them is wrong. If Bill’s statement is true, Stu’s statement is false. But if Stu’s statement is true, then Bill’s statement is false. This is therefore the relationship of contradiction. Stu must mean the contradiction of Bill’s A statement, which is the O statement, i.e. “Some people are not ice cream likers.” But your student’s answer claims that the negation of the A statement is the I statement.


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