NEGATIONS

The negation of a statement is what we get when we precede it by the operator “It is not the case that...” The latter is a truth-functional operator, symbolized by the logical negation symbol, ⁱ-∣^,.

(1) I can HEAR Atlantis full of cheer.

If we symbolize this by H, then its negation -∣H would symbolize any of the following variants:

(2) I can not hear Atlantis full of cheer.

(3) I can’t hear Atlantis full of cheer.

(4) It is not the case that I can hear Atlantis full of cheer.

(5) It is false that I can hear Atlantis full of cheer.

(6) It is untrue that I can hear Atlantis full of cheer.

(2)-(6) are all examples of negative statements. As stated in the previous chapter, our convention is that upper case letters symbolize positive assertions only, so that we must usewhen symbolizing negative statements. As we also saw, no parentheses are used betweenand the statement it operates on. Thus if M symbolizes the statement “I MIND,” and S “SIX turned out to be nine,” the statements below are symbolized as follows:

On the other hand, parentheses are always understood as occurring whenever the four binary operators join statements into compounds, even if they are not explicitly written. Thus the formula -³ (S → -∣M) symbolizes

(10) It is false that I don’t mind if six turned out to be nine.

4.1.2