Talk:Geometry/Inductive and Deductive Reasoning

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NOT: If a statement is preceded by "NOT," then it is evaluating the opposite truth value of that statement. The symbol for "NOT" is For example, if the statement p is "Elvis is dead," then ¬p would be "Elvis is not dead." The concept of "NOT" can cause some confusion when it relates to statements which contain the word "all." For example, if r is "¬". "All men have hair," then ¬r would be "All men do not have hair" or "No men have hair." Do not confuse this with "Not all men have hair" or "Some men have hair." The "NOT" should apply to the verb in the statement: in this case, "have."

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I suggest that someone review this definition of NOT.

The truth-tables at the bottom of the Wiki page indicate that the negation of a true statement is a false statement, and vice versa. This is consistent with notions of classical deductive logic. Yet the above-quoted definition of NOT seems to contradict it.

The definition states that the negation of the proposition p "All men have hair" is "All men do not have hair." Assume that some, but that all, men have hair. In this case, both the proposition p and its negation are false. This contradicts the truth tables.

In contrast, if "All men have hair" is false, then it seems intuitive to conclude that "NOT all men have hair" (or "Some men do NOT have hair") is true. That is, the NOT should apply to a proposition as a whole, not to the verb of the proposition in particular.