Logical Negation: Identifying What to Negate in a Sentence

When negating a sentence, how do you know what specific word you need to negate if it’s a long and complicated sentence?

Students often ask this question, and it’s one that entails a more in-depth response than you may be expecting. We cover this topic in the Logical Reasoning Bible, Chapter 11, in the discussion of the Assumption Negation Technique™. However, even in such a comprehensive discussion, it’s impossible to formulate categorical rules about “which word” to negate in a statement. This section gives an overview of the concept of Logical Negation and how to negate categorical propositions (e.g. all A are B, some A are not B, etc.) and conditional statements (A ➡ B, etc.).

Identifying What to Negate

Because of endless possible variations in syntax—including coordinating conjunctions, phrases in apposition, different forms of negation, words to qualify degrees of likelihood, etc.—it would not be prudent or accurate to attempt to establish a rule that would apply in every situation because there would doubtless exist exceptional cases to confound these efforts. However, there is a concise phrase you can add to introduce any statement to convey the concept of its negation; to wit, you can add “It is not true that…”

Following this phrase, you must include the entire statement you wish to negate and only that statement. For instance, given the conditional statement:

• “Unless Jim reads me the riot act, I’m not going to his stupid shindig.”

It would not work just to say:

• “It is not true that I’m not going to his stupid shindig.”

Why? Because this would fail to encompass the entire conditional. To use this phrase correctly, you would need to structure your negation thus:

• It is not true that unless Jim reads me the riot act, I’m not going to his stupid shindig.

In other words, it could be possible for me to attend the stupid shindig without Jim reading me the riot act. Notice here that there’s a degree of translation required. You have to process the idea and express what the minimum possible expression of its falsehood would entail. This is the distinction we discuss in the LR Bible between polar opposition and logical opposition. For example, in the Bible, the logical negation of “sweet” is “not sweet” rather than “bitter” (the polar opposite).

Steps for Negation

With these ideas of translation, analysis, and logical negation in mind, the general steps for negation are as follows:

1. Express the idea you wish to negate in its entirety.
2. Imagine a condition, the minimum possible condition, the truth of which would contradict this idea.
3. Choose the verb, quantity expression, likelihood expression, or phrase that you would need to negate to express this contradiction.

Practice These Steps

The exercise that follows the above referenced discussion in the Logical Reasoning Bible is an excellent self-test of your proficiency with this process. Let’s take two examples to illustrate:

1. “Marcy reads more books every week than I’ve ever read in a year.”
2. For this statement to be false, I would have to read more books in some years than Marcy read in any given week.
3. My negation could be “Marcy does not read more books every week than I’ve ever read in a year” or “There has been at least one year in which I’ve read more books than Marcy read in one week” or “There is a week in which Marcy read fewer books than I read in some years.”

1. “If Josh picks up the tab for us this evening, I won’t mind paying for dinner tomorrow.”
2. For this statement to be false, it must be possible that even if Josh picks up the tab for us this evening, I still might not want to pay for dinner tomorrow. In other words, Josh could pick up the tab tonight, and tomorrow I still won’t think I should pay for dinner.
3. My negation could be “Josh could pick up the tab for us tonight, and I might not want to pay for dinner tomorrow.”

To sum up, negation requires an understanding of the idea a statement wishes to convey and then the idea of what would be inconsistent with this idea. As rules of thumb, it’s generally safe to negate the…

• Primary verb
• Quantity word
• Likelihood word
• Necessary condition in a conditional statement

Although rules of thumb are handy (so to speak), you’re still the boss here. Follow the steps outlined above to assess the meaning. Even the nearly universally applicable phrase “It is not true that…” still requires some degree of analysis on your part, and this analysis is the crucial step for success with negation.