Statement Negation Drill

[AspiringLawyer]

I am currently completing the Statement Negation Drill in Lesson 5 Homework.

Why is it that when we negate a sentence the language is not absolute? For example, the original statement from #6 is “The sun always rises.” My instinct in negating resulted in “The sun does not always rise” because the logical opposite of always is not always. However, the answer key lists the proper negation as “The sun might not always rise.” Where does the “might” come from?

Another example is #7: “No one except Henry knows the combination to the safe.” My instinct in negating resulted in “Some people beside Henry know the combination to the safe.” Whereas your answer key lists the correct negation as “Some people beside Henry may know the combination to the safe.”

Thank you in advance for your insight.

[Francis O'Rourke]

Your wording of the negation - “The sun does not always rise” - is extremely close to the logical negation of the original statement. It is so close that the difference in word choice between "does not" and "might not" will almost certainly not impact your performance on this exam or your understanding of logical negations. For that reason, I would suggest that you not worry about it.

In case you are curious however, here is the difference. "The sun might not always rise" denies the truth of the statement as a statement. It basically means It is not necessarily true to claim that 'the sun always rises' is true. It may turn out to be true that the sun will or will not always rise. There is a possibility that the sun will not always rise.

The statement “the sun does not always rise” means that it is definitely true that on at least one occasion the sun will not rise or has not risen.

Similarly with drill question #7, the difference is tiny and exactly the same as the difference in the wordings above. As a practical matter, there is no difference between these two word choices.

[StephLewis13]

Hello,

I understand the reasoning above, but I am working on the Statement Negation Drill in the LR Workbook 2020 and have a related question.

1) Number 3 Statement "Only one witness was present when the robbery took place"
Number 3 Negation "Not only one witness was present when the robbery took place"
*The opposite of "only one" is "not only one", however, when examining Number 4, the same principle is not true…

Number 4 Statement "If Smith gets elected, he will serve only one term as mayor"
Number 4 Negation "If Smith gets elected, he might not serve only one term as mayor"

*I do not understand why the same use of the phrase "only one" creates two different results when negating the phrase?? They are both used in the necessary condition, and yet Number 3 (not only) has a much more certain tone than Number 4 (might not)...

Similarly, I do not understand the difference when comparing Number 9 and Number 10 of the Negation Drill
2) Number 9 Statement "Early to bed and early to rise makes a person healthy, wealthy, and wise"
Number 9 Negation "Early to bed and early to rise does not necessarily make a person healthy, wealthy, and wise"

Number 10 Statement "New methods of warfare led to increased casualty rates"
Number 10 Negation "New methods of warfare did not lead to increased casualty rates"

*Again, Number 10 has a level of certainty (did not) while Number 9 is less certain (not necessarily), and yet, they are both discussing causality…. please assist! Thank you.

[StephLewis13]

^^ The only thing I can differentiate between the phrases & their use is the use of past tense versus present/future tense???

[KelseyWoods]

Hi Steph!

Glad to see you're closely reading and analyzing these things! The difference is sort of related to tense. But it actually has more to do with rules vs. not rules.

First, even though the Number 3 statement has conditional terms like "only" and "when," it's not really a conditional statement. Conditional statements are rules. Having the sufficient condition always indicates that the necessary condition must occur. If X happens, then Y happens. Y only occurs when X occurs. If you look closely at statement Number 3, it isn't really a rule. It doesn't say that when there is a robbery, there is a witness. It's only talking about one specific robbery. Also the way "only" is used is not in a way that indicates that something is necessary, rather it just indicates that the number of witnesses is small. You could replace it with a word like "just" -- "Just one witness...". This is not a rule that can be applied to other robberies or that tells us what would happen in a specific eventuality. It's telling us about one thing that did happen. There was a robbery. And there was one witness. Those are both straightforward facts and not a conditional statement. Thus, to negate it, we can focus on the quantity terminology. "Only one" is a phrase to indicate the quantity of witnesses. So we negate it to say "Not only one."

To negate actual conditional statements like we have in Statement 4, we just say that the sufficient condition can occur without the necessary condition. A conditional statement says that if the sufficient condition occurs, the necessary condition must occur. To negate that we just say that if the sufficient condition occurs, the necessary condition doesn't necessarily occur. More info on negating conditional statements is here: https://blog.powerscore.com/lsat/bid-29 ... -the-lsat/

There's a similar explanation for the difference between Number 9 and Number 10. Number 9 is more of a rule--in this case it's a kind of causal rule because something is making--or causing--something else occur but because it's a rule, it is also conditional in nature. It's basically saying, when this cause occurs, then this effect occurs. If you are early to bed and early to rise, that will make you healthy, wealthy, and wise. Because it's a rule, negate it in the same way that you would negate conditional rules as described above: you can have the cause without the effect. Being early to bed and early to rise will not necessarily make you healthy, wealthy, and wise. The negation of "A causes B" is "A does not necessarily cause B."

Number 10 is not a rule because it's just talking about something that has already occurred. It's not a causal rule, it's describing one causal event. There were new methods of warfare and there were increased casualties. But it does not say that every time we have new methods of warfare there will be increased casualties. It only applies to this one war that has already occurred. So negating it is more straightforward. The negation of "A caused B" is simply "A did not cause B."

Ultimately, as Francis noted above, the difference between a "might not" and a "not" is not going to be all that significant and is unlikely to affect your performance. But it's good to be analyzing these things closely and asking questions!

Hope this helps!

Best,
Kelsey

[StephLewis13]

Hi Kelsey,

Yes, it did. Thank you!