Statement Negation (pg 5-36-37)

[Toby]

Hello!

I have several questions about the Statement Negation drill from the Lesson 5 homework of the Live Online Course. My first question has to do with language. As I was doing this drill, I noticed that the language changes from absolute terms to more vague terms. For example, in number 5, "Beatrice will not score above a 90 on the biology exam" is negated to "Beatrice could score above a 90..." Originally, I negated this example to be "Beatrice will score above a 90 on the biology exam." Is my negation too strong? If so, why does the strength/absoluteness of a sentence's language change when we logically negate it?

My second question has to do with #7. I originally logically negated the sentence to "Some one other than Henry knows..." The book states that the correct logical negation for this sentence is "other people besides Henry know..." Is saying "some one" an incorrect negation? On a similar note, is the phrase "not always" the logical opposite of "sometimes"?

Finally, I have a broader question. Should I memorize a list of logical opposites in order to prepare for Assumption questions? If so, where could I find a substantial list of logical opposites?

Thank you so much for all of your help!

[Alexandra Ruby]

Hi Toby,

As you might recall from Lesson 2, there is a difference between a logical opposite and a polar opposite. The drill on 5-36 incorporates the concepts of the Opposition Construct (TM) as explained in L2.

With respect to question #5 on page 5-36, the logical opposite of 'will not' is 'could,' rather than 'will.' More specifically, in logical terms, 'could' is the opposite of 'cannot' or 'will not,' because it includes all other truth possibilities including 'will.' 'Will' only covers two possibilities; either Beatrice will or will not score above 90. It does not account for the fact that she could score over 90, or perhaps below 90.

With respect to number 7, you are correct that 'someone' is the logical opposite of 'no one' and it might be correct if the statement read: "No one knows the combination to the safe." Here, however, the statement is that "no one except Henry knows the combination to the safe" and the logical opposite of 'except Henry' is 'other people besides Henry' which encompasses more logical possibilities than 'someone.'

As for your remaining questions, if you go back to pages 2-1 through 2-3 in Lesson 2 you will find a good review of oppositional subjects with respect to time, space, and quantity. For example, to answer your question, 'not always' is the logical opposite of 'always,' whereas 'sometimes' is the logical opposite of 'never.'

Hope this helps!

[Toby]

Thank you so much for your help.

[ilovemydog]

Hi Powerscore,

I have a question in this section, as well.

For questions 4 and 9, I noticed that the negation became "even if" for the "unless" in 4 and "if" in 9.

Is this the logical opposite wording that I should note to myself when these words come up?

Originally for 4, I put "Happiness may not be impossible unless we profess a commitment to freedom."

I'm having trouble understanding if this still means the same as what Powerscore's answer is (Ans on 5-120).

For 9, I put "If you do not catch the five o'clock train, you may not be able to make it in time."

This, I had lots of difficulty because of the two-parts. I wasn't sure if both has to be negated or only the first part.

Can you clear up on this too? Sorry for so many questions all at once. I want to get it right before I move on!

Thank you

[Francis O'Rourke]

Hi ilovemydog,

Double check the answer key on number 9. The negation provided on page 5-121 does use the phrase "even if."

Is this the logical opposite wording that I should note to myself when these words come up?

"If" and "even if" are not the elements that negate conditional statements. To negate conditional statement, we express the idea that the necessary condition might not happen, even if the sufficient condition occurs.

So in number 4, the negation of the original necessary condition "Happiness is impossible" is "Happiness may still be possible." In number 9, we negate the necessary condition "You might be able to make it in time" by stating that even if the sufficient condition occurs, it is not true that you might be able to make it in time, or more simply "you will not be able to make it in time."

Originally for 4, I put "Happiness may not be impossible unless we profess a commitment to freedom."

That is effectively equivalent to the provided negation on page 5-120. We chose to rephrase the "unless" clause, since it is somewhat more difficult to interpret statements that begin with "unless." You can review pages 2-13 and 2-14 if you are having trouble understanding why the answer provided and your negation are similar. It sounds that you understand this though!

This, I had lots of difficulty because of the two-parts. I wasn't sure if both has to be negated or only the first part.

Can you clear up on this too?

I already gave an example of this above. To clarify though, when you are trying to negate a conditional statement, you want to express the idea that the sufficient condition does not guarantee the necessary condition, or that the necessary condition does not have to follow from the sufficient.

Put a bit more formally, we can say that the negation of If A occurs then B must occur is Even if A occurs, B might not occur, or A occuring does not guarantee that B occurs.

Let me know if this clears up things for you, or it you have any other quesitons!