Negation for Necessary Assumption Questions

[jaf51200]

I'm a little confused with the negation technique. The Manhattan L.R book basically has two rules regarding negation. 1) If there is no modifier, then negate the central verb. For example: "I walk to school" becomes "I did not walk to school" 2) If there's a modifier in the statement then negate that. For example: "John always walks to the beach" becomes "John does not always walk to the beach."

However for pretest 28,S3, Q16, the book negates answer choice A the following way: "some people in Beethoven's time did not ingest mercury " to "everyone in Beethoven's time ingested mercury".

In the above example the modifier and the verb were BOTH negated. Why is that?
Can you also provide some advice or pointers on this negating technique. It such a powerful weapon to have when stuck between choices or just to confirm an answer, but i'm not entirely confident with how to properly negate within the confines of logic.

Looking froward to your response.
Thank you!

[tommywallach]

Hey Alexander,

I hate to say it, but it's just logical. If the sentence says:

Some people don't eat chicken, it inherently implies that some people do. So negating it as "Some people do eat chicken" doesn't actually change the meaning.

The negation would be ALL people eat chicken, because it's the logical opposite.

Hope that clears it up a bit. If you want a rule, I think you could say: "Some people don't do X" will always negate to "All people do X".

-t

[jaf51200]

Thank you!

[samiraa180]

If I were to negate the right answer choice as was suggested in the thread, it would mirror the evidence in the stimulus: " Since mercury was commonly ingested in Beethoven's time..." And that would be considered a premise booster, right?

I get why B is the right answer, I am confused why negating the right answer mirrors a clause in the argument.

[ohthatpatrick]

The negation of "some people in B's time did not ingest Mercury"
is
"EVERYONE in B's time ingested Mercury."

That fact doesn't quite 'mirror' what we were already told in the argument.

As you said, the original premise said that "Since mercury was commonly ingested in Beethoven's time to treat venereal disease"

Knowing that is different from knowing that EVERYONE in B's time ingested Mercury.

If only people with VD ingested mercury, then knowing that someone had ingested mercury would be strong evidence that that person had VD.

But if everyone in B's time ingested mercury, then knowing that someone from B's time had ingested mercury wouldn't allow you to draw any special conclusions about whether that person had / didn't have VD.

To answer the original textbook question:

I'm a little confused with the negation technique. The Manhattan L.R book basically has two rules regarding negation. 1) If there is no modifier, then negate the central verb. For example: "I walk to school" becomes "I did not walk to school" 2) If there's a modifier in the statement then negate that. For example: "John always walks to the beach" becomes "John does not always walk to the beach."

However for pretest 28,S3, Q16, the book negates answer choice A the following way: "some people in Beethoven's time did not ingest mercury " to "everyone in Beethoven's time ingested mercury".

In the above example the modifier and the verb were BOTH negated. Why is that?

All that's being negated in choice (A) is the modifier "some". Negating "some" gives you "none".

So (A) reads "no one in Beethoven's time did not ingest mercury".

As you can see, that's a double-negative, so to clean it up we would say "Everyone in B's time DID ingest mercury."

If we had an idea like "some oranges were rotten", then when we negate it we would get "no oranges were rotten".

Hope this helps.

[samiraa180]

Yeah, that clarifies things, but should I take the absolute statement like "never" or "none" and say "all" or qualify it and say "sometimes". Also, I'm not sure how to approach words like "most" or the "majority". Do I take the minimum?

[ohthatpatrick]

The catch-all technique for negating is just to preface the answer choice with "It is NOT true that ____ ".

But it's also helpful to memorize some of the common translations:

Negating 'all' means 'not all'. (you're going from 100% to 0-99%)

Negating 'none' gives you 'not none', which is the same as 'some'.
(you're going from 0% to 1-100%)

Negating 'most' gives you 'not most', which is basically the same as 'few', although 'few' means less than 50% and 'not most' would technically include 50%.
(you're going from 51-100% to 0-50%)

Although, really, if you see 'most' in a Necessary Assumption answer choice, you should probably just get rid of it. It's almost always wrong. Essentially you're asking yourself whether the argument hinges on something being 50% vs. 51%.

That's almost never a distinction the author needs to make.

This is part of why we always say that strong language is particularly dangerous in Necessary Assumption.

When you negate something strong like 'all' or 'none', you get really weak ideas like 'not all' or 'some'. And remember, negating the correct answer should MASSIVELY harm the argument. It's hard for really weak ideas to do massive harm.

Meanwhile, we LOVE weak, watered down language in Nec. Assump because negating those turns into powerful ideas.

negate "some" and now you have NONE.
negate "can" and now you have CAN'T.
negate "at least sometimes" and now you have NEVER.
negate "it is NOT the case that [this potential objection] would be true" and now you have IT IS THE CASE THAT [this potential objection] IS TRUE.

While we're talking about negating, the one fringe case that occasionally pops up is how/whether to negate a conditional.

If we had an answer like
(A) Whenever students study, they improve
we would not negate either of those ideas, we would just say "it's not true that whenever students study, they improve."

Essentially the negation is saying that there is NOT some inflexible constant connection between those two ideas.

Rather than get bogged down in trying to negate a conditional, you should simply ask yourself if the conditional provides a missing link the author was assuming. Make sure that the language of the argument is strong enough to justify saying that the author assumed there is ALWAYS this CONSTANT connection. Most conditional statements are going to be wrong because they're too extreme.

(Whereas on Sufficient Assumption, the opposite applies. Our task is to completely prove the conclusion so we want strong conditional ideas that leave no room for exceptions.)

[hakopis]

Are there any reasonable differences between
1) Arguments that depend/require etc. and
2) Conclusions that depend/require etc.?

If so, what changes/modifications should be made to our strategy?

As of now, I weed out 3/5 wrong answer through POE and use the negation technique for the last two. I also try to be aware of Strong/Weak language (Correct answers are generally not strong; similar to MBT) as well as whether an answer is too broad or not.

Thanks!

[ghorizon09]

This is how I arrived at the correct answer using negation:

Some people (negated to no people, or no one) in Beethoven's time did not ingest mercury.

The statement "No people DID NOT ingest mercury" can be rephrased to: ALL people ingested mercury.

If all people ingested mercury in Beethoven's time then his having mercury traces in his hair proves nothing. This destroys the conclusion.