Logical Negation Forum

[rbrown0824]

Does anyone currently have a guide or a link that covers logical negation (e.g. A successful person is a smart person vs. A successful person is NOT a smart person)?. I have the LRB and Manhattan 2nd edition, but I'm not following the more difficult ones. Any help would be appreciated. Thanks

[BPlaura]

Here's a quick and dirty summary of negation:

When you negate a statement on the LSAT, you're not giving the opposite of your original statement; you're simply saying that that thing is not the case. In fact, one way of negating a statement is to add "It is not the case that..." in front of it.

For instance, if your statement is "All dogs go to heaven," you could negate it by saying "It is not the case that all dogs go to heaven." Where you might run into trouble is with the interpretation of that statement. Notice that we're not saying that NO dogs go to heaven - just that not all of them do. So, we could rephrase our negated statement to say "Some dogs do not go to heaven."

When you're negating a conditional statement, you're just saying that there is not necessarily a relationship between the sufficient and necessary conditions. Let's say you're negating the statement "Only LSAT instructors are good-looking."

good-looking ---> LSAT instructor

You might think that you'd negate that statement by saying "if you're good-looking, then you're not an LSAT instructor." But you'd be wrong! We're not trying to say that there are no good-looking LSAT instructors; we're simply saying that there is no known relationship between either of those conditions. Being good-looking is not a guarantee that someone is an LSAT instructor, and one does not have to be an LSAT instructor in order to be good-looking. Essentially, we're crossing out the arrow:

good-looking -/-> LSAT instructor

meaning, again, that there is not necessarily any relationship between those two qualities.

I don't have either of those books so I can't take a look at the more difficult examples you referenced, but if you want to post any examples, I'd be happy to walk through them with you - sometimes it's just helpful to hear things explained in a different way, ya know?

[rbrown0824]

My issues were on those questions that contained words such as, "some" and "only." There was a statement, "some people did not ingest mercury" or "only mice eat cheese." I understand the concept of placing, "it is no the case" before the statement, but my issue arises with the interpretation.

[Christine (MLSAT)]

My issues were on those questions that contained words such as, "some" and "only." There was a statement, "some people did not ingest mercury" or "only mice eat cheese." I understand the concept of placing, "it is no the case" before the statement, but my issue arises with the interpretation.

A lot of people get confused when negating statements with 'some', 'always', and 'never'. Fundamentally, this is actually related to what BPLaura was talking about above regarding conditionals, but let's break it out for a second.

To negate "sometimes", it might be tempting to say "sometimes not". So you might think that "sometimes I wear high heels" would negate to "sometimes I don't wear high heels". But it doesn't! Those two statements aren't necessarily contradictory!

If I tell you that I sometimes wear high heels, what would you need to know to call me a liar? You'd need to know that I never wear high heels! So, that shows us that "never" negates "sometimes".

Now, alternately, if I tell you that I sometimes don't wear high heels, what would you need to call me a liar? Well, now you'd have to show that I ALWAYS wear them to call me a liar. So, "always" negates "sometimes not".

We can think about it in the reverse too: If I claim to ALWAYS wear high heels, all you have to do to call me a liar is prove that sometimes I don't wear high heels. And if I claim that I never wear the blasted things, you just need one instance of my wearing them to call me a liar.

So, "some people did not ingest mercury" would negate to "all people ingested mercury".

For words like "only", you could turn in into conditional notation first (If eat cheese --> mouse) and apply BPLaura's comments above (If eat cheese -/-> mouse, or "if eat cheese, then not necessarily a mouse"). You can also think about it as inserting the 'not' before the word 'only'. So, "not only mice eat cheese", or "it's not only mice that eat cheese." In other words, there are other things, other than mice, that eat cheese.

Thoughts?

[rbrown0824]

Thank you so much for your help!! That makes sense, but why is it "All people did ingest mercury" as opposed to "No people did not ingest mercury?" I'm sure that they are effectively the same sentence, but how did you know that it was okay to reduce your version to an easier translation?

Additionally, how would I rectify two "not's" in a sentence, e.g. Administering a placebo is not ethically justified if that treatment is not prescribed by a doctor. I was confused on whether to change the first, the second, or both. And I am also unsure about the rules that govern changing "and" to "or." When is it okay to make this change, and when should I leave them? In the statement "Tony lives without bread or water" why is it not "Tony does not live without bread and water?" Lastly, with the statement, "The prettiest houses are always painted white." If I say, "Not all the prettiest houses are painted white" is that the same as saying, " Some of the prettiest houses are not painted white?" And is saying that something is "not unlikely" the same as saying that it "is likely?" Sorry for all the questions, I'm just wanting to make sure I'm understanding things properly.