#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

# Questions about Logical Opposites, i.e negation

Member
60 karma

If I negate "all", it becomes "not all." But doesn't "not all" imply two distinct possibilities, namely, "some" and "none"? If I negate the statement "all turtles are slow" as "it is not the case that all turtles are slow." Can't it either mean "some turtles are not slow" (there is at least one turtle that is NOT slow out of all the turtles on this earth) or "none of the turtles are slow" (they are ALL FAST AND FURIOUS BEASTS.) When I negate a conditional statement in LSAT, should I be mindful of these two distinct possibilities?

Thanks.

Show Related Discussions

• #### Logical negationThe logical negation of "At least some rhinoceroses whose horns are periodically trimmed off will be able to attract mates," is "none of the rhinocer…

• Member Sage
2111 karma

When you negate ALL you allow for every possibility except all.

Succinctly you mentioned it perfectly that Not All X is equivalent to Some are Not X.

Which allows for All are Not X

• Member
60 karma

Thanks for the reply. What prompted me to ask this question was LSAT 46 - Section 3 - Question 15 (Necessary Assumption Question). The correct answer for this question was "It is to the advantage of some individuals that they be concerned with contributing to societal good."
I skipped this answer choice b/c when I negated the statement in my mind, I translated it as
"It is NOT to the advantage of some individuals that they be concerned with contributing to societal good." And so, I understood it as meaning that "For at least one individual, it is not advantageous for him/her to be concerned with contributing to societal good." This negation didnt seem to affect the argument. After I was reviewing this question it came to my mind that the negation of the statement could also become "It is advantageous for nobody to be concerned with contributing to societal good." in which case, it would most definitely wreck the argument. Does the first interpretation of the negation statement wreck the argument too? (i.e "For at least one individual, it is not advantageous for him/her to be concerned with contributing to societal good.")

btw, I am reading your tips for 170+ and found it to be very insightful. special thanks.

• Member Sage
2111 karma

This question stresses the importance of fully understanding what the conclusion is saying. It mentions that promoting a certain view CAN be damaging to an individual (ie there is some individual for which the promotion of the view is damaging) in order to attack that you must show that this is in fact not the case. That no individual is damaged by this.

B attacks from the perspective of advantage rather than damage which makes it especially tricky but the idea remains you have to show that nobody benefits from the promotion of the view. So it is your 2nd interpretation that counts.

Quick rule of thumb when you are negating is try to place the 'not' in front of intersectional modifiers first (all, some, most) the negation of some is none.

Thanks for the kind words Moose. Are you out on the island? I'm a west coast guy myself!

• Member
60 karma

Thanks for the explanation. My id is Nanaimo because I like Nanaimo bars xD I live in Ontario. Nice to meet another Canadian tho!