Question with Negating ALL Statements

NerfThis

I've repeatedly watched the lesson titled "Advanced: Negate All Statements" and in the video the statement used is:

"All cats are pretentious"

JY states there isn't a word that is a direct opposite of "all" so he uses "some... not..." to directly contradict the statement into:

"Some cats are not pretentious"

.

Here's my problem with this.

If "some" means at least one but not all. How is it that the logical opposite of "All cats are pretentious" is "Some cats are not pretentious"??

If we're dealing with the group "cat" and "things that are not pretentious" wouldn't the statement "some cars are not pretentious" leaves the possibility that ZERO cats are not pretentious? Which directly contradicts the definition of some which is at LEAST one but not all?

I'm confused to why he doesn't just use "not all" as the contradiction to "all" which would leave the range (0-99) which would make things simpler by not directly going against the definition of "some"

Michael.Cinco

I think for teaching purposes keeping away from zero cats would drive the point home of logical vs polar opposites?

Some is also easier to work with in a logical context so when you think of what happens to the argument
some (vs not all) involves one less logical hoop to jump in your mind as you don't have to account for the zero possibility. So the negation may go faster.

I'm with you though if i negate all its always not all in my mind.

Princess

Hey! I feel like this was confusing for me too, so I went back to see how other people process it. So, we know that all is simply a dot that means 100%. Not all could mean 0-99.

Someone( I forgot to copy the username and have lost the website ) had posted the following on a video and it was really helpful:

This may help: if ALL is 100 on the line, then the logical opposite must be everything that is not 100. That includes the range of 0-99. In other words, it is NOT ALL.

Imagine someone says, “Not all of you will pass the LSAT.” Can 100% of people pass? No, because that would be everyone, and not all can pass. Can 99% pass? Yes, because that is not all. Could 1% pass? Yes, because that is not all. Could everybody fail? Yes.

“Not all will pass” is the same as “Some will not pass”, and that includes the possibility that everyone will not pass.

FixedDice

If "some" means at least one but not all.

A ginormous misconception here. "Some" encompasses "all" as well; it can range from at least one to all. Suppose there is a group of 100 entities; "some" denotes all possibilities ranging from 1 entity to 100 entities.

You may want to review the "some" lessons under "Some and Most Relationships."

How is it that the logical opposite of "All cats are pretentious" is "Some cats are not pretentious"??

The logical opposite of "all" (100) is "not all" (0-99). And both "not all" and "some not" mean the same thing: they denote scenarios where, in the hypothetical group of 100 entities, 0-99 entities possess a certain characteristic (or, in other words, 1-100 entities do not possess the said characteristic), whatever it may be. So the logical opposite of "all Cs are P" would be "not all Cs are P," i.e. "some Cs are not P."

If we're dealing with the group "cat" and "things that are not pretentious" wouldn't the statement "some cars are not pretentious" leaves the possibility that ZERO cats are not pretentious? Which directly contradicts the definition of some which is at LEAST one but not all?

Again, "some" can mean anything from one to all. And as explained in the previous paragraph, the statement "some Cs are not P" can mean that "all Cs are not P."

(For the record, "some Cs are not P" does not entail that "ZERO Cs are not P." "Zero Cs are not P" is equivalent to "all Cs are P," which is impossible per "some Cs are not P," or "not all Cs are P." See where you made a mistake?)

I'm confused to why he doesn't just use "not all" as the contradiction to "all" which would leave the range (0-99) which would make things simpler by not directly going against the definition of "some"

Like I said, "some not" is equivalent to "not all." It's just a matter of preference.