Difference between "some are not" and "not all"

Burden.of.Floof

So, I was just listening to the Powerscore Podcast (the first episode on causality), and Dave said the following: If you want to ask a series of confusing questions about concept differentiation, ask someone to describe the difference between some are not, and not all.

Well Dave, I am confused. They seem like the same to me! The only thing I can think of is this:

Some are not implies a positive amount, there has to be at least 1 of a group that is not like any of the other members.
But not all can mean zero: for example if you say that not all of these apples are green, it could be the case that none of them are green.

The problem that I run into with this, is when I think about equivalent statements:
Not all of the apples are green
Some of the apples are not green.

These are logically equivalent.

Does anyone else have some insight? Maybe he just said it offhand and there really is no difference.

Jordan Johnson

I can't remember if you have The Loophole, but "Some" and "Not all" are not equivalent.

All is 100% ; "Not all" is a range that includes 0-99%
None is 0% ; "Some" is a range that includes 1-100%

So while the two modifiers have a large overlap, they actually aren't logically equivalent.

Hope that helps!

Burden.of.Floof

Thanks for your reply @"Jordan Johnson" I appreciate the help! Yeah I definitely understand the difference between just plain some and not all, it was the "some are not part that was throwing me off. Because when you add in the not, they technically should be equivalent, like the examples I gave with the apples.

canihazJD

@"Burden.of.Floof" The "not" in "some are not" is arbitrary.   X←s→/Y could mean the same thing as X←s→Z (or ❤️, or ♤, or △, or 🍆) if we decide it to be so. In other words, you made those two statements equivalent by applying the same variable. But the difference between the two is still what both of you indicated... in their abstract operation.

Burden.of.Floof

Aaaah got it @canihazJD. I was taking what he said a little too literally haha. Thanks!

Burden.of.Floof

or... too specifically? Either way, I understand now.

Glutton for the LSAT

Symbolic logic TA here. In brief: "Not all" and "some are not" are logically equivalent.

The symbolization of "not all" is a negation of a conditional. This is equivalent to a conjunction in which one conjunct is negated.

Example: Not all humans are males
~(H-->M) = H and ~M

Another way to think about it: If you're saying not all humans are males, you're saying there is AT LEAST ONE human and that human is not a male.

clear227

"Some are not" and "not all" are logically equivalent in first order logic. .