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Related Discussions
"Some not...." "Not all"
jennyleejh
Alum Member
I'm looking at the question stimulus and one of the wrong answers and wondering if these two mean exactly the same thing:
"Not all skilled artists are famous"
"Some skilled artists are not famous"
And if so.. could someone kindly explain the logic behind it?
Here are my thoughts so far:
I understand that Not all ranges from (0-99)
and that Some (1-100) but since it is Some..not (subtracting from 100 range, (100-100), (100-1) --> (0,99)?)
so.. number wise.. they seem to indicate the exact same range?
Comments
I am by no means a definitive authority on this but the way I see it is:
They are close but not the same.
If you're looking at only skilled artists who are not famous
"Not all skilled artists are famous" becomes "at least one skilled artist is not famous"
slightly different from
"Some skilled artists are not famous"
which implies at least two.
If all skilled artists equaled 100
Some is an amount between 2-49
Not all is an amount between 1-99
I think
Edit: I mistook the question
Some A are not B is the logical equivalent to not all A are B.
Which is not the same thing as the logical negation of some, which has a potential range of 0-99 in a 0-100 world.
Check video a bit over a minute in for logical negation. https://7sage.com/lesson/advanced-negate-some-statements/
@Jane1990 thanks for the tag, helped clear this up for me!
They do mean the same thing. Your analysis in the OP is correct.
@Bomhillz I think what you are referring to is "none" as the logical opposite (negation) of "some". "Some are not" is the negation of "all", not of "some".
I think @jennyleejh is correct in that "some are not" translates to 0-99, as "not all" translates to 0-99.
They are the same thing.
2-49 (X) 1-100 (O)
1-99 (X) 0-99 (O)
It's so interesting because when you take it into lawgic they technically say the same thing.
Not all skilled artists are famous
not [S->F]
which can be written as
S and /F
Whereas,
Some skilled artists are not famous
S some /F
which can also be written as
S and /F
But I think if you want to get more nuanced, I think of "not all skilled artists are famous" as just saying that's not 100%. It's not the case that every single skilled artist that exists in the world is famous. We're denying that possibility, which would be 0-99. Of the skilled artists in the world, 0-99%, of them do not belong in the group famous.
"Some skilled artists are not famous" implies that there's at least one skilled artist that's not famous. We know of at least one skilled artist that's not famous. For this one, I think you could have a range of 1-100. It could be the case that there's only one or possibly all are not famous. Although the grammar use of "skilled artists are" could imply, as Garth said, at least two.
I think they're both negations of the idea "all skilled artists are famous." The difference in the english, for me, is that in the first set we're denying that skilled artists belong to the group famous. Whereas in the second set we're explicitly saying that at least one skilled artists belongs to the group not famous. Which gets into the whole territory of binary cut of the term famous and what our common sense understanding of that cut entails versus the logical cut. But yes same thing.
Think of it this way, you're pointing to a(t least one) skilled artist on instagram and going "hey you, you don't belong in the group of famous artists with Van Gogh." That's what both are saying.
You are correct, that they essentially mean the same thing.
"Not all skilled artists are famous"
This means roughly, of all the skilled artists, at least 1 of them is not famous. If you take out the "not", you would have just "all skilled artists are famous". That's clear. The first word is just negating "all", so it is like saying "not-all skilled artists are famous". Meaning, at least one of them is not famous. This actually could also (in LSAT world) mean that no skilled artists are famous. All we know is that at least 1 isn't. But if no skilled artists are famous, the original statement would still be true.
"Some skilled artists are not famous"
Some is also a word that means at least 1. That's all we know. At least 1 skilled artist is not famous. Again, not grammatically but in LSAT world, some can also mean all. Because if you discovered that all skilled artists are not famous (or said another way, no skilled artist is famous), it would still be a true statement to say that some skilled artists are not famous. "Some" is contained within the word "all".
Hope that helps!
(And @"gerth.brooks" - I think your analysis is correct only if we're talking about English/American grammar, not the logic that LSAT uses. The relevant lessons here are in the "Some and Most Relationships" section, particularly "Some Statements Meaning")
This matter is complicated—a bit— by the fact that “not all” and “some” don’t mean exactly the same thing within classic first order logic: the latter requires that the “restrictor” of the quantified (i.e. “skilled artists”) be non-empty, whereas the former does not require this. That is “not all skilled artists..” doesn’t entail (though it may implicate) that there be any skilled artists at all, whereas “some skilled artist...” does entail that there is at least one skilled artist.
I don’t think this matters for the LSAT though as I think the test presumed that all noun phrases will denote sets that are non-empty and so you can make the equivalence above. With that caveat, I above explanations are on point
@FixedDice @"Leah M B"
Hmmm maybe this is part of the cause of my LR woes
Reviewing now
Thank you so much everybody for sharing your thoughts
Loving the fruitful discussion!
@"Leah M B" your explanation in terms of "at least 1" really cleared things up ! Really helps since I was struggling to explain the lawgic in words..
But I have one question - reading @acsimon 's post about the little caveat confused me a little because he says that "some" requires "skilled-artists" to be non-empty. I understand that "some" does indicate number starting from 1, but isn't the case different from "some... not"? Just a little clarification would be tremendously helpful!
I believe @acsimon was looking at it from a different perspective, and in one of those phrasings, there wouldn't even have to be any skilled artists at all. But we aren't talking here about the existence of skilled artists, but whether or not they are famous.
I understand the point he was making there, but also I don't think that LSAT writers really go to that level.
ah righty ho that clears things up! Thank you so much. Now that I understand the logic behind it, I can now comfortably memorize that "not all" and "some.. not" are the same!