Negating "Most" when there is a binary cut?

jchanggoaway

Consider this original statement: "Most people are white." Its negation is: "It's not the case that most people are white." i.e. 0-50% people are white. Isn't this the equivalent of "Most people are not white"?

In contrast, given: "Most people are not white" Its negation is "It's not the case that most people are not white." i.e. 0-50% are not white. In this case, I know the negation is not equivalent to "Most people are white". It's not a binary cut here. Compared to the first statement, what changed? I'm not sure how to think about this.

ntrepanier5

I'm not really sure how to think about this either - it's certainly sending my mind through a loop - but thankfully, I've never seen a Most/Some question reach this level of difficulty on the LSAT.

beyondpossum

"0-50% are not white", i.e. "a minority are not white" seems to me to be logically equipollent to "most people are white". I'm missing any paradox that may be here.

beyondpossum

Oh wait, I see, the 50 thing.

jchanggoaway

got it!

beyondpossum

I should correct myself, "0-50% are not white" cannot be translated to "a minority are not white"; rather, it would be translated to a "a minority or exactly half are not white", which would be equivalent to "half or more are white". It's minding the 50/50 scenarios that that's so befuddling here and making the negations complicated.

To make matters worse, here's 'nother thing that might be going on. Philosophers at least since Bertrand Russell have noticed that sentences claiming that sentences denying an entity a property can be ambiguous between claiming no such entity with a property exists or that the entity exists but has no such property. It's summed up on the first page here:

https://www.jstor.org/stable/2252540

So "The King of France is not bald" is ambiguous in meaning between "there is no entity that is the king of France and bald" and "The entity that is the king of France is not bald."

So maybe your cognitive procces interpreting those sentences is vaccilating back and forth between trying to apply these two different sorts of interpretations (which Russell called "primary" and "secondary") which results in the weird uneasy feeling some of us might be getting when we're staring at these "most people are not white" sentences in trying to negate them back and forth.

capturingthemomentmedia

If this helps, "most" refers to anything over 50%. It can be 51% and higher.