Quantifiers - Advanced Flashcards
VALID OR INVALID?
Premise: All H are B.
Premise: Some H are L.
Conclusion: Some B are L.
VALID
When one of the terms in the SOME statement MATCHES THE SUFFICIENT condition of the ALL statement, there must be an overlap between the other two concepts. Here, we know all H are B. So if even one of those H is an L, there must be at least one B that’s an L (at least one of the H is both B and L).
VALID OR INVALID?
Premise: All N are Q.
Premise: Most N are W.
Conclusion: Some Q are W.
VALID
If the LEFT SIDE of a MOST statement MATCHES THE SUFFICIENT of the ALL statement, there must be an overlap between the other concepts. Here, we know all N are Q. If even one of those N is also a W, then there must be at least one Q that is an N.
VALID OR INVALID?
Premise: All Y are Z.
Premise: All Y are V.
Conclusion: Some Z are V.
VALID
If the SUFFICIENT CONDITIONS from two ALL statements MATCH, there must be an overlap between the other two concepts. Here, we know that All Y are Z. If we find out that even one of those Y is also a V, then there must be at least some Z that are V (all the Ys, in this case).
VALID OR INVALID?
Premise: All X are L.
Premise: Some Z are L.
Conclusion: Some X are Z.
INVALID
To get an inference from combining an ALL statement and SOME statement, we need the SUFFICIENT CONDITION to match. There is NO inference if it’s the NECESSARY CONDITION that matches. Here, the Zs that are L might be a completely different group from the Xs that are L. L might be a huge category and the Zs and Xs don’t have to overlap within the L group.
VALID OR INVALID?
Premise: All Q are T.
Premise: Most A are T.
Conclusion: Some Q are A.
INVALID
When combining a MOST statement and ALL statement to produce an inference, the SUFFICIENT CONDITION of the ALL statement must match. If it’s the NECESSARY that matches, there is NO INFERENCE. Here, although All Q are T and Most A are T, the Qs and As might be entirely separate groups. All basketball players are tall and most of my neighbors are tall, but that doesn’t mean some of my neighbors play basketball.
VALID OR INVALID?
Premise: Most U are I.
Premise: Most U are P.
Conclusion: Some I are P.
VALID
When two MOST statements are about the SAME GROUP (in other words, when they’re about the same subject), there must be an overlap between the other qualities. This is because MOST means over half. If over half of U are I, and over half of U are P, then even if you tried to separate I and P as much as possible within the group of U, there’s going to be at least 1 U that is both I and P.
VALID OR INVALID?
Premise: All V are H.
Premise: Most Z are V.
Conclusion: Most Z are H.
VALID
The RIGHT side of a MOST statement matches the SUFFICIENT condition of an ALL statement, you can connect the statements. It’s similar to the connection you can make between two conditional statements. Here, if over half of Z are V…and every V is an H, that means over half of Z must be H, too.
VALID OR INVALID?
Premise: All U are M.
Premise: Some X are U.
Conclusion: Some X are M.
VALID
When one of the terms in a SOME statement matches the SUFFICIENT condition of an ALL statement, there’s an overlap between the other two concepts. Here, if at least one X is a U, and every single U is an M, then at least on X must be an M (the X that are U must also be M).
VALID OR INVALID?
Premise: Most T are Q.
Premise: Most P are Q.
Conclusion: Some T are P.
INVALID
Two MOST statements can produce an inference only if the LEFT side of each statements matches. But if the RIGHT sides match, there is NO inference. Here, the Ts that are Q and the Ps that are Q could be entirely separately from each other.
VALID OR INVALID?
Premise: Most T are O.
Premise: Some T are N.
Conclusion: Some O are N.
INVALID
A MOST statement and a SOME statement will NEVER combine to produce an inference. Here, even though Most T are O and Some T are N, the O and N portions of the T circle don’t have to overlap with each other.
VALID OR INVALID?
Some mammals are known to lay eggs rather than giving live birth. Every mammal is warm-blooded. Thus, we can conclude that there must be at least some warm-blooded creatures that lay eggs.
VALID
Premise 1: Some mammals lay eggs.
Premise 2: All mammals are warm-blooded.
When one of the terms in the SOME statement matches the SUFFICIENT CONDITION of the ALL statement, there’s an overlap between the other two concepts. There must be at least one warm-blooded creature that lays eggs (at least one of the mammals has both qualities).
VALID OR INVALID?
There are many examples of people who dropped out of college yet became successful. We also know that anyone who is hard-working is successful. Clearly, some people who dropped out of college are hard-working.
INVALID
Premise 1: Dropped out of college -some- Successful
Premise 2: Hard-working —> Successful
In order for a SOME statement and an ALL statement to produce an inference, we need the SUFFICIENT condition of the ALL to match one of the terms in the SOME statement. Here, it’s the NECESSARY condition of the ALL that matches (Successful). So there is NO inference. It’s possible that you can become successful through something besides hard-work, such as inheritance or winning the lottery. And it’s possible that the college drop-outs who are successful got there through those other means, not through hard-work.
VALID OR INVALID?
A majority of flawed psychological studies are widely accepted by the public. Anything widely accepted by the public influences mainstream culture. Therefore, most flawed psychological studies influence mainstream culture.
VALID
Premise 1: Flawed psychological studies -MOST-> Widely accepted by the public.
Premise 2: Widely accepted by public —> Influences mainstream culture
When the RIGHT SIDE of a MOST statement matches the SUFFICIENT condition of the ALL statement, you can connect the statements like you do with two conditionals when the necessary condtion of one matches the sufficient condition of the other. Here, if most flawed psych. studies are widely accepted, and everything that’s widely accepted influences mainstream culture, than most flawed psych. studies will fall into the category of things that influence mainstream culture.
