Self-study
Support All too many weaklings are also cowards, and Support few cowards fail to be fools. ████ █████ ████ ██ ██ █████ ███ ██████ ███ ██ ████ █ ████████ ███ █ █████
Method of Reasoning
The argument starts with the statement that "all too many" weaklings are cowards. Since "all too many" is a subjective quantifier — perhaps for this author, even a handful of weaklings being cowards is "too many" — this premise just tells us that some weaklings are also cowards. Then the argument states that few cowards fail to be fools: if few cowards are not fools, this means most cowards are fools. From these two premises, the argument concludes that there is at least one person who is both a weakling and a fool: i.e., at least one weakling is a fool, which we can translate to "some weaklings are fools."
Identify and Describe Flaw
Remember that the premises of this argument are "some weaklings are cowards" and "most cowards are fools." Notice that the group "cowards" is mentioned in both statements. One way to think about these two premises is that they both describe a subset of cowards, "weaklings" being the first subset and "fools" being the other subset.
The problem with this argument is that it assumes these subsets overlap, when we don't have enough information to conclude that they do. We know the subset "fools" takes up more than half of the set "cowards" — but we don't know how big the "cowards" subset is, so we can't conclude that it overlaps with the "fools" subset at all. Thus, the argument's conclusion that some weaklings are fools assumes these subsets will overlap, when that isn't supported by the premises.
As an analogous argument, imagine the statements "some chickens are brown" and "most brown animals are mammals." It would be wrong to conclude "some chickens are mammals" as a result: the groups "chickens" and "mammals" can both be subsets of the group "brown animals" without overlapping with each other. More generally, the pattern we're looking for is an argument that concludes two groups overlap simply because they are subsets of a larger group, without enough information about the size of the subgroups to support that claim.
21.
The flawed pattern of reasoning ██ ███ ████████ █████ ██ ████ ███████ ██ ████ ██ █████ ███ ██ ███ ██████████
a
All weasels are ██████████ ███ ██ ██████████ ████ ██ ██ ██████████████ ██ ████ ███████ ███ ██████████████
The fact that this argument starts with an "all" statement, indicating it uses conditional logic rather than set logic, should be a tip-off that this answer choice isn't what we're looking for. There's no flaw here: if all weasels are carnivores, and all carnivores are nonherbivores, then it follows that at least some (in fact, all) weasels are nonherbivores.
b
Few moralists have ███ ███████ ██ ███ █████████ ██ ███ ██████████ ████ ████████ ███ ███ ██████ ████ ███ ███████ ██ ██████████ ███ ██████████ ██ █████ ████ █████ ██ ██ ███████ ████ ███ ██████ ███ ████ ███ ████ ██████ ███ █████ ████ ██████████
Wrong flaw. Remember that the flawed pattern of the stimulus: the premises established that two groups were each subsets of a larger group, and the argument wrongly concluded that those two groups must overlap. This answer choice gives us two premises about different groups, without telling us that they are subsets of a larger group, and then draws a conclusion about some larger group ("people" in general) with respect to certain traits of the first two groups, saints and moralists.
More abstractly, the flawed pattern we saw in the stimulus was "some A are B," "most B are C," therefore "some A are C." This argument runs: "most A are B" (most moralists are not courageous enough to act according to their principles); "most C are D" (most saints are unable to articulate the principles of their actions); therefore "most E can act like neither A or C" (most people can't act like saints or speak like moralists). Though this conclusion is extremely flawed — is acting like a saint or moralist the same as being one? — this is not what we're looking for.
c
Some painters are ████████ █████ ████ ████████ ███ ██████████ ███ ████ █████████ ███ ████████
This is the correct answer choice. The premises tell us that "some painters are musicians" and "some musicians are dancers." So we know that "painters" and "dancers" are both subgroups of "musicians," but we don't know that these subgroups overlap, as the argument concludes they do. This is the same pattern as in the stimulus.
d
If an act ██ █████████ ████ ██ ██ ███████████ ███ ████ ███ ███ ████████ ██████ ████ ███ █████ ███ ████ ███ ███ ████ ██████ ████ ███ ███████████
The fact that this argument relies entirely on conditional rather than set logic should be a tip-off that this isn't what we're looking for. In any case, there's no flaw here. The premises boil down to stating that autonomy is necessary for freedom, and freedom is necessary for virtue. It follows that autonomy is necessary for virtue, as the conclusion states.
e
A majority of ███ ██████ ██████████ ██████ █ █████ ████ ███ ██ ███ ███ ██████ █ █████ ███ ██ ███████ ██ ███████ ████████ ██ ██ █████ ███ █████ ██ ███ ███████ ██ ███████ ████████
This might be tempting, especially since the language in the conclusion ("at least one") mirrors what we see in the stimulus. But notice, first, that one of the premises is a conditional statementno: one who favors a total ban is opposed to stiffer tariffs. The argument in the stimulus didn't rely on any conditional "all" or "none" statements, so this fact alone should make us suspicious of this answer choice.
And in fact, there's no flaw here. The second premise, "no one who favors a ban is opposed to stiffer tariffs," translates simply to "all those who favor a ban are not opposed to stiffer tariffs." Then, since we already know that "most" voters favor a total ban, it certainly follows that at least one voter is not opposed to stiffer tariffs.