All historians are able to spot trends. But anyone able to spot trends is able to distinguish the significant from th...

Nina July 1, 2014

To continue on the diagramming on answer choice E (my iPad cuts me off)
E)

2nd P: not sure how to diagram
________________________________
C: O + DC - > Not F

And one last question: because of answer choice E's use of terms "and" "or" (for contrapositive) - > could I also eliminate E as a possible option because the stimulus doesn't have these terms?

Naz July 7, 2014

Let's diagram the argument.

"All historians are able to spot trends."

PR1: H ==> ST
not ST ==> not H

"But anyone able to spot trends is able to distinguish the significant from the insignificant."

PR2: ST ==> DSI
not DSI ==> not ST

"Thus, anyone who can distinguish the significant from the insignificant is a historian."

C: DSI ==> H
not H ==> not DSI

The conclusion takes the necessary condition of the second principle rule and deduces the sufficient condition, "ST," which is also the necessary condition of the first principle rule.

From there it deduces the sufficient condition of the first principle rule: "H." As you correctly identified, we cannot deduce anything else from a necessary condition.

Answer choice (A) follows this exact pattern of flawed reasoning.

"All expressions used for emotional impact are expressions used by poets."

PR1: EEI ==> UP
not UP ==> not EEI

"All figures of speech are expressions used for emotional impact."

PR2: FS ==> EEI
not EEI ==> not FS

"So any expression used by poets is a figure of speech."

C: UP ==> FS
not FS ==> not UP

As you can see, the conclusion takes the necessary condition of the first principle rule and deduces the sufficient condition, "EEI," which is the necessary condition of the second principle rule. From there it deduces the sufficient condition of the second principle rule: "FS." This is the exact same flawed reasoning as the argument.

You cannot rule out answer choice (E) because of the words "at least." You don't need to focus on what words are being used, rather, you need to focus on how they are being used.

"At least" does not change how answer choice (E) is diagrammed. Answer choice (E) is incorrect because it doesn't follow the same pattern of flawed reasoning as in the argument.

Let's diagram.

"People living in open and democratic countries have customs that are determined at least in part by an inherited past."

PR1: LODC ==> CD@LIP
not CD@LIP ==> not LODC

(There's no need to split the variable up with an "and." We are focusing on the people who live in that environment, rather than the variables of that environment.)

"But no country's past is a product of free choice."

P2: CP ==> not PFC
PFC ==> not CP

(This has the same structure as a "No As are Bs" statement. We diagram this: A ==> not B.)

"Thus people living in open and democratic countries can never be entirely free."

C: LODC ==> not EF
EF ==> not LODC

The flaw is that we have concluded something about a variable that was never present in the principle rules, i.e. "never being entirely free."

We have no information on how one attains this, so we cannot conclude that those who live in open and democratic countries can "never be entirely free." All we know about those who live in an open and democratic country is that they have customs that are determined at least in part by an inherited past. This is clearly not the same flawed pattern of reasoning as the argument.

Hope that was helpful! Please let us know if you have any other questions.

rockinrobinpa August 22, 2015

Could you please diagram out the information for answer choices B, C, and D also. Thank you

Naz September 2, 2015

Diagram for (B):

"Political systems whose laws originate in elected legislatures are prone to factionalism."

P1: PSEL ==> F
not F ==> not PSEL

"Factionalism leads to civil disorder."

P2: F ==> CD
not CD ==> not F

"Thus political systems not run by autocrats have a tendency to fall into civil disorder."

This is not a Sufficient & Necessary statement. It merely tells us that political systems not run by autocrats are prone to fall into civil disorder but not might. So we have no sufficient or necessary condition.

Diagram for (C):

"Animals that possess horns or antlers use them not to attack prey but for intraspecies combat."

SO: if you are animal that possesses horns or antlers, then you use them for intraspecies combat.

P1: PH or PA ==> UIC
not UIC ==> not PH and not PA

"In fact, animals so equipped never have the claws or fangs that are possessed by predators."

So: animals that possess horns or antlers do not have claws or fangs possessed by predators."

P2: PH or PA ==> not PC and not PF
PC or PF ==> not PH and not PA

"Thus any animal that fights with members of its own species is not a predator."

C: UIC ==> not P
P ==> not UIC

Diagram for (D):

"No one without a deep desire to communicate can be a blues musician."

P1: not DDC ==> not BM
BM ==> DDC

Short-story writers have a deep desire to communicate.

P2: SSW ==> DDC
not DDC ==> not SSW

"So short-story writers could also have become blues musicians."

Again, this is not a Sufficient & Necessary statement since it uses the word "could also have." We have no sufficient or necessary conditions.

Hope that clears things up! Please let us know if you have any other questions.

Irene-Vera March 28, 2019

Hi, sorry could you explain why "could also have" or "have a tendency" would not fall under the spectrum of sufficient and necessary. I understand they are not key works or phrases but we are not always resented with clear statements. Must Sufficient & Necessary statements be straight forward statements that do not allow for any further possibilities?

yuetngan July 24, 2019

Can we not make a chain here? Transitive property?

yuetngan July 24, 2019

I still don't understand the point about not being able to deduce anything from the necessary. You form the conditions based on the ordering/key words used in the sentence right?

Ravi August 5, 2019

@Irene-Vera and @yuetngan,

Happy to help.

@Irene-Vera,

"Could also have" and "have a tendency" are both statements that don't
guarantee anything. In order for a statement to trigger a sufficient
condition, it has to guarantee the necessary condition. Neither of
those statements guarantees anything. Additionally, neither of these
statements indicates something is required, so there's no way that
either can introduce a necessary condition.

Regarding whether or not S&N statements must be straightforward and
not allow for other possibilities, the answer is yes. They can't allow
for other possibilities because if they did, then there wouldn't be a
sufficient and necessary relationship.

@yuetngan,

We can diagram the stimulus:

A - >B

B - >C

C: C, therefore A

The argument is mistakenly thinking that if A - >B - >C, then C - >B - >A.
This is a converse fallacy. You can't deduce anything from the
necessary condition because the necessary condition is the condition
that is required for the sufficient condition. The only thing you can
do is fail the necessary condition, which triggers the failure of the
sufficient condition. This is the contrapositive of the original
statement.


The contrapositive of the stimulus would be

/B - >/A

/C - >/B

We could make a chain that goes from /C - ->/B - >/A

However, we can't say if C, therefore, A, and this is why the stimulus
is flawed.

Does this make sense? Let us know if you have any other questions!