No mathematical proposition can be proven true by observation. It foll

Question

No mathematical proposition can be proven true by observation. It follows that it is impossible to know any mathematical proposition to be true.

The conclusion follows logically if which one of the following is assumed?

(A) Only propositions that can be proven true can be known to be true.

(B) Observation alone cannot be used to prove the truth of any proposition.

(C) If a proposition can be proven true by observation then it can be known to be true.

(D) Knowing a proposition to be true is impossible only if it cannot be proven true by observation.

(E) Knowing a proposition to be true requires proving it true by observation.

VeritasPrepBrian · Accepted Answer

One thing you see a lot of in Assumption questions is a conclusion that rests upon a single premise, and either the conclusion or the premise has a little bit of "extra" language that makes it extra specific and therefore doesn't quite fit with its counterpart.

Here I'd say that the "by observation" is that extra language in the premise. The whole premise is that no mathematical proposition can be proven true  by observation . (Which is pretty specific - that's just one method of proving something) And then the conclusion is more general "it's therefore impossible to know any mathematical proposition to be true." Note that the premise goes far more specific than the conclusion, making the broader conclusion really hard to prove with such a limited, targeted premise. That's a  generalization  error, a common logical gap on CR questions where a limited premise is used to (try to) prove a much broader, more general conclusion. Here it's like saying:

"No door hinges can properly be hung using a hammer. ("a hammer" is one specific tool like "by observation") Therefore, it is impossible to properly hang door hinges."  Basically it's "you can't accomplish a job with this one tool, so therefore you can't accomplish this job." As you read that, if you notice that extra specificity of the premise, you really ought to be thinking "what about other tools?!"

And that's what (E) exposes. If proving something true "requires proving it true by observation" then the argument holds - if observation is the  only way  to prove something, and in this case we can't use observation to prove math rules to be true, then yeah you just can't prove them to be true.

And here's where the Assumption Negation Technique can be really helpful in turning an Assumption question (they tend to be kind of dense and less approachable) into a Weaken question (we're all good at criticizing other people's arguments!). If you negate (E), you pretty much find that objection "hey what if there are other tools to prove something to be true"

Knowing a proposition to be true  requires   does not require  proving it true by observation.

The negated (E) shows that observation isn't the only way to prove something to be true, thereby blowing apart that gap between the narrow premise and the broad conclusion.

One large lesson here: I'd say that this one is like many, many CR questions in that it's harder and more time consuming to try to attack it with pure process of elimination (you mentioned eliminating C and D). If you take the time to analyze the argument and see this one as a generalization error, you can anticipate an answer dealing with the flaw of "hey what if there are other methods besides just observation" and (E) should look really promising. Whereas with dense, kind of abstractly worded (this *definitely* feels like that abstract formal logic LSAT style) answer choices process-of-elimination can be pretty hard if you don't really know what you're looking for.

GMATNinja · Answer

To understand the problem with answer choice (B), first take another look at the conclusion of the passage:
 
Note that the conclusion deals exclusively with  mathematical  propositions. Keep this in mind while reading answer choice (B):
 
The key word in this answer choice is " any ." Answer choice (B) would apply to a broader range of propositions than just the mathematical propositions mentioned in the conclusion (artistic propositions, philosophical propositions, culinary propositions... or whatever). These other types of propositions are not relevant to the conclusion of the passage. Answer (B) does not provide any additional links between the evidence and the specific conclusion of the passage, so it is not an assumption upon which the author relies.

For (E), you don't really need to use the negation technique. (More on the limitations of the negation technique  here .) Instead, you could think of it this way: if (E) is assumed, will the conclusion logically follow from the facts given in the passage? Here's one of those key facts again:
 
And here is answer choice (E), our potential assumption: 
 
Now we know from the passage that mathematical propositions  cannot  be proven true by observation. We also know that knowing a proposition to be true  requires  proving it true by observation. It follows that "it is impossible to know any mathematical proposition to be true."

Answer choice (E) has provided the missing link between the evidence and the conclusion, and so it is the correct answer.

I hope this helps!

yash312 · Answer

No mathematical proposition can be proven true by observation. It follows that it is impossible to know any mathematical proposition to be true.

Meaning analysis: NO mp----> can be proven true---> By observation
 conclusion: it is impossible -----> to know any Mp---> to be true

Prethink: if the MP status to be proven true is not dependant on true by observation; Argument falls
assumption: it is impossible to know to true about any MP without true observation

IMO E

Rest does not affect the argument, if negated
If u negate E, then it matches with the prethink and hence argument falls apart

surbhi1991 · Answer

Hi

How is B Not correct?
Also If we negate E, It doesn't negate the conclusion.

manishcmu · Answer

Hi GMATNinja , even though I picked E, I believe that we need  mathematical proposition   instead of  a proposition . The argument is about  mathematical proposition . By saying a proposition, we are including all kinds of proposition which is not required by the argument. We need something bare minimum. What is your view on this?

GMATNinja · Answer

Think about it this way: the question asks "The conclusion follows logically if which one of the following is assumed?"

So, we need an answer choice that, if stuck into the passage as evidence, makes it so the conclusion MUST be true. Broken down, it should look something like this:

Fact #1 from the passage 
 Correct answer choice 
 Given the two things above, conclusion that MUST be true

Let's try that out with answer choice (E):

Fact from passage: "No mathematical proposition can be proven true by observation." 
 Answer choice (E):  Knowing a proposition to be true requires proving it true by observation.  
 Conclusion: It MUST follow that "it is impossible to know any mathematical proposition to be true."

You are correct that (E) applies to all propositions and not just mathematical propositions. However, that is not a problem for this exact question -- the conclusion "follows logically" if (E) is assumed, so that is the correct answer. A slightly different question (for example, "on which assumption does the argument depend?") would require a bare minimum answer choice.

Given all of that, I'll amend my explanation of answer choice (B) using the same technique:

Fact from passage: "No mathematical proposition can be proven true by observation." 
 Answer choice (B):  Observation alone cannot be used to prove the truth of any proposition.  
 Conclusion: MUST it follow that "it is impossible to know any mathematical proposition to be true"?

Here we learn that observation alone cannot prove the truth of a proposition. But what about other methods of proof? For example, what if mathematical propositions could be proven true just with theoretical calculations? In that case, it  would not follow  that "it is impossible to know any mathematical proposition to be true." Because the conclusion does not necessarily hold true if (B) is assumed, (B) is not the correct answer choice. (E), on the other hand, offers no wiggle room at all -- the conclusion MUST follow if (E) is assumed.

Eliminating (D) is tricky, and comes down to how the phrase "only if" affects the meaning of the sentence. For a good explanation of "if" vs. "only if," please check out  this  article.

Take another look at (D):
 
Based on the logic explained in the article linked above, we can reconstruct this answer choice to read as follows: "IF knowing a proposition to be true is impossible, THEN it cannot be proven true by observation."

We  cannot  infer the inverse, that "IF a proposition cannot be proven true by observation, THEN knowing that proposition to be true is impossible." This would be the more relevant construction, because it would prove that the conclusion follows logically from the answer choice and the evidence in the passage. For this reason, (D) is out.

I hope that helps!

RusskiyLev · Answer

Everybody concentrates on D and E, but I was stuck between E and C. Even though I picked E as the correct choice because it seemed to be straight answer, I had doubts why not to choose C.

GMATNinja , please could you explain what is wrong with option C and why E is more preferable answer choice than C?

Kritisood · Answer

Not understanding how to eliminate D. E and D seem so similar.

VeritasPrepBrian · Answer

They're definitely designed to look similar, but there's a massive keyword in (D) that you should  always  take account of when it show up:  only .

If you look at the placement of "only" in choice (D) - "...impossible only if...", (D) is saying that there's  only one way  to make knowing something to be true impossible, and that's if you can't prove it by observation.

If you take "only" out, (D) and (E) are essentially the same: (D) would say that if you can't prove it by observation, you can't know it to be true, and (E) says that knowing it to be true requires you to be able prove it by observation. But that word "only" in (D) makes it a much more specific and limiting statement. And for (D) to be correct, this argument would require that it's the ONLY way to not know something to be true.

Now ask yourself: what if there were two ways to make it impossible a proposition to be true: 1) is you can't prove it by observation, and 2) is its proof requires the truth of a premise that itself is still unproven (just to make up a second way). Does the existence of #2 ruin the argument? If no mathematical proposition fits #1 (which is what we're told by the stimulus), then we still know that it's impossible to know any mathematical proposition to be true. The argument still holds: If either #1 or #2 is true, it's impossible to know a proposition to be true. All propositions fit case #1, so we cannot know any of them to be true" is still a valid argument.

The "only" in (D) means that there can be no path #2 in my hypothetical - the ONLY way to make something impossible is #1. But we don't need that in order for the argument to hold. As long as path #1 makes knowing something impossible, and all propositions fit #1, then all propositions are impossible to know.

But (E) tells us that #1 is true: if you can't prove it by observation, it's impossible to know it to be true. Without (E) we lose our entire argument - if knowing something to be true DOES NOT require that you can prove it true by observation, then the fact that "no mathematical proposition can be proven true by observation" doesn't tell us whether we know those propositions to be true or not, so the conclusion isn't supported anymore.

TL;DR - that word "only" in (D) is the gamechanger. Without it, (D) and (E) are basically the same, but with it (D) is a totally different statement.

GMATNinja · Answer

Using the analysis explained in  this  post, put (C) into the following format:

Fact #1 from the passage 
 Correct answer choice 
 Given the two things above, conclusion that MUST be true

Here it is with answer choice (C):

Fact from passage: "No mathematical proposition can be proven true by observation." 
 Answer choice (C): "If a proposition can be proven true by observation then it can be known to be true." 
 Conclusion: Does it HAVE to follow that "it is impossible to know any mathematical proposition to be true"?

(C) tells us something about propositions that CAN be proven true by observation: they CAN be known to be true. Cool.

But we really care about mathematical propositions, which CANNOT be proven true by observation. Specifically, we need a link between that fact and the conclusion that is is impossible to know any mathematical proposition to be true.

(C) does not provide that link. Just because propositions that CAN be proven true by observation CAN be known to be true does not mean that observations that CANNOT be proven true by observation CANNOT be known to be true. For instance, what if there was another way to prove mathematical propositions to be true (e.g., by theoretical calculations)? Then it could be possible to know mathematical propositions to be true, even without proving them by observation.

Because the conclusion doesn't logically follow from the information in the passage and answer choice (C), (C) is not the correct answer.

Also (and I probably should have mentioned this earlier), this reads as a pretty LSAT-y LSAT question. I wouldn't worry too much about untangling this particular logical knot if you're studying for the GMAT.

I hope that helps!

KaranB1 · Answer

VeritasPrepBrian   VeritasKarishma   GMATNinja

I'm unable to eliminate A.

If I negate the answer choice I get- Not only propositions that can be proven true can be known to be true.

That means if were to say proposition can be known true  without proving it to be true by any means , would't the conclusion fall apart.

KarishmaB · Answer

Here is the reason why (A) doesn't work.

Premise:No math proposition can be proven true by observation.

Conclusion: No math proposition can be known to be true.

Note that the premise says that math Ps cannot be PROVEN true by OBSERVATION.
The conclusion concludes that no math P can be KNOWN to be true.

So the assumptions are that you need to PROVE a proposition to be true to KNOW that it is true. Also, that OBSERVATION is the ONLY way to prove any P to be true. Note that the question asks for "conclusion logically follows ..." This is a typical LSAT type question. To make the conclusion logically follow, you need to make "premises + assumptions" sufficient for the conclusion. So you necessarily need to cover both aspects in your assumption.

(A) Only propositions that can be proven true can be known to be true.

Great. Takes care of one aspect but not the other. Doesn't say that observation is the only way to prove.

(E) Knowing a proposition to be true requires proving it true by observation.

Perfect. It says that KNOWING it to be true needs PROVING true by OBSERVATION. So both are required to know P to be true.

Answer (E)

P.S - Negation technique only works for the typical GMAT assumptions (missing NECESSARY premises). Here we are looking for missing SUFFICIENT premises.

KaranB1 · Answer

VeritasKarishma  Ma'am you are a true blessing to this community.

KaranB1 · Answer

sunnytiss

by negating this answer choice we get -Observation alone  can  be used to prove the truth of any proposition.

Even if our negated statement is true, conclusion remains intact hence B cannot be author's assumption.

Now of we negate answer choice

we get- Knowing a proposition to be true  does not    require  proving it true by observation.

Now you see that conclusion completely falls apart hence E is the right answer.

JackieO · Answer

The argument says that to prove to be true by observation is a necessary condition for a mathematical proposition to be known true. 
A, B, and C are incorrect as they assume the observational proof to be sufficient.

Correct: E

IN2MBB2PE · Answer

Fastest way to do this is using conditional logic:

P1:  No  mathematical proposition ( MP ) can be proven true by  observation :  MP --> ~ O ----- EQ. 1 
 : It follows that it is  impossible  to know ( K ) any mathematical proposition ( MP ) to be true:  MP --> ~K ------ EQ. 2

Answer Choice E: Knowing  (K)  a proposition to be true  requires  proving it true by observation  (O) : K --> O

Opposite of E:  ~O --> ~K -----EQ. 3

Combining the conditional equation:  MP --> ~O -- > ~K , which means  MP ---> ~K (Eq. 2 /  )

E clearly fills the gap in the conclusion as the conditional works, it does not work for the rest of the answer choices!

ClaireCHEN · Answer

No mathematical proposition can be proven true by observation. It follows that it is impossible to know any mathematical proposition to be true.

The conclusion follows logically if which one of the following is assumed?

Premise: No proposition can be observed true
Conclusion: Impossible to know if any proposition is true

(A) Only propositions that can be proven true can be known to be true. -- NO. Irrelevant to observed to be true

(B) Observation alone cannot be used to prove the truth of any proposition. --NO. Irrelevant to known to be true

(C) If a proposition can be proven true by observation then it can be known to be true. --NO. Irrelevant to observed to be true

(D) Knowing a proposition to be true is impossible only if it cannot be proven true by observation. -- NO, it equals "known to be true is possible when cannot be observed to be true"

(E) Knowing a proposition to be true requires proving it true by observation. -- YES, bcs if we negate E, then it's if observed to be true is not required, then it's possible to know math propositions are true, which counter the conclusion

furherv083 · Answer

E says to prove the proposition to be true, one requires to prove it by observation, emphasis on "requires", its a necessary condition now for proving the proposition true. Now lets visit the premise which says its impossible to prove by observation hence impossible to know if all propositions are true. Therefore if observation is necessary and we know observation cannot prove it to be true, E is the assumption we are looking for.
A -> doesn't make sense to me 
B -> only weakens the argument
C -> kind of strengthens the argument but here the word 'can' is used which indicates there maybe things other than observation which can prove a proposition to be true
D -> also indicates something other than observation may prove a proposition to be true.
Left with E

No mathematical proposition can be proven true by observation. It foll

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