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No mathematical proposition can be proven true

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No mathematical proposition can be proven true  [#permalink]

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New post 24 Dec 2018, 07:17
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A
B
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E

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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.

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Re: No mathematical proposition can be proven true  [#permalink]

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New post 26 Dec 2018, 08:22
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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.
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Re: No mathematical proposition can be proven true  [#permalink]

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New post 25 Dec 2018, 23:42
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This seems super tricky,
Please help gmat1393, broall, nightblade354
Eliminated C & D, unsure about the other options..
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Re: No mathematical proposition can be proven true  [#permalink]

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New post 26 Dec 2018, 10:57
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Thank you VeritasPrepBrian ! :-)

Your post really helps enlighten the negation technique as well as the "try to look for specific things in the options" of a find assumption trick.

+1 Kudos to you sir & Happy Holidays.

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Gladi
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Re: No mathematical proposition can be proven true  [#permalink]

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New post 27 Dec 2018, 12:41
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
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Re: No mathematical proposition can be proven true  [#permalink]

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New post 28 Dec 2018, 09:41
Hi

How is B Not correct?
Also If we negate E, It doesn't negate the conclusion.
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Re: No mathematical proposition can be proven true  [#permalink]

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New post 20 Jan 2019, 04:15
surbhi1991 wrote:
Hi

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

To understand the problem with answer choice (B), first take another look at the conclusion of the passage:
Quote:
it is impossible to know any mathematical proposition to be true.

Note that the conclusion deals exclusively with mathematical propositions. Keep this in mind while reading answer choice (B):
Quote:
(B) Observation alone cannot be used to prove the truth of any proposition.

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:
Quote:
No mathematical proposition can be proven true by observation.

And here is answer choice (E), our potential assumption:
Quote:
(E) Knowing a proposition to be true requires proving it true by observation.

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!
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No mathematical proposition can be proven true  [#permalink]

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New post 20 Jan 2019, 05:34
GMATNinja wrote:
surbhi1991 wrote:
Hi

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

To understand the problem with answer choice (B), first take another look at the conclusion of the passage:
Quote:
it is impossible to know any mathematical proposition to be true.

Note that the conclusion deals exclusively with mathematical propositions. Keep this in mind while reading answer choice (B):
Quote:
(B) Observation alone cannot be used to prove the truth of any proposition.

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:
Quote:
No mathematical proposition can be proven true by observation.

And here is answer choice (E), our potential assumption:
Quote:
(E) Knowing a proposition to be true requires proving it true by observation.

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!


HiGMATNinja, 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?
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Re: No mathematical proposition can be proven true  [#permalink]

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New post 13 Feb 2019, 02:09
This is a bit tricky but can be solved by understanding a broader CR concept, generalization errors. In many assumption questions, the conclusion or the premise will have a little bit of extra information included that will make it just a little too specific to fit with the other part. Here, that extra information is “by observation”, in the premise. This makes the conclusion too broad to fit. So, we have to find the assumption that will bridge this gap.



That assumption is option E. E says that the only way to know that a proposition is true is to prove it true by observation, which makes the conclusion true as if mathematical propositions cannot be proven true by observation and a proposition of any kind can only be proven true by observation then it is impossible to know if mathematical propositions are true.
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No mathematical proposition can be proven true  [#permalink]

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New post 08 Mar 2019, 06:35
Gladiator59 wrote:
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.



Would anybody explain why D is not correct?
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No mathematical proposition can be proven true   [#permalink] 08 Mar 2019, 06:35
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