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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Brian

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