Q9 - Lines can be parallel

[frankdio]

B and E were easy to eliminate. How do I go from there?

[bbirdwell]

Start by identifying the core and evaluating the logic.

Premises:
1. lines can be parallel in E
2. non-E that has most verifications = regarded as correctly describing universe

Conclusion:
If they're right, there are no parallel lines in universe.

What's missing from this? The conclusion says the non-E system w/most verifications has no parallel lines. The evidence doesn't say this!! That's a big assumption, and probly the one we'll find in the choices.

(A) says this exactly. Note that if you negate (A) and say "there ARE parallel lines in the non-E system w/the most verifications," the whole argument falls apart.

Does that help?

[tzyc]

I have a simple grammar quesiton...
Does the most in this question mean "the best" instead of "more than half?"
When I timed this section...
I chose (C) because it contains "any".

Thank you

[sumukh09]

This is a necessary assumption question so we want to be critical with words like "any" in the answer choices because the required assumptions are not generally that broad.

"The most" in this question refers to the majority ie) the non euclidean system has more support than any other system of geometry.

A is correct because if the physicists that support this system are right (that the non euclidean system correctly describes the universe we inhabit) then the universe has no parallel lines. If we negate A then it reads "there ARE parallel lines...." but if the physicists are right about the non euclidean system then there shouldn't be any parallel lines.

[yeh.briann]

Is (c) wrong because it's a sufficient assumption?

[rinagoldfield]

Thanks for your posts.

This is a necessary assumption question, so we need to start with the argument core:

A Non Euclidean system is most verified system of geometry
+
Euclidean geometry has parallel lines
-->
If we accept the verified non-Euclidean geometry, there are no parallel lines.

The next step is to find the assumption. While parallel lines are mentioned in relation to Euclidean geometry, the argument sheds no light as to whether non-Euclidean geometry has parallel lines. Thus, the author assumes that accepting the verified form of geometry means renouncing parallelism.

(A) Speaks to this assumption. It is necessary.

(B) Is a premise booster.

(C) Is too extreme. As yeh.briann writes above, this choice is sufficient, but not necessary. We don’t need to know that EVERY geometric system that has ANY verification lacks parallel lines. We only need to know about the most verified system.

(D) Is incorrect because it talks about “correctly described.” The argument ultimately doesn’t concern which system is correct.

(E) Seems to undermine the premise by casting doubt on the empirically verified geometry.

[mattFbuelow]

So basically answer C is NOT required by the argument because it is TOO strong- it goes further than is necessary to draw the conclusion, correct?
Would this answer be a good example then of the 'goldilocks' answer I've seen Matt Sherman mention- just necessary enough, but not so necessary that it is sufficient alone?

[JosephV]

I got the right answer (A), however I had to put it on hold, rule out all the others and then, by this process of elimination, accept (A).

Here is my question:

Consider two systems - a Euclidean system, call it ES, and a non-Euclidean system, call it NES. Assume that both systems allow for parallel lines.

Could it not be the case that empirically NES is better than ES (as the stimulus says), yet neither one concludes that the universe has parallel lines?

Let me go a little further in trying to explain myself with the following example:

Take the emblem of Mercedes Benz. Any which way you superimpose it onto a Euclidean co-ordinate system, there is no way you'll find that any of the three lines that make up the emblem are parallel. Hence, although the co-ordinate system allows for parallel lines, objectively speaking the reality is that the Mercedes emblem consists of no parallel lines.


I'll greatly appreciate any comments. Thanks.

[ohthatpatrick]

You seem to be worried about the distinction between "allowing for parallel lines" vs. "actively claiming that objective reality contains parallel lines".

I don't think that distinction matters. It would matter if the author were going from "this system allows for parallel lines" to "there are actually parallel lines in our universe".

But this author is going for (assumption:) "this system does NOT allow for parallel lines" to (conclusion:) "there are NOT parallel lines in our universe".

I think you're worried about whether the conclusion could still be true, even if you negate the correct answer. That's not a valid way to test these answers. In some cases, negating the correct answer DOES invalidate the conclusion. But in other cases, it just weakens the argument by destroying the relevance of the evidence.

for example:
All boys like chocolate. Thus, Sam likes chocolate.

When we negate the necessary assumption "Sam is a boy",
we get "Sam is not a boy".

Well, surely Sam-the-girl might still like chocolate. But we still say the author had to assume this, because otherwise there's no connection between "boys" in the evidence and "sam" in the conclusion.

Likewise, the author needs to assume that "NES doesn't allow for parallel lines", because otherwise there's no connection between
"If NES correctly describes our universe" and "then our universe has no parallel lines".

[JosephV]

Thank you for the thorough reply, Patrick!

[nmmizokami]

I am confused about ACs (A) and (C). The difference between the two is that (C) is a more general statement regarding all types of non-Euclidean systems. (A) is thus included within (C).

If (C) is a sufficient assumption, isn’t (A) too? The only system of non-Euclidean geometry that pertains to the argument is that which has the most empirical verification, so why do the other non-Euclidean systems matter?

The conclusion does not follow if you negate (A). Doesn’t negating (C) have the same effect on the argument (There are some parallel lines in every non-Euclidean…). Wouldn’t that make (C) a necessary assumption?