#9 - Lines can be parallel in a Euclidean system of geometry

[ebertasi]

Hi,

I narrowed this down to answer choices A and C and the both seem to fill the gap that the author makes about the parallel lines. The only reasoning I can come up with would be that C is to far reaching that would be the answer to possibly a justify question rather than an assumption in this case? However, when I negated both answer choices the both seemed to destroy the argument. What am I missing here?

Thanks for your help!

[Jon Denning]

That's a good question, and a subtle distinction between A and C. Look again at the stimulus though, and see which one matches the system described. (A) uses the phrase "the non-Euclidian system of geometry that has the most empirical verification," while (C) says "every non-Euclidian system of geometry that has any empirical verification."

Compare those two to the specifics of the stimulus and suddenly it's clear that (A) is a PERFECT match to the system described by the physicists of the conclusion (the one with the most verification), while (C) is talking about any/every system with any verification. That difference is more than enough to discount (C).

I hope that helps!

[ebertasi]

Thank you. I did notice the difference between A being specific and C saying that "every...any," however, "every...any" includes the most empirically verified non-Euclidean system of geometry so that's why I saw it as filling the gap. I probably should have gone with A looking back at it because I did notice that. What if A said something different and completely irrelevant. Would C have been a correct answer for an assumption question with that far-reaching language?

Sorry to drag this out. I know that in this case A was a far better choice, but I am just interested to know exactly if C was wrong just because A was better or if C was wrong because of the language and could simply never answer this assumption question correctly.

Thanks again!

[Dave Killoran]

Hey Elliot,

Let me jump in for a second since I know Jon is out of the office at the moment and probably won't be able to respond until Monday. There's a couple of points relevant to your question I'd like to address.

Could an answer with "every...any" ever be correct in an Assumption question? Sure, you could easily have an answer with strong language like (C) be correct in the right circumstance. The circumstances here, however, aren't right for an answer this broad and far-reaching.

Let me move next to a comment you made, that you felt (A) "includes the most empirically verified non-Euclidean system of geometry so that's why I saw it as filling the gap." This is an interesting point, and shows the difference between Justify and Assumption questions (and I know Justify questions have been giving you trouble, so this may help there). Think about Assumptions as minimalist elements. The correct answer will be very direct, and not include any extraneous elements. So, if there's anything "extra" in an Assumption answer, that answer will be wrong. In considering (C), you thought that it included the assumption needed for the argument (and that implies you thought it was in there along with other stuff). That's fine, but if an Assumption answer includes anything extra (and (C) does), then it's automatically wrong in an Assumption question. The correct answer is literally the bare bones that are needed, and not a speck extra.

Justify questions are entirely different in that respect. You can have "extra" stuff in a Justify answer and it can still be correct. You just need to meet the minimum threshold to justify the conclusion; anything else that's included doesn't take away from meeting that threshold.

So, really, you were close in your idea of how (C) was working here, but it looks like your conception of what you were looking for may have thrown you off.

Please let me know if that helps. Thanks!

[ebertasi]

Hey Dave,

That helps a lot. In fact, your clarification reminded me of the virtual module I had watched with the explanation of the apples for assumption and justify questions. How if the answer was 2 apples, an orange, and a pair, then that would be incorrect as an assumption but correct as a justify. The extraneous information made it wrong even though it included 2 apples which was what it needed to fill the gap. This was a very important piece of information that I had apparently forgotten.

Thanks again for the explanation!

[Noelfranco]

Hello,

I understand how the assumption of C isn’t correct because it is too broad but I am curious why the negation of it seems to weaken the argument nevertheless.

My negation yields “there are parallel lines in every non-Euclidean system of geometry that has any empirical verification.”

Am I getting something wrong or should the negation not be decisive?

[Jeff Wren]

Hi Noel,

Answer C can be tricky to negate, and unfortunately you did negate it incorrectly.

What makes it tricky is the term "no parallel lines," which you assumed is the term that you need to negate. In fact, what you need to negate is the term "every" to "not every."

To simplify, let's replace "no parallel lines" with the variable "Xs"

There are Xs in every non-Euclidean system of geometry.

The negation of this statement would be:

Xs are not in every non-Euclidean system of geometry;

or put another way

Not every non-Euclidean system of geometry has Xs.

It would be incorrect to negate this as:

There are no Xs in every non-Euclidean system of geometry.

This would be the polar opposite rather than the logical opposite, which is what we need.

Replacing "X" with "no parallel lines," you'd get the same thing. The fact that this term is negative makes no difference.

One potentially easier way to negate a tricky statement is to simply add:

"It is not the case that" before the answer choice and think about what that sentence would mean:

It is not the case that there are no parallel lines in every non-Euclidean system of geometry.

What this statement means is that not every non-Euclidean system of geometry has the characteristic of "no parallel lines." This statement has a bunch of negative terms, which is also what makes it tricky.

With Answer C correctly negated, the correct negation no longer weakens the argument because the fact that not every non-Euclidean system of geometry has no parallel lines doesn't mean that the specific non-Euclidean system mentioned in the stimulus has no parallel lines.

[Noelfranco]

Hi Noel,

Answer C can be tricky to negate, and unfortunately you did negate it incorrectly.

What makes it tricky is the term "no parallel lines," which you assumed is the term that you need to negate. In fact, what you need to negate is the term "every" to "not every."

To simplify, let's replace "no parallel lines" with the variable "Xs"

There are Xs in every non-Euclidean system of geometry.

The negation of this statement would be:

Xs are not in every non-Euclidean system of geometry;

or put another way

Not every non-Euclidean system of geometry has Xs.

It would be incorrect to negate this as:

There are no Xs in every non-Euclidean system of geometry.

This would be the polar opposite rather than the logical opposite, which is what we need.

Replacing "X" with "no parallel lines," you'd get the same thing. The fact that this term is negative makes no difference.

One potentially easier way to negate a tricky statement is to simply add:

"It is not the case that" before the answer choice and think about what that sentence would mean:

It is not the case that there are no parallel lines in every non-Euclidean system of geometry.

What this statement means is that not every non-Euclidean system of geometry has the characteristic of "no parallel lines." This statement has a bunch of negative terms, which is also what makes it tricky.

With Answer C correctly negated, the correct negation no longer weakens the argument because the fact that not every non-Euclidean system of geometry has no parallel lines doesn't mean that the specific non-Euclidean system mentioned in the stimulus has no parallel lines.

Hi Jeff,

Thank you very much! This makes sense now. I will be sure to keep that "it is not the case that" trick in my back pocket.