Q25 - At one time, many astronomers assumed that earth

[kyuya]

Tough question, in my opinion

This stimulus is a bit strange because it is someone else describing a past argument, but this isn't really important. I mention it because it threw me off a little bit initially when being timed, but the stimulus cleared up the confusion.

Argument

Premise: earth is motionless, stars revolve around it

Conclusion: stars were not more than a few million miles from Earth.

This is the first half of the stimulus. At this point, if you are anything like me, you're probably thinking "this is a terrible argument".

The second half of this stimulus adds more support to the argument and is ultimately where we find this assumption.

Premise: earth is motionless, stars revolve around it

Conclusion: stars were not more than a few million miles from Earth.

... and then we have if it were more than a few million miles from earth (IE: if the conclusion above was false) the stars would have to move at tremendously great speeds ... there is more but I think it is irrelevant after looking at this question further.

The assumption is then that stars cannot move at tremendously great speeds, and if this were true the argument would fall apart.

Why?

Because the second half of the stimulus states essentially gives the reason that "they would HAVE TO move at tremendously great speeds" implies that this actually cannot happen, because it is for this very reason that the astronomers believe their argument is a good one.

(D) captures this perfectly.

I think the key with these tough NA questions is to break down things to the core of the argument.

I feel like this question was essentially giving no support aside from the assumption that stars would have to move a tremendous speed (presumed not to be the case) , but also does nothing to validate this as true. With it being the sole support, it makes for a good target to attack.

[cacrv]

Can someone explain why E is wrong? If you negate E, it would have say that a star that is more than a million miles from earth could NOT be back in the same place each night. But the astronomers argue that starts could (not) be more than a few million miles from the earth. I know this is getting nitty gritty with the numbers, but I felt pretty strongly that D is a sufficient assumption answer, so I chose E because once you get to the small details of the language (which, I've learned the hard way that small details truly matter on this test) E seems to ruin the argument.

Thanks in advance!

[ohthatpatrick]

Great original post!

The astronomers had this proposition:
"If stars were more than a few million miles away, it would require them moving at tremendous speeds for them to do what they do."

The astronomers had this conclusion:
"Therefore, the stars are NOT more than a few million miles away".

In even MORE formal terms, this says
A --> B
---------
Thus, ~A

How do you produce ~A from that conditional?

You establish ~B.

Consider this analogy:
If this oatmeal had had cinnamon in it, Eddie would have eaten it.
Thus, this oatmeal must not have had cinnamon in it.

What's being assumed?

(assumption: Eddie didn't eat the oatmeal)

Similarly,
If more than a few million miles away, then move at tremendous speeds.
Thus, must not be more than a few million miles away

(assumption: DON'T move at tremendous speeds)

Because (D) triggers some conditional logic, I can see why the previous poster thought it felt kinda like a Sufficient Assumption.

But don't worry, the astronomers argument still isn't airtight. Part of their argument still rests on a dubious assumption the Earth is the motionless center of the universe, around which the stars revolve.

-------- other answers ------
(remember to beware EXTREME ideas on Necessary Assumption)

(A) These guys think that the stars DO revolve around the Earth, so they don't need to assume what would be true if the stars do not revolve around the Earth.

(B) EXTREME - "all" stars at "exactly the same" speed?

(C) This is the opposite of what they believe. They think the Earth DOES remain motionless.

(E) Do the astronomers believe that stars ARE more than a million miles from Earth? They conclude that the stars were not more than a few million miles from Earth. Does that mean the astronomers estimate that the stars ARE a few million miles from Earth, or does it only mean that they are confident that stars could NOT be more than a few million miles away?

It's unclear. If I asked you how your friend Dave's new landscaping business was going and you said, "Not too great. I'm sure he hasn't had more than 10 customers yet", you haven't committed to the idea that he HAS had 9 or 10 customers so far. You're just committing to the idea that his customer total is NOT yet beyond 10.

The previous poster was suggesting that if we negate (E), it sounds like it makes two separate beliefs of the astronomers incompatible:
- the stars are only a few million miles away
- the stars reappear in roughly the same position each night

If we negate (E), it's saying "once you go beyond 1 million miles, you can't reappear in roughly the same spot".

It's implied that stars DO reappear in roughly the same spot. So what does negated (E) tell us about stars?

It says, they must be WITHIN 1 million miles.

Does that hurt the author's argument? He's arguing that the stars are NOT "greater than a few million miles away".

So this actually agrees with his conclusion. If you're NOT greater than, you're less than or equal to.

WITHIN 1 million miles is less than or equal to a few million miles.

[maria487]

I eliminated E because of the "more than a million miles" part because I figured that the argument is limiting the stars' distance to a few million miles. I thought that because E isn't limiting the stars' distance to a range within a few million miles, this AC is not necessary.

With E, I felt like it was not necessary because the ambiguity of language could lend itself to saying that a star 100 miles away could reappear in roughly the same position each night, which seemed to overreach what is necessary. Is my reasoning appropriate?

[ohthatpatrick]

I think your instincts are solid -- the range required by the conclusion is basically "within 3 million miles", and (E) describes a different threshold.

But when you said that E
"could lend itself to saying that a star 100 miles away could reappear in roughly the same position each night"

I think that's a little off. (E) makes no claim whatsoever about stars closer than a million miles.

And when you said that
"I thought that because E isn't limiting the stars' distance to a range within a few million miles, this AC is not necessary. "

That sounds more to me like a Sufficient Assumption style of thinking: 'Which answer, if true, would get me to the conclusion and limit stars to being within a few million miles?'

Our criteria for Necessary Assumption is: 'Which answer, if false, would most weaken the argument?'

When you were talking about an OVERREACH, that is definitely Necessary Assumption thinking. But the potential overreach for (E) would be this:

It seems like the astronomers were assuming that "within a few million" a star could reappear, but (E) sounds like it applies to ANYTHING greater than a million miles.

Did they have to assume that a star that is 10 million miles away could reappear?

No. That would definitely be an overreach.

Ultimately, though, even that logic is not a valid dismissal of (E), because (E) is not saying that ANYTHING greater than a million can reappear; (E) is saying that AT LEAST ONE star that is greater than a million can reappear.

So it's a pretty fiendishly tricky answer. If we negate it, then ONLY stars that are LESS than a million miles away could reappear in the same spot.

That seems to hurt the astronomers' conclusion, if we interpret "the stars are within a few million miles" to include the idea that "some stars are 1-3 million miles away".

But the range of "within a few million miles" just means, roughly, "somewhere between 0 and 3 million miles away".

So negating (E) tells us that stars that reappear in the same spot HAVE to be within one million miles ... and if you're within one million miles, then you're within a few million miles.

Negating (E) doesn't hurt the argument; it agrees with the argument.

[seychelles1718]

Is the 1st sentence a premise or is it just a background info?
"They concluded from this..." indicates it's a premise but doesn't really seem relevant to the author's conclusion.

[ohthatpatrick]

It's a premise for sure, since, as you said, "They CONCLUDED FROM THIS".

They are concluding that the stars are within a few million miles of Earth.
WHY?
1. Earth is motionless, while the stars revolve around it

2. a few million miles from Earth is as far as away as a star could be to take a trip around Earth and arrive at the same point 24 hours later (unless stars were CRAZY fast)


If you didn't have Earth as a fixed point, then they couldn't make their
Distance = Rate * Time
argument about the stars.

The 2nd sentence is a little weird because you wouldn't DIRECTLY conclude that from the fact that the earth is motionless while stars revolve around it.

It's just a loose phrasing. The author doesn't mean they concluded ONLY from the first sentence. Their reasoning included the assumption in the 1st sentence and the D = R * T calculation in the 3rd sentence.

[AlexY297]

Hello so if you negate D it will become "Stars do move at tremendously great speeds." So if they are able to do so, it is possible that they can be more than a few million miles away so they can reappear in roughly the same positions? Am I in the right track here? I think this question is bit difficult since based on the premise that Earth is motionless.

[ohthatpatrick]

Yes, you're correctly explaining how the negation would weaken the reasoning.

In this case, though, maybe it's easier to understand the assumption in its actual form.
Let's look at what their argument was, including the missing assumption.

THEIR ARGUMENT:
If stars were farther than a few million miles away,
then they would have to move at tremendously great speeds to appear where we see them.

[but stars do not move at tremendously great speeds]

Therefore, stars are NOT farther than a few million miles away.

-----------

This was an argument by contrapositive.
If X then Y.
Since ~Y
we can conclude ~X.

Here's a similar example; you can predict what is being assumed:

If Sheila had been at the party last night, she'd be hungover this morning. So, apparently Sheila was not at the party last night.




ASSUMPTION?
(D) Sheila is not hungover this morning

[BarryM800]

I'm totally lost with this question. Can any expert break the stimulus down? My interpretation is that this is about many astronomers' argument, starting with the first sentence as their conclusion. The second and third/last sentence also start with "they," providing premises in support of the astronomers' conclusion. As far as I can see, there's no other argument, though the first sentence sounds like introducing an opposing. Does the author provide his argument, as I cannot find any clues? Based on the question stem, are we supposed to identify the necessary assumption of the astronomers' argument? Thanks!

[Laura Damone]

You're correct that the question is asking for an assumption required by the reasoning of the "many astronomers" who assumed earth was static, the stars revolved around it, and could therefore not be more than a few millions miles from earth.

However, their conclusion is the second sentence, not the first one: "They concluded from this..." is your structural indicator phrase. The support for this conclusion is the final sentence + the assumption stated in the first sentence.

So, the argument looks like this:

Explicit Assumption that functions as a premise: Earth is still and stars revolve around it.
Conclusion: Stars are not more than a few million miles away.
Premise: If stars were more than a few million miles away, they'd have to move at tremendously great speeds to circle Earth in a day and end up in roughly the same position each night.

To reach the conclusion using the premise provided, you need to engage premise's contrapositive. In order to do so, you need to establish the negation of its necessary condition: stars don't travel at tremendously great speeds. Since the argument doesn't establish this, it's necessary to assume it in order to draw the conclusion.

Hope this helps!