QUESTION TEXT: Lines can be parallel in a Euclidean…
QUESTION TYPE: Necessary Assumption
CONCLUSION: There are no parallel lines in our universe, if those physicists are right.
REASONING: The non-Euclidean system of geometry with the most empirical verification (real world proof) is seen by some physicists think it accurately describes our universe.
Euclidean geometry can have parallel lines.
ANALYSIS: The argument didn’t tell us whether or not the non-Euclidean system can have parallel lines. A necessary assumption is that they cannot.
- CORRECT. If there are parallel lines in the system then this argument is wrong.
- This just tells us that more physicists think the system is correct. But that doesn’t tell us whether or not our universe has parallel lines or what the geometry system is like. So this isn’t necessary.
- This would be a sufficient assumption. But it’s only necessary that the particular non-Euclidean system in question has no parallel lines.
- This isn’t necessary. The argument was describing what would be true if the physicists were correct. It was not arguing that the physicists were necessarily correct.
- It doesn’t matter how many physicists think the system is correct. The argument isn’t claiming that the system is correct. Instead, it’s telling us what would be true if the system were correct.
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