Logical Reasoning

PT110 · S3 · Q9 Lines can be parallel in

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Lines can be parallel in a Euclidean system of geometry.

Conclusion

If these physicists are right, (if non-Euclidean geometry correctly describes our universe), then there are no parallel lines in our universe.

Evidence

Euclidean geometry thinks that lines can be parallel.

Evaluate

This author is assuming that non-Euclidean geometry rejects every part of Euclidean geometry. The argument would be the same if it said,

We could represent this flawed thinking as an illegal negation.

The author establishes this: If Euclidean Geo, then parallel lines Then erroneously reasons this: If non-Euclidean Geo, then not parallel lines

That's an illegal negation, a.k.a. confusing Necessary and Sufficient.

Goal

So what is the author assuming? She thinks that in non-Euclidean geometry, lines can't be parallel. She thinks that, .

9.

Which one of the following is an assumption that is required by the argument?

  1. Correct

    There are no parallel lines

    Why this is right

    The author is saying, "If non-Euclidean geometry correctly describes our universe, then there are no parallel lines in our universe", so the author is definitely assuming that there are no parallel lines according to non-Euclidean geometry. If we negated this, it would badly weaken the argument (which is true of every correct answer on Necessary Assumption). If we said, "Hey, author, there are parallel lines in non-Euclidean, that would basically ruin his argument."

    Skill tested: Necessary Assumption · how this choice captures the argument's function is the move to repeat next time.

    75% picked this

  2. Most physicists have not doubted

    Out of Scope: most physicists

    The word "most" is wrong 99% of the time we see it on Necessary Assumption. In this argument, the author is saying, "If these several physicists are right, then ____ ." He doesn't need to assume anything about any other physicists.

    5% picked this

  3. There are no parallel lines

    Too Strong

    Too Strong: every / any Out of Scope: other non-Euclid systems We might not have noticed until this answer that the argument implies that there are multiple non-Euclidean systems of geometry, because the premise specifies that we're talking about the non-Euclidean system with the most empirical verification. The author's argument is only about that specific non-Euclidean system, so she doesn't need to assume anything about any other non-Euclidean system.

    9% picked this

  4. The universe is correctly described

    Never Assumes the Trigger

    This conclusion is a conditional: if these physicists are right (i.e. if that most verified non-Euclidean system correctly describes our universe), then there are no parallel lines When we make conditional claims, like, "If humans lived on Mars, there would still be racism", we aren't assuming that humans will one day live on Mars. When I say, "If Presidents were allowed to serve 10 terms, then we would at some point have the same President for forty years", I'm not assuming that Presidents will be allowed to serve 10 terms. Any time we're dealing a conditional conclusion, we'll usually see a trap answer directed at this misunderstanding. The author isn't assuming the trigger is true. We can't strengthen the argument in any way by saying the trigger is true. We can't weaken the argument by saying the trigger is false.

    10% picked this

  5. Only physicists who are not

    Too Strong: only

    The author has told us that several prominent physicists believe X. This answer is taking that statement and saying, "So what you're saying is .... the only physicists who would doubt X are non-prominent ones?" That's a ridiculously bad interpretation. If say "several Senators like mayonnaise with their french fries", it's possible that many Senators don't like mayo with their fries. We can't twist that into, "The only people who don't like mayo on their fries are non-Senators".

    1% picked this

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