Self-study
Lines can be parallel in a Euclidean system of geometry. ███ ███ █████████████ ██████ ██ ████████ ████ ███ ███ ████ █████████ ████████████ ██ ████████ ██ ███████ █████████ ██████████ ██ █████████ ██████████ ███ ████████ ██ ████████ ██ █████ ██████████ ███ ██████ ██ ███ ████████ █████ ███ ██ ████████ ██████
Argument Summary
Some physicists believe that a particular non-Euclidean geometry (the one with the most empirical verification) correctly describes our universe. The conclusion: if they're right, our universe has no parallel lines.
The premises tell us a non-Euclidean geometry describes the universe. The conclusion tells us the universe has no parallel lines. Where does "no parallel lines" come from? The stimulus invites the reader to fill it in by leading with "lines can be parallel in a Euclidean system," nudging us to infer "so they're not parallel in non-Euclidean systems." That's a trap. "Non-Euclidean" just means "not Euclidean." That doesn't imply non-Euclidean systems don't have parallel lines. Some might let lines be parallel. So the argument assumes that the specific system in play (the one with the most empirical verification) lacks parallel lines.
Anticipation
For a Necessary Assumption question, we want to pick a claim the argument needs to be true in order for its conclusion to follow. The conclusion introduces a new concept ("no parallel lines") that the premises don't establish. The required assumption almost certainly bridges that gap by telling us the particular non-Euclidean system in play actually lacks parallel lines.
9.
Which one of the following ██ ██ ██████████ ████ ██ ████████ ██ ███ █████████
a
There are no ████████ █████ ██ ███ █████████████ ██████ ██ ████████ ████ ███ ███ ████ █████████ █████████████
This is necessary. The argument needs it to bridge the gap between "this non-Euclidean system describes our universe" and "our universe has no parallel lines." If you negate (A), then the system has parallel lines. In that case, even granting that the physicists are right and the system accurately describes the universe, the universe would have parallel lines too. The conclusion wouldn't follow if (A) were false. Since negating (A) destroys the argument, (A) is necessary.
b
Most physicists have ███ ███████ ███ ████ ████ ███ ████████ ██ █████████ █████████ ██ ███ █████████████ ██████ ██ ████████ ████ ███ ███ ████ █████████ █████████████
The conclusion is conditional ("IF these physicists are right"). The argument doesn't claim the physicists ARE right or that the view enjoys wide acceptance. Whether other physicists doubt the view is therefore irrelevant. The conditional "if X, then Y" can be true regardless of how many people accept X.
c
There are no ████████ █████ ██ █████ █████████████ ██████ ██ ████████ ████ ███ ███ █████████ █████████████
Too broad. The argument only relies on the specific non-Euclidean system with the most empirical verification lacking parallel lines. Other non-Euclidean systems with some empirical verification could have parallel lines without affecting the argument at all.
d
The universe is █████████ █████████ ██ ███ █████████████ ██████ ██ ████████ ████ ███ ███ ████ █████████ ████████████ ██ █████████ ██████████ ████████ ████ ██ ███
The argument doesn't assume the physicists are right. It only draws a conditional conclusion ("IF they're right, then..."). So the argument doesn't need to bridge from "physicists believe X" to "X is actually true." That bridge isn't part of the reasoning.
e
Only physicists who ███ ███ █████████ █████ ███ ████ ████ ███ ████████ ██ █████████ █████████ ██ ███ █████████████ ██████ ██ ████████ ████ ███ ███ ████ █████████ █████████████
Not necessary, because the existence of doubt or lack of doubt has no bearing on the reasoning. The conclusion is based on the hypothetical situation in which the non-Euclidean system accurately describes the universe. Whether anyone doubts the theory or not is irrelevant; for the purpose of evaluating the argument, we simply accept the hypothetical situation as true.