Lines can be parallel in a Euclidean system of geometry. But the non–Euclidean system of geometry that has the most ...

Ravi on November 23, 2020

@liwenwong28, we can diagram this statement.

1) Euclidean geometry-->parallel lines

2) Correctly describes universe-->non-Euclidean geometry

The author then concludes

3) Correctly describes-->no parallel lines

Th author's committing the inverse fallacy here. The author is negating both terms of the first conditional statement without switching them. The author then connects statement two with statement one to fallaciously conclude the third statement

C is incorrect because the conclusion is about one type of non-Euclidean geometry, which is the one that has the most empirical justification. Other types of non-Euclidean geometry do not affect the argument, so this answer choice is not necessary for the argument.

A is correct because the negation destroys the argument. The negation of A says, "there are parallel lines in the non-Euclidean system of geometry that has the most empirical verification." A in its original form can be diagrammed as

Non-Euclidean geometry-->no parallel lines

This is the necessary assumption (and flaw) the author is making, as they are negating both terms of the first conditional statement without switching their order. Thus, this is the correct answer choice, as this is an assumption that the author's argument depends on.