Self-study
At one time, many astronomers assumed that Earth remains motionless while the stars revolve around it. ████ █████████ ████ ████ ████ ███ █████ ████ ███ ████ ████ █ ███ ███████ █████ ████ ██████ ████ ████████ ████ ██ ███ █████ ████ ███████ █████ ████ █████ ████ ██ ████ ██ ████████████ █████ ██████ ██ █████ ██ ██████ █████ ██████ ███ ███ ███ ████████ ██ ███████ ███ ████ █████████ ████ ██████
Summary
The astronomers conclude that the stars are not more than a few million miles from Earth.
Why?
Because if the stars were farther away, they’d have to move at tremendously great speeds.
Notable Assumptions
The astronomers are trying to trigger the contrapositive of the conditional premise. They’re assuming that the stars do NOT move at tremendously great speeds.
25.
Which one of the following ██ ██ ██████████ ████████ ██ ███ █████████ █████████ ██████
a
If the stars ██ ███ ███████ ██████ ██████ ██ ██ ████████ ███ ██ █████ ████ █████ ██ ██ ████ ████ █ ███ ███████ █████ ████ ██████
Not necessary, because for the purpose of the astronomer’s argument, we’re going along with their assumption that Earth remains motionless while the stars revolve around it. So what would be true if the stars do NOT revolve around Earth isn’t necessary to the astronomer’s argument, which is based on the stars revolving around earth.
b
All stars move ██ ███████ ███ ████ █████ ████ ████ ███ █████████ ██████ ██████
Not necessary, because all that the argument needs to assume is that the stars do not move at tremendously great speeds. But the stars can move at slightly different speeds, as long as none of them are moving tremendously fast.
c
Earth does not ██████ ██████████ █████ ███ █████ ███████ ██████ ███
Not necessary, because for the purpose of the astronomer’s argument, we’re going along with their assumption that Earth remains motionless while the stars revolve around it. So even if the Earth does not in fact remain motionless, that doesn’t affect the reasoning of the astronomer’s argument.
d
Stars do not ████ ██ ████████████ █████ ███████
Necessary, because if it were not true — if stars DO move at tremendously great speeds — then we have no reason from the astronomers’ premise to believe that the stars can’t be more than a few million miles from Earth. The astronomers must assume (D) in order to trigger the contrapositive of their conditional premise.
e
A star that ██ ████ ████ █ ███████ █████ ████ █████ █████ ████████ ██ ███████ ███ ████ ████████ ████ ██████
Not necessary, because even if a star that is more than “a million miles” from Earth CANNOT reappear in the same position, the astronomers never argued that it would be able to. The conclusion is just that there’s a limit to how far away the stars can be. But if that limit is even closer than “a few million miles from Earth,” that doesn’t undermine the astronomers’ argument. Maybe stars need to be under a million miles from Earth; this is consistent with the astronomers’ reasoning.