Page 192, Question 4

[btownsquee]

Why is the final line of this question not considered to be a conditional statement? Furthermore, if it is taken to be a conditional statement, it seems to be the Mistaken Negation of the second sentence. Can you please explain why we should not take the last sentence into account for this problem?

The following is my reasoning:

SA = stable angle
LM = large moon
SL = support life
X = negation

Sentence 1: N/A
Sentence 2: SA -> LM
Sentence 3: SL -> SA
Sentence 4: X(SL) -> X(LM)

My reasoning does not match the answer key in the book. Is my reasoning ok?

Thank you!

[Adam Tyson]

Thanks for the question, btownsquee. As I read it, that last sentence, about Mars, has no conditional elements to it. There is no "if...then" relationship present. Instead, it's just a recitation of unconditional facts - Mars has small moons, an unstable orbital angle, and can't support life.

We could stretch to make this conditional by latching onto the "only" part of the statement - only small moons. I might read that as "if something is a moon around Mars, it is small." I could go further and really work to make this conditional - "if a planet is Mars, then it must have small moons, an unstable orbital angle, and be unable to support life." But none of that is necessary or even helpful here. It's too much work! It also doesn't do anything to change or impact in any way the earlier conditional claims.

How do we know to essentially ignore this sentence? "For example" is my clue. The author is just telling us about one case where the conditions are all negated. He doesn't present it as "since Mars is incapable of supporting life, it must therefore have no large moon", which is what your diagram suggests he said. Rather, it says only that Mars doesn't support life, isn't stable, and has no large moon. You could just as easily interpret that as a contrapositive (no large moon, therefore no stable orbit and therefore no support life) as you could call it a mistaken negation. The author simply doesn't present it as a conditional claim, so we shouldn't treat it as one.

Take another look at that sentence, and ignore the rest of the stimulus. All by itself, with no context, would you treat it as a conditional claim? If so, what would be your indicators for the sufficient and necessary conditions? Once you've done that, you should have an easier time seeing why you should pretty much ignore it for the purpose of your prephrase and selection of the best answer. Let me know if that help!

[btownsquee]

Thank you! I understand that it is not a conditional statement.