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An argument states that: Maria won this year's sailboat race by beating Sue, who has in each of the four last years. We can conclude from this that Maria trained hard.
Premise: Maria won this year by beating Sue who won the last 4 years
Conclusion: Maria trained hard.
I was between these two answers and chose the first one incorrectly:
1. If Maria trained hard, she would win the sailboat race
2. Maria could beat a four time winner only if she trained hard
The explanation says that the first one (the one I picked) is a mistaken reversal, but how am I supposed to know how to conditionally diagram this??
Why couldn't it be diagrammed as if maria trained hard she won, instead of if maria won she trained hard?
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Glad to help @emilycyoung1650 ! Love to see things clicking into place for people!
Oh I completely understand now!! That makes so much sense @jhaldy10325
With this answer choice, it’s important to remember what the question is asking us to do. We have to logically force “Maria trained hard” to be true. This statement just doesn’t do that. This is saying that IF she trained hard she won.
The statement is contingent on whether or not she trained hard, so there’s nothing it can do to force her to have trained hard, even if we can affirm the necessary condition. Affirming the necessary frees the sufficient condition to be fulfilled or not. The rule no longer matters.
I should add that very frequently the conditional structures are more complex than this one. So there may be a lot of options that could work for your sufficient term. It’s typically the least obvious option. So if our argument in the stimulus is:
A —> B —> C
conclusion: A —> D
you’re probably looking for C —> D.
But it’s worth noting that B —> D or technically even A —> D would justify the conclusion just as successfully. So in this more complex conditional chain, you’ve just got the additional step of making sure it’s true that A —> C.
@jhaldy10325 ^^
Ok because I was really confused as to why this wouldnt have been the answer: If Maria trained hard, she would win the sailboat race. Can you explain that real quick?
Pretty much, yeah. If you do that and then find a sufficient you can plug in that the stimulus can confirm, that conditional statement will always justify the conclusion.
@jhaldy10325 So in these sort of arguments/statements, can you always just put the conclusion as the necessary?
Hey, no problem @emilycyoung1650 ! So, the first thing I see here is that the conclusion is “Maria trained hard.” That’s where we’re trying to get to, so I know I need to throw that into a necessary position. So in my answer choices I’m looking for something along the lines of:
_?_ —> Maria trained hard.
You could throw this into the sufficient slot by negating it, but that seems very counterintuitive to me. We’re trying to force the conclusion to be true, and a really easy way to do that is to make the conclusion a necessary assumption in a conditional and then affirm the sufficient. If we affirm the sufficient then the necessary must be true (Woah, that’s a really meta conditional statement, lol), so we just need to look for something affirmative in the stimulus to make the sufficient in our conditional. In this case, all we really know is that Maria beat Sue. So by making that our sufficient, we affirm the sufficient and force out the necessary which is our conclusion.
So with the answer choices, "if" introduces a sufficient assumption and “only if” introduces a necessary assumption. That’s why those two statements are reversals of each other.
Why couldn't it be diagrammed as if maria trained hard she won
So with this statement, we’re not accomplishing the justification of the conclusion. Our conclusion is Maria trained hard and we need to force that to be true. We know that she won, but affirming a necessary doesn’t trigger the sufficient, so this statement fails to force out the conclusion.
@jhaldy10325 could you help with this post question as well? Thank you for all of your help!!
@danielnoahpearlberg295.noah.pearlberg so always put the conclusion as the necessary condition?
Because the conclusion is that Maria trained hard. Think of that as B. We can arrive at that conclusion if we are given the following two premises: (i) If A then B; (ii) A. Then, if those premises are true, the conclusion B must be true as well.
You are suggesting the following premises: (i) If B then A; (ii) A. Even if those premises are true, the conclusion B doesn't follow. That's the mistaken reversal.