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#21 - The presence of bees is necessary for excellent

Charlie Melman
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Hi bk1111,

You're right about the conclusion and the support for it. The argument says:

Excellent pollination :arrow: presence of bees

Establishing a beehive or two :arrow: presence of bees.

Keeping bees is economical :arrow: use for homegrown honey.

It concludes that:

Not (use for homegrown honey) :arrow: Not (keeping bees is economical) :arrow: Not (establishing a beehive or two) :arrow: not (presence of bees) :arrow: not (excellent pollination).

The Mistaken Negation comes in the form of, "Not (establishing a beehive or two) :arrow: not (presence of bees)." The flaw that the correct answer choice points out is that saying that, "Not (keeping bees is economical) :arrow: Not (establishing a beehive or two)" isn't enough; maybe there will be bees even if we don't establish a hive.

Hope that makes sense.
Jon Denning
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Had a student ask me about this question via email this morning, and since I know it's both a tricky question and the subject of a lot of conversation here, I wanted to post my reply. Consider this as an additional run through rather than improvement on, or correction of, anything posted in this thread previously :)

The argument has a lot of conditionality in it, and centers around the idea that to have excellent pollination gardens need bees. Diagrammed you could show it as: Ex Pollination :arrow: Bees. Meaning if we can say for sure that bees won’t be in the garden, then we’ll also know excellent pollination is impossible (that’s the contrapositive idea at the heart of this).

It then goes on to outline one way to guarantee the presence of bees: establish a beehive. In other words, if you want to make sure your garden has bees, you can set up a beehive or two and then be all set! That looks like:
Beehive :arrow: Bees. Of course, that wouldn’t ensure excellent pollination—bees are required for it, but don’t guarantee it—but it’s a way to at least be sure that excellent pollination is possible.

So far so good.

And finally: to make beehives (“keeping bees”) economical, the gardener must have a use for homegrown honey. Meaning gardeners who don’t have a use for homegrown honey probably won’t have beehives, as those hives wouldn’t be economical (another contrapositive). Again, if you wanted to show this relationship in a diagram it would be:
Beehives :arrow: Use for Honey (with the implied idea that this means “for a beehive to be economical/attractive” the gardener must have a use for honey), and then the contrapositive that we’re told: No Use for Honey :arrow: No Beehives.

But what does that mean for bees and pollination? Or, put another way, what would we know about the bees in a garden if that gardener doesn’t keep any beehives?

The answer? Nothing. Saying that one way to have bees won’t happen (no hives kept) doesn’t mean for sure that bees still won’t be there! More broadly, negating a sufficient condition (beehives) doesn’t automatically negate the necessary (bees). So when the argument goes on to conclude that gardens without beehives won’t have excellent pollination, the author has mistakenly overlooked the possibility that bees, the necessary condition for excellent pollination, can still be in gardens, even if beehives aren’t.

And therein lies the argument’s flaw. Just because one way to get bees won’t happen (in those cases where gardeners don’t have a use for honey and thus don’t keep beehives), doesn’t mean bees themselves won’t happen, so excellent pollination remains possible! This is akin to the classic Mistaken Negation error, where losing the sufficient tells you nothing about the necessary, despite an author’s attempts to draw that conclusion.

Answer choice (D) describes that mistake perfectly. Excellent pollination’s requirement (bees) could still be met even if we lose one way to ensure that requirement (no beehives).

Answer choice (B) on the other hand presents a Mistaken Reversal flaw, but that doesn’t happen in this argument. There’s nothing in the stimulus about bees guaranteeing pollination. Rather, the author thinks that losing hives means losing bees altogether—thus removing pollination’s requirement and triggering a contrapositive of No Bees :arrow: No Ex Pollination—but of course that’s not necessarily the case from just eliminating beehives, as discussed above.

So this is a pretty complicated question and definitely deserves another look on your end, but hopefully this helps to clear it up a bit and resolve any confusion!
Jon Denning
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bk1111
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Jon Denning wrote:Had a student ask me about this question via email this morning, and since I know it's both a tricky question and the subject of a lot of conversation here, I wanted to post my reply. Consider this as an additional run through rather than improvement on, or correction of, anything posted in this thread previously :)


I just wanted to say thank you so much for this analysis. This question has given me trouble for some time now and I revisited it today. It makes a lot more sense this time around!
rahimlsat
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Jon Denning wrote:Had a student ask me about this question via email this morning, and since I know it's both a tricky question and the subject of a lot of conversation here, I wanted to post my reply. Consider this as an additional run through rather than improvement on, or correction of, anything posted in this thread previously :)

The argument has a lot of conditionality in it, and centers around the idea that to have excellent pollination gardens need bees. Diagrammed you could show it as: Ex Pollination :arrow: Bees. Meaning if we can say for sure that bees won’t be in the garden, then we’ll also know excellent pollination is impossible (that’s the contrapositive idea at the heart of this).

It then goes on to outline one way to guarantee the presence of bees: establish a beehive. In other words, if you want to make sure your garden has bees, you can set up a beehive or two and then be all set! That looks like:
Beehive :arrow: Bees. Of course, that wouldn’t ensure excellent pollination—bees are required for it, but don’t guarantee it—but it’s a way to at least be sure that excellent pollination is possible.

So far so good.

And finally: to make beehives (“keeping bees”) economical, the gardener must have a use for homegrown honey. Meaning gardeners who don’t have a use for homegrown honey probably won’t have beehives, as those hives wouldn’t be economical (another contrapositive). Again, if you wanted to show this relationship in a diagram it would be:
Beehives :arrow: Use for Honey (with the implied idea that this means “for a beehive to be economical/attractive” the gardener must have a use for honey), and then the contrapositive that we’re told: No Use for Honey :arrow: No Beehives.

But what does that mean for bees and pollination? Or, put another way, what would we know about the bees in a garden if that gardener doesn’t keep any beehives?

The answer? Nothing. Saying that one way to have bees won’t happen (no hives kept) doesn’t mean for sure that bees still won’t be there! More broadly, negating a sufficient condition (beehives) doesn’t automatically negate the necessary (bees). So when the argument goes on to conclude that gardens without beehives won’t have excellent pollination, the author has mistakenly overlooked the possibility that bees, the necessary condition for excellent pollination, can still be in gardens, even if beehives aren’t.

And therein lies the argument’s flaw. Just because one way to get bees won’t happen (in those cases where gardeners don’t have a use for honey and thus don’t keep beehives), doesn’t mean bees themselves won’t happen, so excellent pollination remains possible! This is akin to the classic Mistaken Negation error, where losing the sufficient tells you nothing about the necessary, despite an author’s attempts to draw that conclusion.

Answer choice (D) describes that mistake perfectly. Excellent pollination’s requirement (bees) could still be met even if we lose one way to ensure that requirement (no beehives).

Answer choice (B) on the other hand presents a Mistaken Reversal flaw, but that doesn’t happen in this argument. There’s nothing in the stimulus about bees guaranteeing pollination. Rather, the author thinks that losing hives means losing bees altogether—thus removing pollination’s requirement and triggering a contrapositive of No Bees :arrow: No Ex Pollination—but of course that’s not necessarily the case from just eliminating beehives, as discussed above.

So this is a pretty complicated question and definitely deserves another look on your end, but hopefully this helps to clear it up a bit and resolve any confusion!


The problem I'm having with this is how were we suppose to presume that "gardeners who don’t have a use for homegrown honey probably won’t have beehives". I diagrammed the statement as:

Beesecon :arrow: HH

But you're saying that that is akin to:

Beehives :arrow: HH

But how can you say that with certainty?
Rachael Wilkenfeld
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Hi rahimlsat,

Good question. We can jump from your conditional (if beehives are economical, then the gardener must have a use for homegrown honey), to Jon's (if there are beehives, then the gardener must have a use for homegrown honey) by using the conclusion. The conclusion tells us that gardeners who don't have a use for homegrown honey TEND not to have beehives. That will connect back to the relationship in the sentence before (keeping bees is economical, however, only if the gardener has a use for homegrown honey). By connecting the two statements, we get that if there are beehives, the gardener must have a use for the homegrown honey. Otherwise, it wouldn't be economical, and the gardener probably won't have one.

Hope that helps,
Rachael