Q21 - Most kinds of soil

[ohthatpatrick]

What does the Question Stem tell us?
Match the Flaw

Break down the Stimulus:
Conclusion: Some soil has both clay and sand, and some soil has both clay and organic material.
Evidence: Most soil has clay. Most soil has sand, organic material, or both.

Any prephrase?
The conclusion is attempting a Most+Most Quantity Overlap inference. This is an inference in which you know "If Most A's are B and Most A's are C, then Some B are C." The author tries to prove an overlap between clay and sand and an overlap between clay and organic material. Let's start with that first idea. Can we prove an overlap between clay and sand? Do we know that "most soil has clay" and "most soil has sand"? Not quite. We know that "most soil has clay" and "most soil has sand or organic material". Well ... that's not good enough. We could fairly conclude "there must be some soil that has both clay and sand/organic material", but we can't prove that there is clay+sand AND clay+organic material.

So we're looking to replicate a flawed argument in which we have two premises: "Most A's are B" and "Most A's are C or D". And then we need a conclusion that says "some B is C, and some B is D".

Correct answer:
E

Answer choice analysis:
A) This conclusion is conditional. The original was not.

B) This conclusion is "Most A's are C's". We're looking for Some A's are C's and Some A's are D's."

C) This conclusion is also conditional.

D) The conclusion matches. Let's give it a read. Most P's are C. And Most P's that are S are also T. Hmm, that second premise doesn't match what we need. We want to hear "Most P's are S or T".

E) Conclusion matches. We have "Most P's are C" and "Most P's are S or T". And then we conclude that "Some C's are T, and Some C's are S".

Takeaway/Pattern: On Match the Flaw, are primary concern is matching the flaw, not matching every structural ingredient. But for THIS flaw, it was so structural in nature, that we DO have good reason to scan for ingredient matches/mismatches. That made finding the right answer much easier than usual. A, B, and C took only a glance. Once we see the conclusion is a mismatch, we should bail and check the next answer choice.

In case the flaw still doesn't make sense, here's a more mathematical explanation. The Most+Most inference is what it is because if you know two majority facts about the same group, i.e. "Most A's are B and Most A's are C", then there has to be an overlap between B and C. At a minimum, 51% of A's are B and 51% of A's are C. There has to be an overlap, because there's no way you could fit the 51% of A's that are C into the 49% of A's that are not-B. That's how we know there's AT LEAST SOME spillover of B's into C's, or vice versa.

But with these facts, we didn't have to have a spillover. Let's say that 51% of soil has clay and 49% of soil does not have clay. And we'll say that 40% of soil has sand and 50% has organic material. We've complied with all the facts. But we have no way of arguing that the 40% of soil that has sand must for some reason overlap with the 51% of soil that has clay. The 40% of soil that has sand could safely fit within the 49% of soil that does NOT have clay. There doesn't have to be an overlap.

#officialexplanation

[ganbayou]

Hi,

I chose A...
I thought the structure is Most of X contains A and all of X contain either B or C, or both.
Thus, there are some of A that contain B and C.
Actually I thought this is not a flaw because it's the combination between All and Most statement so we can infer Some...
What makes A wrong and E correct?

Thanks,

[andrewgong01]

What does the Question Stem tell us?
Match the Flaw



In case the flaw still doesn't make sense, here's a more mathematical explanation. The Most+Most inference is what it is because if you know two majority facts about the same group, i.e. "Most A's are B and Most A's are C", then there has to be an overlap between B and C. At a minimum, 51% of A's are B and 51% of A's are C. There has to be an overlap, because there's no way you could fit the 51% of A's that are C into the 49% of A's that are not-B. That's how we know there's AT LEAST SOME spillover of B's into C's, or vice versa.

But with these facts, we didn't have to have a spillover. Let's say that 51% of soil has clay and 49% of soil does not have clay. And we'll say that 40% of soil has sand and 50% has organic material. We've complied with all the facts. But we have no way of arguing that the 40% of soil that has sand must for some reason overlap with the 51% of soil that has clay. The 40% of soil that has sand could safely fit within the 49% of soil that does NOT have clay. There doesn't have to be an overlap.

I have two questions,

First, how did we know this was two "most" inferences because I read "virtually every kind" as an all statement
In other words, Most soil have clay and all soil has either sand or organic material

Second, regarding the over lap you wrote, I can see now that yes we do not need to have any soil with clay that also has sand. If the original condition was that all soil needs to have either sand or organic material then there has to be an overlap since if none of your soil has sand then they must have organic material. But if we go with "Most" in your above example, I still see the overlap:

51% of soil has clay , 40% of soil has sand and 50% has organic material. We can say that the clay and sand does not overlap. But doesn't the organic material and clay have to overlap by at least 1% since now 50% of the soil has organic material and that 51% of the soil has clay and ,in turn, be consistent with the conclusion drawn by the original argument?

[MingL143]

I chose "D" because, there is possibility that there is no overlapping between soil that contain clay only and soil that contain organic material only.

[ohthatpatrick]

(D) is vulnerable to the same objection that the original argument was vulnerable to:
in both cases, the author concluded there must be an overlap when there does not need to be an overlap.

However (E) also does that. So how do you differentiate between whether (D) or (E) better matches the pattern of flawed reasoning in the original?

You'd have to try to line up ingredient for ingredient.

The 1st sentence is the problem. A matching ingredient would say
"Virtually every pharmacy sells either shampoo or toothpaste."

Instead, it says
"Virtually every pharmacy that sells shampoo also sells toothpaste.

We need to hear "Almost all pharmacies have S or T", not "Almost all S-pharmacies have T."

The pharmacies-that-sell-shampoo are a subset of all pharmacies. We don't want to hear "virtually all [of this subset] has this 2nd trait also". We need, "virtually all [of the big set] has either trait 1 or trait 2".

I just said the same thing three different ways. Hopefully one of those made sense.

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The previous poster asked about "virtually all" = "most"?
They're not identical, since 'most' just means more than 50%, and virtually all has no specific minimum, but it feels like it would be at least 90%.

However, it's safer to equate virtually all with "most" than with "all".
ALL doesn't leave any room for exceptions.
MOST and VIRTUALLY ALL do leave room for exceptions.

That poster was also asking about my numerical example:
51% of soil has clay , 40% of soil has sand and 50% has organic material.

We can say that the clay and sand does not overlap. But doesn't the organic material and clay have to overlap by at least 1% since now 50% of the soil has organic material and that 51% of the soil has clay and ,in turn, be consistent with the conclusion drawn by the original argument?

Yes, the soil and organic material would have to overlap. But the conclusion is still wrong, because it makes two separate claims, one of which is wrong. The conclusion says clay+sand overlaps and that clay+organic material overlaps. With the example we just showed, we could only prove the 2nd claim. The 1st one is in doubt.

That's why I said in my breakdown of the argument that the conclusion would be correct if it had concluded "there must be some soil that contains both clay and either sand or organic material."

For that claim, you only need clay to overlap with AT LEAST ONE one of sand / organic material.
For the author's actual conclusion, he needs clay to overlap with BOTH of those qualities at least once.