#14 - Archaeologist: An ancient stone building at our

[lilmissunshine]

Hello,

I picked (D) over (B), because I thought (B) was mistaken reversal. Here are my diagrams:

Premise 1: human dwellings only limestone/naturally occur
Premise 2: Our building has 3 kinds of stones including unnaturally occurred stones
Conclusion: Our building was not a dwelling

So we are looking for: unnaturally occurred stones dwelling, which is the reverse of (B). I chose (D) because of the difference between "human dwelling" and "dwelling".

Could you explain it for me? Thanks a lot!

[Adam Tyson]

This question involves Formal Logic rather than purely Conditional Reasoning, lilmiss. "Most" and "some" are common key words for making that distinction, and Mistaken Reversals are not as much of an issue in Formal Logic as in Conditional Reasoning. Here's what I mean:

If most of the buildings were made of only limestone, then it must be true that at least some limestone things were buildings. You can take the "most" going in one direction and infer a "some" going back in the other direction.

If you happen to have the LR Bible, there is a chapter on Formal Logic that you might benefit from.

Now, I happen to be a numbers guy - I like to use simple numbers to gain a better understanding of Formal Logic questions, and I will walk through some numbers here to show you what I mean.

I'm going to start by pretending there are 10 buildings at the site. If most were made of limestone only, that's 6 buildings. Most were dwellings, so that is also 6 dwellings. I'm not sure how much those two groups overlap - maybe all 6 are the same, or maybe there are only two that are both limestone and dwellings.

My author wants to prove that this building, with other stone in it, was not a dwelling. How am I going to help that?

If answer B is true, then most of the 4 buildings that were not dwellings were made with other kinds of stone. So there are at least three buildings that were not dwellings and made of multiple types of stone. Now I know that my two groups either do not overlap or only do so a little - 6 dwellings, 4 non-dwellings, at least 3 of the latter made with multiple kinds of stone, at least 5 of the former being only limestone. At most one non-dwelling is limestone only and at most 1 dwelling is multi-stone. So, my multiple stone building is much more likely to be a non-dwelling than a dwelling!

Try any other combination of numbers you like, and it should work out the same.

I don't think we have to worry too much about the "dwelling" vs "human dwelling" aspect of this argument, because "dwelling" commonly means a place where people (humans) live, and is not used to mean where any non-humans live (unless we start talking about alien civilizations, which is a bit of a stretch for our purposes!) It does look to me like maybe you were treating this as more of a Must Be True question, rather than a Strengthen question, so perhaps that's why answer B threw you off? If it is true that this multi-stone building was probably not a dwelling, then it makes sense to prephrase that most of the multi-stone buildings are not dwellings. But we don't know that it is true - we want to help suggest that it is!

[lsacgals101]

I am having trouble understanding why answer A doesnt strengthen the argument (though I understand why B does). Could you help me figure out how to approach answer A?

[lsacgals101]

I think i chose answer A because of how I diagrammed the problem... which leads me to the question of HOW one would diagram question 14? See my diagramming and thought process below.

My diagramming:
ES = excavation site
A building (ES) = Q + G + L

Premise 1:
Limestone Natural Occurs in Area

Premise 2:
Human dwellings (most) Buildings at ES Limestone only

Conclusion:
A building (ES) ~Human dwelling


My inference from premise 2 is:
Human dwellings Limestone only

This inference led me in the direction of answer A, although I knew it wasn't a perfect fit... but i also didn't know if I diagrammed premise 2 correctly, since the stimulus says: most of the buildings at site...had limestone as only component, and most were human dwellings. Does the second "most" in that sentence refer to the buildings at the site? or the buildings at the site that had limestone as the only component?

I am definitely getting turned around by this problem and would really appreciate your help.

[Brook Miscoski]

lsacgirls,

I suggest reviewing Adam's explanation. I wouldn't diagram this stimulus and don't believe a diagram is a helpful way of understanding it unless you are very careful about the diagram.

The archaeologist has pointed out that most of the buildings in the area are limestone only and most of the buildings are dwellings. He concludes that a building that also has other stones is probably not a dwelling.

The problem with his reasoning is that the "mosts" don't have to include each other except minimally. I'm a bit more abstract than Adam--I think "most just means slightly more than 50%." That means that most of the buildings can be "limestone only," and most of the buildings can be "dwellings," even if only a very tiny percentage of the "limestone only" buildings are "dwellings." Adam gives you the numbers explanation.

The correct diagram, if you use one, is to realize that the archaeologist has only shown:

LO D,

because you cannot chain "mosts" together and keep the "most."

That means that we basically have no idea what to believe about whether a limestone only building is a dwelling, or whether a dwelling is likely to contain other stones. We have to fix that.

(A) provides D Limestone Only OR Limestone Plus

Thus, (A) doesn't help us at all because just says that dwellings use limestone and maybe other stones. That's the opposite of what we need.

(B), as you understand, strengthens the argument.

I think it's easier to see that (A) doesn't work if you focus on Adam's analysis or my analysis--understand that in these kinds of scenarios this problem always needs to be solved, it's not something you learn from the diagramming so much as it is something that you learn could be represented by a proper diagram.

[Jenmstearns]

Hi,

I’m second-guessing my process on this question because I felt confident and prephrased something pretty close to B, which I picked, but I went a totally different route. I saw the second to last sentence as “Limestone human dwelling”, and then that the conclusion was going to be to a mistaken negation unless we supplied the argument with the contrapositive of that premise, putting the conclusion of “not dwelling” as a sufficient condition and “not limestone” or “not local” as the necessary condition. Ignoring all of the “most” and “some” aspects, I looked for and found the answer that was “not dwelling not limestone/local”. It made sense in my head under timed conditions, but did I just get lucky or is that a valid mental process? What did I miss?

Thanks!
Jenny

[Claire Horan]

Hi Jenny,

The conditional reasoning you just went through isn't valid, but I think it may have helped you see what components would be present in the answer. Since the other answer choices are not strong contenders, you ended up making the right choice. So, it wasn't all luck!

Previous posts explain why "some" and "most" are important qualifiers, and you should not force them into your usual conditional reasoning scheme. If you have trouble with formal logic but think you have a contend, try testing it by running through the argument with your chosen answer, reading each premise, then the chosen answer, then the conclusion to make sure it fits together. Often we understand arguments in ways we aren't able to diagram perfectly or put into words.

Good work!

[oq058420]

I'm going to start by pretending there are 10 buildings at the site. If most were made of limestone only, that's 6 buildings. Most were dwellings, so that is also 6 dwellings. I'm not sure how much those two groups overlap - maybe all 6 are the same, or maybe there are only two that are both limestone and dwellings.

My author wants to prove that this building, with other stone in it, was not a dwelling. How am I going to help that?
If answer B is true, then most of the 4 buildings that were not dwellings were made with other kinds of stone. So there are at least three buildings that were not dwellings and made of multiple types of stone. Now I know that my two groups either do not overlap or only do so a little - 6 dwellings, 4 non-dwellings, at least 3 of the latter made with multiple kinds of stone, at least 5 of the former being only limestone. At most one non-dwelling is limestone only and at most 1 dwelling is multi-stone. So, my multiple stone building is much more likely to be a non-dwelling than a dwelling!

Try any other combination of numbers you like, and it should work out the same.

Maybe I'm making some mistake, but this doesn't seem to be true for certain combinations of numbers.

Suppose there are twenty buildings at the site: 10 limestone-only dwellings, 2 limestone-only non-dwellings, 5 non-limestone-only dwellings, and 3 non-limestone-only non-dwellings. In this scenario, both general premises are true: most buildings at the site are limestone-only (12 out of 20), and most buildings at the site are dwellings (15 out of 20). Moreover, answer choice (B) is true: most non-dwellings are non-limestone-only (3 out of 5). But it is not true that most non-limestone-only buildings at the site are non-dwellings: on the contrary, there are 8 non-limestone-only buildings and only 3 of them are non-dwellings. So the mere fact that a given building is non-limestone-only doesn't seem to lead to the conclusion that the building is probably a non-dwelling.

I don't see why this scenario wouldn't matter just as much as the original quoted scenario, or why the combination of numbers 10, 2, 5, and 3 wouldn't be as important as the combination of numbers 5, 1, 1, and 3. And I don't see any problems stemming from simplifying matters by treating non-limestone-only and multi-stone and at-least-partially-foreign-stone as equivalent. So I don't see how adding (B) to the two general premises helps us get from the premise x is non-limestone-only to the conclusion probably, x is non-dwelling (or, alternatively, helps us get to most non-limestone-only buildings at the site are non-dwellings).

Can anyone explain why (B) is correct?

[Luke Haqq]

Hi oq058420!

I can certainly address why answer choice (B) is correct. The numbers you provided in your hypotheticals seemed to make sense to me in skimming them and looking at the premises in the stimulus. One thing missing from your post was the variable of "occur[ring] naturally in the area," which seems to be key to why answer choice (B) is correct.

The conclusion is, "Therefore, the building we are studying probably was not a dwelling." How does the author arrive at this? The author notes that the building is made from 3 different types of stone, but only 1 of them is found naturally in the area. The author seems to make an inference that the presence of the other 2 types of stone indicates that it's not a dwelling, but if so, this isn't stated.

In addition to the numerical hypotheticals you suggested, you might also find it helpful to think of the middle two sentences of the stimulus in terms of a Venn diagram, or something similar--there'd be one encompassing circle for "buildings," one within it covering more than half for "dwellings," and the same amount for "limestone." Since they both cover more than half, those inner two circles overlap, i.e., we know that there are some dwellings are made from limestone.

Answer choice (B) states, "Most of the buildings at the site that were not dwellings were made, at least in part, from types of stone that do not occur naturally in the area." This connects the sentence about not being from the area to the conclusion. It makes sense to conclude from the types of stone it is made out of--which included stones not from the area--that this building is not a dwelling if, as (B) supposes, most non-dwellings utilized stones that were not from the area.