Q20 - All savings accounts are

[hdw217]

Hi, I cannot for the love of Christ tell why the reasoning here is flawed. i can match it well in the answers and get C but am puzzled why is this flawed?

[timmydoeslsat]

Hi, I cannot for the love of Christ tell why the reasoning here is flawed. i can match it well in the answers and get C but am puzzled why is this flawed?

I first want to thank you for the laugh. I think we have all been there at some point in frustration!

This stimulus is flawed in a way that is frequently tested on the LSAT. To see how this is flawed, I will demonstrate an intuitive example:

All cities in Alaska are cold places.

Some cold places have NFL teams.

Therefore, some cities in Alaska have NFL teams.

We know the two statements given as evidence are true. The problem is that we do not have the logical warrant to combine the statements. We know that some cold places have NFL teams, but this could be just Chicago or just Buffalo. This does not have to include a city in Alaska.

In a quick formulaic approach, you cannot infer anything logically about a quantifying statement on the necessary condition side of a conditional statement.

City Alaska ---> Cold Place

Cold Place some NFL teams

We cannot make an inference.

Answer choice (C) replicates this error of reasoning.

[ohthatpatrick]

Ironically, Timmy, before I saw you had already typed a response to the original question, I had my own NFL-related quantity inference example on deck for my own response to the original question.

Great minds think alike.

When it comes to quantity inferences, there are primarily two possibilities to make a LEGAL quantity inference:

All A are B
Most/Some A are C
= Some B are C (Some C are B ... same diff)

Most A are B
Most A are C
= Some B are C (Some C are B ... same diff)

The important characteristic to note is that in both cases, you have two facts about group A, or as Timmy was saying, the sufficient condition.

(Of course, 'MOST' statements aren't conditional, so it would be technically wrong to call one side sufficient and the other necessary, but 'MOST' statements are only meant to be read left to right, so we could still think of the left side idea as the 'sufficient')

[WaltGrace1983]

Just wanted to add a bit of analysis to the wrong answers here! While, as already stated, "most" and "some" don't really warrant conditional language, I find it helpful to visualize it with arrows.

Savings Account → Interest-Bearing

(Some) Interest-Bearing → Tax-Free

⊢ (Some) Savings Account → Tax-Free

The problem, as already mentioned, is that we are unsure if there is overlap between the Interest-Bearing Savings Accounts and those specific Interest-Bearing accounts that are Tax-Free. Thus, we want to find something that is similar in form: All X are Y, some Y are Z, therefore some X are Z.

(A) (Some) P → A → I ⊢ (Some) P → I
Perfectly logical. If we know that some P are A and all A are I, Some P must absolutely be I.

(B) P → A → I ⊢ (Some) P → I
Perfectly logical. You know, you could even take the conclusion even farther by saying that ALL P are I. Why? Because we know that ALL P are A and ALL A are I, therefore, ALL P must absolutely be I.

(C) P → A, (Some) A → I ⊢ (Some) P → I
As you can see, there is a disconnection between "A" and "(Some) A." We don't know if "A" as it applies to the P's that are A has any overlap between the "(Some) A." I hope that makes sense. As you can see, this is a perfect match for the original argument.

(D) P → A, (Some) P → I ⊢ (Some) A → I
Perfectly logical. If we know that all P are A and some P are I, there absolutely must be an overall between those that are A and I. We know that at least some P will be both A and I!

(E) P → A → ~I ⊢ (Some) P → ~I
Perfectly logical. Like (B) this conclusion can also go farther. If we know that all P are A and, if you are an A you are most certainly not an I (all A's are ~I's), we can say that ALL P's are actually ~I!

So not only are the 4 wrong answers inaccurate representations of the flaw, they are actually not flawed at all!

[AyakiK696]

Just to reconfirm, is answer choice D wrong because the second statement utilizes the sufficient condition of the first statement? So rather than:

All A are B
Some B are C
Some A are C

It gives us:

All A are B
Some A are C
Some B are C?

In order words, because it flips the order of the last two statements?

[ohthatpatrick]

Correct.

And switching the last two ideas isn't just a picky technicality.

Because the last two ideas get switched, (D) is a 100% airtight argument! It's not flawed at all.

Whenever we get
All A's are B
+
Some A's are C
===we=can==infer====
Some B's are C

[mk513]

Hi, I cannot for the love of Christ tell why the reasoning here is flawed. i can match it well in the answers and get C but am puzzled why is this flawed?

Blessed is the name of Jesus Christ