Formal Logic

[PB410]

Hi,

I'm going over the formal logic section in my Logical Reasoning Question type training. Questions 2 and 3 brought up a question. They are from prep test 1. section 4. Q24 (parallel reasoning) and prep test 2. section 2. Q20.(parallel flaw).
My question involves valid inferences from combined logic chains involving "some" statements.
Question 24 I diagrammed as
P: Contemporary Advertising -------> Try Persuade
P: CA ---(some)----> Morally Reprehensible
C: P------(Some)---> MR

I connected the statements as:
MR <------(some)-----> CA ---------> P
the conclusion above follows:
Mr <------(some)------>P which is equal to P -------(some) ----->MR


Question 20 is a parallel flaw, but I believe it makes the same inferences as question 24. I am not sure if what I am doing is valid. I diagrammed 20 as
P: Savings Accounts -------> Interest Bearing
P: IB ------(some)-----> Tax Free
C: Tax Free -----(some)-----> Savings Accounts
It looks like the connections to reach the conclusion are
SA ------> IB ------(some) ---->TF
isn't it valid to view this as
SA ----> IB <----(some)---->TF which is equal to the conclusion they state: TF -----(some) ---->SA

Don't the two questions follow the same inferences and aren't they both valid? I am confused because one of the questions is a normal parallel reasoning while the other is a parallel flaw. Unless I have made a mistake in my diagramming and understanding of when it is valid to combine some logic chains?

[KelseyWoods]

Great question, PB!

Your diagramming of the statements in each question is correct. Great job! But notice that there is actually a key different between these arguments and diagrams: in the first question, the one with the valid logical argument, your "some" relationship is before your "all" relationship. In the second question, the one with the logical flaw, your "some" relationship is after your "all" relationship.

Let's consider an example of these types of relationships in a different scenario. Here are my rules:

All cats have tails. (Cats Tails)
Some cats have gray fur. (Cats Gray fur)

If I combine those 2 rules I get:

Gray fur Cats Tails

So basically, since some things with gray fur are cats, and all cats have tails, there must be some things with gray fur that have tails (because at least all those gray fur cats have tails!).

Now let's add another rule:

Some things with tails are reptiles. (Tails reptiles)

If I combine that with my "all" relationship above, I get:

Cats Tails reptiles

Notice that now that the "some" relationship is at the end of my "all" relationship, I can't make the same connection and conclude that some cats are reptiles. Just because all cats have tails, and some things with tails are reptiles, does NOT mean that some cats are reptiles. Those 2 groups (cats with tails & reptiles with tails) do not have to overlap.

Basically, you can make inferences when your "some" relationships connect with your sufficient conditions, but you can't make the same inferences when those "some" relationships connect with your necessary conditions.

Hope this helps!

Best,
Kelsey

[PB410]

Thanks, Kelsey!

And thanks for providing the example. It was super helpful!