Law School Discussion

[Try it] a sufficient-necessary condition LR question from Dec '97, Sec 2, #10

theunderdog

Nonetheless found this question to be challenging, even though I found the credited answer.  Will post the answer along with the diagrams as an addendum to this post (so don't read further after this post if you want to try this question).  For you curious readers, this is from Dec '97, Sec 2, #10 and also from the homework in the Lesson One TestMasters Coursebook, p. 37.


All material bodies are divisible into parts, and everything divisible is imperfect.  It follows that all material bodies are imperfect.  It likewise follows that the spirit is not a material body.

The final conclusion above follows logically if which one of the following is assumed?

(A)  Everything divisible is a material body.
(B)  Nothing imperfect is indivisible.
(C)  The spirit is divisible.
(D)  The spirit is perfect.
(E)  The spirit is either indivisble or imperfect.

theunderdog

Answer is (D).

My diagram for the stimulus was as follows:
MB = material bodies
D = divisible
P = perfect
P = imperfect
S = spirit

MB -> D
D -> P
First conclusion:  MB -> P
Second conclusion:  S -> MB

(A) D -> MB [Incorrect Reversal]
(B) P -> D [Incorrect Reversal]
(C) S: D [meets a necessary condition of MB, so it leaves the possibility open it could be MB)
(D) S: P [does NOT meet a necessary condition of MB, making it impossible for S to be MB, therefore making the secondary conclusion]
(E) S: D or P [1/2 right, 1/2 wrong answer - the latter part of this answer is wrong, because it meets a necessary condition of MB, which is to be imperfect.]

Intuition

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Yea, it's D.

I have no clue what all that diagramming stuff is. The answer was pretty apparent though.

I too think charting these is over the top.  In this case the answers that jump at me are A and D.  I find the easiest method is generally to plug each answer into the argument prior to the conclusion. Doesn't always work, but often does...

E.G.:
All material bodies are divisible into parts, and everything divisible is imperfect.  It follows that all material bodies are imperfect.  Everything divisible is a material body.  It likewise follows that the spirit is not a material body.

Doesn't work.  Nothing is known about the spirit to say that.

But...

All material bodies are divisible into parts, and everything divisible is imperfect.  It follows that all material bodies are imperfect.  The spirit is perfect.  It likewise follows that the spirit is not a material body.

Ding ding ding...it works.

Much simpler than writing out contrapositives and such.


 

EvieO

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In response to OldStyle -- diagramming works for some people, and for others it doesn't.  Personally, I have found it useful when I want to make sure that my intuitive answer is correct - seeing it diagrammed on paper reassures me. It also makes it possible to arrive at the correct answer more quickly than you could by going through each answer individually in a "test-and-check" method.  Eventually you internalize it and won't need to actually write it out (this coming from some one who never took a course or did LRB, but just used simple diagramming on her own).

Theunderdog, I think you did a great job here, but I think you could reach the conclusion even more simply:


MB -> D
D -> P
First conclusion:  MB -> P
Second conclusion:  S -> MB


Take the contrapositive of your first conclusion and stack it above the second:

P -> MB
S -> MB

In this way, it's easy to see that S:P will provide the correct link.

theunderdog

I too think charting these is over the top.  In this case the answers that jump at me are A and D.  I find the easiest method is generally to plug each answer into the argument prior to the conclusion. Doesn't always work, but often does...

E.G.:
All material bodies are divisible into parts, and everything divisible is imperfect.  It follows that all material bodies are imperfect.  Everything divisible is a material body.  It likewise follows that the spirit is not a material body.

Doesn't work.  Nothing is known about the spirit to say that.

But...

All material bodies are divisible into parts, and everything divisible is imperfect.  It follows that all material bodies are imperfect.  The spirit is perfect.  It likewise follows that the spirit is not a material body.

Ding ding ding...it works.

Much simpler than writing out contrapositives and such.


 

Not necessarily.  Diagramming is an effective way to break arguments into their parts and understand the relationships between premises and conclusions.  With a lot of diagramming practice, you should be able to evaluate arguments internally without much error.