Daily Drills 20 - Section 20 - Question 3

P: X → YP: X → not YC: ?

mikeheath June 27, 2020

How is it possible for x then not x?

Is this something covered in the paradox section?

Replies
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Victoria July 7, 2020

Hi @mikeheath,

Thanks for the question.

Try not to worry too much about the missing premise drills! They are more of a warmup to ensure that you understand how S&N statements and diagrams work before you apply the skills to actual passages. Personally, I found the missing premise drills to be more difficult than some of the actual questions as the logic made more sense to me when it wasn't in such an abstract form.

Let's start by diagramming the contrapositives for each premise.

X --> Y
Not Y --> Not X

X --> Not Y
Y --> Not X

We can then use the transitive property to conclude:

X --> Y --> Not X
X --> Not X

The conclusion, therefore, is "not X" which is why answer choice (B) is correct. However, since this is impossible, then the ultimate conclusion is that X does not exist.

This sort of concept will be covered to an extent in the paradox section, but not in this abstract way. When addressing paradox questions, you are usually looking for the answer choice which would help to resolve the paradox which is inherent in a passage's reasoning.

Hope this is helpful! Keep up the good work and please let us know if you have any further questions.

Victoria July 7, 2020

My mistake, I meant argument completion drills!

mikeheath July 7, 2020

Thank you!