"None" & "None" Relationship

[faysun1007]

Dear Dave,

While reading the Formal Logic Inference Relationships table towards the end of the Formal Logic chapter, I have a question regarding the "None" "None" relationship which the table shows that it will never yield an inference.

Assuming the following relationships;

None of As are Bs & None of Bs are Cs

I believe above can be translate to A B C

Based on the table, there is no inference can be made, for example A C

Could you please help to explain the rationale behind it as I'm having a hard time conceptualize it.

Many thanks,

Fay

[Dave Killoran]

Hi Faysun,

Thanks for the question! Perhaps the simplest way to think of this is with two people who dislike the same person. For example, if Alain dislikes Bita, and Carlos dislikes Bita, what does that tell us, if anything, about the relationship between Alain and Carlos? Nothing at all actually: Alain and Carlos could still be friends, or they could even be enemies. We don't know anything other than the fact that they both dislike Bita, and this highlights why the two none relationships don't yield a solid inference. Anything is still possible, and because of that, we can't draw a direct inference.

Please let me know if that helps. Thanks!

[faysun1007]

Hi Dave, thanks so much for the quick reply! Yes, it really helped!!

Fay