Making an inference with All and None

[Takhmina]

In chapter 11: formal logic i quite don't understand why it is impossible to create inference from
A <--/--> B -----> C
The bible says that i need to use inherent inference, but I can't use additive inference.
logically if all A's are not B's and if all B's are C's then all A's are not C's.
or i miss something? in my logic?

[Dave Killoran]

Hi Takhmina,

Thanks for the question! It's not that it's logically impossible to create an inference from this relationship, it's just that you can't create the one you want to create

The only inference that can be derived here is "some Cs are not As." This is created by using the inherent "some" relationship as you go from C over to B, and then combining that with the negative relationship between B and A.

The inference you want to create doesn't work because the arrow between B and C is pointed in the wrong direction. To analogize, consider the following situation:

• Construction workers (A) and doctors (B) never overlap (A B)
  Every doctor (B) has an undergraduate college degree (C) (B C)
  
  Does that mean that no construction worker has a college degree? (A C)? No, it still could be true that some construction workers have college degrees.

Let me not that in your analysis, you wrote, "logically if all A's are not B's and if all B's are C's then all A's are not C's. " I italicized the portion where the terms change (from "not B" to "B"), and I think that switch may be the point that is causing you an issue here, because it's not a simple transitive chain.

As a reference for anyone else reading, this inference is covered in more detail on pages 327-328, and uses the concept at the bottom of page 320.

Please let me know if that helps. Thanks!