Two Rules of Diagram Creation: Linkage inferences involving "some"

[Emma Beck]

Hello,

I was working on p.420 (2017 editing) of the Formal Logic chapter and wondered if we can make the following inference with the diagram on the bottom of the page. Here's the diagram:
A B
B C

The rule goes on to explain how we shouldn't duplicate variables; we should just diagram the above as A B C.

I am wondering if making the following inference A C would be correct. After all, if some As are some Bs, and all of those "some Bs" are Cs, then isn't it inevitable that at least some As are also Cs? Is that a correct inference? It wasn't on the page so perhaps I am wrong.

I'd greatly appreciate your help!
Thank you,
Emma

[Dave Killoran]

Hi Emma,

Yes, very good--that is a valid inference! It's also one you'll begin to see quite frequently as it comes up in the section immediately following the one you are working on, in item 4 about the Some Train.

Fyi, I'm going to move this post into our LRB Forum section on Formal Logic.

And a side note for other readers: this is page 443 in the 2022 edition.

Thanks!