The Some Train

[ThePhilosopher]

Hey,

I'm hoping Dave could clear this up, but if anyone is able to that would be great. In "The 11 Principles of Making Formal Logic Inferences," for the 4th principle "The Some Train," there are two diagrams given (Page 445, 2024 edition):
1) A B C
and
2) A B C

We are told that in first diagram, we can deduce the additive inference: A C.
However, we are told the same cannot be done with the second diagram.

An explanation is given as to why on the following page (page 446 on my version), yet it isn't entirely clear.

Using Rule #2 of Diagram Creation, "There is no traditional direction in logic," we can rewrite the second diagram as,
C B A.
As such, the issue of the "direction of the arrow" being the issue is circumvented.

From this rewritten diagram, we can deduce C A which, with the rule of reversibility discussed earlier in the Chapter, can be written as A C.

The discussion on the second diagram with the track and journey analogy does not clarify the confusion as the issue of as rewritten diagram does not suffer from a not having a "track away."

If there was an error made, please let me know where and why and thank you in advance.

[Dave Killoran]

Hey Philosopher,

Sure happy to help here

Using Rule #2 of Diagram Creation, "There is no traditional direction in logic," we can rewrite the second diagram as,
C B A.
As such, the issue of the "direction of the arrow" being the issue is circumvented.

Ok, while the re-draw of the diagram is correct, you haven't circumvented the problem. Functionally and directionally, it's the same diagram so nothing really has changed. More on this at the end.

From this rewritten diagram, we can deduce C A which, with the rule of reversibility discussed earlier in the Chapter, can be written as A C.

Unfortunately, no, you cannot. Imagine there are 10 Cs, and a million Bs. Then, just a few of those B's are also As. Do those few As have to overlap with your 10 Cs? No, which shows that mathematically you haven't made the inference here. Let's get to the why now.

The discussion on the second diagram with the track and journey analogy does not clarify the confusion as the issue of as rewritten diagram does not suffer from a not having a "track away."

If there was an error made, please let me know where and why and thank you in advance.

The "track away" is a track away from the "some" relationship. When we look at C B A. , the arrow from C still goes "into" B, which is the opposite direction we need to be "away" from B some A. So that's where the arrow is. It's tricky at first, but now that you've encountered this issue, you won't have it again

Thanks!

[ThePhilosopher]

I see,

Thank you for your help.

I know you speak against the use of Venn diagrams, but in this case visualizing it made it very easy to understand.

I will include it here in case anyone else has this confusion in the future!

[Dave Killoran]

Ironically enough, I love Venn diagrams! They are great for helping to understand problems just like this one. Unfortunately, during the LSAT, drawing them out isn't feasible for most people, hence we use a different approach

Here's more on how Venn becomes an issue during LR sections: https://blog.powerscore.com/lsat/bid-15 ... agramming/