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So I'm understanding all the concepts of this chapter, but in action i'm having trouble.

When I hit a <--/-->, does the some train stop there? For instances, #1 of the drill is Some As are Bs, No Bs are Cs, and All Cs are Ds. I diagram it all correctly, but I would've thought that you could conclude that some A->D. #2 All Xs are Ys, Some Ys are Zs, and Most Xs are Ws. I wanted to make X -> Y into a some and make it a <--->, which I thought would lead me to be able to conclude that some w->Z. But then you get to #3, No Es are Fs, All Fs are Gs, and All Gs are Hs. Why is it on this one that I can turn it all into somes and work my way back up to the /E? Can someone help me identify where i'm going wrong?
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 Dave Killoran
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Hi Z,

You are actually running into multiple problems here, which is why this probably seems quite confusing. A few thoughts:

The :dblline: doesn't stop the inferences in the Some Train. It just turns the relationship into a negative one. Compare the following two relationships:

  • 1. A :some: B :dbl: C

    Inference: A :some: C

    2. A :some: B :dblline: C

    Inference: A :some: C

Same inference, one just has a negative on C.

Second, you should go back and review the Rules of Reversibility. They play a role in some of your confusion as far as I'm seeing.

Third, go use the book site code in the front cover of the 2023 versions, or see Chapter 1 for the book site in other versions. I wrote an expanded set of explanations for each of the items in this drill that takes the inferences step-by-step :-D There are also some additional discussions of each drill in this forum.


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