Page 79, Linkage Discussion: W not in 2 or 6?

[Dave Killoran]

Earlier today, we received the following question:

In re: Logic Games Bible (2016), page 79 The explanation for the linkage diagram says that W cannot be in slot 4. However, since W and X cannot speak consecutively, doesn't that mean that W could not be in slots 2 or 6 either, forcing it into slot 1?

Here is the answer:

Thanks for the question! This is a good example of an error you want to avoid, so it’s good that you’ve come across it while you are studying. We know that X is limited to slots 3 or 5, hence W can’t be in slot 4. But, the rotation of X is critical here: if X was fixed in, say, slot 3, then we would know that W could not be in slot 2. But X can be in either 3 or 5, and when X is in 5, it becomes possible for W to be in slot 2. And, when X is in slot 3, W could be in slot 6, and thus we cannot infer that W can never be in slot 2 or 6.

There’s also a related discussion of not-block inferences on page 87, in the Avoiding False Inferences section. You might find that helpful as well.

Please let me know if that helps. Thanks!