This question pertains to the Formal Logic Additive Inference Drill, Q#4, which reads:
Some Ts are Us
All Us are Vs
All Ts are Ss
The answer key to this drill lists three additive inferences as correct:
U S
T V
S V
The first two additive inferences make sense. However, the last additive inference (S V) is a bit confusing and I wonder how we can arrive at the answer provided the 11 Principles listed in the LR Bible Formal Logic chapter. Principle #9 concerns "some" and most" combos. The principle states there will be no inference, when two "some"s are next to each other (e.g., A B C).
Returning to drill question #4, we can arrive at the equation V U S. We arrive at this equation by substituting one of the first two inferences into the original diagram. However, what we are left with is a "some" combo (i.e., two "some"s next to each other). We are supposed to derive S V, according to the answer key. However, Principle #9 tells us specifically that there will be no inference if two "some"s are next to each other. How then are we supposed to derive V S? Are there exceptions to the "some" "some" combo like there are for the "most" combo?
The drill answer key says "see the book website for an expanded explanation." So, I am seeking clarification.
Thanks for any assistance!
Formal Logic Additive Inference Drill, Q#4
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Hi mcharlt,
For ease of explanation let's use "at least one" for "some". So if we are given: Some Ts are Us All Us are Vs All Ts are Ss And we want to know how S V This means that: Every T gets an S, At least one T(which also has an S) gets a U, Every U gets a V. So there is at least one TSUV (which is probably more clearly diagrammed as TS UV). Hope that helps! Malila
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